thermal separation library: examples of use · thermal separation library: examples of use ......

Thermal Separation Library: Examples of Use

Karin Dietl∗ Kilian Link† Gerhard Schmitz‡

Abstract

This paper deals with the Thermal Separation Library,which is intended to be used for absorption and rec-tification processes. Two example calculations showhow the simulation speed can be increased by choos-ing the right way to set up the equations. One examplerefers to the ordering of the substances in the substancevector and one refers to the modelling of equilibriumprocesses. An example of use presented is the CO2

absorption in a post-combustion carbon capture plant.The transient simulation results are compared to mea-surement data obtained in a Siemens pilot plant.

Keywords: thermal separation, carbon capture, ab-sorption / desorption

1 Introduction

Dynamic analysis of thermal separation processesgains in importance, be it in batch processing, systemcontrol, start-up strategies or shut down behaviour incontinuous processing ([9]).

General modelling approaches for these problems(or a part of these problems) have been reportedin literature. READYS ([16]) as well as a modeldeveloped in [12] can be used for dynamic simulationof equilibrium columns. A model which considersdynamic simulation of multiphase systems is pre-sented in [2]. [11] describes steady-state and dynamicnon-equilibrium models. A tool for dynamic processsimulation - DIVA - is proposed by [5], which hasa sequential simulation approach. DYNSIM wasdeveloped by [3] and is a tool for design and analysisof chemical processes. In [13] a modelling languagegPROMS is proposed to model combined lumped anddistributed systems which was then successfully usedin several publications in order to model separationprocesses (e.g. [23]).

∗Hamburg University of Technology, [email protected]†Siemens, [email protected]‡Hamburg University of Technology, [email protected]

The developed models have been tested on severaldifferent processes, mostly on a single column. Thereare also examples where more complex system designsare presented ([6]).

The aim of this paper is to describe a modellinglibrary which can be used for flexible modelling andsimulation of complex separation systems. As an ex-ample a fully integrated absorption/desorption loop forcarbon capture is simulated. Simulation results will becompared to measurement data obtained in a Siemenspilot plant. The process is shown in figure 5 and willbe discussed in more detail in section 4.1.

2 Modelling Approach

It is commonly agreed on that when developing amodel of multicomponent system including chemicalreactions, a simple equilibrium-based model which ne-glects mass transfer, is often not sufficient and a morephysical approach - the rate-based approach ([18]) - isneeded (e.g. [19], [17], [10]). The simulation modelsare built using the object-oriented Thermal SeparationLibrary ([8]) which was developed in order to modeldynamic absorption and rectification processes.

2.1 Model equations

2.1.1 Balance equations

The balance equations are established separately forthe vapour and liquid bulk phase as described in [8].There is therefore a mole balance for each compo-nent i of vapour and liquid phase. Additionally thereshould also be summation equations in the bulk phases(∑i yi = 1 and∑i xi = 1). However, in general systemsof ordinary differential equations can be more easilysolved than differential algebraic equations and intro-ducing a differential equation instead of an algebraicequation is rewarded with faster computation times.Therefore these two algebraic equations are replacedby the total amount of substance balance for vapourand liquid phase.For liquid and vapour phase there is one energy bal-ance each (see [8]).

Proceedings 8th Modelica Conference, Dresden, Germany, March 20-22, 2011

28

Nomenclature

A heat transfer areaa specific areac concentrationH Henry coefficientk mass transfer coefficientM molar massN molar flow raten number of discrete elementsnS no. of substances which are in both phasesnliq

S , nvapS number of liquid / vapour substances

[R] rate matrix for mass transfer coefficientsT temperatureu specific inner energyx liquid compositiony vapour compositionZ factor for equilibrium stage

Greek symbolsεvap,ε liq vapour or liquid hold up[Γ] thermodynamic correction matrixγ activity coefficientφ fugacity coefficientSubscriptsi componentij stagejr reactionSuperscriptsliq liquidsat saturationvap vapour∗ thermodynamic equilibriumAbbreviationsnLF number of liquid feedsnVF number of vapour feeds

