with safety constraints. OSHA has established guidelines that must be followed in any
plant when dealing with chemicals defined as highly hazardous. Limits for temperature,
pressure, flow rates, and compositions need to be regulated. Alarms should be in place to
warn operators when a limit is near so that steps can be taken to ensure the safety of
people in the plant. An example of this is a safe temperature limit for a CSTR. The alarm
signals that the temperature is too high and action is needed to prevent a runaway
scenario. If the corrective action is not taken, or not taken quickly enough, a critical alarm
can signal a computer program to automatically shut down the entire process or specific
Some industries may expect product quality to be closely regulated by the FDA or other
government agencies. Typically, this will be in a process where the final product is
directly used by people and the margins for error are small. These processes include food
processing and manufacturing consumer products, especially pharmaceuticals. These
industries usually require systems in place that frequently validate alarms, as well as
documentation for all critical alarm events. Measurements such as the weight percent of a
pharmaceutically active compound in a solution must be carefully monitored, with
recorded uncertainty analysis.
6.2.2 Environmental Safety
Emissions of solids, liquids, and gases in a plant are heavily regulated by government
agencies. Regulations apply for processes that emit chemicals to the atmosphere (either
directly or following a scrubber), processes that discharge material into a body of water,
or processes that require containment control devices like check valves and rupture disks.
Alarms are frequently used to comply with these regulations by measuring things such as
pH and organic solvent concentration. Typically, a warning alarm will alert personnel that
a threshold may be breached if action is not taken, allowing time to avoid an incident
requiring a formal report. Critical alarms can alert operators that a threshold has been
passed and automatically trigger the appropriate action, such as a systematic shutdown of
6.3 Regulatory Agencies
Federal and national agencies maintain smaller state subsections of various programs and
administrations. In most cases, the state level requires stricter compliance and lower
limits. Solely state-controlled programs usually handle the air and water quality since any
regulation violation results in the consequences for the immediate community.
6.3.1 Federal and Na:onal Agencies or Programs
Plant safety and environmental safety programs regulated on the national or federal level
are monitored by three main agencies; the Environmental Protection Agency (EPA), the
U.S. Department of Labor, the Food and Drug Administration, and the Department of
Homeland Security. These three governing bodies have created numerous acts,
committees, administrations and policies that protect the welfare of the employee,
community, and environment.
The EPA at the federal level, provides acts, laws, and regulations, that help maintain and
improve the air and water quality. The risk management program (RMP) is a mandatory
program that "require facilities that produce, handle, process, distribute, or store certain
chemicals to develop a Risk Management Program" . A Risk Management Plan (RMP)
must be submitted to the EPA for approval. Overall, risk management is a large part of
process control as control systems must adequately function and maintain compliance of
an entire facility. Failure logic for instrumentation, redundant sensors, and critical alarms
are essential in maintaining compliance, but a RMP is crucial for handling low-likelihood
The U.S. Department of Labor maintains the Occupational Safety and Health
Administration (OSHA) which provides rules and regulations for employers and
employees on safe workplace practices. Although individual states may maintain their
own occupational health and safety plans, OSHA is the governing body and authority on
those programs. Inspections are performed to ensure that all employees have a clean and
safe working environment that is hazard-free and risk-mediated. OSHA also maintains
the Process Safety Management Program (PSM) which regulates requirements for
facilities that handle highly hazardous chemicals. A list of chemicals that qualify include
chlorine, formaldehyde, and hydroflouric acid. Requirements of PSM include frequent
process hazard analysis (PHA), pre-startup safety review (PSSR), and incident
investigations. A cooperative program that OSHA maintains is The Voluntary Protection
Programs (VPP). These programs aim to bring together management and labor to provide comprehensive safety and health guidelines and regulations that keep all employees safe
while on the job. Each facility must submit application for entry into the program and
upon acceptance will follow a set of standards to ensure continued safety. The following
is a detailed description of why PSM should be important to chemical engineers, and also
some highlights of the main aspects of PSM as required by OSHA.
6.3.2 Process Safety Management (PSM) ‐‐ Why is this important to chemical engineers?
See the following links to videos provided by the United States Chemical Safety Board
describing a few catastrophic events that have occurred in the chemical engineering
2005 Texas City Rerinery Explosion
Besides the catastrophic nature of events that can occur from neglecting Process Safety,
large chemical facilities are granted a privilege and license to operate by the different
federal regulatory agencies. If these regulatory agencies perform an audit on a specific
facility, and find that their regulations are not being followed, then extremely large fines
can be levied to the company, even to the extent of shutting the facility down
permanently by removing that facility's privilege to operate. In the case of PSM, it is
OSHA who deals out these fines. For example, in 2009 OSHA attempted to levy a record
87 million dollar fine to an integrated oil company, which has not been finalized in the
legal system yet, but gives a good example of how important it is for companies
operating in the U.S., if they want to continue to operate safely and economically, to
follow all government regulations as closely as possible.
Unexpected releases of toxic, reactive, or flammable liquids and gases in processes
involving highly hazardous chemicals have been reported for many years in various
industries that use chemicals with such properties. Regardless of the industry that uses
these highly hazardous chemicals, there is a potential for an accidental release any time
they are not properly controlled, creating the possibility of disaster. As a result of
catastrophic incidents in the past, and to help ensure safe and healthful workplaces,
OSHA has issued the Process Safety Management of Highly Hazardous Chemicals
standard (29 CFR 1910.119), which contains requirements for the management of
hazards associated with processes using highly hazardous chemicals. OSHA’s standard
29CFR 1910.119 emphasizes the management of hazards associated with highly
hazardous chemicals and establishes a comprehensive management program that
integrates technologies, procedures, and management practices. A detailed list of these
standards can be found on the United States Department of Labor website: http://
www.osha.gov/SLTC/processsafetymanagement/standards.html An effective process safety management program requires a systematic approach to evaluating the whole
process. Using this approach the process design, process technology, operational and
maintenance activities and procedures, training programs, and other elements which
impact the process are all considered in the evaluation. Process safety management is the
proactive identification, evaluation and mitigation or prevention of chemical releases that
could occur as a result of failures in process, procedures or equipment. OSHA prescribes essential tools to the success of process safety management including:
Process Safety Information
Process Hazard Analysis
Operating Procedures and Practices
Pre‐Startup Safety Review
Management of Change
The thought is, with the simultaneous implementation of all of these things at a facility
dealing with large amounts of highly hazardous chemicals, the risk of a catastrophic
incident resulting from an unplanned release will be minimized. Following is a detailed
discussion of each of these tools prescribed by OSHA.
Process Safety Information (PSI)
Complete, accurate, and up-to-date written information concerning process chemicals,
process technology, and process equipment is essential to an effective process safety
management program. The compiled information will be a necessary resource to a variety
of users including the team that will perform the process hazards analysis, those
developing the training programs and operating procedures, contractors whose employees
will be working with the process, those conducting the pre-startup safety reviews, local
emergency preparedness planners, and insurance and enforcement officials. PSI includes,
but is not limited to:
Material and safety data sheets (MSDS)
A block Elow diagram showing the major process equipment and
interconnecting process Elow lines
Process Flow Diagrams (PFDs)
Piping and Instrument Diagrams (P&IDs)
Process design information, including the codes and standards relied on to
establish good engineering design
Process Hazards Analysis (PHA)
A process hazards analysis (PHA) is one of the most important elements of the process
safety management program. A PHA is an organized and systematic effort to identify and
analyze the significance of potential hazards associated with the processing and handling
of highly hazardous chemicals. A PHA is directed toward analyzing potential causes and
consequences of fires, explosions, releases of toxic or flammable chemicals, and major spills of hazardous chemicals. The PHA focuses on equipment, instrumentation, utilities,
human actions, and external factors that might impact the process. These considerations
assist in determining the hazards and potential failure points or failure modes in a
A team from each process unit in the facility will be tasked with conducting a PHA for
their process unit at regularly scheduled intervals as defined by OSHA. One example is in
an oil refinery, where a PHA has to be conducted and documented for each process unit
every five calendar years. The competence of the team conducting the PHA is very
important to its success. A PHA team can vary in size from two people to a number of
people with varied operational and technical backgrounds. The team leader needs to be
fully knowledgeable in the proper implementation of the PHA methodology that is to be
used and should be impartial in the evaluation. The other full or part time team members
need to provide the team with expertise in areas such as process technology, process
design, operating procedures and practices, alarms, emergency procedures,
instrumentation, maintenance procedures, safety and health, and any other relevant
subject as the need dictates. The ideal team will have an intimate knowledge of the
standards, codes, specifications and regulations applicable to the process being studied.
There are various methodologies for conducting a PHA. Choosing which one is right for
each individual facility will be influenced by many factors, including the amount of
existing knowledge about the process. For more information on the different
methodologies for conducting a PHA, see Center for Chemical Process Safety of the
American Institute of Chemical Engineers
Operating procedures provide specific instructions or details on what steps are to be taken
or followed in carrying out the task at hand. The specific instructions should include the
applicable safety precautions and appropriate information on safety implications. For
example, the operating procedures addressing operating parameters will contain operating
instructions about pressure limits, temperature ranges, flow rates, what to do when an
upset condition occurs, what alarms and instruments are pertinent if an upset condition
occurs, and other subjects. Another example of using operating instructions to properly
implement operating procedures is in starting up or shutting down the process.
Operating procedures and instructions are important for training operating personnel. The
operating procedures are often viewed as the standard operating practices (SOPs) for
operations. Control room personnel and operating staff, in general, need to have a full
understanding of operating procedures. In addition, operating procedures need to be
changed when there is a change in the process. The consequences of operating procedure
changes need to be fully evaluated and the information conveyed to the personnel. For
example, mechanical changes to the process made by the maintenance department (like
changing a valve from steel to brass or other subtle changes) need to be evaluated to
determine whether operating procedures and practices also need to be changed. All
management of change actions must be coordinated and integrated with current operating
procedures, and operating personnel must be alerted to the changes in procedures before
the change is made. When the process is shut down to make a change, the operating procedures must be updated before re-starting the process.
All employees, including maintenance and contractor employees involved with highly
hazardous chemicals, need to fully understand the safety and health hazards of the
chemicals and processes they work with so they can protect themselves, their fellow
employees, and the citizens of nearby communities. Training conducted in compliance
with the OSHA Hazard Communication standard (Title 29 Code of Federal Regulations
(CFR) Part 1910.1200) will inform employees about the chemicals they work with and
familiarize them with reading and understanding MSDSs. However, additional training in
subjects such as operating procedures and safe work practices, emergency evacuation and
response, safety procedures, routine and non-routine work authorization activities, and
other areas pertinent to process safety and health need to be covered by the employer's
In establishing their training programs, employers must clearly identify the employees to
be trained, the subjects to be covered, and the goals and objectives they wish to achieve.
The learning goals or objectives should be written in clear measurable terms before the
training begins. These goals and objectives need to be tailored to each of the specific
training modules or segments. Employers should describe the important actions and
conditions under which the employee will demonstrate competence or knowledge as well
as what is acceptable performance.
Careful consideration must be given to ensure that employees, including maintenance and
contract employees, receive current and updated training. For example, if changes are
made to a process, affected employees must be trained in the changes and understand the
effects of the changes on their job tasks. Additionally, as already discussed, the evaluation
of the employee's absorption of training will certainly determine the need for further
Pre‐Startup Safety Review
For new processes, the employer will find a PHA helpful in improving the design and
construction of the process from a reliability and quality point of view. The safe operation
of the new process is enhanced by making use of the PHA recommendations before final
installations are completed. P&IDs should be completed, the operating procedures put in
place, and the operating staff trained to run the process, before startup. The initial startup
procedures and normal operating procedures must be fully evaluated as part of the pre-
startup review to ensure a safe transfer into the normal operating mode.
