Crate distillation_shortcut_unit

Distillation shortcut unit operation

This is an example unit operation implementation featuring a shortcut distillation unit operation using the Fenske-Underwood-Gilliland-Kirkbride approach.

Fenske

The Fenske equation (Fenske, “Fractionation of Straight-Run Pennsylvania Gasoline”, Industrial and Engineering Chemistry, Vol. 24: 482, 1932) is used to estimate distillate and bottoms composition and the minimum number of stages.

From the slate of components, two components are selected that are called the Light Key (LK) component, and Heavy Key (HK) component. The desired recovery is specified for the LK:

${''r''}_{\text{LK}}=\frac{{''f''}_{\text{LK},\text{dist}}}{{''f''}_{\text{LK},\text{feed}}}$

and for the heavy component recovery

${''r''}_{\text{HK}}=\frac{{''f''}_{\text{HK},\text{bot}}}{{''f''}_{\text{HK},\text{feed}}}$

Initial distillate and bottom compositions are estimated.

The separation is based on calculation of the relative volatility for each component:

${''\alpha ''}_{\text{i}}=\frac{{''K''}_{\text{i}}}{{''K''}_{\text{HK}}}$

where the K value for each compound is calculated for the dew point (DP) at distillate conditions, and bubble point (BP) at bottoms conditions, and the average K value is given by

${''K''}_{\text{i}}=\sqrt{{''K''}_{\text{i},\text{DP},\text{dist}}{''K''}_{\text{i},\text{BP},\text{bot}}}$

The minimum number of stages follows from:

${''N''}_{\text{min}}=\frac{\text{ln}\left(\frac{{''f''}_{\text{LK},\text{dist}}{''f''}_{\text{HK},\text{bot}}}{{''f''}_{\text{HK},\text{dist}}{''f''}_{\text{LK},\text{bot}}}\right)}{\text{ln}\left({''\alpha ''}_{\text{LK}}\right)}$

The bottom component flow rates are:

${''f''}_{\text{i},\text{bot}}=\frac{{''f''}_{\text{i},\text{feed}}}{1+\left(\frac{{''f''}_{\text{HK},\text{dist}}}{{''f''}_{\text{HK},\text{bot}}}\right)''\alpha ''_{\text{i}}^{{''N''}_{\text{min}}}}$

and the distillate component flow rates are:

${''f''}_{\text{i},\text{dist}}={''f''}_{\text{i},\text{feed}}-{''f''}_{\text{i},\text{bot}}$

The unit operation operates isobarically, so product pressure equals feed pressure. The distillate product is at the dew point temperature for the distillate composition, and the bottoms product it at the bubble point temperature for the distillate composition.

Given the new distillate temperature and composition, and the new bottoms temperature and composition, the K values and relative volatilities are updated, and the above calculation is repeated until converged values are obtained.

Underwood

The Underwood equation (Underwood, “Fractional distillation of multi-component mixtures. Calculation of minimum reflux ratio”, J. Inst. Petrol., 32, 614, 1946) is used to estimate the minimum reflux ratio.

The minimum reflux ratio is determined from

${''R''}_{\text{min}}=\sum \frac{{''\alpha ''}_{\text{i}}{''x''}_{\text{i},\text{dist}}}{{''\alpha ''}_{\text{i}}-''\theta ''}-1$

where Underwood parameter $\theta$ is the root of equation

$1-''q''=\sum \frac{{''\alpha ''}_{\text{i}}{''x''}_{\text{i},\text{feed}}}{{''\alpha ''}_{\text{i}}-''\theta ''}$

where q is the feed quality, defined as

$''q''=\frac{{''h''}_{\text{feed,DP}}-{''h''}_{\text{feed}}}{{''h''}_{\text{feed,DP}}-{''h''}_{\text{feed,BP}}}$

where ${''h''}_{\text{feed,DP}}$ is the enthalpy of the vapor phase at the dew point temperature of the feed, and ${''h''}_{\text{feed,BP}}$ is the enthalpy of the liquid phase at the bubble point temperature of the feed.

