An Integrated Educational Thermodynamics Software Program ThermoSolver An Integrated Educational Thermodynamics Software Program Connelly Barnes

What is ThermoSolver? Programmed by Connelly Barnes. Software program used to teach Chemical Engineering (ChE) thermodynamics. Available for free from Web (Google it). Allows students to "explore" thermodynamics – make nontrivial calculations, and compare different thermodynamic models.

Motivation Thermodynamic equations can become complicated, must be solved by lookup tables or computer algorithms. Tables are available for a limited set of pure species.

Motivation (continued) Computer solutions: spreadsheets, scripts, Computer Algebra System worksheets can be used, but it's hard to let the student use different number of species, thermodynamic models, etc. We would like students to not have the burden of programming every solution, especially for routine calculations.

Objectives Standalone educational software program. Easy to use interface – reduce all "barriers" to using the software. Research and develop algorithms needed to solve equations. Integrate with chapter problems in Engineering and Chemical Thermodynamics by Milo Koretsky.

Use at Universities At OSU, ThermoSolver used in ChE thermo course, graduate reactors course, plant design. In plant design, ThermoSolver not specifically named, but 10/39 students used it. Don't track usage by other Universities, but Web search reveals it has been used at Univ. Notre Dame, Indiana and Univ. of Colorado at Boulder.

Features Database, 350+ chemical compounds. Calculate saturation pressure, temp. Solve equations of state (LK and PR). Find pure, mixed fugacity coefficients. Fit excess Gibbs energy models to experimental data. Bubble point and dew point calculations. Plot phase diagrams for binary systems.

Features (continued) Calculate Keq for single chemical reaction. Multiple chemical reaction equilibria. Plotting. HTML docs provided, numerical methods and equations described.

Tour of Program: Saturation Pressure Calculator Solve for saturation pressure or saturation temperature. Saturation pressure/temp determines where liquid/vapor phase transition occurs. Example problem: Find saturation pressure of 1,4-dioxane (C4H8O2) at 50 oC.

Tour of Program: Equation of State Solver Finds one of the state properties pressure, molar volume, or temperature given the other two, using the LK or PR equations of state. Example problem: Find molar volume of propane at 35 bar and 50 oC. Compare w/ ideal gas: 0.77 L/mol.

Tour of Program: Fugacity Coefficient Solver Finds the pure fugacity coefficient or the fugacity coefficient of a species in a mixture, using the LK or PR equation of state.

Tour of Program: Fugacity Coefficient Solver

Tour of Program: Models for excess Gibbs energy Fits activity coefficient models to experimental data for binary Vapor-Liquid Equilibrium (VLE) systems. Objective function. Example: Chloroform-heptane.

Tour of Program: Bubble point / Dew Point Calculator Dew point: gaseous system, when first drop of liquid forms – achieved by decreasing temperature or increasing pressure. Bubble point: liquid system, when first bubble forms. Solver finds temp./pressure where first bubble or dewdrop forms, and composition of chemicals in bubble or dew-drop.

Tour of Program: Bubble point / Dew Point Calculator

Tour of Program: Binary Phase Diagrams Make plots of phase transitions in binary vapor-liquid systems. Example: Plot pressure vs. liquid mole fraction for methylcyclohexane-benzene system at 50 oC.

Tour of Program: Equilibrium Constant Solver Finds KT at a single temperature, for a single chemical reaction. Plots KT vs T.

Tour of Program: Equilibrium Constant Solver

Tour of Program: Multiple Chemical Reaction Equilibria Gas-solid equilibrium. Found by minimizing excess Gibbs energy.

Tour of Program: Multiple Chemical Reaction Equilibria

Tour of Program: Multiple Chemical Reaction Equilibria

Numerical Algorithms Newton root finder with backtracking. Downhill simplex method for minimization. Iterative substitution.

Multidimensional Newton Method Vector-valued function F: Rn -> Rn. Newton step Iterate

Newton Backtracking Use full Newton step δ if norm ||F||2 is less than its value at xi, otherwise try δ/2, δ/4, δ/8, ... until ||F||2 is less than its value at xi. This is guaranteed to happen, as δ is a descent direction for ||F||2.

Simplex Method J.A. Nelder and R. Mead, "A simplex method for function minimization," Computer Journal 7 (1965) 308-313. Simple, derivative free method for finding minimum of function of form F: Rn -> R. Does not use derivatives, so constrained minimization possible by setting F to infinity.

Algorithms Equation of state solver: Newton method. Excess Gibbs energy model fitting: Simplex. Bubble point / dew point: Custom iterative methods based on those of Smith, Van Ness, and Abbott. Multiple chemical reaction equilibria: Newton and simplex. Typically converges, however Dr. Koretsky found a problem where this method does not converge.

Conclusion Objectives met? User interface is straightforward to use. Numerical methods converge with one known exception. A practical tool integrated with problems in a textbook.

Acknowledgements Milo Koretsky, Mentor. Rubin Landau, Computational Physics.