For existing processes that have been shut down for turnaround or modification, the
employer must ensure that any changes other than "replacement in kind" made to the
process during shutdown go through the management of change procedures. P&IDs will
need to be updated, as necessary, as well as operating procedures and instructions. If the
changes made to the process during shutdown are significant and affect the training
program, then operating personnel as well as employees engaged in routine and non-
routine work in the process area may need some refresher or additional training. Any incident investigation recommendations, compliance audits, or PHA recommendations
need to be reviewed to see what affect they may have on the process before beginning the
Employers must review their maintenance programs and schedules to see if there are
areas where "breakdown" is used rather than the more preferable on-going mechanical
integrity program. Equipment used to process, store, or handle highly hazardous
chemicals has to be designed, constructed, installed, and maintained to minimize the risk
of releases of such chemicals. This requires that a mechanical integrity program be in
place to ensure the continued integrity of process equipment.
Elements of a mechanical integrity program include identifying and categorizing
equipment and instrumentation, inspections and tests and their frequency; maintenance
procedures; training of maintenance personnel; criteria for acceptable test results;
documentation of test and inspection results; and documentation of manufacturer
recommendations for equipment and instrumentation.
Management of Change
To properly manage changes to process chemicals, technology, equipment and facilities,
one must define what is meant by change. In the process safety management standard,
change includes all modifications to equipment, procedures, raw materials, and
processing conditions other than "replacement in kind." These changes must be properly
managed by identifying and reviewing them prior to implementing them. For example,
the operating procedures contain the operating parameters (pressure limits, temperature
ranges, flow rates, etc.) and the importance of operating within these limits. While the
operator must have the flexibility to maintain safe operation within the established
parameters, any operation outside of these parameters requires review and approval by a
written management of change procedure. Management of change also covers changes in
process technology and changes to equipment and instrumentation. Changes in process
technology can result from changes in production rates, raw materials, experimentation,
equipment unavailability, new equipment, new product development, change in catalysts,
and changes in operating conditions to improve yield or quality. Equipment changes can
be in materials of construction, equipment specifications, piping pre-arrangements,
experimental equipment, computer program revisions, and alarms and interlocks.
Employers must establish means and methods to detect both technical and mechanical
Temporary changes have caused a number of catastrophes over the years, and employers
must establish ways to detect both temporary and permanent changes. It is important that
a time limit for temporary changes be established and monitored since otherwise, without
control, these changes may tend to become permanent. Temporary changes are subject to
the management of change provisions. In addition, the management of change procedures
are used to ensure that the equipment and procedures are returned to their original or
designed conditions at the end of the temporary change. Proper documentation and
review of these changes are invaluable in ensuring that safety and health considerations
are incorporated into operating procedures and processes. Employers may wish to
develop a form or clearance sheet to facilitate the processing of changes through the
management of change procedures. A typical change form may include a description and
the purpose of the change, the technical basis for the change, safety and health
considerations, documentation of changes for the operating procedures, maintenance
procedures, inspection and testing, P&IDs, electrical classification, training and
communications, pre-startup inspection, duration (if a temporary change), approvals, and
authorization. Where the impact of the change is minor and well understood, a check list
reviewed by an authorized person, with proper communication to others who are affected,
may suffice. For a more complex or significant design change, however, a hazard
evaluation procedure with approvals by operations, maintenance, and safety departments
may be appropriate. Changes in documents such as P&IDs, raw materials, operating
procedures, mechanical integrity programs, and electrical classifications should be noted
so that these revisions can be made permanent when the drawings and procedure manuals
are updated. Copies of process changes must be kept in an accessible location to ensure
that design changes are available to operating personnel as well as to PHA team members
when a PHA is being prepared or being updated.
Incident investigation is the process of identifying the underlying causes of incidents and
implementing steps to prevent similar events from occurring. The intent of an incident
investigation is for employers to learn from past experiences and thus avoid repeating
past mistakes. The incidents OSHA expects employers to recognize and to investigate are
the types of events that resulted in or could reasonably have resulted in a catastrophic
release. These events are sometimes referred to as "near misses," meaning that a serious
consequence did not occur, but could have.
Employers must develop in-house capability to investigate incidents that occur in their
facilities. A team should be assembled by the employer and trained in the techniques of
investigation including how to conduct interviews of witnesses, assemble needed
documentation, and write reports. A multi-disciplinary team is better able to gather the
facts of the event and to analyze them and develop plausible scenarios as to what
happened, and why. Team members should be selected on the basis of their training,
knowledge and ability to contribute to a team effort to fully investigate the incident.
Each employer must address what actions employees are to take when there is an
unwanted release of highly hazardous chemicals. Emergency preparedness is the
employer's third line of defense that will be relied on along with the second line of
defense, which is to control the release of chemical. Control releases and emergency
preparedness will take place when the first line of defense to operate and maintain the
process and contain the chemicals fails to stop the release.
Employers will need to select how many different emergency preparedness or third lines of defense they plan to have, develop the necessary emergency plans and procedures,
appropriately train employees in their emergency duties and responsibilities, and then
implement these lines of defense. Employers, at a minimum, must have an emergency
action plan that will facilitate the prompt evacuation of employees when there is an
unwanted release of a highly hazardous chemical. This means that the employer's plan
will be activated by an alarm system to alert employees when to evacuate, and that
employees who are physically impaired will have the necessary support and assistance to
get them to a safe zone. The intent of these requirements is to alert and move employees
quickly to a safe zone. Delaying alarms or confusing alarms are to be avoided. The use of
process control centers or buildings as safe areas is discouraged. Recent catastrophes
indicate that lives are lost in these structures because of their location and because they
are not necessarily designed to withstand overpressures from shock waves resulting from
explosions in the process area.
Preplanning for more serious releases is an important element in the employer's line of
defense. When a serious release of a highly hazardous chemical occurs, the employer,
through preplanning, will have determined in advance what actions employees are to
take. The evacuation of the immediate release area and other areas, as necessary, would
be accomplished under the emergency action plan. If the employer wishes to use plant
personnel-such as a fire brigade, spill control team, a hazardous materials team-or
employees to render aid to those in the immediate release area and to control or mitigate
the incident, refer to OSHA's Hazardous Waste Operations and Emergency Response
(HAZWOPER) standard (Title 79 CFR Part 1910.1 20). If outside assistance is necessary,
such as through mutual aid agreements between employers and local government
emergency response organizations, these emergency responders are also covered by
HAZWOPER. The safety and health protection required for emergency responders is the
responsibility of their employers and of the on-scene incident commander.
An audit is a technique used to gather sufficient facts and information, including
statistical information, to verify compliance with standards. Employers must select a
trained individual or assemble a trained team to audit the process safety management
system and program. A small process or plant may need only one knowledgeable person
to conduct an audit. The audit includes an evaluation of the design and effectiveness of
the process safety management system and a field inspection of the safety and health
conditions and practices to verify that the employer's systems are effectively
implemented. The audit should be conducted or led by a person knowledgeable in audit
techniques who is impartial towards the facility or area being audited. The essential
elements of an audit program include planning, staffing, conducting the audit, evaluating
hazards and deficiencies and taking corrective action, performing a follow-up review, and
documenting actions taken.
6.3.3 Other Federal En::es
The Food and Drug Administration (FDA) is an agency of the United States Department
of Health and Human Services. The FDA regulates food, drugs, cosmetics, biologics,
medical devices, radiation-emitting devices and vetenary products manufactured in the
United States. The main goal of the FDA is to maitain that the products they regulate are
safe, effective, and secure. The FDA is also responsible that the products are accurately
represented to the public. State and local governments also help regulate these products in
cooperation with the FDA. The FDA does not regulate alcohol, illegal drugs, and meat
The Department of Homeland Security has recently taken a role in regulating chemical
plants because of 9/11. Chemical plants are seen by the government as targets for
terrorists and security in and around the plant is a major concern. Although the laws are
typically state run, the Department of Homeland Security has required mandatory
national security standard to chemical plants throughout the nation. Although the
mandates were fought by legislative for years, the Department of Homeland Security has
influence in the security in chemical plants. The law requires the plant to prepare a
vulnerability test and submit a site security plan. In order to validate these activities,
audits and site visits are/will be performed by government officials.
6.3.4 State Regula:ons
State regulations vary greatly from state-to-state depending on the main concern. For
instance, beach quality is more important in California than Nebraska due to the
geographical location. Similarly state legislative acts and administrations can expect high
performance from the chemical industry as it has the capability to affect all parts of a
community for many generations.
U.S. National ProEile on the Management of Chemicals. http://www.epa.gov/oppfead1/
U.S. Department of Labor. Occupational Safety & Health Administration. Process Safety
U.S. Department of Labor. Occupational Safety & Health Administration. State Occupational
Health and Safety Plans. http://www.osha.gov/dcsp/osp/index.html
U.S. Department of Labor. Voluntary Protection Programs. http://www.osha.gov/dcsp/vpp/
Environmental Protection Agency. Regulatory Information by Business Sector. http://
Environmental Protection Agency. Regulatory Information by Environmental Topic. http://
Environmental Protection Agency. State SpeciEic Regulatory Information Search Engine.
Environmental Protection Agency. Risk Management Plan. http://www.epa.gov/oem/
United States Chemical Safety and Hazard Regulation Board. Homepage. http://
U.S. Department of Health & Human Services. Food and Drug Administration. http://
United States Chemical Safety Board (CSB). http://www.csb.gov
Center for Chemical Process Safety (CCPS). http://www.aiche.org/ccps
Chapter 5. Logical Modeling
Sec3on 1. Boolean models: truth tables and state transi3on
Title: Boolean Models
Authors: Joseph Casler, Andry Haryanto, Seth Kahle and Weiyin Xu
Date Presented: Thursday, September 26, 2006
Date Revised: Thursday, September 21, 2006
Stewards: (September 12, 2007) Adhi Paisoseputra, Andrew Kim, Hillary Kast, Stephanie Cleto
First round reviews for this page
Rebuttal for this page
1.1 Introduc,on to Boolean Models
A Boolean is a variable that can only attain two values: True or False. In most
applications, it is convenient to represent a True by the number 1, and a False by the
number 0. A Boolean model, or Boolean network, is a collection of Boolean variables
that are related by logical switching rules, or Boolean functions, that follow an If-Then
format. This type of Boolean model is known as an autonomous model and will be the
primary type of model discussed in this article.
In chemical engineering, Boolean models can be used to model simple control systems.
Boolean functions can be used to model switches on pumps and valves that react to
readings from sensors that help keep that system operating smoothly and safely.
A simple application for level control of a CSTR is included in worked-out example 1. In
this example, Boolean function is used to close the inlet stream and open the outlet
stream when the level is higher than a specified point.
1.1.1 Boolean Func:ons
Boolean functions are logical operators that relate two or more Boolean variables within
a system and return a true or false. A Boolean expression is a group of Boolean functions,
which will be described individually below. When computing the value of a Boolean
expression, Parentheses are used to indicate priority (working from inside out as in
algebra). After that, LOGICAL INVERSION will always be first and LOGICAL
EQUIVALENCE will be last, but the order of operation for the AND, OR, and
EXCLUSIVE OR functions are specified with parenthesis.
Descriptions and examples of these functions are given below. A quick reference of each
of the functions can be found after the examples.
LOGICAL INVERSION is a function that returns the opposite value of a variable. The
function is denoted as a prime on the variable (e.g. A' or B') For example, if we say that
A is true (A=1), then the function A' will return a false (A'=0). Similarly, if we say that A
is false (A=0) then the function A' will return true (A'=1).