2.1.2 Rate Equations

In [8] the molar flow rates at stagej over the phaseboundary are calculated as

~Ni, j = ki, j ·a j · ( ~ci, j − ~c∗i, j) (1)

This approach however is only valid for binary sys-tems, and using the concentration difference as driv-ing force is only applicable for isothermic condi-tions. Therefore this was replaced by the more generalMaxwell-Stefan equations as described by [22]:

~Nvapj = Nvap

total, j ·~y j +cvapj ·a j · [R

vapj ]−1

· [Γvapj ] · (~y j −~y∗j )

(2)

~Nliqj = Nliq

total, j ·~x j +cliqj ·a j · [R

liqj ]−1

· [Γliqj ] · (~x j −~x∗j )

(3)

The thermodynamic correction matrices[Γ] are nec-essary, since here the difference of the mole fractionas driving force is used and not the difference in thechemical potential. The[Γ]-matrices contain the com-position derivatives of the activity coefficient (liquid)or fugacity coefficient (vapour), which can be foundfor several activity coefficent models in [21]. The[R]-matrices are calculated using the binary mass transfercoefficients. How to obtain the[R]-matrices via the bi-nary mass transfer coefficients is described in detail in[22].The total molar flow rates in (2) and (3) are obtainedby summing the molar flow rates for each component.

It is also important to note that the vectores~Nvapj and

~Nliqj in eq. (2) and (3) contain only the molar flow rate

Nj,i of nvapS −1 andnliq

S −1 substances respectively, thatis this equation is not established for every substance.The missing equations are the summation equations atthe phase boundary:

∑i

y∗i = 1 , ∑i

x∗i = 1 (4)

2.1.3 Inert Substances

An equation describing the thermodynamic equilib-rium does only exist for thenS components, which ex-ist in both phases, but not for inert substances. Themissing equations for the inert substances are obtainedby setting the molar flow rate over the phase boundaryof the inert substances to zero:

Nvapi, j = 0

Nliqi, j + Nfilm

r,i, j = 0

}

if substancei is inert (5)

2.2 Numerical Solutions

In order to solve the resulting system of differential-algebraic equations using numerical integration, asmany state variables as differential equations areneeded. For the columns, the following variables arechosen as state variables:cvap

j,i , cliqj,i , uvap

j , uliqj , εvap

j andTvap

j (or Mvapj which is as suitable), withj = 1...n and

i = 1...nvapS or i = 1...nliq

S respectively. Using this set


29

of state variables, all other variables can be calculatedvia algebraic relations. Intensive rather than extensivequantities were chosen as state variables, since the dif-ferential equations were set up using these intensivevariables.

2.3 Library Structure

The library structure of the column models is repre-sented in figure 1 which shows a class diagram ofthe library. The three different column types (packedcolumn, tray column, spray column) all inhert fromFeedStage (which is denoted with an arrow pointingat the parent class). TheFeedStage-model inheritsfrom the BaseStage-model which contains the bal-ance equations and some of the constitutive equationsfor n discrete elements. It also contains instances ofthe medium models, the reaction models etc. Thesemodels are declared as replaceable, where replaceabil-ity is denoted using a dotted line with a diamond.The extending column classes supply the geometry,the instances of the pressure loss and liquid holdupmodel, the heat transfer model between the two phasesand the mass transfer models. Each column type isstructured the same way; but only the structure of thepacked column is shown in the diagram due to read-ability.

3 Examples

As stated in the introduction it should be possible tomodel and simulate a complex separation process us-ing the Thermal Separation Library. In the following acomplete absorption/desorption loop is presented. Be-fore doing so some small examples show how a dif-ferent writing of the modelling equations can increasesimulation speed.

