Calculating Fugacities in OLI Studio

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Camilla Flowers
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1 Calculating Fugacities in OLI Studio If you are working at high pressures where only a water (aqueous) and hydrocarbon (second liquid) phase are present, you can still culate fugacities using values generated in the OLI software. Fugacity can be computed indirectly when the gas phase is absent. The fugacity is computed automatily by OLI Studio software when a gas (vapor) phase is present. When a gas is absent, usually due to high pressures, the fugacity can be computed indirectly using thermodynamic values generated by the software. Using H2S as an example, the software constructs the elements that contribute to the following Gibbs Energy equation. G H2 S,vap = G H2 S,vap + RT ln f H2 S = G H2 S,vap + RT ln(φ H2 Sy H2 SP T ) G H2 S,vap - Standard State Gibbs Energy, which is a function of temperature only. φ H2 S - Fugacity coefficient y H2 S - Vapor phase e fraction P T - Total Pressure (1) Similar equations exist for the water (AQ) phase and hydrocarbon (ORG) phase 1. We will use H2S as an example G H2 S,Aq = G H2 S,Aq + RT ln a H2 S,Aq = G H2 S,Aq + RT ln(γ H2 S,AqX H2 S,Aq) G H2 S,org = G H2 S,org + RT ln a H2 S,org = G H2 S,org + RT ln(γ H2 S,orgX H2 S,org) At equilibrium, the following is true: (2) (3) In equilibrium the value of GH2S is computed for each phase that exists The values of G H2 S for each phase that exists is known (computed) The values of G H2 S is known, even if the phase does not exist 1 The standard states for the aqueous and organic phases are different from the gas phase. The aqueous-phase standard-state is the state of a species at infinite dilution in water at the hypotheti concentration of 1 m. As such, it depends on both T and P. The organic phase standard-state differs depending on the model. In the OLI AQ model, it is the same as for the gas phase and in the OLI MSE model it is the same as for the aqueous phase. 1

2 When the phases are in equilibrium, the following relationship is true: G H2 S,vap = G H2 S,Aq = G H2 S,Org (4).and the value of GH2S in each phase is equal Thus, elements in equations (1) to (3) can be rearranged to solve for fugacities or activities of a missing, or unmeasured phase. For example, there is no gas-phase at 15C and 1 bar. Therefore, the fugacity can be computed from the aqueous H2S concentration by combining equation (4) and (1): G H2 S,aq = G H2 S,vap + RT ln( H2 SY H2 SP T ) = G H2 S,vap + RT ln f H 2 S f H2 S (5) The Standard state G H2 S,vap value is based on a reference pressure of 1 bar, or;f H2 S = 1bar. The equation is rearranged to: G H 2S,aq G H2S,vap f H2 S(bar) = e RT (6) A similar fugacity relationship can be made when the H2S concentration in the oil phase is known. G H 2S,org G H2S,vap f H2 S(bar) = e RT (7) Standard State Gibbs Energy of the vapor-phase H2S (G H2 S,vap) By definition, the value of G H2 S,vap is independent of composition. 2

3 Therefore, G H2 S,vapcan be computed using temperature only; without needing the gas phase composition, or existence. These values can there be used directly in the above equations, regardless of the phases present. Example: Low temperature, Vapor-Water phases present Software culations at ambient T & P, where the gas & water phases are present Consider the low temperature and pressure state first. The screenshots below are the output of a flash culation at 25C, 1 atm, and.1% H 2S vapor (.1 atm PP). The Gibbs Energy for the water (aq) and gas (vap) phase, G H2 S,vap = G H2 S,aq = , are equal because the phases are in equilibrium. Also computed (automatily) is the standard state Gibbs energy of H 2S in the gas phase, G H2 S,aq = Lastly, the gas phase, H2S fugacity coefficient is culated automatily, φ H2 S =.994, because the gas phase is present. Software output shows the Gibbs Energy of each phase and the fugacity 3

4 Internal consistency therefore, requires equation (5) to be an equality: G H2 S,aq = G H2 S,vap + RT ln(φ H2 SY H2 SP T ) = ln( ) (= ) The fugacity is the (φ H2 SY H2 SP T ) term, and has a value of: = 9.94e 5, or.6% below the ideal partial pressure of 1e -4 bar. Thus, this example displays the internal consistency of these equations. Example: High Temperature/Pressure case, oil phase only (no vapor) When no gas phase is present, use thermodynamic relationships to culate The next example is a 5:5 CH 4:Decane 5 mixture containing, 5e H 2S. The conditions are 15C and 15 bar, where no gas phase exists, and thus no fugacity is shown. The software culates the Gibbs energy of H 2S in the 2nd Liquid phase: G H2 S,org = The standard state Gibbs energy for H 2S in the vapor is G H2 S,vap =

5 The Gibbs energy of the phase and the standard state Gibbs energy can be used to culate fugacity We can use equation (7) to compute the gas phase fugacity by entering the date from the above tables. f H2 S = e G H 2S,oil G H 2S,vap RT = e ( ) =.16 Since the reference fugacity is 1 bar, f H2 S =.16 bar. If this mixture were a hypotheti 1% vapor, then the partial pressure could be computed by setting 5 the gas-phase e fraction y H2 S = 5e, and: 5 P H2 S = 5e 15 bar =.75 bar. The fugacity coefficient is then computed from equation (1): φ H2 S = f.16 bar = y H2 SP T.75 bar =.21 The OLI Studio will automate the fugacity culation when there is no gas phase present beginning with release V For more information please contact Pat McKenzie, Business Development Director for OLI at pat.mckenzie@aqsim.com or x112 5

CH2351 Chemical Engineering Thermodynamics II Unit I, II Phase Equilibria. Dr. M. Subramanian

CH2351 Chemical Engineering Thermodynamics II Unit I, II Phase Equilibria Dr. M. Subramanian Associate Professor Department of Chemical Engineering Sri Sivasubramaniya Nadar College of Engineering Kalavakkam