# 1: Overview

- Page ID
- 7618

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)This is **Part I, ****Overview **of a ten-part series of technical articles on Distillation Science, as is currently practiced on an industrial level. It is organized as it would be used for the industrial process design of distillation columns, which may differ from the way it is introduced to students academically. As a part of distillation column design, these articles also involve the vapor-liquid equilibria (VLE) of binary systems, with potential extension to multi-component systems.

It is assumed that the reader has a basic understanding of distillation, as a means of separating two or more volatile fluids by the difference between their boiling points; and also the purpose of a distillation column's various components. A variety of texts exist that explain these concepts on a basic level. From such pre-requisites, the purpose of this series of articles is to expand these basics to the degree necessary for commercial applications with real fluids - which typically do not follow ideal behavior. It is also assumed that the reader is familiar with the concepts of molar units, mole fractions, the bonding of chemical elements, vapor pressure, latent heat of vaporization, and a compound's critical point - all of which are found in college freshman-level textbooks. In discussing mathematical relationships, it is assumed that the concepts of differentiation and integration are known to the reader.

While chlorosilanes and their electronic impurities are used as recurring examples, the technology developed here has great application in other mildly polar and hydrogenated compounds, which are normally excluded from theoretical treatment in many texts. The chlorosilane homologue starts with silane (SiH_{4}),_{ }and concludes with silicon tetrachloride (SiCl_{4}), as the Si-H bonds are incrementally swapped for Si-Cl bonds.

Chlorosilanes (and many of the electronic impurities) are non-naturally occurring compounds, but are key to the manufacture of high-purity silicon (solar photovoltaics and modern electronic integrated circuits, aka “computer chips”); as well as silicon-based chemicals such as silicones and organic/inorganic coupling agents. Applications for distillation science are found in both bulk separations of these fluids, as well as the purification by high-reflux processing, to parts-per-billion levels.

Furthermore, this technology is applicable to a wide variety of other non-organic fluids such as refrigerants, biologic pre-cursors, and pharmaceutical pre-cursors (i.e., not the final biological or pharmaceutical product, but rather the compounds used as catalysts and building-block agents for assembling these specialized chemical products).

To make the discussion of Distillation Science more generic, temperature, pressure, and molar volume ( T, P, and V) are often expressed in dimensionless reduced units, designated respectively as T_{r} , P_{r} , and V_{r}. T_{r} = T/T_{c} ; P_{r}=P/P_{c} ; V_{r }= V/V_{c} . By definition, T_{r} =1, P_{r }=1, and V_{r }=1 simultaneously at the critical point. When temperature and pressure are given as T and P, these are in absolute units of Kelvins and atmospheres. For those more familiar with pressures in other absolute units such as PSIA, bar absolute, and Pascals absolute, converting those units to absolute atmospheres is easily done using internet-accessible conversion tables and calculators.

**Part II, Existing Vapor****Pressure****Equations**deals with the pure component VP relationships commonly found in textbooks, as well as their limitations. This article lays the basis for subsequent articles.**Part III, Critical Properties and Acentric****Factor**deals with the tabulation of these properties for selected fluids based on globally collected data. Data analysis and validation are discussed, as well as estimation techniques for those fluids for which data is either poor or non-existent. Critical properties are used to convert temperature, pressure, and specific volume from conventional units used in both chemistry and chemical engineering, to the reduced form of**Part IV**. In**Parts V**and**VII**, the value of the acentric factor is important.**Part IV, New Vapor****Pressure****Equation****Part II**and the results of**Part III**, to show how a new vapor pressure equation allows the practice of distillation applications at the elevated pressures more common to industry. The culmination of this article is a thermodynamically consistent equation that is valid between the atmospheric boiling point and the critical point, and which allows evaluation of other required distillation properties such as saturated phase densities and latent heat of vaporization.**Part V, Equation of State**deals with the recommendations for best EOS, as well as the mathematical techniques for solving such non-intrinsic EOS equation forms.**Part VI,****Fugacity**deals with the departure of apparent pure-component vapor pressure in binary mixtures, as is commonly found in practical application of distillation science. The equations for evaluating fugacity coefficents are given.**Part VII,****Liquid Activity Coefficient**deals with the application and estimation of Liquid Activity Coefficients, as commonly found in practical application of distillation science. Various Liquid Activity Coefficient models are reviewed along with some limited data and a recommended estimation technique given where data is lacking.**s****Part VIII, VLE Analysis****Methods**discusses the recommended methodology used when data-collecting binary systems, to assure that systemic errors are minimized. This topic also deals with validation whenever data collection is done on reactive fluids, which can disproportionate or dimerize during study.**Part IX, Putting It All****Together**shows how to combine the components of the above distillation science articles in a practical application.**Part X, Convergence****Strategy**illustrates how solutions are best obtained for additional fluids using non-intrinsic or nested-loop equation methods, such as the recommended vapor pressure equations. While this topic is more mathematical or computer-science oriented than chemistry-centered, it is a necessary technique to understand when dealing with modern technology. No complex mathematics are required.

Notation | Usage | Units | Notation | Usage | Units |
---|---|---|---|---|---|

NBP | Normal Boiling Point | °K | q | Watson exponent | - |

P, VP | Pressure, Vapor Pressure | atmospheres | ΔH_{vap} |
Latent heat of Vaporization | Cal/g-mol |

P |
Critical Pressure | atmospheres | ΔH_{vb} |
Latent heat @ T_{b} |
Cal/g-mol |

P |
Reduced Pressure | - | T-S ΔH_{vb} |
Thek-Stiel VP equation parameter | Cal/g-mol |

R |
Gas constant | Cal/g-mol°K | Z | compressibility | - |

T | Temperature | °K | Z_{v} & Z_{L} |
compressibility of saturated vapor & liquid | - |

T |
Temperature @ Normal Boiling Point | °K | ΔZ_{vap} |
(Z_{v}-Z_{L}) @ vaporization |
- |

T |
Critical Temp | °K | α | Riedel derivative | - |

T |
Reduced Temp | - | α_{c} |
α @ critical | - |

T |
Reduced T_{b} |
- | \(\psi \nonumber\) | Vapor Pressure derivative | - |

V |
Critical Volume | cc/g-mol | ø | fugacity coefficient | - |

k |
H bonding parameter | - | \(\gamma \nonumber\) | liquid activity coefficient | - |

k_{ij} |
Binary Interaction Coefficient | - | ω | acentric factor | - |

## Units

The units used in these articles are temperatures in °K, pressures in atmospheres (absolute), and molar volumes in cc/gram-mole. Molecular weight (MW), and compressibility (Z) are dimensionless. For the above units, the value of the gas constant (R) is 82.057 atm-cc/mole-°K.