3.1 Ordering of Substances in MediumModel

In general any order of the substances in the mediummodel can be chosen. However since for a non-equilibrium model the equations for the molar flowrates eq. (2) and (3) exist only fornvap

S −1 andnliqS −1

substances respectively, and the molar flow rate for thelast substance in the medium model is defined via thesummation equations (4), the ordering becomes im-portant in case the fraction of the last substance be-comes very small (in the order of the tolerance of thenumerical solver). In this case the calculation can be-come very slow and the composition of the last sub-

stance at phase boundary may even be calculated to benegative. This is known as cancellation problem (seee.g. [4]). Figure 2 shows an example for the absorptionof N2 and O2 in H2O. The simulation time decreasesby the factor 5 if not O2 is the last substance in themedium model.So it can be stated having substances with very lowconcentrations at the last place in the substance vec-tor decreases simulation speed. If this is not possible(i.e. no substance is always large enough to be suit-able as last component) it is also possible to apply theMaxwell-Stefan equations to all components and om-mit the summation equations at the phase boundary.This also reduces the CPU-time, but in some test casesthe sums of the mole fractions at the phase boundarywere observed to deviate about 10% from 1.

0 20 40 60 80 1000

50

100

150

200

Time (s)

CP

U ti

me

(s)

N2, H

2O, O

2

N2, O

2, H

2O

Figure 2: Influence of the ordering of the substances inthe medium model. Simulation speed is increased, ifin the liquid phase a substance with a high mole frac-tion (H2O) is the last substance in the medium model(i.e. the CPU time for simulation is smaller).

3.2 Equilibrium Model

As stated in chapter 2 the stages were modelled as non-equilibrium stages, i.e. mass transfer is taken into ac-count. However sometimes it is advantageous to de-scribe the separation column using equilibrium stages,e.g. if no suitable correlations for the mass transfer areavailable.There are basically two different approaches to modelsuch an equilibrium stage: The first possibility is toimplement a new set of equations which describe theequilibrium stage. However the additional algebraicconstraint of the compositions at phase boundary and


30

3n+ nLF

nVF nLF

3n+ nVF

Interfacial

Area

Interfacial

Area Corr.

Equilibrium Constant

Heat Transfer

Corr.

Pressure

Loss Corr.

R Liquid R Vapour Pressure

Loss

Wall

Models

Geometry

Liquid

Holdup

Wall

Model

Heat

Transfer

Holdup

CorrMass Transfer Corr.

Liquid Vapour

Reaction Models Liq. Medium Models Vap. Medium Models

Reaction Medium Liquid Medium Vapour

Base Stage

Feed Stage

Tray ColumnPacked ColumnSpray Column

Vapour Port In Vapour Port Out Liquid Port In Liquid Port Out Heat Port

Correlations for

φ φsat γ

φφ φsat γ

Thermodynamic FactorΓliq Thermodynamic FactorΓvap

Figure 1: UML class diagram of an absorption or rectification process. The arrow denotes inheritance,i.e. FeedStage inherits fromBaseStage only. The line with the diamond denotes composition. Dotted linesmean that the object is replaceable. The composition of spray column and tray column are analogue to thecomposition of the packed column.


31

in the bulk phase being equal result in a large nonlin-ear system of equations.The second possiblity is to approach the thermody-namic equilibrium (xi → x∗i ) using the non-equilibriumequations and increasing the binary mass transfer co-efficients to infinity. Using this approach the system isless strongly coupled, but still it has to be noted thatthe equations (2) to (4) introduce a high non-linearityto the system. Together with a very high value for thebinary mass transfer coefficients, necessary in order toapproach equilibrium, the computation time can be-come very large (see figure 3). Since the equation (2)- (4) do not give any information for the equilibriummodel they are replaced by the much more simplereq. (6)-(7):

Nvapj,i = Zvap

j,i · (y j,i −y∗j,i) (6)

Nliqj,i = Zliq

j,i · (x j,i −x∗j,i) (7)

wereZ is an adjustable factor. IfZ approaches in-finity, the difference between the composition at thephase boundary and in the bulk phase vanishes andequilibrium is attained. A very high value forZ lead toa very accurate result. An indicator for the accuracy isthe difference of the composition at the phase bound-ary to the composition in the bulk phase. This dif-ference should become zero for an equilibrium model.However for a very high value forZ, the computationtime may become very large or - even worse - thereare convergence problems with the nonlinear solver.Since a optimal value forZ, which leads to an accept-able compromise between computing time and accu-racy is not constant during simulation,Z is continu-ously adapted to minimize the difference between bulkand phase boundary composition using the equationsof a simple PI controller.Equations (6) and (7) are then replaced by equations(8) and (9), whereZ are functions of the error(y j,i −

y∗j,i) and (x j,i − x∗j,i) respectively and some controllerparameters which are constant during simulation.