A=1, B=A' then B=0
The AND function relates two or more Boolean variables and returns a true if-and-only-if
both variables are true. A dot is used to denote the AND function, or it is simply omitted.
For example "A and B" can be written as "A•B" or as "AB." In this example, the AND
function will only return a true if-and-only-if both Boolean variables A and B have a
value of 1.
AB = 1
AB = 0
A=1, B=1, C=1 ABC = 1
A=1, B=0, C=1 ABC = 0
The OR function relates two or more Boolean variables and returns a true if any
referenced variables are true. A plus is used to denote the OR function. For example "A or
B" can be written as "A+B." In this example, the OR function will return true if either
Boolean variable, A or B, has a value of 1.
A+B = 1
A+B = 1
A+B = 0
A=0, B=0, C=1 A+B+C = 1
A=0, B=0, C=0 A+B+C = 0
The EXCLUSIVE OR function relates two or more Boolean variables and returns true
only when one of the variables is true and all other variables are false. It returns false when more than one of the variables are true, or all the variables are false. A
circumscribed plus is used to denote the EXCLUSIVE OR function. For example "A
EXCLUSIVE OR B" can be written as "A
B = 0
B = 1
B = 1
B = 0
A=0, B=0, C=0 A
C = 0
A=1, B=0, C=0 A
C = 1
A=1, B=0, C=1 A
C = 0
A=1, B=1, C=1 A
C = 0
The LOGICAL EQUIVALENCE function equates two Boolean variables or expressions.
The LOGICAL EQUIVALENCE function, denoted as =, assigns a Boolean variable a
true or false depending on the value of the variable or expression that it is being equated
with. For example, A LOGICAL EQUIVALENCE B can be written as A = B. In this
example, the value of A will be assigned the value of B.
1.1.2 Boolean Networks
As stated in the introduction, a Boolean network is a system of boolean equations. In
chemical engineering, Boolean networks are likely to be dependant on external inputs as
a means of controlling a physical system. However, the following sections pertain mostly
to synchronous autonomous systems. An autonomous system is one that is completely
independent of external inputs. Every Boolean variable is dependent on the state of other
Boolean variables in the system and no variable is controlled by an external input. A
synchronous system is one that logical switching (the changing of Boolean variables)
occurs simultaneously for all variables based on the values prior to the incidence of
Here is an example of an autonomous boolean network:
A = B+C'
B = AC
C = A'
1.2 Truth Tables
A truth table is a tabulation of all the possible states of a Boolean Model at different time
frames. A simple truth table shows the potential initial states at time, Ti, and the
corresponding subsequent states at time Ti+1, of a Boolean network. Truth tables can
provide one with a clearer picture of how the rules apply and how they affect each
situation. Hence, they help to ensure that each output only has one control statement so
that the Boolean rules do not conflict with each other.
1.2.1 Construc:ng Truth Tables
1) Draw up a table with the appropriate number of columns for each variable; one for
each input and output.
2) The left side of the column should contain all possible permutations of the input
variables at time Ti. One method to accomplish this might be to list all possible
combinations in ascending binary order.
3) The right side of the column should contain the corresponding outcome of the output
variables at the subsequent time Ti+1. A generic example of this with 2 variables can be
A quick way to check that you have all of the possible permutations is that there should
be 2x possible permutations for X input variables.
1.2.2 Example of a Truth Table
The sample system we will be using is based on hydrogen fuel cell technology. The
equation for the operation of hydrogen fuel cells is H2 + O2 -> H2O. One aspect of Proton
Exchange Membrane (PEM) fuel cells (a type of fuel cell) is that the performance of the
fuel cell is highly dependent on the relative humidity of the system (if humidity rises too
high, the fuel cell will flood and H2 and O2 will be unable to reach the cell. If humidity
falls too low, the fuel cell will dry up and the performance will drop.) The task is to create
a Boolean model for this simplified water management system.
The system produces steam within the system, and there is a vent to release steam if the
system becomes too saturated. In our system, we will assume that the inputs are
stoichimetric and react completely. Also we will assume that pressure buildup from steam
is negligible compared to the change in relative humidity. The only variable in question is
the %relative humidity in the system.
note: this is not how water management actually works in a fuel cell system,
but it is a simple example.
A will represent the moisture controller response (0 indicates relative humidity or %RH <
80%, 1 indicates %RH >80%)
B will represent the valve status (0 is closed, 1 is open)
The corresponding Boolean functions for this model are given below (normally you
would have to design these yourself to meet the criteria you desire):
A = A
B = A
For this example with 2 input variables, there are 22 = 4 possible permutations and 22 = 4
rows. The resultant permutations for the outputs are: For A where Y=1, the number of 0s
and 1s are 2(Y-1)=2(1-1)=1. For B where Y=2, the number of 0s and 1s are 2(Y-1)=2(2-1)=2.
The resultant truth table is below:
1.3 State Transi,on Diagrams
A state transition diagram is a graphical way of viewing truth tables. This is
accomplished by looking at each individual initial state and its resultant state. The
transition from one state to another is represented by an arrow. Then they are pieced
together like a jigsaw puzzle until they fit in place. When one state leads to itself it simply
points to itself. The following example is based on the truth table in the previous section.
In this example, there are two state cycles. A state cycle is a combination of states around
which the system continually enters and reenters. For a finite number of states, there will
always exist at least one state cycle. A state cycle is also a pathway or a flowchart that
shows the "decision making process" of a Boolean network. This feature is a direct result
from two attributes of Boolean networks:
1. Finite number of states
2. Deterministic (there is a certain set of rules that determines the next state that will be
In the example presented in the previous section, there were two state cycles. One
advantage of state cycles is it easily allows you to see where your model will end up
cycling and if there are any states that are not accounted for properly by your model. In
the previous diagram, if the moisture controller indicated the humidity was below the set
value, it would close the valve or hold the valve closed. If the moisture controller
indicated that the humidity was above the set value, it would either open the valve or hold
Consider this alternate system.
In this example, the state cycle says that if the meter says that the humidity is below the
set point it would cycle the vent valve open and closed. This would hurt the system and is
not a desired outcome of the model.
For safety and functionality issues, a process control engineer would want to consider all
possiblities in the design of any Boolean network modeling a real system.
1.4 Limita,ons of Boolean Networks
1.4.1 Advantages of Boolean Networks
Unlike ordinary differential equations and most other models, Boolean
networks do not require an input of parameters.
Boolean models are quick and easy to compute using computers.
Boolean networks can be used to model a wide variety of activities and
Boolean networks can be used to approximate ordinary differential
equations when there are an inEinite number of states.
1.4.2 Disadvantages of Boolean Networks
Boolean networks are restrained to computing very simple math. They
cannot be used for calculus and to calculate large quantities.
Boolean models have relatively low resolution compared to other models.
It is very time consuming and complicated to build Boolean networks by
1.5.1 Worked out Example 1
A hypothetical CSTR needs to have its liquid level maintained below a safety mark by
means of a sensor, L1, on the corresponding mark and a control valve placed on the inlet
and outlet streams – V1 and V2 respectively. A typical application of the afore-mentioned
system could involve heterogeneously catalyzed liquid reaction(s) with liquid product(s).
Solution to Example 1
Water level sensor
water level desirable too high
position closed open
Assume that the CSTR is empty and being filled up. CSTR, being empty, sets the value of
L1 to zero. Filling up the CSTR could be done by opening valve 1 - V1 assuming a value
of one - and closing valve 2 - V2 assuming a value of zero.
In coordinate form, the initial state is as such: (L1, V1, V2) = (0, 1, 0)
Let h be the water level and WL1 be the safety mark defined in the CSTR. The system
could assume one of the following states at any one time:
1) h < WL1 : desirable water level
Maximizing production of the chemical prompts the system
to remain in its current state - that is, its initial
state. (L1, V1, V2)final = (0, 1, 0) final state
2) h > WL1 : water level too high
Prevention of flooding requires that the tank be emptied.
As such, valve 1 (V1) should be closed to stop the input
while valve 2 (V2) should be open to empty the extra water
above the safety water mark. (L1, V1, V2)' = (1, 1, 0)
trigger to valve (L1, V1, V2)final = (1, 0, 1)
1.6 Quick Reference
1.7 Sage's Corner
Boolean Models: A mechanism for
constructing truth tables
Slides without narration
Slides without narration Truth Tables
James E. Palmer and David E. Perlman (1993). Schaum's Outline of Theory and Problems of
Introduction to Digital Systems, McGraw‐Hill Professional. ISBN 0070484392
Stuart A. Kauffman (1993). The Origins of Order Self‐Organization and Selection in Evolution, Oxford University Press. ISBN 0195079515
Sec3on 2. Logical control programs: IF... THEN… WHILE…
Title: Logical control programs: IF, THEN, WHILE...
Video lecture available for this section!
Authors: Stephanie Fraley, Michael Oom, Benjamin Terrien, John Zalewski
Stewards: Ross Bredeweg, Jessica Morga, Ryan Sekol, Ryan Wong
Date Presented:September 26, 2006 /Date Revised: September 13, 2007
First round reviews for this page
Rebuttal for this page
A logical control program is a set of conditional statements describing the response of a
controller to different inputs. A controller is a computer used to automate industrial
processes (See Wikipedia). Process engineers use control logic to tell the controller in a
process how to react to all inputs from sensors with an appropriate response to maintain
normal functioning of the process. Control logic (sometimes called process logic) is
based on simple logic principles governed by statements such as IF X, THEN Y, ELSE Z
yet can be used to describe a wide range of complex relationships in a process. Although
different controllers and processes use different programming languages, the concepts of
control logic apply and the conditions expressed in a logical control program can be
adapted to any language.
The concepts behind logical control programs are not only found in chemical processes;
in fact, control logic is used in everyday life. For example, a person may regulate his/her
own body temperature and comfort level using the following conditional logic
statements: IF the temperature is slightly too warm, THEN turn on a fan; IF the
temperature is way too warm, THEN turn on the air conditioning; IF the temperature is
slightly too cold, THEN put on a sweatshirt; IF the temperature is way too cold, THEN
turn on the fireplace. The person takes an input from the environment (temperature) and if
it meets a certain prescribed condition, she executes an action to keep herself
comfortable. Similarly, chemical processes evaluate input values from the process against
set values to determine the necessary actions to keep the process running smoothly and
safely (aforementioned example illustrated below).
The following sections elaborate on the construction of conditional logic statements and
give examples of developing logical control programs for chemical processes.
2.2 Logic Controls
Logical controls (IF, THEN, ELSE, and WHILE) compare a value from a sensor to a set
standard for the value to evaluate the variable as True/False in order to dictate an
appropriate response for the physical system. The control program for a chemical process
contains many statements describing the responses of valves, pumps, and other
equipment to sensors such as flow and temperature sensors. The responses described by
the system can be discrete, such as an on/off switch, or can be continuous, such as
opening a valve between 0 and 100%. The goal of a control program is to maintain the
values monitored by the sensors at an acceptable level for process operation considering
factors like product quality, safety, and physical limitations of the equipment. In addition
to describing the normal activity of the process, a control program also describes how the
process will initialize at the start of each day and how the controller will respond to an
emergency outside of the normal operating conditions of the system. Unlike a linear
computer program, logic programs are continuously monitoring and responding without a
specific order. Before constructing logical control programs, it is important to understand
the conditional statements, such as IF-THEN and WHIlE statements, that govern process
The following logic controls found below are written in pseudocode. Pseudocode is a
compact and informal way of writing computer program algorithms. It is intended for
human reading instead of machine reading, and does not require stringent syntax for
people to understand. Pseudocode is typically used for planning computer program
development and to outline a program before actual coding occurs.
