Phase Equilibrium Equations Research Articles

Intrinsic correlation between the generalized phase equilibrium condition and mechanical behaviors in hydrate-bearing sediments

The phase equilibrium and mechanical behaviors of natural gas hydrate-bearing sediment are essential for gas recovery from hydrate reservoirs. In heating closed systems, the temperature-pressure path of hydrate-bearing sediment deviates from that of pure bulk hydrate, reflecting the porous media effect in phase equilibrium. A generalized phase equilibrium equation was established for hydrate-bearing sediments, which indicates that both capillary and osmotic pressures cause the phase equilibrium curve to shift leftward on the temperature-pressure plane. In contrast to bulk hydrate, hydrate-bearing sediment always contains a certain amount of unhydrated water, which keeps phase equilibrium with the hydrate within the hydrate stability field. With changes in temperature and pressure, a portion of pore hydrate and unhydrated water may transform into each other, affecting the shear strength of hydrate-bearing sediment. A shear strength model is proposed to consider not only hydrate saturation but also the change in temperature and pressure of hydrate-bearing sediment. The model is validated by experimental data with various hydrate saturation, temperature and pressure conditions. The deformation induced by partial dissociation was studied through depressurization tests under constant effective stress. The reduction in gas pressure within the hydrate stability field indeed caused sediment deformation. The dissociation-induced deformation can be reasonably estimated as the difference in volume between hydrate-bearing and hydrate-free sediments from the compression curves.

Effects of Salty Additives in Drilling Fluids on Hydrate Formation Dynamics and Phase Equilibrium

In the drilling process for deepwater and hydrate formations, adding salty components to drilling fluids is an important way to avoid secondary generation of hydrates in the annulus, and the effect of salt solutions on the hydrate generation lays a basis for drilling fluid design. In this study, an evaluation device for the effect of drilling fluid additives on hydrate formation and phase equilibrium is designed based on their interaction characteristics. In addition, hydrate generation experiments were carried out for pure water and three commonly used salty additives for drilling fluids. As such, the hydrate phase equilibrium equations under different conditions are established, and the hydrate phase change latent heat is further calculated. The results show that hydrate formation can be divided into four stages, i.e., gas dissolution, hydrate crystal nucleation, hydrate particle mass aggregation, and stabilization. Compared with pure water, sodium chloride and potassium formate solutions can effectively inhibit hydrate formation. At lower ambient temperature, the higher the concentration of potassium formate, the lower the phase equilibrium pressure. On the contrary, at higher ambient temperature, the higher the concentration of potassium formate, the higher the phase equilibrium pressure. The incomplete presence of sodium silicate in water in the form of ions is found to promote methane hydrate formation. Based on the experimental results of methane hydrate generation in potassium formate and sodium silicate solutions with different mass concentrations, the phase equilibrium calculation models for methane hydrate in both salt solutions were finally established. The latent heat of the phase change distribution of hydrate under different conditions was further calculated. The results of this paper can provide a theoretical basis for the study of deepwater drilling fluid systems and multicomponent annular flow.

Pore pressure built-up in hydrate-bearing sediments during phase transition: A poromechanical approach

Due to the density contrast between the hydrate and methane gas, the pore pressure is accumulated in the sediment during the decomposition process of methane hydrate. This accumulation of pore pressure decreases the magnitude of effective stress, further triggering potential geological disasters such as landslide. This paper establishes a theoretical framework to investigate the evolution of fluid pressure in the hydrate-bearing sediments during the decomposition process. This model consists of two parts: an unsaturated thermo-poromechanical constitutive law as well as a phase equilibrium equation. Compared with the existing studies, the present work incorporates the effect of pore volume change into the pressure built-up model. In addition, the capillary effect is considered, which plays a nontrivial role in fine-grained sediments. Based on this model, the evolution of fluid pressure is investigated in undrained conditions. It is shown that four mechanisms mainly contribute to the pressure built-up: the density contrast between decomposing hydrate and producing fluid, the variation of pore volume, the compaction of hydrate due to variation of capillary pressure, and the thermal deformation of pore constituents induced by temperature change. Among these mechanisms, the density contrast dominates the pore pressure accumulation. Under the combined effect of these contributions, the evolution of fluid pressure exhibits a strong nonlinearity during the decomposition process and can reach up to dozens of mega Pascal. Nevertheless, this high-level pressure built-up results in a significant tensile strain, yielding potential fracturing of the sediment.

