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Natural gas and oil produced from shale accounts for a signicant portion in the global production. Due to the large surface area and high organic content in shale formations, adsorption plays a major role in the storage of the hydrocarbons within the rock and their phase equilibrium. This study provides a comparison of several engineering models for gas adsorption in shale based on the recent literature data for pure and binary gases. For pure components, Langmuir, the modied Toth-Langmuir, and the Multicomponent Potential Theory of Adsorption using Dubinin-Radushkevich potential (MPTA-DRA) were compared. The three models show similar deviations lower than 10%. For binary gases, Multicomponent Langmuir (ML), Ideal Adsorbed Solution Theory (IAST) and MPTA were evaluated, where MPTA shows the lowest deviation with 17.9%. Additionally, we presented an analysis of the phase envelope shift under the in uence of the capillary pressure and the adsorption lm. ML and IAST were used to calculate the adsorption amount whereas MPTA was used to gen- erate articial adsorption data over large temperature range and for other homologous hydrocarbons to estimate the ML and IAST parameters. The adsorption lm thickness was considered in the calculation of the eective capillary radius and the corresponding capillary pressure. The combined eects modify the saturation pressure in the whole temperature range except at the critical point. The biggest impact was found on the bubble point branch away from the critical point where the interfacial tension of the system is more pronounced.

Confined fluids such as oil and gas mixtures inside tight reservoirs are systems that can experience high capillary pressure difference between the liquid and gas phases. This capillary pressure difference has an effect on the phase equilibrium and in some cases is considerably high. We presented an algorithm which can reliably compute the whole phase envelope for multicomponent mixtures when there is a capillary pressure difference. It uses an equation of state for the phase equilibrium and the Young-Laplace equation for the capillary pressure model. The algorithm proves to be robust and efficient for test mixtures with wide ranges of compositions at different capillary radii and vapor fractions. The calculation results show that the phase envelope changes everywhere except at the critical point. The bubble point and the lower branch of the dew point show a decrease in the saturation pressure, whereas the upper branch of the dew point shows an increase. The cricondentherm is shifted to a higher temperature. We also presented a mathematical analysis of the phase envelope shift due to capillary pressure based on linear approximations. The resulting linear approximation equations can predict the correct direction of the phase envelope shift. Combined with the multicomponent Clapeyron equation, the equations reveal why the shift changes direction for the saturation pressure at the cricondentherm and for the saturation temperature at the cricondenbar. The equations can be used to estimate the magnitude of shift, and the approximation is close for the change in the bubble point pressure.

Gas injection is a widely used enhanced oil recovery method, and its application is expected to increase in the foreseeable future. In order to build a method of characteristics solution to a two-phase gas injection system, we must construct the composition route from the injection gas to the initial oil where all the intersecting key tielines must be identified. Calculation of these intersecting tielines requires a series of special negative flashes, which allow not only phase fractions outside the physical interval [0,1] but also negative feed compositions. The phase compositions from one negative flash are used to recombine the feed for the next negative flash. Despite the apparent complexity due to multicomponent phase equilibrium and transport, for pure component gas injection, negative flash and elimination of components can be performed in an alternating manner. In particular, if K-values are constant, there exists a simple feature that the vapor fraction roots (β-roots) for the Rachford–Rice equat...

The cubic-plus-association (CPA) equation of state is applied in this work to mixtures containing acetic acid and water. A previously developed modification of the model, the so-called CPA-Huron−Vidal (CPA-HV), is used. New CPA parameters have been estimated based on the vapor pressure, liquid density, enthalpy of vaporization, and vapor-phase compressibility factor data. The CPA-HV parameters have been fitted to, among others, experimental vapor compressibility factor data and experimental relative volatility data at different temperature ranges. The purpose of the work was to investigate whether the CPA-HV model can describe the vapor−liquid equilibrium for acetic acid−water over a temperature range of 200 K and at the same time represent the behavior of pure acetic acid and acetic acid−water mixtures with respect to enthalpies of vaporization and compressibility factors. It is shown that satisfactory results are overall obtained, but if an excellent match is needed over the whole temperature range, the...

This article shows how controlled variables (CVs) of the regulatory control layer in a liquefied natural gas (LNG) plant can be chosen as linear combinations of measurements using self-optimizing control principles. By self-optimizing control, the CVs are chosen such that the set points of the CVs remain close to steady-state optimal despite disturbances, thus reducing the need for online reoptimization. Several methods for calculation of linear combinations within this framework are compared. Self-optimizing control design can also be used in the process design phase to place measurements by reducing a maximum candidate set of measurements to a best possible subset of measurements giving an acceptable loss. This article proposes a relatively simple method for successive selection (SS) of measurements and compares this approach to a more comprehensive branch-and-bound (BB) method for selection of measurements. The results indicate that, although the BB method gives lower average losses for very small subsets, the methods are comparable with respect to average losses for medium and large subsets, and the SS method outperforms the BB method in terms of computational load.