2.2.1 IF‐THEN statements
IF-THEN statements compare a value from a sensor to a set value and describe what
should happen if the relationship holds. The IF-THEN statement takes the form IF X,
THEN Y where X and Y can be single variables or combinations of variables. For
example, consider the following statements 1 and 2. In statement 1, both X and Y are
single variables whereas in statement 2, X is a combination of two variables. The ability
in conditional logic to combine different conditions makes it more flexible than incidence
graphs, which can only describe monotonic relationships between two variables (See
incidence graphs). A monotonic relationship is one where if X is increasing, Y is always decreasing or if X is increasing, Y is always increasing. For complex processes, it is
important to be able to express non-monotonic relationships.
1. IF T>200 C, THEN open V1
2. IF T> 200 C and P> 200 psi, THEN open V1.
Where T is Temperature, P is pressure, and V represents a valve.
In statement 1, if the temperature happens to be above 200 C, valve 1 will be opened.
In statement 2, if the temperature is above 200 C and the pressure is above 200 psi, then
the valve will be opened.
Otherwise, no action will be taken on valve 1
If the conditions in the IF statement are met, the THEN statement is executed, and
depending on the command, the physical system is acted upon. Otherwise, no action is
taken in response to the sensor input. In order to describe an alternate action if the IF
condition does not hold true, ELSE statements are necessary.
2.2.2 ELSE statements
The simple form of an IF-THEN-ELSE statement is IF X, THEN Y, ELSE Z where again
X, Y, and Z can be single variables or combinations of variables (as explained in the IF-
THEN section above). The variable(s) in the ELSE statement are executed if the
conditions in the IF statement are not true. This statement works similar to the IF-THEN
statements, in that the statements are processed in order. The ELSE statement is referred
to last, and is a condition that is often specified to keep the program running. An example
is the following:
IF P>200 psi, THEN close V1
ELSE open V4
In this statement, if the pressure happens to be 200psi or less, the THEN statement
will be skipped and the ELSE statement will be executed, opening valve 4.
Sometimes, if X, Y or Z represent many variables and several AND or OR statements are
used, a WHILE statement may be employed.
2.2.3 CASE statements
CASE statement is an alternative syntax that can be cleaner than many IF..THEN and
ELSE statements. The example shown in the table below shows its importance.
IF..THEN and ELSE
ELSE IF T
Thus CASE statements make the code easier to read for debugging.
2.2.4 WHILE statements
The WHILE condition is used to compare a variable to a range of values. The WHILE
statement is used in place of a statement of the form (IF A>B AND IF A
statements simplify the control program by eliminating several IF-AND statements. It is
often useful when modeling systems that must operate within a certain range of
temperatures or pressures. Using a WHILE statement can allow you to incorporate an
alarm or a shut down signal should the process reach unstable conditions, such as the
limits of the range that the WHILE statement operates under. A simple example
illustrating the use of the WHILE statement is shown below.
A tank that is initially empty needs to be Eilled with 1000 gallons of water 500
seconds after the process has been started‐up. The water Elow rate is exactly 1
gallon/second if V1 is completely open and V1 controls the Elow of water into the
Using a IF...THEN statement the program could be written as follows:
IF t > 500 and t < 1501 THEN set V1 to open
ELSE set V1 to close.
The WHILE statement used to describe this relationship is as follows:
WHILE 500 < t < 1501 set V1 to open
ELSE set V1 to close.
It may not seem like much of a change between the two forms of the code. However, this
is a very simple model. If modeling a process with multiple variables you could need
many IF...THEN statements to write the code when a single WHILE condition could
V1 controls reactants entering a reactor that can only run safely if the temperature
is under 500K.
The WHILE can be used to control the process as follows:
WHILE T < 500 set V1 to open
ELSE set V1 to close. ALARM.
This example shows how a WHILE condition can be used as a safety measure to prevent
a process from becoming unstable or unsafe.
In addition to lists of IF-THEN-ELSE-WHILE statements, control logic can be
alternately represented by truth tables and state transition diagrams. Truth tables show all
the possible states of a model governed by conditional statements and state transition
diagrams represent truth tables graphically. Oftentimes, these are used in conjunction
with booleans, variables that can only have two values, TRUE OR FALSE. A Boolean
model or Boolean function follows the format of IF-THEN statements described here. A
description of Boolean models, truth tables, and state transition diagrams is given here.
2.2.5 GO TO statements
The GO TO statement helps to break out of current run to go to a different configuration.
It can be an important operator in logical programming because a lot of common
functions are accessed using GO TO. However, many programmers feel that GO TO
statements should not be used in programming since it adds an extra and often
unnecessary level of complex that can make the code unreadable and hard to analyze.
Even though the GO TO operator has its downsides, it is still an important operator since
it can make help to simplify basic functions. It can simplify code by allowing for a
function, such as a fail safe, be referenced multiple times with out having to rewrite the
function every time it is called. The GO TO operator is also important because even
advanced languages that do not have a GO TO function often have a different operator
that functions in a similar manner but with limitations. For example, the C, C++ and java
languages each have functions break and continue which are similar to the GO TO
operator. Break is a function that allows the program to exit a loop before it reaches
completion, while the continue function returns control to the loop without executing
the code after the continue command. A function is a part of code within a larger
program, which performs a specific task and is relatively independent of the remaining
code. Some examples of functions are as follows:
FUNCTION INITIALIZE: It runs at the beginning of a process to make sure all the
valves and motor are in correct position. The operation of this function could be to close
all valves, reset counters and timers, turn of motors and turn off heaters.
FUNCTION PROGRAM: It is the main run of the process.
FUNCTION FAIL SAFE: It runs only when an emergency situation arises. The operation
of this function could be to open or close valves to stop the system, quench reactions via
cooling, dilution, mixing or other method.
FUNCTION SHUTDOWN: It is run at the end of the process in order to shutdown.
FUNCTION IDLE: It is run to power down process.
All the functions mentioned above except FUNCTION IDLE are used in all chemical
2.2.6 ALARM statements
The ALARM statement is used to caution the operators in case a problem arises in the
process. Alarms may not be sufficient danger to shut down the process, but requires
outside attention. Some example when ALARM statements are used in the process are as
-If the storage tank of a reactant is low, then ALARM.
-If the pressure of a reactor is low, then ALARM.
-If no flow is detected even when the valve is open, then ALARM.
-If the temperature of the reactor is low even after heating, then ALARM.
-If redundant sensors disagree, then ALARM.
In conclusion ALARM functions are very important in order to run a process safely.
2.3 Control Language in Industry
As stated before, these commands are all in pseudocode, and not specific to any
programming language. Once the general structure of the controller is determined, the
pseudocode can be coded into a specific programming language. Although there are many
proprietary languages in industry, some popular ones are:
- Visual Basic
- Database programming (ex. Structured Query Language/SQL)
Pascal and Fortran are older languages that many newer languages are based on, but they
are still used with some controllers, especially in older plants. Any experience with
different computer languages is a definite plus in industry, and some chemical engineers
make the transition into advanced controls designing, writing, and implementing code to
make sure a plant keeps running smoothly.
2.4 Logical Func,ons in Microsol Excel
Microsoft Excel has basic logical tools to help in constructing simple logical statements
and if needed more complex logical systems. A list of the functions is shown below.
TRUE().............................................Returns the logical value, TRUE.
FALSE()...........................................Returns the logical value, FALSE.
AND(logical_expression_A,B,C).........Returns TRUE if all the expressions are true.
OR(logical_expression_A,B,C)...........Returns TRUE if one of the expressions are true.
NOT(logical_expression)....................Returns the opposite of the expected logical value.
If the expression is TRUE, it will return FALSE
IFERROR(value,value_if_error)............Returns the value unless there is an error in which it will return the value_if_error.
IF(logical_expression,value_if_true,value_if_false)..............Checks the validity of the
expression and returns TRUE or FALSE likewise.
The IF() function will be most useful in logical programing. It is essentially an IF THEN
or IF ELSE function returning one of two values based on the logical expression it is
testing. Excel also allows logical functions within functions. This allows for logical
expressions involving more than one IF statement within itself for example. Use of these
tools will be practical in quickly setting up control programs and other systems in
2.5 Construc,ng a Logical Control Program
Understanding the conditional statements used in control logic is the first step in
constructing a logical control program. The second step is developing a thorough
understanding of the process to be controlled. Knowledge of the equipment, piping, and
instrumentation (contained on a P&ID diagram), operating conditions, chemical compounds used, and safety concerns is necessary. Particularly it is important to know
the measured and controlled variables. For example, the pressure limits of a tank must be
known in order to develop a control plan to ensure safety; ignoring this constraint could
lead to explosion and injury. Once the necessary controls are known, one can develop a
plan using the logical statements described previously. The third step is constructing a
logical control program is understanding that there is not always a right answer, meaning
there are many different ways to ensure the same desired outcome.
Worked out Examples 1, 2, and 3 demonstrate the construction of simple logical control
programs. The more complex the situation, the longer the logical control plan becomes
yet the process is still the same. An example of a more complex logical control program
is given here.This example is from the 2005 ChE 466 class at the University of Michigan
and describes an entire chemical process from the delivery of raw materials to the output
of the final product.
2.6 Determining Fail Safe Condi,ons
Fail safe is the practice of designing a system to default to safe conditions if anything or
everything goes wrong. The goals of fail safe conditions are to:
Protect plant personal
Protect the local community around the plant
Protect the environment
Protect plant equipment
In order to establish safe conditions, fail safe programs must specify the desired positions
of all valves and status of all motors and controlled equipment. For example, in an
exothermic reactor, fail safe conditions would specify opening all cooling water valves,
closing all feed valves, shutting off feed pump motors, turning on agitator motor, and
open all vent valves.
Control programs frequently define fail safe conditions at the beginning of the program.
These conditions are then activated using a GO TO command when process conditions
exceed the maximum or fall below the minimum allowable values.
All processes must be evaluated for conditions that could cause hazards and fail safe
procedure must be designed counteract the effects.
2.7 Worked Out Example 1: Reboiler
Disclaimer: This is a fictional example of an isolated unit operation, neglecting possible
outcomes on the rest of the plant.
Reboilers are used in industry to cool down process streams by creating steam from
water. This chemical process involves a phase change from liquid (water) to gas (steam)
and it is important to monitor flowrates, temperatures, and pressures. Below is a diagram
of a reboiler. The controlled variables are F1, F2, and F3; these are controlled by
manipulating the corresponding valves. The measured variables are P1, T1, and T2.
Considering the operating conditions and constraints given below, write a logical control
program for the reboiler.
The operating constraints are as follows:
T1 must not exceed 350 ˚C
T2 must be between 100 and 200 ˚C
P1 cannot exceed 150 psi
The normal operating conditions for the controlled variables are as follows:
F1 is 20 gal/min
F2 is 10 gal/min
F3 is closed
The first step is understanding the system to be controlled. Looking at the diagram, one
can see that F1 controls the flow rate of the service water, F2 controls the flow rate of the
process stream, and F3 controls the vent to the atmosphere. T1 is the temperature of the
process stream entering the reboiler and T2 is the temperature of the process stream
exiting the reboiler. P1 is the pressure inside the reboiler.
Below is a possible control program to ensure the operating constraints are met; there
may be other solutions to achieve the same objective:
IF T2 > 200 ˚C, THEN F1 = 30 gal/min
IF T2< 100 ˚C, THEN F1 = 10 gal/min
IF P1 > 150 psi, THEN open F3
IF T1 > 350 ˚C, THEN F2 = 2 gal/min
In order to control the exit temperature of the process stream, one can increase or
decrease the service water from the normal flow rate. Opening the vent to the atmosphere
reduces the pressure if it reaches an unsafe value. If the entering temperature is too high
for the process stream, reducing the entering flow rate will ensure the exit temperature is
not too high for the remainder of the process. Note: reducing the process stream may
negatively impact the rest of the plant.
