To obtain a semi-theoretical equation for the excess Gibbs energy of a liquid mixture, Guggenheim's quasi-chemical analysis is generalized through introduction of the local area fraction as the primary concentration variable. The resulting universal quasi-chemical (UNIQUAC) equation uses only two adjustable parameters per binary. Extension to multicomponent systems requires no ternary (or higher) parameters.

The UNIQUAC equation gives good representation of both vapor-liquid and liquid-liquid equilibria for binary and multicomponent mixtures containing a variety of nonelectrolyte components such as hydrocarbons, ketones, esters, amines, alcohols, nitriles, etc., and water. When well-defined simplifying assumptions are introduced into the generalized quasi-chemical treatment, the UNIQUAC equation reduces to any one of several well-known equations for the excess Gibbs energy, including the Wilson, Margules, van Laar, and NRTL equations.

The effects of molecular size and shape are introduced through structural parameters obtained from pure-component data and through use of Staverman's combinatorial entropy as a boundary condition for athermal mixtures. The UNIQUAC equation, therefore, is applicable also to polymer solutions.

Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems

An equation of state for associating liquids is presented as a sum of three Helmholtz energy terms: Lennard-Lones (LJ) segment (temperature-dependent hard sphere + dispersion), chain (increment due to chain formation), and association (increment due to association). This equation of state has been developed by extending Wertheim’s theory obtained from a resummed cluster expansion. Pure component molecules are characterized by segment diameter, segment-segment interaction energy, for example, Lennard-Jones u and E, and chain length expressed as the number of segments. There are also two association parameters, the association energy and volume, characteristic of each site-site pair. The agreement with molecular simulation data is shown to be excellent at all the stages of development for associating spheres, mixtures of associating spheres, and nonassociating chains. The model has been shown to reproduce experimental phase equilibrium data for a few selected real pure compounds.

New reference equation of state for associating liquids

This report is an update of NREL's ongoing process design and economic analyses of processes related to developing ethanol from lignocellulosic feedstocks The US Department of Energy (DOE) is promoting the development of ethanol from lignocellulosic feedstocks as an alternative to conventional petroleum-based transportation fuels DOE funds both fundamental and applied research in this area and needs a method for predicting cost benefits of many research proposals To that end, the National Renewable Energy Laboratory (NREL) has modeled many potential process designs and estimated the economics of each process during the last 20 years This report is an update of the ongoing process design and economic analyses at NREL We envision updating this process design report at regular intervals; the purpose being to ensure that the process design incorporates all new data from NREL research, DOE funded research and other sources, and that the equipment costs are reasonable and consistent with good engineering practice for plants of this type For the non-research areas this means using equipment and process approaches as they are currently used in industrial applications For the last report, published in 1999, NREL performed a complete review and update of the process design and economic model formore » the biomass-to-ethanol process utilizing co-current dilute acid prehydrolysis with simultaneous saccharification (enzymatic) and co-fermentation The process design included the core technologies being researched by the DOE: prehydrolysis, simultaneous saccharification and co-fermentation, and cellulase enzyme production In addition, all ancillary areas--feed handling, product recovery and purification, wastewater treatment (WWT), lignin combustor and boiler-turbogenerator, and utilities--were included NREL engaged Delta-T Corporation (Delta-T) to assist in the process design evaluation, the process equipment costing, and overall plant integration The process design and costing for the lignin combustor and boiler turbogenerator was reviewed by Reaction Engineering Inc (REI) and Merrick & Company reviewed the wastewater treatment Since then, NREL has engaged Harris Group (Harris) to perform vendor testing, process design, and costing of critical equipment identified during earlier work This included solid/liquid separation and pretreatment reactor design and costing Corn stover handling was also investigated to support DOE's decision to focus on corn stover as a feedstock for lignocellulosic ethanol Working with Harris, process design and costing for these areas were improved through vendor designs, costing, and vendor testing in some cases In addition to this work, enzyme costs were adjusted to reflect collaborative work between NREL and enzyme manufacturers (Genencor International and Novozymes Biotech) to provide a delivered enzyme for lignocellulosic feedstocks This report is the culmination of our work and represents an updated process design and cost basis for the process using a corn stover feedstock The process design and economic model are useful for predicting the cost benefits of proposed research Proposed research results can be translated into modifications of the process design, and the economic impact can be assessed This allows DOE, NREL, and other researchers to set priorities on future research with an understanding of potential reductions to the ethanol production cost To be economically viable, ethanol production costs must be below market values for ethanol DOE has chosen a target ethanol selling price of $107 per gallon as a goal for 2010 The conceptual design and costs presented here are based on a 2010 plant start-up date The key research targets required to achieve this design and the $107 value are discussed in the report« less

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Lignocellulosic Biomass to Ethanol Process Design and Economics Utilizing Co-Current Dilute Acid Prehydrolysis and Enzymatic Hydrolysis for Corn Stover

New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures☆

The temperature and acentric factor dependence of the attractive term of the Peng—Robinson equation of state have been modified. The introduction of a single pure compound parameter allows the accurate reproduction of the vapor pressure data for a wide variety of substances. Nonpolar, polar nonassociating and associating compounds are equally well represented by the cubic PRSV equation of state. The conventional one-binary-parameter mixing rule allows the correlation of the vapor—liquid equilibrium data for a wide variety of binary systems. Only for systems formed by a polar compound (associating or not) and a saturated hydrocarbon, are results poorer than those obtained with conventional excess Gibbs energy functions.

PRSV: An improved peng—Robinson equation of state for pure compounds and mixtures

A critical discussion is given of the use of local compositions for representation of excess Gibbs energies of liquid mixtures. A new equation is derived, based on Scott's two-liquid model and on an assumption of nonrandomness similar to that used by Wilson. For the same activity coefficients at infinite dilution, the Gibbs energy of mixing is calculated with the new equation as well as the equations of van Laar, Wilson, and Heil; these four equations give similar results for mixtures of moderate nonideality but they differ appreciably for strongly nonideal systems, especially for those with limited miscibility. The new equation contains a nonrandomness parameter α12 which makes it applicable to a large variety of mixtures. By proper selection of α12, the new equation gives an excellent representation of many types of liquid mixtures while other local composition equations appear to be limited to specific types. Consideration is given to prediction of ternary vapor-liquid and ternary liquid-liquid equilibria based on binary data alone.

Henri Renon

Papers

Local compositions in thermodynamic excess functions for liquid mixtures