Measurement and thermodynamic modeling of wax precipitation in asphalt binder

Considering asphalt as a mixed system composed of multiple solid and liquid phases based on the principle of phase equilibrium and regular solution theory, in this paper, the activity coefficient was used to describe the non-ideality of solid and liquid phases. According to the phase equilibrium equation, mass equilibrium equation, and normalization equation, the solid–liquid fraction under the equilibrium condition was calculated, and then the precipitation temperature of paraffin wax in asphalt and the precipitation amount at each temperature were determined. The gas chromatography-mass spectrometry experiment was conducted to measure the paraffinic, naphthenic and aromatic distribution of the asphalt as the input parameter of the prediction model. After the calculation results of the wax precipitation temperature (WPT) and wax precipitation curve (WPC) were compared with measured values acquired from experimental methods (viscosity method, Fourier-transform infrared spectroscopy (FTIR) method), it was found that the trend of WPC is approximately similar, but the WPT of the theoretical model was significantly higher than that of FTIR. The authors believe that this was caused by the overestimation of the thermodynamic properties of the aromatic components. After reducing the melting point and enthalpy of the aromatic components to a certain extent, satisfactory results were obtained.

Modeling and Simulation of a Packed Column Batch Still for Fruit Wine Distillations

Batch distillations are extensively used worldwide to produce fruit wine spirits with distinctive aromas. These processes are typically operated manually, based on the experience of the distiller. However, dynamic optimization and automatic control strategies could be valuable for ensuring a more consistent product and quickly adapting to new market tendencies. Consequently, reliable process models are required for the application of these methods. The novelty of this study is developing a highly efficient method to reliably simulate and calibrate a rigorous first-principles model of a packed batch column still. We applied the method of lines (MOL) to transform the partial differential equations describing the packed column dynamics into an ordinary differential equation (ODE) system. The nonlinear phase equilibrium equations were pre-solved, and several polynomials were fitted to get explicit algebraic equations. The final differential-algebraic system (DAE) comprises 31 ODEs, 113 explicit algebraic equations, and two implicit algebraic equations. Variables scaling, smoothing of discontinuities, and applying an algebraic loop within Simulink to solve the implicit algebraic equations resulted in 600 times faster simulations than a naïve approach. The model was regressed using pilot-scale experimental data and subjected to extensive validation using independent data. Sensitivity and residual analysis established that a better heat loss model could improve ethanol concentration prediction. This new heat losses model reduced the average ethanol concentration error by more than five times. The developed model can be applied to design reliable control systems and optimal operating strategies for packed column batch distillations.

Comparison of freezing and hydration characteristics for porous media

AbstractThe processes of freezing–thawing and hydration–dissociation change the content of liquid water that coexists with ice or hydrate in porous media, such as frozen soils and hydrate‐bearing sediments, changing their physicomechanical properties. In this study, a generalized phase equilibrium equation is presented for both frozen soils and hydrate‐bearing sediments by considering the capillary and osmotic pressures. The liquid water content is related to temperature depression, plotted as the soil freezing characteristic curve (SFCC) or the soil hydration characteristic curve (SHCC), by combining the generalized phase equilibrium equation and the soil‐water characteristic curve (SWCC). From the SFCC or the SHCC, the phase equilibrium surface can be calculated in the space of temperature, pressure, and liquid water content. The proposed generalized phase equilibrium equation and the model of SFCC and SHCC can help to estimate the physicomechanical properties that depend on the fraction of the liquid or solid phase in porous media. Finally, the SHCC is employed to analyze the dissociation of hydrate‐bearing sediments using various methods.