This article describes a dynamic, control relevant, mechanistic model of the TEALARC liquified natural gas process. The model is to be used for both steady-state and dynamic controllability analysis. The model therefore needs to be computationally light, but still include enough complexity such as to study the impact of capacity constraints on the control structure. Structured assumptions have been used to obtain simplified representations of gas/liquid flows and thermodynamic properties. The steady-state operating points of the dynamic model have been adapted to a given steady-state process design model. The paper demonstrates that the model is well suited for operability analysis. Steady-state and dynamic characteristics are illustrated.

An association model, the cubic-plus-association (CPA) equation of state (EoS), is applied for the first time to a class of multifunctional compounds (alkanolamines). Three alkanolamines of practical and scientific significance are considered; monoethanolamine (MEA), diethanolamine (DEA), and methyl diethanolamine (MDEA). Vapor pressures and liquid densities, as well as solvatochromic parameters and mixture liquid−liquid equilibria (LLE) data with alkanes are used to estimate the five pure-compound parameters. Vapor−liquid equilibria (VLE) calculations for cross-associating mixtures, especially those with water, are used in the validation of the parameters. The influence on the results of the association scheme, cross-association combining rules, interaction parameters, and the data available is discussed also, in connection with other aqueous cross-associating mixtures previously studied using the CPA equation of state (alcohols, amines, and glycols).

Acetic acid is a very important compound in the chemical industry with applications both as solvent and intermediate in the production of, e.g., polyesters. The design of these processes requires knowledge of the phase equilibria of mixtures containing acetic acid and a wide variety of compounds over extended temperature and pressure ranges. From the scientific point of view, modeling of such equilibria is challenging because of the complex association and solvation phenomena present. In this work, a previously developed association equation of state (cubic-plus-association, CPA) is applied to a wide variety of mixtures containing acetic acid, including gas solubilities, cross-associating systems (with water and alcohols), and polar chemicals like acetone and esters. Vapor−liquid and liquid−liquid equilibria are considered for both binary and ternary mixtures. With the exception of a somewhat inferior performance for the water−acetic acid VLE, which does not seem to affect substantially the performance fo...

Two equations of state (PC-SAFT and CPA) are used to predict the monomer fraction of pure associating fluids. The models each require five pure-component parameters usually obtained by fitting to experimental liquid density and vapor pressure data. Here we also incorporate monomer fractions measured using spectroscopy, resulting in models that better predict the monomer fraction (fraction of molecules not participating in hydrogen bonding), without sacrificing the accuracy of the liquid density and vapor pressure correlations. Thus, it is clear that monomer fraction prediction depends on the way the parameters were obtained. The selection of appropriate association schemes is also investigated using spectroscopic data. For pure water a four-site scheme is shown to be the most appropriate scheme. In the case of pure alcohols, a three-site scheme is best for methanol; two- or three-site schemes perform about equally for ethanol; for higher alcohols a two-site scheme is preferred. This is in accordance with ...

CPA (Cubic-Plus-Association) is an equation of state that is based on a combination of the Soave−Redlich−Kwong (SRK) equation with the association term of the Wertheim theory. The development of CPA started in 1995 as a research project funded by Shell (Amsterdam), and the model was first published in 1996. Since then, it has been successfully applied to a variety of complex phase equilibria, including mixtures containing alcohols, glycols, organic acids, water, and hydrocarbons. Focus has been placed on cases of industrial importance, e.g., systems with gas-hydrate inhibitors (methanol, glycols), glycol regeneration and gas dehydration units, oxygenate additives in gasoline, alcohol separation, etc. This manuscript, which is the first of a series of two papers, offers a review of previous applications and illustrates current focus areas related to the estimation of pure compound parameters, alcohol−hydrocarbon vapor−liquid equilibria (VLE) and solid−liquid equilibria (SLE), as well as aqueous systems. Th...

Equations of state that incorporate the Wertheim association expression are more difficult to apply than conventional pressure explicit equations, because the association term is implicit and requires solution for an internal set of composition variables. In this work, we analyze the convergence behavior of different solution methods and demonstrate how a simple and efficient, yet globally convergent, procedure for the solution of the equation of state can be formulated.