There are multiple roots for $''\theta ''$, and the root that is used is between 1 and ${''\alpha ''}_{\text{LK}}$. In case there are α values that are in between 1 and ${''\alpha ''}_{\text{LK}}$, a warning is issued and the root that is closest to 1 is used.

The unit does not check whether for retrograde flash results, which is outside the scope of this example.

Gilliland

The Gilliland equation (Gilliland, “Estimate the number of theoretical plates as a function of reflux ratio”, Ind. Eng. Chem. 32(9): 1220-1223, 1940, doi 10.1021/ie50369a035) is used to estimate the number of stages:

$''Y''=1-\text{exp}\left(\right(\frac{1+54.4''X''}{11+117.2''X''}\left)\right(\frac{''X''-1}{\sqrt{''X''}}\left)\right)$

where

$''Y''=\frac{''N''-{''N''}_{\text{min}}}{''N''+1}$

and

$''X''=\frac{''R''-{''R''}_{\text{min}}}{''R''+1}$

The reflux ratio $R$ is determined from the minimum reflux ratio using an adjustable parameter:

$''R''=''k''{''R''}_{\text{min}}$

where $k$ must exceed 1. The default value for $k$ is 1.15.

Kirkbride

The location of the feed stage is estimated from the Kirkbride correlation (Kirkbride, “Process Design Procedure for Multicomponent Fractionators”, Petr. Ref. 23(9), 321, 1944):

$\frac{{''N''}_{\text{top}}}{{''N''}_{\text{bot}}}={\left[\frac{{''f''}_{\text{bot}}}{{''f''}_{\text{dist}}}\frac{{''x''}_{\text{HK},\text{feed}}}{{''x''}_{\text{LK},\text{feed}}}{\left(\frac{{''x''}_{\text{LK},\text{bot}}}{{''x''}_{\text{HK},\text{dist}}}\right)}^2\right]}^{0.206}$

where $''f''$ are molar flow rates, $''x''$ are mole fractions, and the number of trays above the feed ${''N''}_{\text{top}}$ and the number of trays below the feed ${''N''}_{\text{bot}}$ sum up to the number of trays $''N''$.

Parameters

The unit operation has the following input parameters:

• HK: selection of the heavy key component,
• LK: selection of the light key component,
• ${''r''}_{\text{LK}}$, light component recovery, mol/mol,
• ${''r''}_{\text{HK}}$, heavy component recovery, mol/mol,
• $''k''$, factor of reflux ratio $''R''$ above minimum reflux ratio ${''R''}_{\text{min}}$.
• the maximum number of iterations
• the convergence tolerance for the component flow rates relative to the total feed rate; also used for convergence of the Underwood equation

The unit has the following output parameters:

• $''N''$, number of stages
• $''R''$, reflux ratio, mol/mol
• ${''N''}_{\text{feed}}$, feed stage location.

Installation and usage

cobiaRegister.exe distillation_shortcut_unit.dll

An installer for Windows is made available through the AmsterCHEM web site.

After installation, the unit operation can be used in any CAPE-OPEN compliant flowsheeting environment.

Modules

distillation_shortcut_unit 🔒

gui 🔒

integer_parameter 🔒

material_port 🔒

parameter_collection 🔒

port_collection 🔒

real_parameter 🔒

shared_unit_data 🔒

string_parameter 🔒

Statics

PMCS 🔒

A list of all the PMCs that need to be registered

Functions

capeCreateObject

COBIA PMC object creation entry point

capeRegisterObjects

COBIA PMC registration entry point

capeUnregisterObjects

COBIA PMC unregistration entry point

register_pmcs_for_all_users 🔒

This function is called by functions generated by the pmc_entry_points macro to check if the unit operation is registered for all users.

register_types 🔒

Type registration entry point for the module.

unregister_types 🔒

Type unregistration entry point for the module.