2.8 Worked out Example 2: Thermostat
Chemical engineers are increasingly involved in biological applications. In many
biological processes, temperature control can be very critical to the process. Take, for
example, a simulated cell on a computer chip. Let's say that it is imperative for the chip to
remain at 97oF ± 1oF, very similar to the temperature of the human body. Some of the
reactions and processes on the chip will not function at temperatures outside this range
and can become irreversibly damaged unless the power supply to the chip is turned off.
The power is turned on and off by a switch S1. There are flows of cool water with an
automatic valve V1 and warm water with an automatic valve V2 for cooling and heating
purposes. The chip is attached to a thermostat to sense and control the temperature, T.
Write out a controlled logic scheme to maintain the chip temperature and to prevent
Hint: Heat or cool the chip before reaching the limits (about half a degree)
To control the temperature, the chip must be heated or cooled depending on the
IF (T<96.5) THEN V2 is open
ELSE V2 is closed
IF (T>97.5) THEN V1 is open
ELSE V1 is closed
The control is executed before the temperature limit is reached to allow for lag time in the
heating or cooling water flow.
Also, to ensure that the chip is not damaged, the power needs to be shut off if the
temperature goes above 98oF or below 96oF
ELSE S1 is off
2.9 Worked out Example 3: Chemical Reactor
There is an exothermic chemical reaction occurring in a CSTR (Continuous Stirred Tank
Reactor) that involves two reactants being fed at a 1:1 ratio. All valves are set to be 50%
open normally. Write a control program that keeps the level in the CSTR vessel less than
8 meters (the tank is 10 meters tall) and the reactor temperature below 450 degrees
While L1 > 8 set V3 to 100% open and close V1 and V2
Else set V1 and V2 and V3 to 50% open
If T2 > 450 THEN set V5 and V4 to 100% open
Else set V5 and V4 to 50% open
This solution gives an example of using AND statements to control multiple valves with
just one condition.
2.10 Worked out Example 4: Programming and Alarms
There is a process that is run by the P&ID shown below.
Based on this process and the steps listed below, write out a detailed control program for
the process. Use comments (denoted with #) if necessary to explain the logic behind the
1) Measure Qw units of water into a tank
2) Add Qc units of dried chickpeas
3) Let dried chickpeas soak for 20 hours without mixing
4) Drain off soaking water to waste (assume the filter in the tank will not allow whole
chickpeas through the pump) 5) Add Qw units of fresh water to the tank.
6) Heat the tank to Tcook and maintain the pressure at 4 atm. Note that your tank is rated
to withstand pressures between 0.5 and 6 atm, while outside of that range the tank may
implode or explode.
7) Cook chickpeas for 20 minutes.
8) After cooking, turn off heat and allow the system to return to ambient temperature
(Tamb) and ambient pressure. Beware of a strong vacuum forming in the tank as the
water vapor condenses!
9) Drain cooking water to drain.
10) Pump in Qs units of the tahini spice mix
11) Blend the mixture for 10 minutes to produce a smooth hummus paste.
12) Pump out product to packaging.
13) Fill tank with clean water and agitate to clean the reactor.
14) Pump wash water to drain.
Turn off M1, M2, M3, M4
Close V1, V2, V3, V5, V6, V7, SV1
Set all timers to zero
Set all totalizers to zero
Turn off M1, M2, M3, M4
Close V1, V2, V3, V5, V7, SV1
#Step 1 – Measure Qw unites of water into a tank
Turn on M1
WHILE FC1tot < Qw:
Adjust V1 to FC1set
IF LC1 < LC1min:
Turn off M1
#FC1tot is the total amount of Eluid that has gone through the Elow meter
#FC1set is the set point (amount the valve is open) for V1 that FC1 has already
programmed into it
#LC1min is the minimum acceptable level of Eluid in S001
#Step 2 – Add Qc units of dried chickpeas
WHILE FC4 < Qc:
Adjust SV1 to FC4set
IF LC4 < LC4min:
#FC4set is the set point for SV1 that FC4 has already programmed into it
#LC4min is the minimum acceptable level of Eluid in S003. LC4 is not on the P&ID,
however, it makes sense to have one on it so the level on the tank can be properly
#Step 3 – Let dried chickpeas soak for 20 hours without mixing
WAIT 20 hours
#Step 4 – Drain off soaking water to waste
Turn on M3
WHILE FC3tot < Qw:
Adjust V7 to FC3set2
Turn off M3
#FC3tot is the total amount of Eluid that has gone through the Elow meter
#FC3set2 is the set point for V7 that FC3 has already programmed into it
#Step 5 – Add Qw units of fresh water to the tank
Turn on M1
WHILE FC1tot < Qw:
Adjust V1 to FC1set
IF LC1 < LC1min:
Turn off M1
#Step 6 – Heat the tank to Tcook and maintain the pressure at 4 atm.
WHILE TC1 < Tcook:
Adjust v5 to Tcook
IF OR (PC1 < 0.5, PC1 > 6):
GO TO FAILSAFE
IF PC1 < PC1set:
Adjust V6 to PC1set
IF LC3 > LC3max:
GO TO FAILSAFE
#PC1set is the setting that V6 must be set to for the tank to have 4 atm of pressure
#LC3max is the maximum level that the contents of the tank are allowed to get to.
Anything higher indicates a problem with one of the Elow meters.
#Step 7 – Cook chickpeas for 20 minutes#
WAIT 20 minutes
#Step 8 –After cooking, turn off heat and allow the system to return to ambient
temperature and pressure
IF PC1 > PC1amb:
Adjust V6 to PC1set2
IF OR (PC1 < 0.5, PC1 > 6):
GO TO FAILSAFE
WHILE TC1 > Tamb:
#PC1amb is the ambient pressure of 1 atm that the system needs to get to
#PC1set2 is the second setting on PC1 which effects how open V6 is
#Step 9 – Drain cooking water to drain
Turn on M3
WHILE FC3tot < Qw:
Adjust V7 to FC3set
Turn off M3
#Step 10 – Pump in Qs units of the Tahini spice mix
Turn on M2
WHILE FC2tot < Qs:
Adjust V2 to FC2set
IF LC2 < LC2min:
Turn off M2
#FC2tot is the total amount of Eluid that has gone through the Elow meter
#FC2set is the set point for V2 that FC2 has already programmed into it
#Step 11 – Blend the mixture for 10 minutes to produce a smooth hummus paste
Turn on M4
WAIT 10 minutes
Turn off M4
#Step 12 – Pump out product to packaging
Turn on M3
WHILE LC3 > 0:
Adjust V3 to FC3set
Turn off M3
#FC3set is the set point for V3 that FC3 has already programmed into it
#Step 13 – Fill tank with clean water and agitate to clean the reactor
Turn on M1
WHILE LC3 < LC3max:
Adjust V1 to FC1set
IF LC1 < LC1min:
Turn off M3
Turn on M4
WAIT 10 minutes
Turn off M4
#Step 14 – Pump was water to drain
Turn on M3
WHILE LC3 > 0:
Adjust V7 to FC3set2
Turn off M3
2.11 Worked Out Example 5: Another Chemical Reactor (taken from Prof. Barkel's
WRITING THE CONTROL PROGRAM
xA = input amount of A
yB = input amount of B
LL = low level
LH = high level
Lmax = maximum high level
Lmax = maximum low level
Things to note:
Be sure to use If, Then statements.
Lines in italics are comments used to organize the program.
Equal means within +/- 0.05 % of the value being held equal.
Initialize This is used to set all control devices to the position you want them in.
1. Turn off all valves
2. Shut off all motors
Fail Safe This is used to shut down the process in case something goes wrong and must
be terminated immediately.
1. Turn off all valves except V5, V7, V9, V6
2. Shut off all motors except M2
If T1>Tmax, then go Fail Safe.
2. Open V6, V9, V1. [so that systems doesn't build up pressure]
3. If L1> LL, then turn on M1. [fill with A]
4. If L2>= Lag, turn on M2. [start stirrer]
5. If F1>= xA, turn off V1, shut off M1. [stop flow of A]
6. Open V5, V7. [allow for cooling]
7. If P1>= PL, then open V2. [fill with B]
8. If L4>=L4min, open V8, turn on M4. [release product AB]
9. If L2< Lag, then shut off M2. [so motor doesn't run dry]
10. If L4< L 4 L, close V8. [stop outflow of product AB]
11. If T1>< TH, then open V5. [cool reactor temperature]
12. If T2>< TH, then open V5. [cool upper product stream]
13. If T1<< TL, then close V5. [stop cooling of reactor]
14. If F2>=< yB, then turn off V2. [stop flow of B]
15. Close V8, M4, leave V6, V9 open. [shut down process but allow it to vent]
16. Pump out BAB.
2.12 Worked Out Example 6
A + B --> AB
The reaction is exothermic
A, B, AB are all liquids
It goes to 100% completion
XA = total amount of A used
YB = total amount of B used
B is added slowly into a full charge of A
The temperature is maintained at TR
Upon completion of the reaction, the AB is cooled to TP
ZC, an amount of solvent C is added to the AB to make the final product
Using only the equipment and instrumentation shown, write the control logic for this
BATCH reaction. Use If, Then logic.
Use of subscripts:
Ag for agitator
L for low-bottom of control range
H for high-top of control range
Min for minimum - lowest level allowed
Max for maximum - highest level allowed
tot for totalizer
Process Control Logic
Equal means within +/‐ 0.05% of the value being held equal.
Shut all valves
Turn off all motors
Set all FCtot = 0
2) Fail safe
Shut off V1, V2, V3, V4
Turn off M1, M2, M3
Turn off M4, Open V4
Turn on M5 if LC4>Lag, else turn off M5
3) If T1> Tmax, then go Fail Safe
4) If L2> L 2 min, then turn on M2, open V2
5) If L2< L 2 min, then turn off M2, shut off V2
6) If FC 2 tot = XA, then turn off M2, shut off V2
7) If L4>Lag, then turn on M5
8) If L1> L 1 max, then go Fail Safe
9) If L1> L 1 min, then turn on M1, open V1
10) If L1< L 1 min,then turn off M1, shut off V1
11) If FC 1 tot = YB, then turn off M1, shut off V1
12) If T1> T 1 H, then open V5
13) If T1< T 1 L, then close V5
14) If L4> L 4 H, then close V1, turn off M1
15) If T1> TP, then open V5
16) If T1= TP, then close V5
17) If L3> L 3 min, then turn on M3, open V3
18) If L3< L 3 min, then turn off M3, shut off V3
19) If FC 3 tot = ZC, then turn off M3, shut off V3
20) If LC4
21) Open V4
22) Turn on M4
23) If L4< L 4 min, then turn off M4, shut off V4
2.13 Sage's Corner
Narrated Presentation of Example 1
Narrated Presentation of Example
Savitch, Walter. "Problem Solving with C++ The Object of Programing". Boston: Pearson
Education, Inc. 2005.
Stanford Encyclopedia of Philosophy
Woolf, Peter. "Possible Useful Notes", Notes for Boolean Logic, September 22, 2005.
Woolf, Peter. "Project 1 Sample Solution", October 6, 2005.
Woolf, Peter. "Useful DeEinitions", Terms Review, October 11, 2005.
Chapter 6. Modeling Case Studies
More information on chemical process modeling in general at ECOSSE example 1
and ECOSSE example 2
Sec3on 1. Surge tank model
Video lecture available for this section!