Investigation of gas solubility and its effects on natural gas reserve and production in tight formations

In this study, the natural gas solubility in brine and its influence on natural gas reserve and production in a tight gas reservoir have been investigated by the integration of laboratory experiments, phase equilibrium calculations, and numerical evaluation. Experimentally, a visualized PVT cell has been used to measure natural gas solubility at various pressures, temperatures, and salinity. Theoretically, the solubilities of natural gas and natural gas components are calculated using the phase equilibrium theory and equation of state (EOS), which are calibrated by the experimental data first. A sensitivity analysis is implemented to investigate the effects of pressure, temperature, and salinity on natural gas solubility. Subsequently, with the assistance of numerical simulation, the influence of the dynamic gas solubility on the natural gas reserve and production is examined in a tight gas reservoir in Middle Permian Shihezi Formation, Ordos Basin, China. The natural gas solubility is found to be 2.91 m3/m3 at initial reservoir conditions, which contributes to an increase of 1.33% in natural gas reserve. For natural gas and formation brine with specific composition, the gas solubility decreases gradually with the reservoir pressure reduction in the production process. The production prediction indicates that the cumulative gas production from tight formation requires calibration if the dynamic gas solubility is considered. In the field-scale simulation, the cumulative gas production after 10 years is 0.52% higher than the case not considering the dynamic natural gas solubility.

Technical-environmental assessment of CO2 conversion process to dimethyl carbonate/ethylene glycol

Abstract Utilization of CO2 to produce value-added chemicals is a promising approach to mitigate greenhouse gas emissions. In this work, a new process for the conversion of CO2 to dimethyl carbonate (DMC) and ethylene glycol (EG) was rigorously simulated and assessed in term of the technical performance and the environmental impact. The proposed model involves the conversion of CO2 catalyzed by ionic liquid-based catalysts, the reactive distillation with the reaction kinetics model, the pressure-swing distillation with rigorous phase equilibrium equations, and complex material-energy nexus between each unit. The results show that the carbon utilization efficiency of this process reaches 99% and the negative CO2 emission is 0.14 ton CO2/ton product achieving CO2 reduction. The green degree value of the entire process is 176.30 gd/h indicating that this new process can be evaluated as an environmental friendly process. Additionally, the retrofitted heat exchanger network designed via the pinch technique achieves 48.70% saving in heating utility consumption and increasing the green degree by 193.89 gd/h.

A conservative sequential fully implicit method for compositional reservoir simulation

A conservative sequential fully implicit method is derived for compositional reservoir simulation. Multi-phase flow in porous media comprises coupled complex processes: i.e. elliptic flow equation, hyperbolic transport equation and highly nonlinear phase equilibrium equation. These processes contain very different mathematical characteristics that cannot be efficiently solved by one numerical method. As a result, the fully implicit method may become numerically complex and inefficient because the Jacobian includes the derivatives w.r.t. the variables from all of the different processes involved.Jenny et al. (2004) [12] and Lee et al. (2015) [20] demonstrated that flow (pressure) and transport (saturation) for multi-phase flow without compositional effect can be efficiently solved by a sequential fully implicit method. However, the characteristics of the phase equilibrium equations are very different from those of the transport equations. This paper proposes an iterative method that solves the flow, transport and phase equilibrium equations in a sequential manner. The transport of hydrocarbons through porous media is governed by the multi-phase Darcy's equation, which is used to compute the phase velocities. The hydrocarbon components belonging to the same phase are transported with the same phase velocity. Upon arrival in the destination grid cell, these components are redistributed via a phase equilibrium calculation. This observation leads to simplification of the governing equations by reducing primary variables to four (i.e., pressure and three phase saturations). The nonlinear solution scheme composed of the stages outlined above is proven to preserve mass conservation, while a new degree of freedom, “thermodynamic flux”, is introduced to ensure volume conservation. The sequential algorithm is solved iteratively until pressure, saturation, and phase composition are fully converged.It is well-known that sequential solution schemes may require many iterations or fail to converge if the phase equilibrium calculation involves phase transition with a large volume change. This indicates that the current governing equations may not adequately describe fluid flux during rapid phase transition. With numerical examples we demonstrate that such numerical difficulties are successfully resolved via the thermodynamic flux term.

