Thermodynamics: Determining Fugacity in a Vapor Mixture Using Equations of State

A walk through of an example problem determining the fugacity of methane in a vapor mixture using an equation of state, as well as applying the Lewis Fugacity Rule: Consider a ternary system of methane (a), ethane (b), and propane (c) at 25°C and 15 bar. Assume this system can be represented by the virial equation truncated at the second term: z=1+B_mix/v_m You can assume that the mixture obeys the following mixing rule for Bmix: Bmix = yayaBaa + 2yaybBab + 2yaycBac + ybybBbb + 2ybycBbc + ycycBcc At 25°C, the second virial coefficients [cm3/mol] are given by: Baa = -42, Bab = -93, Bac = -139, Bbb = -185, Bbc = -274, Bcc = -399 a. Develop an expression for the fugacity coefficient of methane in the mixture. b. Estimate the fugacity and the fugacity coefficient of methane for a mixture with 20 mole % methane, 30 mole % ethane, and 50 mole % propane. c. Repeat (a) and (b) using the Lewis Fugacity Rule. Purdue University Omega Chi Epsilon Text: Engineering and Chemical Thermodynamics by Koretsky 2nd edition ---------------------------------------------------------------------------------------------------------- Topics: fugacity, vapor mixture, gas phase , vapor mixture fugacity, equations of state, Thermodynamic relations, example problem, non-ideal behavior, Lewis Fugacity Rule, chemical thermodynamics, chemical engineering, thermodynamic properties, how to, engineering, Purdue University, chemical engineering, Purdue university chemical engineering, CHE 211, Introduction to thermodynamics, fugacity, vapor mixture, gas phase , vapor mixture fugacity, equations of state, Thermodynamic relations, example problem, non-ideal behavior, Lewis Fugacity Rule, chemical thermodynamics, chemical engineering, thermodynamic properties, how to, engineering, Purdue University, chemical engineering, Purdue university chemical engineering, CHE 211, Introduction to thermodynamics, fugacity, vapor mixture, gas phase , vapor mixture fugacity, equations of state, Thermodynamic relations, example problem, non-ideal behavior, Lewis Fugacity Rule, chemical thermodynamics, chemical engineering, thermodynamic properties, how to, engineering, Purdue University, chemical engineering, Purdue university chemical engineering, CHE 211, Introduction to thermodynamics Consider a ternary system of methane (a), ethane (b), and propane (c) at 25°C and 15 bar. Assume this system can be represented by the virial equation truncated at the second term: z=1+B_mix/v_m You can assume that the mixture obeys the following mixing rule for Bmix: Bmix = yayaBaa + 2yaybBab + 2yaycBac + ybybBbb + 2ybycBbc + ycycBcc At 25°C, the second virial coefficients [cm3/mol] are given by: Baa = -42, Bab = -93, Bac = -139, Bbb = -185, Bbc = -274, Bcc = -399 a. Develop an expression for the fugacity coefficient of methane in the mixture. b. Estimate the fugacity and the fugacity coefficient of methane for a mixture with 20 mole % methane, 30 mole % ethane, and 50 mole % propane. c. Repeat (a) and (b) using the Lewis Fugacity Rule. Consider a ternary system of methane (a), ethane (b), and propane (c) at 25°C and 15 bar. Assume this system can be represented by the virial equation truncated at the second term: z=1+B_mix/v_m You can assume that the mixture obeys the following mixing rule for Bmix: Bmix = yayaBaa + 2yaybBab + 2yaycBac + ybybBbb + 2ybycBbc + ycycBcc At 25°C, the second virial coefficients [cm3/mol] are given by: Baa = -42, Bab = -93, Bac = -139, Bbb = -185, Bbc = -274, Bcc = -399 a. Develop an expression for the fugacity coefficient of methane in the mixture. b. Estimate the fugacity and the fugacity coefficient of methane for a mixture with 20 mole % methane, 30 mole % ethane, and 50 mole % propane. c. Repeat (a) and (b) using the Lewis Fugacity Rule. Consider a ternary system of methane (a), ethane (b), and propane (c) at 25°C and 15 bar. Assume this system can be represented by the virial equation truncated at the second term: z=1+B_mix/v_m You can assume that the mixture obeys the following mixing rule for Bmix: Bmix = yayaBaa + 2yaybBab + 2yaycBac + ybybBbb + 2ybycBbc + ycycBcc At 25°C, the second virial coefficients [cm3/mol] are given by: Baa = -42, Bab = -93, Bac = -139, Bbb = -185, Bbc = -274, Bcc = -399 a. Develop an expression for the fugacity coefficient of methane in the mixture. b. Estimate the fugacity and the fugacity coefficient of methane for a mixture with 20 mole % methane, 30 mole % ethane, and 50 mole % propane. c. Repeat (a) and (b) using the Lewis Fugacity Rule.