Authors: (September 6, 2007) Cara Canady, David Carpenter, Che Martinez, Jeremy Minty, Bradley Novak
Used to regulate fluid levels in systems, surge tanks act as standpipe or storage reservoirs
that store and supply excess fluid. In a system that has experienced a surge of fluid, surge
tanks can modify fluctuations in flow rate, composition, temperature, or pressure.
Typically, these tanks (or “surge drums”) are located downstream from closed aqueducts
or feeders for water wheels. Depending upon its placement, a surge tank can reduce the
pressure and volume of liquid, thereby reducing velocity. Therefore, a surge tank acts as a
level and pressure control within the entire system.
Since the flow to the surge tank is unregulated and the fluid that is output from the surge
tank is pumped out, the system can be labeled as unsteady-state [MIT], but the approach
to an approximate solution (below) utilizes techniques commonly adhered to when
solving similar steady-state problems.
The technology behind surge tanks has been used for decades, but researchers have had
difficulty fully finding a solution due to the non-linear nature of the governing equations.
Early approximations involving surge tanks used graphical and arithmetical means to
propose a solution, but with the evolution of computerized solving techniques, complete
solutions can be obtained. [Wiley InterScience].
1.2 Deriva,on of Ordinary Differen,al Equa,on
To accurately model a surge tank, mass and energy balances need to be considered across
the tank. From these balances, we will be able to develop relationships for various
characteristics of the surge tank
1.2.1 Diagram of Surge Tank System
A surge tank relies on the level sensor to determine whether or not fluid stored in the tank
should be removed. This regulated outflow is pumped out in response to calculations
made by a controller that ultimately opens and closes the control valve that releases the
fluid from the tank.
1.2.2 Governing Equa:ons of Surge Tank Model
A surge tank's components must be divided up and evaluated individually at first, then as
a whole. First, the expression for the inlet stream must be obtained. The simplistic sine
function will be used as the basis for the expression of a stream because it typically
describes the tidal surge pattern of a low-viscous fluid, like water. The flowrate, w, will be
given in units of kg h-1.
where a and b are constants determined by the specific problem circumstance.
A mass balance must now be performed on the tank as a system. Using the concept that
mass in = mass out, and assuming that the tank is a perfect cylinder devoid of diversions, an expression can be derived:
rate mass in ‐ rate mass out = accumulated Lluid in tank
Where, at time t=0, the amount of fluid in the surge tank is constant; thus h(0) = h 0.
Substituting the original equation for the inlet stream, wi, into the expression for the
height of the tank, h(t), the governing equation for the height of the tank is obtained:
Integrating by parts,
where x is formed from the constants a and b during integration.
1.3 Secondary uses of Surge Tanks
Surge tanks are most commonly used to protect systems from changes in fluid levels;
they act as a reservoir that stores and supply excess fluid. In addition, the tanks shield the
systems from dramatic changes in pressure, temperature, and concentration. They can
also allow one unit to be shut down for maintenance without shutting down the entire
There can be moments of high pressure, called hammer shock, in a system when the
liquid (incompressible) flow is stopped and started. The energy that liquids possess while
traveling through pipes can be categorized as potential or kinetic. If the liquid is stopped
quickly, the momentum that the liquid carries must be redirected elsewhere. As a result,
the pipes vibrate from the reactive force and weight of the shock waves within the liquid.
In extreme cases, pipes can burst, joints can develop leaks, and valves and meters can be
The extreme amounts of pressure are dampened when the fluid enters the surge tanks.
The surge tank acts as a buffer to the system, dispersing the pressure across a greater
area. These tanks make it possible for a system to more safely execute their tasks.
The temperature of a fluid can either be controlled or changed through the use of a surge
tank. The surge tank allows for a rapid change in fluid temperature. This is exemplified
by the process of pasteurization; the milk needs to be at a high temperature for just a
short period of time, so it is exposed to the high temperature and then moved to the surge
tank where it can be stored and cooled (see heated surge tank).
A substance can enter the surge tank at room temperature, and it will instantaneously mix
with the rest of the tank. Substances entering the tank will also subsequently rise to meet
the high temperature and then exit the surge tank quickly thereafter.
Concentration inside the surge tank is kept relatively constant, thus the fluid exiting the
surge tank is the same as the fluid in the tank. This is favorable when there is a
concentration gradient in the incoming fluid to the surge tank. The tank homogenizes the
entering fluid, keeping the concentration of the reactants the same throughout the system,
therefore eliminating any concentration gradient.
1.4 Modeling Surge Tank: Example 1
Suppose we are to design a surge tank that deals with flow swings of +/- 40% over a 10
minute period modeled by the following equation:
where flow is m3h-1 and time in hours. The outlet flow rate, w o, is desired to be 500 m3h-1.
The surge tank is 30m tall and has a cross sectional area of 5m2. The initial height of the
fluid (ρ = kg / m 3) is 10m.
[A.] Model this hypothetical example.
[B.] The surge tank has upper and lower limit controls that open or close the valve if the level gets too high or low. What is the highest maximum set point that can be used
without the surge tank overflowing?
[A.] First we should write out the Material Balance:
Substituting (1) into (2), we get
To complete the design, we must have the cross-sectional area A of the surge tank, this
would be given.
If we were to apply the following condition,
and were to substitute (4) into (2), we discover
[B.] Using the Microsoft Excel model provided, the highest possible maximum set point
is 23m. Media:Model Surge Tank.xls
1.5 Modeling Surge Tanks: Example 2
In this example, we simulate random fluctuations that might be observed in a real world
process stream. A random number generating function (in MS Excel) is used to generate
pseudo-random fluctuations of
200 kg/h about an average value of 1000 kg/h for the
inlet stream, wi( t) over a period of 5 hours. The result is as follows:
Examine the effect that these fluctuations have on the fluid level in surge tanks of various
volumes. To vary the volume, assume tanks of constant height hmax=20m, and vary the
cross sectional area from A=1 m 2 to A=5 m 2. Use the following parameters for the surge tank: Initial fluid level h 0=10m, ρ=1 kg / m 3, w 0=1000 kg / m 3, t 0=0 h and tf=5h.
In the solution to the first example problem, we used a trigonometric function to simulate
fluctuations in the inlet stream, and we obtained an analytical solution to the differential
equation. Since we are using a pseudo-random fluctuating inlet stream in this example,
we will solve this problem via numerical methods. Using the pseudo-random data for
wi( t), we perform a numerical integration on the previously derived expression:
This integration was performed with the trapezoid rule (in MS Excel, using a slight
modification of the posted Excel model), using the specified surge tank parameters, with
A=1 m 2, 2 m 2, and 5 m 2 l. The following results were obtained:
We see that increasing the volume of the surge tank by increasing the cross sectional area
A reduces the magnitude of the fluctuations of the fluid level h in the surge tank. For A=1
m 2 and 2 m 2, the capacity of the surge tank is exceeded and it overflows.
1.6 Modeling Surge Tanks: Example 3
An operator quickly adds 50 gallons from a drum of water into a cylindrical surge tank
with a diameter of 4 feet. The initial volume of liquid in the tank is 40 cubic feet and the
total height of the tank is 5 feet. The inflow and exit flow rates are initally 6 cubic feet per
minute. The resistance has a linear relationship with liquid height.
(a) Derive a first order linear model for the tank height and determine the value of R for
(b) Will the tank overflow when the drum is added?
(c) Show the height h(t) after the drum of water is added; treat the change in h(t) as
(d) Does the tank height return to steady state? What is it?
Assume the operator adds the water at t = 0, so when t < 0, the tank is under steady state
which can be described as: qIN − qOUT = 0 (1)
where R is the resistance and h is the height of the
liquid. Initial volume of the tank is:
into equation 1
0 = 6 − hSS / R
At time t > 0, the 50 gallons (6.685 cubic feet) of water is added to the system which
disrupts the steady state and the corresponding initial condition of the system is:
V 0 = VSS + Voperator = 40 + 6.685 = 46.685 ft 3
The corresponding dynamic linear model:
with intitial condtion: h 0 = 3.7151 ft
After adding the drum, h 0 = 3.7151 which is lower than 5 feet. The system will not
overflow at t 0. Because the liquid level is higher than the steady state level and
, the out flow rate will be larger than qIN which pushes the liquid
level drop. As a result, water will not over flow.
Define deviation variables. h' = h − hSS ; qIN' = qIN − qINSS = 0 and substitute into equation (2)
Solve the linear model above (Eq. 3): (Either by direct integration or laplace transform
and inverse lapace transform)
Put h' = h − hSS into equation 4:
ft which was the original steady state
1.8 Sage's Corner
If you are a sage for this page, please link your narrated powerpoint presentation here.
Kundur, Prabha. Power System Stability and Control, McGraw‐Hill 1994.
Cheng‐Nan Lin and John S. Gladwell. Non‐dimensional Surge Tank Analysis, State of
Washington Water Research Center, Washington State University 1970.
Slocum, Stephen Elmer. Elements of Hydraulics, McGraw‐Hill 1915.
MIT OpenCourseWare. http://www.ocw.cn/OcwWeb/Chemical‐Engineering/
Design of a surge tank to smooth out Eluctuations in Elow. DeEinition of important process
Use the Harvard Referencing style for references in the document.
For more information on when to reference see the following wikipedia entry.
Sec3on 2. Heated surge tank
see also ECOSSE
Authors: Angela Antosiewicz, Christopher Kline, Peter Heisler, Paul Niezguski
Stewards: Karen Staubach, Soo Kim, Kerry Braxton-Andrew, Joshua Katzenstein
Date Released: September 6, 2007
Date Revised: September 9, 2007
A surge tank is an additional safety or storage tank that provides additional product or
material storage in case it becomes needed. Heat exchange can be added to surge tanks,
which provides temperature control for the tank. Within a system these tanks can appear
as distillation columns, reboilers, heated CSTR’s, and heated storage. They can increase
production rates by allowing a batch of product to finish reacting while the initial tank is
reloaded, provide constant system parameters during start up and shut down, or create
additional storage space for product overflow or backup material.
Uses for Heated Surge Tanks:
Fuel surges caused by motion of a vehicle: If fuel cannot be drawn from the
primary tank, the engine resorts to a surge tank. The heat maintains the fuel’s
Caramelization: During the formation of caramel, the mixture must be
maintained at a speciEic temperature for a predetermined amount of time.
Once the ingredients are thoroughly dissolved, the mixture is transferred to a
heated surge tank and maintained until the caramel has thickened and is
ready to be drawn out.
Mixing of gases: Bulk gas lines can be connected to a heated surge tank with a
pressure sensor. The pressure sensor would control the temperature. By
heating the gas when it Eirst enters the tank, there is no risk of explosion later
due to expansion.
Heated pools: Surge tanks are used to catch and store displaced water from a
pool. If the pool is heated, a heated surge tank should be used to maintain the
temperature of the water.
De‐aeration: Heated surge tanks are often used with de‐aerators. They heat
the component that will enter the de‐aerator, because if the component is not
preheated, the de‐aerator must wait until the component reaches the correct
temperature. This could waste a lot of time and energy.
Chemical Baths: Often in industry, things need to be treated with a chemical
bath. The chemicals usually need to be at a certain temperature so that it will
adhere to the object. A heated surge tank is perfect for this application.
Reboilers: Liquids coming off of a distillation column can be reheated to
enter the column again at a higher temperature to drive the separation
process. Many industries use this tool to obtain a more efEicient separation
and produce a higher net proEit.
Product or Material Backup: Heated surge tanks can also be used as simple
storage in two ways. First, a surge tank can be used excess product not yet
sold or otherwise moved out of the production system. Second, heated surge
tanks can serve as backup for chemical or fuel supplies to a production plant,
such as outdoor gasoline tanks for a backup generator in case of power
2.2 Basic Design for Heated Surge Tanks
Above is a basic example of a heated surge tank. While surge tanks can have multiple
inputs and outputs, for simplicity we have only included one of each here.