Elastoplastic analytical investigation of wellbore stability for drilling in methane hydrate-bearing sediments

Methane hydrates (MHs) are popular clean energy resources. The dissociation of MHs near the wellbore wall during drilling in marine methane hydrate-bearing sediments (MHBS) significantly reduces the bearing capacity of the wellbore and increases the risk of wellbore instability. In this study, a new elastoplastic analytical solution for wellbore stability during drilling in MHBS is provided, taking into account the reduction in the stiffness and strength of the formation after the hydrates dissociate, the conduction/diffusion and convection of heat/ion transfer, and the partial coupling among the seepage, temperature, salt concentration and mechanical fields.An axisymmetric plane strain problem is simplified by diving the infinite region into several annular regions with different physical properties. The distribution of pore pressure at a specific time for this multi-region problem is first obtained by introducing an influence radius estimated by the common unsteady flow solution. Accordingly, the conduction/diffusion and convection effects on the temperature and salt concentration fields are provided for balanced, underbalanced and overbalanced drilling conditions, and the dissociated region is finally addressed through the hydrate phase equilibrium equation fitted by numerous experimental data. Then, the mechanical responses of the wellbore in an elastic-brittle-plastic formation are analytically analysed by employing unified strength theory, considering two principal stress orders and three plastic zone locations.The analytical solution agrees very well with the numerical results determined under the same assumptions, and the solutions of the influence radii of the pressure and temperature and distribution of the pressure and effective stress around the wellbore are consistent with the results from complex numerical simulations. A detailed parametric study is carried out to investigate the specific influence of the drilling fluid properties, the size of the dissociated region and the reduction in Young's modulus/cohesion due to hydrate dissociation on wellbore stability during drilling in MHBS.

Phase Equilibrium Condition for Pore Hydrate: Theoretical Formulation and Experimental Validation

AbstractBased on the chemical potential equilibrium of water, a generalized equation of phase equilibrium is presented for pore hydrate, which relates the temperature depression of hydrate to the capillary pressure and osmotic pressure. The relationship between capillary pressure and unhydrated water content can be characterized by a soil‐water characteristic curve (SWCC). Uniting the SWCC and the phase equilibrium equation yields the equation of soil hydration characteristic curve (SHCC), which expresses the relationship between the unhydrated water content and temperature depression of pore hydrate. A series of experiments are performed, validating the phase equilibrium equation and the concept of SHCC. From the SHCC, the phase equilibrium surface can be determined in the space of temperature, pressure, and unhydrated water content. The thermodynamic state of pore hydrate moves on the equilibrium surface when the hydrate forms or dissociates. The projections of the equilibrium surface indicate the dissociation process of pore hydrate caused by thermal stimulation or depressurization. The salt solution changes the equilibrium surface to the direction that requires lower temperature and higher pressure and slows down the dissociation rates of hydrate to temperature and pressure.

Fast prediction of the quasi phase equilibrium in phase field model for multicomponent alloys based on machine learning method

The phase field model for multicomponent alloys are usually coupled with the thermodynamic database. But it will take much time to solve the quasi phase equilibrium equations. In order to reduce such time and keep the enough accuracy, we develop a new model to predict the quasi phase equilibrium based on the machine learning method. As an example, the quasi phase equilibrium during the isothermal solidification of Al-Cu-Mg alloy is studied in detail. A neural network model with 3 inputs, 4 outputs and a hidden layer of 150 nodes is constructed. The “training data” are prepared by solving the quasi phase equilibrium equations with least square method. The neural network model is trained by different amount of data set, which can fully cover the ranges of all the variables. The accuracy and performance of the neural network model are discussed in detail. Its high accuracy and fast speed demonstrated that this will be a convenient method to acquire the quasi phase equilibrium data in phase field model for multicomponent alloys.

Study on the hydrate formation region in a wellbore during Subsea Mudlift Drilling

Subsea Mudlift Drilling is a newly developed technology that provides a good solution to the problem of narrow pressure window in deep-water areas. However, current researches on Subsea Mudlift Drilling seldom focus on hydrate formation in a wellbore. Considering the shortcomings of current researches, a heat transfer model is established in this paper considering the specific flow path during Subsea Mudlift Drilling. A numerical model for the pressure profile during Subsea Mudlift Drilling is also established considering the lift force by the subsea pump. On basis of these models, a prediction method for the hydrate formation region is proposed, combining the hydrate phase equilibrium equation. In addition, a series of numerical simulations are conducted, which indicate that hydrate is easier to form during Subsea Mudlift Drilling than during conventional drilling. In order to reduce the hydrate formation region, a smaller head for the subsea pump, smaller diameter of the return line, larger displacement of the drilling fluid, and higher concentrations of inhibitors are suggested during Subsea Mudlift Drilling. On the basis of the numerical simulation results, an optimization method of hydraulic parameters for Subsea Mudlift Drilling is proposed. Conclusions and suggestions in this paper can help engineers to reduce hydrate formation during subsea Mudlift Drilling.