Nvapj,i = Zvap

j,i (y j,i −y∗j,i ,contr. parameter) · (y j,i −y∗j,i)

(8)

Nliqj,i = Zliq

j,i (x j,i −x∗j,i ,contr. parameter) · (x j,i −x∗j,i)

(9)

Figures 3 and 4 show that using eq. (6) and (7)(solid line) or eq. (8) and (9) (dotted line) insteadof eq. (2), (3) and (4) (dashed line) lead to a lowercomputation time and a higher accuracy of the result.Adapting the variableZ during the simulation using aPI controller (dotted line) further increases accuracy

0 20 40 60 80 1000

200

400

600

800

Time (s)

CP

U ti

me

(s)

eq. (2) − (5)eq. (6), (7)eq. (8), (9)

Figure 3: Computation time using three different setsof equations to model an equilibrium stage. The firstset uses exactly the same equations as for a non-equilibrium model (eq. (2) to (4)) with a constant,but high mass transfer coefficient. The second andthird set use simplified yet sufficient detailed equationswhich increases simulation speed.

without increasing the computation time, compared toeq. (6) and (7) whereZ is constant.In this example, the first set of equations has moretime states than the last two (178 scalars instead of162 scalars; for eight stages) but about the sameamount of time varying variables (around 12000). Thesize of the nonlinear system of equations obtained byDymola is higher, for the first set of equations: eightblocks of 20 iterations variables are necessary insteadof eight blocks of 15 iteration variables (the otherblocks are identical with lesser iteration variables.

The same approach is also chosen when reactionequilibrium should be assumed: in this case the con-troller minimizes the difference between the reactionequilibrium constant and the product of the activities.


32

0 20 40 60 80 1000

0.5

1

1.5

2x 10

−3

Time (s)

y* − y

bulk (

mol

/mol

)

eq. (2) − (5)

eq. (6), (7)

eq. (8), (9)

Figure 4: Largest difference iny∗− y using three dif-ferent sets of equations to model an equilibrium stage.

4 Dynamic Analysis of CO2 CapturePlant

4.1 Plant Layout and Data

The simulation of the carbon capture plant refers tothe same pilot plant as presented in [7]. It is a slip-stream pilot plant operating under real conditions. Theabsorber as a diameter of approx. DN200 and the ab-sorber height is approx. 35 m. The plant layout isshown in figure 5.

RICH

SOLVENT

TANK

AB

SO

RB

ER

GA

S

CO

OL

ER D

ES

OR

BE

R

COOLING

WATER

CO2

FLUE GAS

INLET

RE

BO

ILE

R

FLUE GAS

OUTLET

COOLING

WATER

Figure 5: Carbon capture pilot plant as it can be foundin [7].

The plant consists basically of a flue gas cooler, anabsorber and a desorber (see figure 5). The flue gasfirst enters the flue gas cooler, where it is cooled down

Table 1: Physical properties and other parameters

Property Reference

Pressure loss vapour [20]Interfacial heat transfer coeff. Chilton-ColburnMass transfer coefficient [15]Liquid holdup [14]Diffusion coeff. vapour [1]Interfacial area [15]

using pure water. In the absorber, the saturated fluegas is then brought in contact with a liquid containinga high amount of dissolved amino acid salt. Here, theCO2 is absorbed by the liquid and nearly CO2-free gasleaves the absorber. The loaded liquid is now heatedup in a heat exchanger before it enters the desorber,where the CO2 is stripped from the liquid usingwater vapour, which is obtained in a thermosyphon.The gas leaving the desorber (containing water andCO2) is cooled down and such water is removed viacondensation. The pure CO2 is then liquified andstored; the pure water is fed back to the desorber.The now unloaded liquid from the desorber bottomis partly evaporated in a thermosyphon and partly ledback to the absorber via two heat exchangers in orderto cool down to the absorber temperature.The solvent used is an amino-acid salt solution, asdescribed in [7]. The underlying chemical reactionis shown in figure 6. In the model, it is assumedthat reaction takes place in the film only and reactionkinetics are not considered.