Connected to the tank is a temperature control, which controls the heater. Depending on
the temperature of the fluid, this control will increase or decrease the heating to the tank.
This will keep the fluid at the necessary temperature to meet the process requirements.
There is also a level control connected to the tank to indicate when the tank has neared
maximum capacity. When this happens, the control will open the valve at the bottom of
the tank, allowing the product to flow further down the process. The control can also slow
or stop the flow coming through the input valve. These mechanisms will prevent the tank
from overfilling. The position of the level control depends on the type of material in the
process, the phase of the material, the type of level control, and the requirements of the
2.3 Useful Equa,ons
The basic equations that govern heated surge tanks are shown below. First, a simple mass
balance is done on the system. Second, the energy balance was simplified using the
assumptions listed below. Most problems involving this type of tank can be described by
these equations. Additional considerations may require additional variables and
1) The substance coming into the tank is uniform.
2) No reaction is taking place.
3) The tank is well mixed, which means the temperature profile is constant throughout the
2.3.1 Mass Balance
Since there is no generation from reactions inside the heated surge tank, we obtain the
rate of accumulation or level inside the tank by subtracting what is coming out from what
is coming in.
2.3.2 Energy Balance
The temperature change with respect to time is essential for the purpose of configuring a
system to reach steady state. When turning a system on or off, there is a time period in
which the system is in unsteady state. During this time, the system is difficult to model.
In steady state, the system is easier to model because once steady state is reached the left
hand term will become zero.
2.4 Case Study ‐ Water Purifica,on at IBM
At IBM’s manufacturing facility outside Burlington, Vermont, a heated surge tank is used
in the de-ionized water system. In order to wash semi-conductor wafers in manufacturing,
the water has to be about 1,000,000 times cleaner than the incoming city water. All of this
purification is done on site.
The water comes in from the municipal water source at a constant flow rate, but
manufacturing demand is not constant. In order to compensate for this, when the demand
in manufacturing is low, a surge tank is used to store extra water for high demand
periods. Because the large tank is located outside and the winter in Vermont is very cold,
the tank is heated to prevent the water inside from freezing.
During normal operation of the system, the surge tank is bypassed. When a flow
controller downstream has low demand, the inlet valve opens, letting water into the surge
tank. A level controller monitors the tank to make sure it doesn’t overfill and can shut off
the inlet valve and let water out. A temperature controller controls the heater jacket to
maintain the water around 50°C. When the demand for water increases, the flow
controller near the outlet can shut off the inlet valve to the tank, and/or further open the
outlet valve to access the extra water supply in the tank.
2.5 Worked out Example 1 ‐ Determining Temperature of Hea,ng Fluid for Tank
A heated surge tank is being designed to hold paraffin wax coming from a distillation
column at an oil refinery. High pressure steam will be used as a heating fluid in the heat
exchanger to heat up and maintain the paraffin at 51°C (to maintain high viscosity and
prevent solidification). The physical parameters of the tank (volume of 5 m3) and heat
exchanger within it are given. The tank is originally filled with paraffin at room
temperature. At what temperature must the high pressure steam be to sufficiently heat the
paraffin; will a proposed temperature of 130°C be adequate?
The paraffin comes into the tank at 37°C at a volumetric flow rate of 0.0005 m3/s. The
heat exchange coefficient is equal to 50 W/m2/K and the area of the heat exchanger is 2.0
2. The heat capacity of the paraffin is 2900 J/Kg/K and the density is 800 Kg/m3.
Worked out Answer to Example 1
vin= 0.0005 m3/s
U= 50 W/m2/K
A= 2 m2
Ta= 130°C= 403K
Cp= 2900 J/Kg/K
rho= 800 Kg/m3
Tin= 37°C= 310K
V= 5 m3
t(0)= 0 s
t(f)= 36000 s
With a heating fluid at a temperature of 130°C, the fluid only reaches a temperature of
44°C (317K). A higher capacity heating fluid must be used.
Trying a heating fluid at 277°C, we generate the plot below.
The plot shows that the tank will reach a temperature of about 55.5°C (328.5K) with a
heating fluid at 277°C. This will be sufficient to maintain the paraffin in the liquid phase.
2.6 Worked out Example 2 ‐ Time to Reach Steady State aler Hea,ng Failure
For the same surge tank from problem 1, if the heater fails for 2 hours after 10 hours of
operation and is then restarted, how long will it take after it is restarted to reach steady
Answer: Approximately 20 hours
The first manipulation that must be done to your Polymath code is to create an "if-then-
else" statement for the dT/dt line for the case before hour 10, the case between hour 10
and hour 12, and the case after hour 12. For the time ranging between 10 and 12 hours,
because the heating element has failed, the differential equation over this period must
reflect that. Thus, the section (U*A*(Ta-T)) from the differential equation is dropped and
the equation appears as follows: d(T)/d(t)= (-vin*rho*Cp*(T-Tin))/(Cp*V*rho). For any
other time in this simulation, the normal dT/dt equation is used. In order to determine
where the surge tank reaches steady state again, the final time is increased until dT/dt
appoximately reaches zero. The graph generated in Polymath will look like the following,
using the code below as a parameter:
2.7 Sage's Corner
Use the Harvard Referencing style for references in the document.
For more information on when to reference see the following wikipedia entry.
Sec3on 3. Bacterial chemostat
Authors: Shoko Asei, Brian Byers, Alexander Eng, Nicholas James, Jeffrey Leto
Date Released: September 18, 2007
Stewards: Jeffrey Falta, Taylor Lebeis, Shawn Mayfield, Marc Stewart, Thomas Welch
Date Revised: September 25, 2007
Stewards: Sarah Hebert, Valerie Lee, Matthew Morabito, Jamie Polan
Date Revised: September 27, 2007
Bioreactors are used to grow, harvest, and maintain desired cells in a controlled manner.
These cells grow and replicate in the presence of a suitable environment with media
supplying the essential nutrients for growth. Cells grown in these bioreactors are
collected in order to enzymatically catalyze the synthesis of valuable products or alter the
existing structure of a substrate rendering it useful. Other bioreactors are used to grow
and maintain various types of tissue cultures. Process control systems must be used to
optimize the product output while sustaining the delicate conditions required for life.
These include, but are not limited to, temperature, oxygen levels (for aerobic processes),
pH, substrate flowrate, and pressure. A bacterial chemostat is a specific type of bioreactor.
One of the main benefits of a chemostat is that it is a continuous process (a CSTR),
therefore the rate of bacterial growth can be maintained at steady state by controlling the
volumetric feed rate. Bacterial chemostats have many applications, a few of which are
Pharmaceuticals: Used to study a number of different bacteria, a specific example being
analyzing how bacteria respond to different antibiotics. Bacteria are also used in the
production of therapeutic proteins such as insulin for diabetics.
Manufacturing: Used to produce ethanol, the fermentation of sugar by bacteria takes
place in a series of chemostats. Also, many different antibiotics are produced in
Food Industry: Used in the production of fermented foods such as cheese.
Research: Used to collect data to be used in the creation of a mathematical model of
growth for specific cells or organisms.
The following sections cover the information that is needed to evaluate bacterial
3.2 Bacterial Chemostat Design
The bacterial chemostat is a continuous stirred-tank reactor (CSTR) used for the
continuous production of microbial biomass.
3.2.1 Chemostat Setup
The chemostat setup consists of a sterile fresh nutrient reservoir connected to a growth
chamber or reactor. Fresh medium containing nutrients essential for cell growth is
pumped continuously to the chamber from the medium reservoir. The medium contains a
specific concentration of growth-limiting nutrient (Cs), which allows for a maximum
concentration of cells within the growth chamber. Varying the concentration of this
growth-limiting nutrient will, in turn, change the steady state concentration of cells (Cc).
Another means of controlling the steady state cell concentration is manipulating the rate
at which the medium flows into the growth chamber. The medium drips into culture
through the air break to prevent bacteria from traveling upstream and contaminating the
sterile medium reservoir.
The well-mixed contents of the vessel, consisting of unused nutrients, metabolic wastes,
and bacteria, are removed from the vessel and monitored by a level indicator, in order to
maintain a constant volume of fluid in the chemostat. This effluent flow can be controlled
by either a pump or a port in the side of the reactor that allows for removal of the excess
reaction liquid. In either case, the effluent stream needs to be capable of removing excess
liquid faster than the feed stream can supply new medium in order to prevent the reactor
Temperature and pressure must also be controlled within the chemostat in order to
maintain optimum conditions for cell growth. Using a jacketed CSTR for the growth
chamber allows for easy temperature control. Some processes such as biological
fermentation are quite exothermic, so cooling water is used to keep the temperature at its
optimum level. As for the reactor pressure, it is controlled by an exit air stream that
allows for the removal of excess gas.
For aerobic cultures, purified air is bubbled throughout the vessel's contents by a sparger.
This ensures enough oxygen can dissolve into the reaction medium. For anaerobic
processes, there generally is not a need for an air inlet, but there must be a gas outlet in
order to prevent a build up in pressure within the reactor.
In order to prevent the reaction mixture from becoming too acidic (cell respiration causes
the medium to become acidic) or too basic, which could hinder cell growth, a pH
controller is needed in order to bring pH balance to the system.
The stirrer ensures that the contents of the vessel are well mixed. If the stirring speed is
too high, it could damage the cells in culture, but if it is too low, gradients could build up
in the system. Significant gradients of any kind (temperature, pH, concentration, etc.) can
be a detriment to cell production, and can prevent the reactor from reaching steady state
Another concern in reactor design is fouling. Fouling is generally defined as the
deposition and accumulation of unwanted materials on the submerged surfaces or
surfaces in contact with fluid flow. When the deposited material is biological in nature, it
is called biofouling. The fouling or biofouling in a system like this can cause a decrease
in the efficiency of heat exchangers or decreased cross-sectional area in pipes. Fouling on
heat exchanger surfaces leads to the system not performing optimally, being outside the
target range of temperature, or spending excess energy to maintain optimum temperature.
Fouling in pipes leads to an increase in pressure drop, which can cause complications
down the line. To minimize these effects, industrial chemostat reactors are commonly
cylindrical, containing volumes of up to 1300 cubic meters, and are often constructed
from stainless steel. The cylindrical shape and smooth stainless steel surface allow for
3.2.2 Design Equa:ons
The design equations for contiuous stirred-tank reactors (CSTRs) are applicable to
chemostats. Balances have to be made on both the cells in culture and the medium
The mass balance on the microorganisms in a CSTR of constant volume is:
[Rate of accumulation of cells, g/s] = [Rate of cells entering, g/s] – [Rate of cells
leaving, g/s] + [Net rate of generation of live cells, g/s]
The mass balance on the substrate in a CSTR of constant volume is:
[Rate of accumulation of substrate, g/s] = [Rate of substrate entering, g/s] –
[Rate of substrate leaving, g/s] + [Net rate of consumption of substrate, g/s]
Assuming no cells are entering the reactor from the feed stream, the cell mass balance
can be reworked in the following manner:
Similarly, the substrate mass balance may be reworked in the following manner:
Putting equations 1, 2, and 3 together gives the design equation for cells in a chemostat:
Similarly, equations 4, 5, and 6 together gives the design equation for substrate in a
Assumptions made about the CSTR include perfect mixing, constant density of the
contents of the reactor, isothermal conditions, and a single, irreversible reaction.
Many laws exist for the rate of new cell growth.