On the solubility of gases in dilute solutions: Organic food for thoughts from a molecular thermodynamic perspective

Despite the long history behind the experimental determinations of gas solubility and the consequent wealth of experimental data for binary systems we are still confronted with lingering issues regarding their reliability, the approximations behind their modeling, and the consistency among resulting solvation quantities. In the present effort we discuss cautiously these issues through the thermodynamic scrutiny of the coexistence phase equilibrium equations involving sparingly soluble species according to the recently proposed rigorous molecular-based solvation formalism [Chialvo: Fluid Phase Equilibria https://doi.org/10.1016/j.fluid.2017.10.031 and Journal of Chemical Physics, 148 (2018)]. We address the fundamentals underlying the isothermal-isobaric phase equilibria associated specifically with the solubility of carbon dioxide in aqueous systems, their thermodynamic limit of stability, as well as the link between the latter and the microstructure of the pair of incipient phases. Moreover, we show how the resulting equilibrium phase composition can provide relevant solvation quantities to test the thermodynamic consistency of the experimental data. Finally, we illustrate the arguments explicitly through the analysis of experimental evidence from a few selected sources in the literature, and discuss the implications behind the findings.

Modeling and optimization for asymmetric separation of atenolol enantiomers and application

This paper reports the asymmetric separation of atenolol (AT) enantiomers using n-hexyl (L)-tartrate (LT) and boric acid (BA) as chiral selector in a cascade of centrifugal contactor separators (CCSs). A multistage extraction model governing phase equilibrium equations and mass balance equations was established. The model was applied to predict and optimize the asymmetric separation of AT enantiomers. The effects of important factors on the multistage separation process, including the extract to wash phase ratio (O/W), the feed to wash phase ratio (F/W), the concentrations of LT and BA, and the location of feed stage, were simulated and optimized by the multistage extraction model. Under the optimal conditions for asymmetric separation, ATS was purified with enantiomeric excess (ee) of 0.9416 when F/W was 0.50.

A stable algorithm for calculating phase equilibria with capillarity at specified moles, volume and temperature using a dynamic model

Capillary pressure can significantly affect the phase properties and flow of liquid-gas fluids in porous media, and thus, the phase equilibrium calculation incorporating capillary pressure is crucial to simulate such problems accurately. Recently, the phase equilibrium calculation at specified moles, volume and temperature (NVT-flash) becomes an attractive issue. In this paper, capillarity is incorporated into the phase equilibrium calculation at specified moles, volume and temperature. A dynamical model for such problem is developed for the first time by using the laws of thermodynamics and Onsager's reciprocal principle. This model consists of the evolutionary equations for moles and volume, and it can characterize the evolutionary process from a non-equilibrium state to an equilibrium state in the presence of capillarity effect at specified moles, volume and temperature. The phase equilibrium equations are naturally derived. To simulate the proposed dynamical model efficiently, we adopt the convex-concave splitting of the total Helmholtz energy, and propose a thermodynamically stable numerical algorithm, which is proved to preserve the second law of thermodynamics at the discrete level. Using the thermodynamical relations, we derive a phase stability condition with capillarity effect at specified moles, volume and temperature. Moreover, we propose a stable numerical algorithm for the phase stability testing, which can provide the feasible initial conditions. The performance of the proposed methods in predicting phase properties under capillarity effect is demonstrated on various cases of pure substance and mixture systems.

Effects of rock pore sizes on the PVT properties of oil and gas-condensates in shale and tight reservoirs

Shales make up a large proportion of the rocks with extremely low permeability representing many challenges which can be complex in many cases. A careful study of rock and fluid properties (i.e. PVT of shales) of such resources is needed for long-term success, determining reservoirs quality, and increased recovery factor in unique unconventional plays. In this communication, a comprehensive thermodynamic modelling is undertaken in which capillary pressure is coupled with the phase equilibrium equations. To this end, the data associated with both shale oil and gas-condensates of Eagle Ford shale reservoir located in South Texas, U.S., is used. Different properties, including bubble and dew point pressures, capillary pressure, interfacial tension, liquid and gas densities, and liquid and gas viscosities, are predicted observing the effects of rock pore sizes by the thermodynamic modelling performed in this study. The results demonstrate that the thermodynamic model developed in this study is capable of simulating the PVT properties of oil and gas-condensates in shale and tight reservoirs. For a binary mixture 25:75 C1/C6, the bubble point pressure at different reservoir temperature is increased by increasing the pore sizes from 10 to 50 nm. Furthermore, an increase in pore sizes from 10 to 50 nm can increase the dew point pressure for a studied binary mixture 75:25 C1/C6.

