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First draft of inertial electro-chemical potential concept
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,45 @@ | ||
| within Chemical; | ||
| model DropOfCommons "Model for global parameters" | ||
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| parameter Chemical.Utilities.Units.Inertance L=1e-5 "Inertance of the molar flow through electro-chemical process" annotation (Dialog(tab="Advanced")); | ||
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| parameter Modelica.Units.SI.MolarFlowRate n_flow_reg = 0.01 "Regularization threshold of molar flow rate" | ||
| annotation(Dialog(group="Regularization")); | ||
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| parameter AssertionLevel assertionLevel = AssertionLevel.error "Global assertion level"; | ||
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| annotation (defaultComponentName="dropOfCommons", | ||
| defaultComponentPrefixes="inner", | ||
| missingInnerMessage=" | ||
| Your model is using an outer \"dropOfCommons\" component but | ||
| an inner \"dropOfCommons\" component is not defined. | ||
| Use Chemical.DropOfCommons in your model | ||
| to specify system properties.",Icon(coordinateSystem(preserveAspectRatio=false), graphics={ | ||
| Ellipse( | ||
| extent={{-80,-60},{80,-100}}, | ||
| fillColor={175,175,175}, | ||
| fillPattern=FillPattern.Solid, | ||
| pattern=LinePattern.None), | ||
| Polygon( | ||
| points={{0,100},{16,36},{80,-32},{0,-100},{-82,-30},{-18,36},{0,100}}, | ||
| lineColor={194,138,221}, | ||
| smooth=Smooth.Bezier, | ||
| fillColor={158,66,200}, | ||
| fillPattern=FillPattern.Solid), | ||
| Polygon( | ||
| points={{6,42},{20,16},{44,-14},{22,-38},{6,42}}, | ||
| smooth=Smooth.Bezier, | ||
| fillColor={194,138,221}, | ||
| fillPattern=FillPattern.Solid, | ||
| pattern=LinePattern.None), | ||
| Polygon( | ||
| points={{-6,-76},{-40,-62},{-56,-30},{-30,-44},{-6,-76}}, | ||
| pattern=LinePattern.None, | ||
| smooth=Smooth.Bezier, | ||
| fillColor={90,34,117}, | ||
| fillPattern=FillPattern.Solid)}), Diagram( | ||
| coordinateSystem(preserveAspectRatio=false)), | ||
| Documentation(revisions="<html> | ||
| <p>2023, Marek Mateják</p> | ||
| </html>")); | ||
| end DropOfCommons; |
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,211 @@ | ||
| within Chemical; | ||
| package Processes | ||
| model Process "Electro-chemical process" | ||
| extends Interfaces.SISOFlow; | ||
| extends Interfaces.ConditionalKinetics; | ||
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| parameter Real kE(unit="mol/J")=0 "Kinetic turnover coefficient"; | ||
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| equation | ||
| //the main equation | ||
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| n_flow = - kC * du * exp(-kE*abs(du)); | ||
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| annotation ( Documentation(revisions="<html> | ||
| <p><i>2009-2015 by </i>Marek Matejak, Charles University, Prague, Czech Republic </p> | ||
| </html>", info="<html> | ||
| <p>Diffusion of the substance as equilibration of electro-chemical potentials.</p> | ||
| </html>"), | ||
| Icon(graphics={Rectangle(extent={{-100,40},{100,-40}}, lineColor={28,108,200})})); | ||
| end Process; | ||
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| model Reaction "Chemical Reaction" | ||
| extends Interfaces.ConditionalKinetics; | ||
| import Chemical.Utilities.Types.InitializationMethods; | ||
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| parameter StateSelect n_flowStateSelect = StateSelect.default "State select for n_flow" | ||
| annotation(Dialog(tab="Advanced")); | ||
| parameter InitializationMethods initN_flow = Chemical.Utilities.Types.InitializationMethods.none "Initialization method for n_flow" | ||
| annotation(Dialog(tab= "Initialization", group="Molar flow")); | ||
| parameter Modelica.Units.SI.MolarFlowRate n_flow_0 = 0 "Initial value for n_flow" | ||
| annotation(Dialog(tab= "Initialization", group="Molar flow", enable=(initN_flow == InitializationMethods.state))); | ||
| parameter Utilities.Units.MolarFlowAcceleration n_acceleration_0 = 0 "Initial value for der(n_flow)" | ||