Table 1 provides an overview of the most importantphysical properties.

4.2 Thermodynamic equilibrium

4.2.1 Phase equilibrium CO2

A very simple approach proposed by Siemens waschoosen to model the phase equilibrium of CO2 be-tween liquid and gas phase. This approach combinesthe dissolution of CO2 in the liquid and the stepwisereaction with the dissolved salt to the final productin a single phase equilibrium equation. The mainadvantage is that only very few components in theliquid phase have to be modelled, namely H2O, thedissolved salt called AAS (amino acid salt) and thefinal reaction product. All reaction intermediate prod-ucts as well as dissolved molecular CO2 in the liquidphase have not to be considered, the latter due to the


33

Figure 6: Reaction scheme in the amino acid salt solution, as presented in [7]

assumption that the reaction is nearly instantenous andthe CO2 concentration in the liquid is negligible. Thismeans that if a molar flow rateNCO2 of gaseous CO2crosses the phase boundary, a source term increasesthe molar quantity of the reaction product and a sinkterm decreases the molar quantity of the educts (H2O,AAS) such accounting for the stoichiometrics.Since CO2 is nonexistent in the model of the liquidphase the phase equilibrium is described using theCO2 vapour mole fraction on the one side and themole fraction of the reaction product on the other side:

p·yCO2 =xProduct

1+xProduct·H(T) · γ(T,xProduct) (10)

The Henry coefficientH is temperature dependent andthe activity coefficientγ is additionally dependent onthe concentration of the product in solvent. For bothcoefficients Siemens provides a correlation, which areas follows:

lnH = a+bT

(11)

lnγ = e(c+d·T+e·T2)·

xProduct

1+xProduct(12)

The parametersa, b, c, d, e have been adjusted usingmeasurement data.It has to be stated that this approach has drawbacksconcerning the accurateness of the results, neverthe-less they are all in the right order of magnitude andthe main factors influencing the result are considered.This approach is therefore suitable for dynamic simu-lation, where the dynamics are in the focus of the studyand a high simulation speed is needed but very correctsteady-state results are not of such importance.

4.2.2 Phase equilibrium water

The water equilibrium is calculated using

p·yH2O = xH2O · psat· γ ·φsat (13)

For the calculation of the water saturation pressure,the saturation pressure of pure water is multiplied bya factor smaller 1 to match the higher saturation tem-perature. The activity coefficientγ is set equal to one,even though it should be smaller than one in reality.At Siemens steady-state calculations were performedusing AspenPlus where much more detailed mediummodels than the ones here where used. These Aspen-Plus calculations revealed that the activity coefficientdid not differ significantly from one in the consideredtemperature and concentration range. Therefore, sincethe proposed modelling of the thermodynamic equi-librium is anyway not suitable in order to obtain veryaccurate steady-state results, setting the water activitycoefficient equal to one does not increase the overallerror very much.

4.3 Medium models

4.3.1 Gas mediums

Both gases, the flue gas, consisting of N2, CO2, O2

and H2O and the CO2-water vapour mixture in thedesorber, are modelled as ideal gas, even though thisassumption is more questionable for the CO2-watervapour mixture, due to the high water vapour content(about 70%-90%) at the saturation temperature of wa-ter (around 100◦C). However the error due to differ-ences in density and enthalpy are not important.


34

4.3.2 Liquid mediums

The pure water in the flue gas cooler is modelled us-ing the waterIF97 medium model from the ModelicaStandard Library.The solvent is also modelled based on the water IF97standard, but density and heat capacity are adjusted tomatch the solvent values (for a solvent containing ap-prox. 30 weight -% AAS). All solvent medium proper-ties are temperature and in parts also pressure depen-dent, but independent of composition.As stated in 4.2.2 the solvent model consists onlyof three components in order to increase simulationspeed.