The cubic-plus-association (CPA) equation of state has been previously applied to vapor−liquid, liquid−liquid, and solid−liquid equilibria of mixtures containing associating compounds (water, alcohols, glycols, acids, amines). Although some high-pressure applications have been presented, emphasis was given to low pressures and liquid−liquid equilibria. In this work, CPA is applied to two classes of mixtures containing polar chemicals for which high-pressure data are available: acetone-containing systems and dimethyl ether mixtures. They are of both scientific and industrial importance. Moreover, CPA is applied to high-pressure solid−liquid equilibria (SLE) for alcohol−alkane mixtures. In the case of acetone−hydrocarbon mixtures, satisfactory results are achieved if acetone is allowed to self-associate. Satisfactory high-pressure acetone−water vapor−liquid equilibrium (VLE) is obtained, comparable to conventional models such as MHV2. Very good results are also obtained for multicomponent vapor−liquid−liqu...

The cubic-plus-association (CPA) equation of state is applied to phase equilibria of mixtures containing alcohols, glycols, water, and aromatic or olefinic hydrocarbons. Previously, CPA has been successfully used for mixtures containing various associating compounds (alcohols, glycols, amines, organic acids, and water) and aliphatic hydrocarbons. We show in this work that the model can be satisfactorily extended to complex vapor−liquid−liquid equilibria with aromatic or olefinic hydrocarbons. The solvation between aromatics/olefinics and polar compounds is accounted for. This is particularly important for mixtures containing water and glycols, but less so for mixtures with alcohols. For water/hydrocarbons, a single binary interaction parameter which accounts for the solvation is fitted to the experimental liquid−liquid equilibria (LLE) data. The interaction parameter of the physical term of the model (the Soave-Redlich-Kwong (SRK) equation of state) can be obtained from mixtures with aliphatic hydrocarbon...

The cubic-plus-association (CPA) equation of state has been extended to modeling mixtures containing amines. Special focus was given to primary and secondary amines, which are known to self-associate, thus forming hydrogen bonds in mixtures with alkanes. Pure-compound parameters have been determined from vapor pressure and liquid density data, but phase equilibrium data were also used as guidance for selecting the optimum sets among those which best represent the pure-compound properties. Diethylamine was modeled as a two-site molecule, whereas the two primary amines considered (methylamine, ethylamine) were modeled using both the two-site and three-site schemes. Both schemes perform overall equally well, when care is exercised in the parameter estimation, by giving more weight on the vapor pressures rather than the liquid densities. Thus, only results using the two-site scheme are shown. Excellent binary vapor−liquid equilibria have been obtained for amine + aliphatic hydrocarbons with a low value of the...

The cubic-plus-association (CPA) equation of state (EoS) is applied, using different combining rules, to vapor−liquid equilibria (VLE) and liquid−liquid equilibria (LLE) of alcohol−water systems. It is demonstrated that the Elliott combining rule (ECR) with a common temperature-independent interaction parameter provides very adequate VLE correlations over extended temperature and pressure ranges, yielding also a very satisfactory description of the azeotropic behavior. LLE of heavy alcohol−water systems is best described with the CR-1 combining rule and a single interaction parameter. Satisfactory predictions of multicomponent, multiphase equilibria of water−alcohol−alkane systems at various conditions are achieved using solely one interaction parameter per binary. A study of the dominant binary systems for the prediction of the multicomponent systems demonstrates that both the binary alcohol−water and alcohol−hydrocarbon systems are crucial for the prediction of the partition coefficients of alcohols. Fi...

Using simplified PC-SAFT we have modeled gas solubilities at high temperatures and pressures for the gases methane and carbon dioxide in each of the three polymers high-density polyethylene (HDPE), nylon polyamide-11 (PA-11), and poly(vinylidene fluoride) (PVDF). In general the results are satisfactory, using in most cases a single, temperature-independent value of the binary interaction parameter. In the cases of methane in HDPE and PVDF, a temperature-dependent binary interaction parameter was required. New pure component polymer parameters for PA-11 and PVDF were obtained using a recently developed prediction scheme which does not rely on binary experimental data.

Partial pressures of carbon dioxide (CO2) over aqueous solutions of monoethanolamine (MEA), diethanolamine (DEA), and N-methyldiethanolamine (MDEA) have been correlated using a simple approach where only one chemical equilibrium reaction is taken into account and assuming ideal gas and ideal liquid properties. The approach combines the Henry's law constant and the chemical reaction equilibrium constant for the formation of carbamate for primary and secondary alkanolamines (MEA, DEA) or bicarbonate for tertiary alkanolamines(MDEA), resulting in an explicit expression for calculating the partial pressure of CO2 over an aqueous alkanolamine solution. Accurate values for the partial pressure of CO2 are obtained for a limited loading, temperature, and pressure range that is useful in modeling CO2 capture from coal-fired power plants. Heat of absorption values derived from the model agree with experimental data from the literature.