| annotation(Dialog(tab= "Initialization", group="Molar flow", enable=(initN_flow == InitializationMethods.derivative))); | ||
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| parameter Modelica.Units.SI.Time TC=0.1 "Time constant for electro-chemical potential adaption" annotation (Dialog(tab="Advanced")); | ||
| parameter Utilities.Units.Inertance L = dropOfCommons.L "Inertance of the flow" | ||
| annotation(Dialog(tab="Advanced")); | ||
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| parameter Integer nS=0 "Number of substrate types" | ||
| annotation ( HideResult=true, Evaluate=true, Dialog(connectorSizing=true, tab="General",group="Ports")); | ||
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| parameter Modelica.Units.SI.StoichiometricNumber s[nS]=ones(nS) | ||
| "Stoichiometric reaction coefficient for substrates" | ||
| annotation (HideResult=true); | ||
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| parameter Integer nP=0 "Number of product types" | ||
| annotation ( HideResult=true, Evaluate=true, Dialog(connectorSizing=true, tab="General",group="Ports")); | ||
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| parameter Modelica.Units.SI.StoichiometricNumber p[nP]=ones(nP) | ||
| "Stoichiometric reaction coefficients for products" | ||
| annotation (HideResult=true); | ||
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| parameter Real kE(unit="mol/J")=0 "Kinetic turnover coefficient" | ||
| annotation(Dialog(group="Chemical kinetics")); | ||
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| Modelica.Units.SI.MolarFlowRate rr(stateSelect=n_flowStateSelect) "Reaction molar flow rate"; | ||
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| Interfaces.Inlet substrates[nS] annotation (Placement(transformation( | ||
| extent={{10,-10},{-10,10}}, | ||
| rotation=180, | ||
| origin={-100,0}), iconTransformation( | ||
| extent={{10,-10},{-10,10}}, | ||
| rotation=180, | ||
| origin={-100,0}))); | ||
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| Interfaces.Outlet products[nP] annotation (Placement(transformation( | ||
| extent={{10,-10},{-10,10}}, | ||
| rotation=180, | ||
| origin={100,0}), iconTransformation( | ||
| extent={{10,-10},{-10,10}}, | ||
| rotation=180, | ||
| origin={100,0}))); | ||
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| Modelica.Units.SI.MolarEnthalpy h_mix; | ||
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| protected | ||
| outer DropOfCommons dropOfCommons; | ||
| Modelica.Units.SI.ChemicalPotential du; | ||
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| initial equation | ||
| if initN_flow == InitializationMethods.state then | ||
| rr = n_flow_0; | ||
| elseif initN_flow == InitializationMethods.derivative then | ||
| der(rr) = n_acceleration_0; | ||
| elseif initN_flow == InitializationMethods.steadyState then | ||
| der(rr) = 0; | ||
| end if; | ||
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| equation | ||
| //the main equation | ||
| du = ((p * products.u) - (s * substrates.u)); | ||
| rr = - kC * du * exp(-kE*abs(du)); | ||
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| //reaction molar rates | ||
| rr*s = substrates.n_flow; | ||
| rr*p = -products.n_flow; | ||
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| products.h = h_mix*ones(nP); | ||
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| if | ||
| (rr>0) then | ||
| h_mix*(products.n_flow*ones(nP)) + substrates.n_flow*substrates.h = 0; | ||
| else | ||
| h_mix = 0; | ||
| end if; | ||
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| if nP>0 then | ||
| (p * products.r) = (s * substrates.r) - der(rr)*L; | ||
| for i in 2:nP loop | ||
| //first product is based on inertial potential, | ||
| //other products are provided as source | ||
| der(products[i].u).*TC = products[i].r; | ||
| end for; | ||
| end if; | ||
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| annotation ( | ||
| Icon(coordinateSystem(preserveAspectRatio=false,extent={{-100,-100},{ | ||
| 100,100}}), graphics={ | ||
| Rectangle( | ||
| extent={{-100,-30},{100,30}}, | ||
| lineColor={0,0,127}, | ||
| fillColor={255,255,255}, | ||
| fillPattern=FillPattern.Solid), | ||