4.4 Simulation results

In this section the simulation results are presentedand compared to measurement data obtained in theSiemens pilot plant.Two different test cases are investigated:

• Test case 1: Increase of Flue gas flow rate from75% to 100% at t = 0 min.

• Test case 2: Decrease of steam flow rate at re-boiler from 90% to 75% at t = 0 min.

Figure 7 - 9 show the comparision between simula-tion and measurements of test case 1. All temperaturesare plotted referring to an arbitrary reference tempera-ture. The CO2 mass flow rate is described in percent,whereas 100% is arbitrarily set to the measurementvalue obtained at t=0 min. It can be seen that thesteady-state results differ, which is due to the verysimplified modelling of the thermodynamic equilib-rium. The dynamic response between simulation andmeasurement are quite similar, even though in thesimulation the new steady-state is obtained after ashorter time.

For test case 2 the comparision between simulationand measurements are shown in figure 10 - 14 . Again,all temperatures are plotted referring to an arbitraryreference temperature. As for test case 1 the steady-state results differ, but the dynamic behaviour is simi-lar. In figure 12 not only the measured CO2 mass flowrate at the desorber outlet is plotted, but also the massflow rate of the absorbed CO2 in the absorber. Thelatter value was obtained from measurement data, us-ing measured mass flow rates, temperatures and vol-ume fractions at the absorber in- and outlet. These twomass flow rates should be equal in steady-state (which

0 20 40 60−1

0

1

2

3

4

5

6

7

8

Time (min)

(Tliq ou

t − T

ref)

in K

, Abs

orbe

r

simulationmeasurement

Figure 7: Liquid outlet temp., absorber (test case 1)

0 20 40 600

0.01

0.02

0.03

0.04

0.05

Time (min)

x CO

2, Abs

orbe

r ou

tlet


Figure 8: CO2 outlet mole fraction (test case 1)

0 20 40 6092

94

96

98

100

102

104

106

108

Time (min)

mCO

2in

%,des

orb

eroutl

et


Figure 9: CO2 mass flow rate, desorber (test case 1)


35

0 20 40 602

3

4

5

6

7

8

Time (min)

(Tliq ou

t − T

ref)

in K

, Abs

orbe

r


Figure 10: Liquid outlet temp., absorber (test case 2)

0 20 40 600.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Time (min)

x CO

2, Abs

orbe

r ou

tlet


Figure 11: CO2 outlet mole fraction (test case 2)

0 20 40 6070

75

80

85

90

95

100

105

Time (min)

mdo

t CO

2 in %

desorber (meas.)absorber (meas.)desorber (sim.)absorber (sim.)

Figure 12: CO2 mass flow rate (test case 2)

was the case in test case 1), however there is a dif-ference of about 20%. Since this difference does notoccur in the simulation, it explaines why measurementand simulation fit well for the CO2 mass flow rate atthe desorber outlet, but not for the CO2 mole fractionsin the absorber and consequently not for the amount ofCO2 absorbed.

0 20 40 6053

54

55

56

57

58

59

Time (min)

(Tliq ou

t − T

ref)

in K

, des

orbe

r


Figure 13: Liquid outlet temp., desorber (test case 2)

0 20 40 6043

44

45

46

47

48

49

50

Time (min)

(Tva

pou

t − T

ref)

in K

, Des

orbe

r


Figure 14: Vapour outlet temp., desorber (test case 2)

5 Summary

This work proposed a Modelica-library model for dy-namic simulation of tray and packed columns for sep-arations processes such as absorption and rectification.It is shown that it is advantageous to describe an equi-librium model using modified equations of the non-equilibrium model. Also the influence of the ordering


36

of the substances in the medium vector was shown.It was also shown that using the Thermal Separa-tion Library a complex system, namely an absorp-tion/desorption loop for carbon capture is modelledand simulated dynamically. The simulation resultswere compared to measurement data obtained in aSiemens pilot plant. It showed good agreement, eventhough there were differences in the stationary resultswhich is due to the very simplified modelling of thethermodynamic equilibrium.

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