Modeling of the Methyl Methacrylate Atom Transfer Radical Suspension Polymerization Process: Polymerization and Particle Kinetics

In this work, a mathematical model is developed to characterize the batch atom transfer radical suspension polymerization (batch suspension ATRP). For the first time, the morphological and molecular properties of particles, as well as their dynamics in methyl methacrylate ATRP can be simultaneously simulated by solving the model that consists of ATRP kinetic equations, moment equations, a phase equilibrium equation for calculating equilibrium monomer distributions in various phases, and a particle population balance model. The proposed model is verified using the open experimental data. Based on the verified model, two key operating factors including the ratios of monomer to initiator and water to monomer are studied in order to investigate the batch suspension ATRP kinetics. In addition, the model is also used to predict the droplet/particle size distribution. The effects of breakage rate, coalescence rate, and agitation speed on the droplet volume density distribution and the Sauter mean diameter are discussed in details. The simulated results demonstrate that the coupled model can describe the batch suspension ATRP kinetics and its droplet kinetics. image

Fully implicit compositional simulator for modeling of asphaltene deposition during natural depletion

This paper describes development of a fully implicit compositional simulator for modeling of asphaltene deposition during natural depletion. In this paper, a new approach for multiphase flash calculation has been developed. This approach provides a more detailed description of the kinetic part of asphaltene deposition which needs to be explained more clearly. Due to a large number of unknowns, there are many ways to solve such a system by choosing different sets of independent variables. A new set of independent variables in a fully implicit model is considered for asphaltene deposition modeling. By incorporating an asphaltene precipitation model into a compositional simulator where the phase equilibrium equations, the volumetric constraint equation, the component transport equations, the multiphase flash equations and the deposition equation are solved simultaneously; a simulator for asphaltene deposition was developed with respect to natural depletion. The pure solid model is used to model asphaltene precipitation. The solid particles are considered to be separated into three parts: precipitated, flocculated and deposited solid. A first-order chemical reaction is used which models forward and reverse rates for the conversion of precipitated asphaltene to flocculated asphaltene. Also, a deposition model including adsorption, pore throat plugging, and re-entrainment was used. The simulator can also predict formation damage including porosity and permeability reduction in each block.

Application of the Firefly and Luus–Jaakola algorithms in the calculation of a double reactive azeotrope

The calculation of reactive azeotropes is an important task in the preliminary design and simulation of reactive distillation columns. Classically, homogeneous nonreactive azeotropes are vapor–liquid coexistence conditions where phase compositions are equal. For homogeneous reactive azeotropes, simultaneous phase and chemical equilibria occur concomitantly with equality of compositions (in the Ung–Doherty transformed space). The modeling of reactive azeotrope calculation is represented by a nonlinear algebraic system with phase equilibrium, chemical equilibrium and azeotropy equations. This nonlinear system can exhibit more than one solution, corresponding to a double reactive azeotrope. In a previous paper (Platt et al 2013 J. Phys.: Conf. Ser. 410 012020), we investigated some numerical aspects of the calculation of reactive azeotropes in the isobutene + methanol + methyl-tert-butyl-ether (with two reactive azeotropes) system using two metaheuristics: the Luus–Jaakola adaptive random search and the Firefly algorithm. Here, we use a hybrid structure (stochastic + deterministic) in order to produce accurate results for both azeotropes. After identifying the neighborhood of the reactive azeotrope, the nonlinear algebraic system is solved using Newton's method. The results indicate that using metaheuristics and some techniques devoted to the calculation of multiple minima allows both azeotropic coordinates in this reactive system to be obtains. In this sense, we provide a comprehensive analysis of a useful framework devoted to solving nonlinear systems, particularly in phase equilibrium problems.