| Text( | ||
| extent={{-100,-72},{100,-40}}, | ||
| lineColor={128,0,255}, | ||
| textString="%name"), | ||
| Polygon( | ||
| points={{-60,6},{-60,4},{54,4},{54,4},{18,14},{18,6},{-60,6}}, | ||
| lineColor={0,0,0}, | ||
| fillColor={0,0,0}, | ||
| fillPattern=FillPattern.Solid), | ||
| Polygon( | ||
| points={{54,-8},{54,-6},{-60,-6},{-60,-6},{-24,-16},{-24,-8},{54,-8}}, | ||
| lineColor={0,0,0}, | ||
| fillColor={0,0,0}, | ||
| fillPattern=FillPattern.Solid)}), | ||
| Documentation(revisions="<html> | ||
| <p><i>2013-2020 by </i>Marek Matejak, Charles University, Prague, Czech Republic </p> | ||
| </html>", info="<html> | ||
| <p><b>s<sub>1</sub>·S<sub>1</sub> + .. + s<sub>nS</sub>·S<sub>nS</sub> <-> p<sub>1</sub>·P<sub>1</sub> + .. + p<sub>nP</sub>·P<sub>nP</sub></b> </p> | ||
| <p>By redefinition of stoichometry as v<sub>i</sub> = -s<sub>i</sub>, A<sub>i</sub> = S<sub>i</sub> for i=1..nS v<sub>i</sub> = p<sub>i-nS</sub>, A<sub>i</sub> = P<sub>i-nS</sub> for i=nS+1..nS+nP </p> | ||
| <p>So the reaction can be written also as 0 = ∑ (v<sub>i</sub> · A<sub>i</sub>) </p> | ||
| <h4><span style=\"color:#008000\">Equilibrium equation</span></h4> | ||
| <table cellspacing=\"2\" cellpadding=\"0\" border=\"0\"><tr> | ||
| <td><p>K = <a href=\"modelica://ModelicaReference.Operators.'product()'\">product</a>(a(S)<a href=\"modelica://ModelicaReference.Operators.ElementaryOperators\">.^</a>s) / <a href=\"modelica://ModelicaReference.Operators.'product()'\">product</a>( a(P)<a href=\"modelica://ModelicaReference.Operators.ElementaryOperators\">.^</a>s ) = <a href=\"modelica://ModelicaReference.Operators.'product()'\">product</a>(a(A)<a href=\"modelica://ModelicaReference.Operators.ElementaryOperators\">.^</a>v) </p></td> | ||
| <td><p>dissociation constant</p></td> | ||
| </tr> | ||
| <tr> | ||
| <td><p>Δ<sub>r</sub>G = ∑ (v<sub>i</sub> · Δ<sub>f</sub>G<sub>i</sub>) = Δ<sub>r</sub>H - T·Δ<sub>r</sub>S = -R·T·<a href=\"modelica://ModelicaReference.Operators.'log()'\">log</a>(K) </p></td> | ||
| <td><p>molar Gibb's energy of the reaction</p></td> | ||
| </tr> | ||
| <tr> | ||
| <td><p>Δ<sub>r</sub>H = ∑ (v<sub>i</sub> · Δ<sub>f</sub>H<sub>i</sub>) </p></td> | ||
| <td><p>molar enthalpy of the reaction</p></td> | ||
| </tr> | ||
| <tr> | ||
| <td><p>Δ<sub>r</sub>S = ∑ (v<sub>i</sub> · Δ<sub>f</sub>S<sub>i</sub>) = <a href=\"modelica://Modelica.Constants\">k</a>·<a href=\"modelica://ModelicaReference.Operators.'log()'\">log</a>(Δ<sub>r</sub>ω) </p></td> | ||
| <td><p>molar entropy of the reaction</p></td> | ||
| </tr> | ||
| </table> | ||
| <h4><span style=\"color:#008000\">Notations</span></h4> | ||
| <table cellspacing=\"2\" cellpadding=\"0\" border=\"0\"><tr> | ||
| <td><p>A<sub>i</sub></p></td> | ||
| <td><p>i-th substance</p></td> | ||
| </tr> | ||
| <tr> | ||
| <td><p>v<sub>i</sub></p></td> | ||
| <td><p>stochiometric coefficients of i-th substance</p></td> | ||
| </tr> | ||
| <tr> | ||
| <td><p>K</p></td> | ||
| <td><p>dissociation constant (activity based)</p></td> | ||
| </tr> | ||
| <tr> | ||
| <td><p>a(A<sub>i</sub>)=f<sub>i</sub>*x<sub>i</sub></p></td> | ||
| <td><p>activity of the substance A</p></td> | ||
| </tr> | ||
| <tr> | ||
| <td><p>f<sub>i</sub></p></td> | ||
| <td><p>activity coefficient of the substance A</p></td> | ||
| </tr> | ||
| <tr> | ||
| <td><p>x<sub>i</sub></p></td> | ||
| <td><p>mole fraction of the substance A</p></td> | ||
| </tr> | ||
| <tr> | ||
| <td><p>Δ<sub>f</sub>H<sub>i</sub></p></td> | ||
| <td><p>molar enthalpy of formation of i-th substance</p></td> | ||
| </tr> | ||
| <tr> | ||
| <td><p>Δ<sub>f</sub>G<sub>i</sub></p></td> | ||
| <td><p>molar Gibbs energy of formation of i-th substance</p></td> | ||
| </tr> | ||
| <tr> | ||
| <td><p>Δ<sub>f</sub>S<sub>i</sub></p></td> | ||
| <td><p>molar entropy of formation of i-th substance</p></td> | ||
| </tr> | ||
| <tr> | ||
| <td><p>Δ<sub>r</sub>ω</p></td> | ||
| <td><p>change of number of microstates of particles by reaction</p></td> | ||
| </tr> | ||
| <tr> | ||
| <td></td> | ||
| <td></td> | ||
| </tr> | ||
| </table> | ||
| </html>")); | ||
| end Reaction; | ||
| end Processes; |
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