The Gibbs-Helmholtz Equation and the Thermodynamic Consistency of Chemical Absorption Data Paul M. Mathias* ,† and John P. O’Connell ‡ † Fluor Corporation, 3 Polaris Way, Aliso Viejo, California 92698, United States ‡ Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904-4741, United States ABSTRACT: The Gibbs-Helmholtz (G-H) equation connects vapor-liquid equilibrium (VLE) and calorimetric data. If experimental measurements for the heat of solution are not available, they may be estimated through the G-H equation. Further, if both VLE and heat-of-solution data are available, their mutual thermodynamic consistency can be evaluated through the G-H equation, to develop the most accurate and reliable model. This kind of analysis is particularly useful for chemical-absorption systems, such as the capture of CO 2 using aqueous solutions of amines, where regeneration energies are significant. In this work, the G-H equation is derived to unambiguously relate the commonly used form to the rigorous and general form, including for systems where phase equilibrium is accompanied by chemical reactions in any phase. The effect of approximations and the range of applicability of the common G-H equation are first applied to data generated for a simple VLE system by an equation of state, with different reliability found for the vapor and liquid phases. Next, consistency is evaluated for many VLE and calorimetric data for CO 2 absorption in aqueous MEA (monoethanolamine). It is shown that some VLE and/or calorimetric data sets are likely to be in error and that the experimental VLE and CO 2 heat of solution at the highest temperatures are currently uncertain. ■ INTRODUCTION Chemical solvents like alkanolamines are well suited for gas- treating applications, such as natural-gas purification and CO 2 - capture, because they provide strong selectivity for acid-gas components (e.g., CO 2 and H 2 S). 1 More than 80 years ago, Bottoms 2 first recommended amines as chemical solvents and also invented the absorption-stripping process used today. Amine scrubbing is widely expected to be the dominant technology for CO 2 capture from power plants, particularly for coal-fired plants. 3 There is considerable ongoing research to develop improved solvents and process configurations for CO 2 capture. 3,4 Proper execution of these efforts requires an accurate and reliable thermodynamic model for the system of interest. 5 Thermodynamic correlations for chemical absorption are typically phenomenological or semiempirical models, 6-8 but they may also be totally empirical. 9 Regardless of the type of model used, the experimental database is critically important since the data enable accurate model calculations and help establish the model uncertainty. It is therefore very important to test the thermodynamic consistency of the experimental database by applying thermodynamic relations such as the Gibbs-Duhem (G-D) equation and Gibbs-Helmholtz (G-H) equations. 10-12 For chemical absorption systems, both consistency analysis and energy estimations have commonly been treated by a Gibbs-Helmholtz (G-H) equation, which relates the differ- ential enthalpy of solution of a gaseous component i to the temperature derivative of its fugacity in the liquid phase at its bubble point at fixed “apparent” composition. Δ ̅ ≡ ∂ ∂ − * ≈ ∂ ∂ σ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ H H n h R f T ln (1/ ) i i TPn i i x 0 0 , , ,{ } j 0 0 (1) Here, ΔH ̅ 0i is the differential enthalpy of solution of component i, which is defined as the difference between the partial molar enthalpy of component i and its ideal-gas enthalpy at the same temperature. The standard state is the pure- component ideal gas at reference pressure (100 kPa). As indicated in Appendix A, ΔH ̅ 0i may be considered to be the enthalpy change resulting from adding an infinitesimal amount of component i from the ideal gas at the given temperature to the liquid solvent solution at the given temperature, pressure, and with “apparent” number of moles of other components held constant divided by the infinitesimal moles of component i added. Note that no phase change should occur in this step. This quantity is also identified as the differential heat of solution. Appendix A also shows the relationship of ΔH ̅ 0i to the commonly measured integral heat of solution. The “apparent” composition refers to the composition of the molecular components (reactants) in solution. As a specific example, in the case of CO 2 absorption in aqueous monoethanolamine (MEA), the apparent composition refers to the composition of CO 2 , MEA, water, and possibly other inert components such as oxygen, nitrogen, and argon. In reality, some fraction of the CO 2 , MEA, and water will react to form ionic species, and the extent of the chemical conversion changes with apparent composition, temperature, and pres- sure. 13,14 The temperature derivative on the right side of eq 1 is taken with a solvent solution at given apparent composition (denoted by fixed vector of apparent composition {x 0 }) while it is maintained at its bubble point (denoted by the subscript σ), and hence, the total pressure will change as the derivative is Received: November 19, 2011 Revised: February 27, 2012 Accepted: March 6, 2012 Published: March 6, 2012 Article pubs.acs.org/IECR © 2012 American Chemical Society 5090 dx.doi.org/10.1021/ie202668k | Ind. Eng. Chem. Res. 2012, 51, 5090-5097