Two algorithms for evaluating liquid−liquid equilibria (LLE) for binary and ternary polymer solutions are presented. The binary algorithm provides the temperature versus concentration cloud-point curve at fixed pressure, whereas the ternary algorithm provides component 1 versus component 2 concentration coexistence curves at fixed pressure and temperature. The algorithms automatically trace the entire liquid−liquid coexistence curves in steps by adjusting the step size, generating initial estimates, and subsequently solving the phase-equilibrium problem by a second-order method. The algorithms are used for investigating the correlative and predictive capabilities of the thermodynamic model PC-SAFT. The investigation shows that the model correlates well experimental LLE data for binary as well as ternary systems but further predicts the behavior of the ternary systems with reasonably good accuracy, even by using interaction parameters obtained from binary vapor−liquid equlibrium data.

The simplified PC-SAFT equation of state (von Solms et al. Ind. Eng. Chem. Res. 2003, 42, 1098) has been applied to the pure-component properties and vapor−liquid equilibria of mixtures of polyamid...

The application of the cubic-plus-association (CPA) equation of state has been extended to mixtures containing cross-associating compounds such as glycols and water. In this case, combining rules are required in the association term of CPA for the cross-association energy and volume parameters. Different types of such combining rules have been suggested over the past years for association models such as statistical associating fluid theory. These are tested in this work for CPA in terms of their correlation and prediction capabilities for vapor−liquid equilibria of glycol−water systems. Comparisons with the Soave−Redlich−Kwong equation of state are also provided. It has been found that the arithmetic mean combining rule for the cross-association energy parameter and the geometric mean for the cross-association volume parameter provide overall the best results for cross-associating systems containing glycols and water. Moreover, preliminary results show that the CPA model can be used to predict multicompon...

Two modifications to perturbed-chain statistical associating fluid theory are proposed which simplify the calculation of phase-equilibrium properties for nonassociating and associating systems, polymers, and simple molecules without loss of accuracy. A simple linear extrapolation scheme is proposed to obtain parameters for linear alkanes up to polyethylene. It is shown that computing times are greatly reduced using these modifications and compare favorably with traditional equations of state for nonassociating and associating systems.

The ability of the Unifac-FV and Entropic-FV models to predict phase equilibria for dendrimer systems is investigated in this work. Different approaches are considered for the estimation of the den...

A Langmuir adsorption model is used to represent the conditions at which structure H hydrates may form. The two smaller cavities of structure H hydrates are of similar size and are modeled using the same Langmuir constants. Parameters in a simple two-parameter Langmuir expression have been estimated for methane and nitrogen as guest molecules of the smaller cavities and for 12 possible guest molecules of the large cavity. The latter ones are all hydrocarbons with from 5 to 8 carbon atoms. Experimental hydrate formation temperatures are correlated with an average absolute temperature deviation of 0.15 K. Hydrate formation data for two ternary mixtures not used in the parameter estimation are modeled with approximately the same accuracy.

A detailed model for a wet flue gas desulfurization (FGD) pilot plant, based on the packed tower concept, has been developed. All important rate-determining steps, absorption of SO2, oxidation of H...

Several recent proposals for using excess free energy models in constructing mixing rules for cubic equations of state have been analyzed. The reproduction of the base model behavior at the correlating temperature and the nature of the extrapolation to higher temperatures have been examined. The Wong−Sandler, LCVM, and MHV-1 mixing rules in an equation of state result in excess Gibbs free energies with contributions in addition to those from the base activity coefficient model. As a result, considerable degradation of calculated equilibrium behavior can occur. The excess enthalpies produced by these mixing rules are generally more positive than would be found from the temperature derivative of the G excess models, with only the MHV-2 mixing rule giving a reasonably quantitative reproduction. The success of the Wong−Sandler mixing rule in extrapolating to higher temperatures appears to derive in part from this positive addition to the excess enthalpy.

The method of successive substitution for phase equilibrium calculations can only converge to a minimum of the mature Gibbs free energy, and it is commonly assumed that, given proper initial estimates, convergence will always occur. Unfortunately, although the exemptions are rare, the assumption is incorrect. Divergence, regardless of the quality of the initial estimate, can occur in matures that exhibit strong negative deviations from ideal solution behavior, such as polymer solutions and gas hydrates. Unless special precautions are taken, algorithms that implement successive substitution as part of the solution procedure are likely to fail on such matures. We present an analysis of the thermodynamic conditions that may lead to divergence of successive substitution and present some numerical examples. In addition we briefly discuss some methods capable of solving the appropriate equilibrium equations under conditions where successive substitution fails

Free-volume theories have been used the last century in various areas of science including polymer thermodynamics and studies related to viscosity and diffusion. Irrespective of the exact free-volu...