The Monod equation is the most commonly used model for the growth rate response
curve of bacteria.
where rg = cell growth rate
Cc = cell cencentration
μ = specific growth rate
The specific cell growth rate, μ, can be expressed as
where μ max = a maximum specific growth reaction rate
Ks = the Monod constant
Cs = substrate concentration
Tessier Equation and Moser Equation
Two additional equations are commonly used to describe cell growth rate. They are the
Tessier and Moser Equations. These growth laws would be used when they are found to
better fit experimental data, specifically at the beginning or end of fermentation.
where λ and k are empirical constants determined by measured data.
The death rate of cells, rd, takes into account natural death, kd, and death from toxic by-
product, kt, where Ct is the concentration of toxic by-product.
Death Phase The death phase of bacteria cell growth is where a decrease in live cell
concentration occurs. This decline could be a result of a toxic by-product, harsh
environments, or depletion of nutrients.
In order to model the amount of substrate and product being consumed/produced in
following equations, yield coefficients are utilized. Ysc and Ypc are the yield coefficients
for substrate-to-cells and product-to-cells, respectively. Yield cofficients have the units of
g variable/g cells. Equation (14) represents the depletion rate of substrate:
Equation (15) represents the rate of product formation:
3.3 Control Factors
The growth and survival of bacteria depend on the close monitoring and control of many
conditions within the chemostat such as the pH level, temperature, dissolved oxygen
level, dilution rate, and agitation speed.
As expected with CSTRs, the pumps delivering the fresh medium and removing the
effluent are controlled such that the fluid volume in the vessel remains constant.
Different cells favor different pH environments. The operators need to determine an
optimal pH and maintain the CSTR at it for efficient operation. Controlling the pH at a
desired value during the process is extremely important because there is a tendency
towards a lower pH associated with cell growth due to cell respiration (carbon dioxide is
produced when cells respire and it forms carbonic acid which in turn causes a lower pH).
Under extreme pH conditions, cells cannot grow properly, therefore appropriate action
needs to be taken to restore the original pH (i.e. adding acid or base).
Controlling the temperature is also crucial because cell growth can be significantly
affected by environmental conditions. Choosing the appropriate temperature can
maximize the cell growth rate as many of the enzymatic activates function the best at its
optimal temperature due to the protein nature of enzymes.
One of the important features of the chemostat is that it allows the operator to control the
cell growth rate. The most common way is controlling the dilution rate, although other
methods such as controlling temperature, pH or oxygen transfer rate can be used.
Dilution rate is simply defined as the volumetric flow rate of nutrient supplied to the
reactor divided by the volume of the culture (unit: time-1). While using a chemostat, it is
useful to keep in mind that the specific growth rate of bacteria equals the dilution rate at
steady state. At this steady state, the temperature, pH, flow rate, and feed substrate
concentration will all remain stable. Similarly, the number of cells in the reactor, as well
as the concentration of reactant and product in the effluent stream will remain constant.
Negative consequences can occur if the dilution rate exceeds the specific growth rate. As
can be seen in Equation (16) below, when the dilution rate is greater than the specific
growth rate (D > μ), the dCC/dt term becomes negative.
This shows that the concentration of cells in the reactor will decrease and eventually
become zero. This is called wash-out, where cells can no longer maintain themselves in
the reactor. Equation (17) represents the dilution rate at which wash-out will occur.
In general, increasing the dilution rate will increase the growth of cells. However, the
dilution rate still needs to be controlled relative to the specific growth rate to prevent
wash-out. The dilution rate should be regulated so as to maximize the cell production
rate. Figure 1 below shows how the dilution rate affects cell production rate(DCC), cell
concentration (CC), and substrate concentration (CS).
Figure 1: Cell concentration, cell production, and substrate concentration as a
function of dilution rate
Initially, the rate of cell production increases as dilution rate increases. When Dmaxprod is
reached, the rate of cell production is at a maximum. This is the point where cells will not
grow any faster. D = μ (dilution rate = specific growth rate) is also established at this
point, where the steady-state equilibrium is reached. The concentration of cells (CC) starts
to decrease once the dilution rate exceeds the Dmaxprod. The cell concentration will
continue to decrease until it reaches a point where all cells are washed out. At this stage,
there will be a steep increase in substrate concentration because fewer and fewer cells are
present to consume the substrate.
Oxygen transfer rate
Since oxygen is an essential nutrient for all aerobic growth, maintaining an adequate
supply of oxygen during aerobic processes is crucial. Therefore, in order to maximize the
cell growth, optimization of oxygen transfer between the air bubbles and the cells becomes extremely important. The oxygen transfer rate (OTR) tells us how much oxygen
is consumed per unit time when given concentrations of cells are cultured in the
bioreactor. This relationship is expressed in Equation (18) below.
Oxygen Transfer Rate (OTR) = QO2CC
Where CC is simply the concentration of cell in the reactor and QO2 is the microbial
respiration rate or specific oxygen uptake rate. The chemostat is a very convenient tool to
study the growth of specific cells because it allows the operators to control the amount of
oxygen supplied to the reactor. Therefore it is essential that the oxygen level be
maintained at an appropriate level because the cell growth can be seriously limited if
inadequate oxygen is supplied.
A stirrer, usually automated and powered with a motor, mixes the contents of the
chemostat to provide a homogeneous suspension. This enables individual cells in the
culture to come into contact with the growth-limiting nutrient and to achieve optimal
distribution of oxygen when aerobic cultures are present. Faster, more rigorous stirring
expedites cell growth. Stirring may also be required to break agglutinations of bacterial
cells that may form.
Q1: Why is a chemostat called a chemostat?
A1: Because the chemical environment is static, or at steady state. The fluid volume,
concentration of nutrients, pH, cell density, and other parameters all are assumed to
remain constant throughout the operation of the vessel.
Q2: What are some concerns regarding chemostats?
A2: a) Foaming results in overflow so the liquid volume will not be constant. b) Changing
pumping rate by turning the pump on/off over short time periods may not work. Cells
respond to these changes by altering rates. A very short interval is needed for it to
respond correctly. c) Fragile and vulnerable cells can be damaged/ruptured when they
are caught between magnetic stirring bar and vessel glass. d)Bacteria contamination
occurs because bacteria travel upstream easily and contaminate the sterile medium. This
can be solved by interrupting the liquid path with an air break.
Q3: The Monod equation uses a Michaelis-Menten relationship which is based on a
quasi-state assumption. (T/F)
Q4: An important feature of chemostat is the dilution rate. Define dilution rate.
A4: Dilution Rate = volume of nutrient medium supplied per hour divided by the volume
of the culture.
Q5: What are the advantages/disadvantages over choosing a chemostat instead of a batch
reactor for bioreactions?
A5: Advantages: 1. A chemostat has better productivity than a batch reactor. There is a
higher rate of product per time per volume. A batch process wastes time. 2. A chemostat
is operated at steady state, therefore it has better control maintaining the same conditions
for all product produced.
Disadvantages: 1. A chemostat is less flexible than a batch reactor. A batch reactor can
be used to make more than one product. 2. It is harder to maintain a sterile system in a
chemostat. A batch reactor is easier to clean.
Q6: What is the physical meaning of the Monod constant?
A6: The Monod constant is a substrate concentration at which the growth rate of the
biomass of microbial cells participating in the reaction is half the maximum growth rate.
3.5 Worked out Example 1
Note: The context and values given in this problem are not factual.
Researchers at the University of Michigan are using a bacterial chemostat to model the
intestinal tract of a pig in order to study the metabolism of E. Coli bacteria in that
particular environment. The growth chamber of the chemostat has a volume of 500 dm3.
The initial concentration of E. Coli bacteria inoculated in the chemostat growth chamber
is 1 g/dm3. A 100g/dm3 substrate feed is fed to the chemostat at a volumetric flow rate of
20 dm3/hr. How much time is required for this biochemical process to reach steady rate
from the point of startup? Assume the growth rate is the Monod equation for bacteria
bacterial cell growth, shown above.
Additional data pertaining to the problem is given: μmax = 0.8; Ks = 1.7 g/dm3; Ys/c = 8;
Yp/c = 5; m = 0; rd = 0;
Answer = 3.7 hours
The Chemostat was modeled in Excel using the design equations above and Euler's
Method. A graph of Cell Concentration (g/dm3) vs Time(hr) was then plotted. When the
Cell Concentration become stable, steady state has been reached and the time can be read
off the graph. Below is a screen shot of the model and the graph created.
Excel Model Screen Shot
This graph clearly shows that steady state is reached 3.7 hours after start up.
3.6 Worked out Example 2
Note: The context and values given in this problem are not factual.
After calculating the time required to reach steady state, the researchers decide to start up
the chemostat. While do so, the control valve for the inlet substrate feed malfunctions.
The flow rate of substrate into the chemostat is accelerating at 40 dm3/hr2. Determine
how long they have to correct the problem before wash-out occurs and all of the bacteria
in the chemostat is lost.
Modeling the Malfunction
Answer = 20 hours
The Chemostat was modeled in Excel using the design equations above and Euler's
Method. A graph of Cell Concentration (g/dm3) vs Time(hr) was then plotted. When the
Cell Concentration becomes zero wash-out of the bacteria took place. Below is a screen
shot of the model and the graph created.
Excel Model Screen Shot
This graph clearly shows wash-out occurs 20 hours after start up. We can see in example
that process controls are extremely important for Bacterial Chemostats.
The template model used for both Worked Out Example 1 and 2 can be downloaded here
Media: Bacterial Chemostat Template.xls
3.7 Sage's Corner
"Chemostat." McGraw‐Hill Dictionary of ScientiLic and Technical Terms. McGraw‐Hill
Companies, Inc., 2003. Accessed September 16, 2007. Available http://www.answers.com/
Fogler, H. Scott (2006). Elements of Chemical Reaction Engineering. New Jersey: Prentice Hall
PTR. ISBN 0‐13‐047394‐4
Kelly, C. "Ch 9 ‐ Reactors" 17 February, 2004. Retrieved 2007‐09‐24. Available http://
Smith, H.L. (2006). "Bacterial Growth". Retrieved on 2007‐09‐15.
Strandberg, Per Erik (2004). "Mathematical models of bacteria population growth in
bioreactors: formulation, phase space pictures, optimisation and control". Retrieved on
Strandberg, Per Erik (2003). "The Chemostat". Retrieved on 2007‐09‐15.
"What is a Bioreactor?" Transgalactic Ltd., 25 May, 2005. Retrieved 2007‐09‐24. Available
Sec3on 4. ODE & Excel CSTR model w/ heat exchange
Title: ODE & Excel CSTR Modeling with Heat Exchange
Authors: Jason Bourgeois, Michael Kravchenko, Nicholas Parsons, Andrew Wang
Date Presented: 10/3/06 Date Revised: 10/19/06
First round reviews for this page
Rebuttal for this page
CSTR with Heat Exchange
A CSTR (Continuous Stirred-Tank Reactor) is a chemical reaction vessel in which an
impeller continuously stirs the contents ensuring proper mixing of the reagents to achieve
a specific output. Useful in most all chemical processes, it is a cornerstone to the
Chemical Engineering toolkit. Proper knowledge of how to manipulate the equations for
control of the CSTR are tantamount to the successful operation and production of desired
The purpose of the wiki is to model dynamic conditions within a CSTR for different
process conditions. Simplicity within the model is used as the focus is to understand the
dynamic control process.
For the purposes of this Wiki, we have made the following assumptions to explain CSTR
with heat exchange modeling.
The agitator within the CSTR will create an environment of perfect mixing
within the vessel. Exit stream will have same concentration and temperature
as reactor Eluid.
Single, 1st order reaction
To avoid confusion, complex kinetics are not considered in the following
We assume that the necessary parameters to solve the problem have been