# Browsing by Subject "Equation of state"

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Item A proxy Peng-Robinson EOS for efficient modeling of phase behavior(2021-05) Zhao, Mark; Okuno, Ryosuke, 1974-Show more Equation-of-state (EOS) compositional simulation is commonly used to model the interplay between phase behavior and fluid flow for various reservoir and surface processes. Because of its computational cost, however, there is a critical need for efficient phase-behavior calculations using an EOS. The objective of this research was to develop a proxy model for the fugacity coefficient based on the Peng-Robinson EOS for rapid multiphase flash in compositional flow simulation. The proxy model as implemented in this research is to bypass the calculations of fugacity coefficients when the Peng-Robinson EOS has only one root, which is often the case at reservoir conditions. The proxy fugacity model was trained by artificial neural networks (ANNs) with over 30 million fugacity coefficients based on the Peng-Robinson EOS. It accurately predicts the Peng-Robinson fugacity coefficient by using four parameters: Am, Bm, Bi, and ΣxiAij. Since these scalar parameters are general, not specific to particular compositions, pressures, and temperatures, the proxy model is applicable to petroleum engineering applications as equally as the original Peng-Robinson EOS. A case study shows the proxy fugacity model gave a speed-up factor of 3.4% in comparison to the conventional EOS calculation. Case studies also demonstrate accurate multiphase flash results (stability and phase split) and interchangeable proxy models for different fluid cases with different (numbers of) components. This is possible because it predicts the Peng-Robinson fugacity in the variable space that is not specific to composition, temperature, and pressure. For the same reason, non-zero binary iteration parameters do not impair the applicability, accuracy, robustness, and efficiency of the model. As the proxy models are specific to individual components, a combination of proxy models can be used to model for any mixture of components. Tuning of training hyperparameters and training data sampling method helped reduce the mean absolute percent error to less than 0.1% in the ANN modeling. To the best of our knowledge, this is the first generalized proxy model of the Peng-Robinson fugacity that is applicable to any mixture. The proposed model retains the conventional flash iteration, the convergence robustness, and the option of manual parameter tuning for fluid characterization.Show more Item Development of a Thermodynamically Consistent, Fully Implicit, Composittonal, Equation-Of-State, Steamflood Simulator(1991-05) Brantferger, Kenneth Mark; Pope, Gary A.; Sepehrnoori, KamyShow more A thermodynamically consistent, three-dimensional, fully implicit, compositional, equation-of-state, steamflood simulator is developed. The formulation uses a single set of primary variables-overall component mole numbers, total fluid enthalpy, and pressure-to linearize the finite difference forms of the component conservation equations, the energy conservation equation, and the pore volume constraint. These primary variables constitute a thermodynamically independent set; subsequently, they may be applied throughout the reservoir, supplanting the use of variable substitution. The resulting nonlinear system of equations is solved using the Newton-Raphson method to update the primary variables. At each Newton iteration, phase equilibria is computed isenthalpically using an original Newton-type entropy maximization algorithm, combined with a Gibbs stability test, that yields the number of phases, the phase mole numbers, and temperature of the fluid mixture. The thermodynamic fluid properties such as enthalpy and density are calculated using the Soave-Redlich-Kwong cubic equation-of-state. Comparisons are made between numerical simulations and compositional steamflood experiments that illustrate the importance of phase behavior on the residual oil saturation to steam.Show more Item Development of an equation-of-state thermal flooding simulator(2009-05) Varavei, Abdoljalil; Sepehrnoori, Kamy, 1951-Show more In the past thirty years, the development of compositional reservoir simulators using various equations of state (EOS) has been addressed in the literature. However, the development of compositional thermal simulators in conjunction with EOS formulation has been ignored, in particular. Therefore in this work, a fully implicit, parallel, compositional EOS-based simulator has been developed. In this model, an equation of state is used for equilibrium calculations among all phases (oil, gas, and aqueous). Also, the physical properties are calculated based on an equation of state, hence obviating the need for using steam tables for calculation of water/steam properties. The governing equations for the model comprise fugacity equations between the three phases, material balance, pore volume constraint and energy equations. The governing partial differential equations are solved using finite difference approximations. In the steam injection process, the solubility of oil in water-rich phase and the solubility of water in oil phase can be high. This model takes into account the solubility of water in oil phase and the solubility of hydrocarbon components in water-rich phase, using three-phase flash calculations. This simulator can be used in various thermal flooding processes (i.e. hot water or steam injections). Since the simulator was implemented for parallel computers, it is capable of solving large-scale thermal flooding problems. The simulator is successfully validated using analytical solutions. Also, simulations are carried out to compare this model with commercial simulators. The use of an EOS for calculation of various properties for each phase automatically satisfies the thermodynamic consistency requirements. On the other hand, using the K-value approach, which is not thermodynamically robust, may lead to results that are thermodynamically inconsistent. This simulator accurately tracks all components and mass transfer between phases using an EOS; hence, it will produce thermodynamically consistent results and project accurate prediction of thermal recovery processes. Electrical heating model, Joule heating and in-situ thermal desorption methods, and hot-chemical flooding model have also been implemented in the simulator. In the electrical heating model, electrical current equation is solved along with other governing equations by considering electrical heat generation. For implementation of the hot-chemical heating model, first the effect of temperature on the phase behavior model and other properties of the chemical flooding model is considered. Next, the material and energy balance and volume constraints equations are solved with a fully implicit method. The models are validated with other solutions and different cases are tested with the implemented models.Show more Item Material properties of liquid iron at planetary core conditions(2020-05) Grant, Sean Campbell; Ditmire, Todd; Lin, Jung-Fu; Keto, John; Ao, Tommy; Bernstein, Aaron; Demkov, AlexanderShow more The outer core of the Earth is composed primarily of liquid iron, and the inner core boundary is governed by the intersection of the melt line and the geotherm. Traditional static compression techniques have provided a wealth of information on the solid phase of iron, but struggle in the liquid phase, leaving this important phase relatively unexplored. We use dynamic compression to diagnose the high-pressure liquid state of iron by utilizing the shock-ramp capability at Sandia National Laboratories’ Z-Machine. This technique enables measurements of material states off the Hugoniot by initially shocking samples and subsequently driving a further, shockless compression. Planetary studies benefit greatly from isentropic, off-Hugoniot experiments since they cover states that are representative of the adiabatic profiles found in planets. We used this method to drive iron to pressure and temperature conditions similar to those of the Earth’s core, along an elevated-temperature isentrope in the liquid from 275 GPa to 400 GPa, providing valuable information near the melt line. We are also developing an ellipsometry diagnostic for these experiments to optically probe the conductivity of the sample. We derive the equation of state using a hybrid backward integration – forward Lagrangian technique on particle velocity traces to determine the pressure-density history of the sample. Our results are in excellent agreement with SESAME 92141, a previously published equation of state table. With our data and previous experimental data on liquid iron we derive new parameters for a Vinet-based equation of state. The table and our parameterized equation of state provide an updated means of modeling liquid iron cores in planetary interiors, to which we provide an example.Show more Item Simple thermodynamic modeling of liquids(2017-05) O'Keefe, Sean Patrick; Sanchez, Isaac C., 1941-; Truskett, Thomas M; Johnston, Keith P; Okuno, RyosukeShow more Theoretical thermodynamic models that accurately capture liquid behavior do so at the cost of ease of use, and do not explicitly reduce to simple relationships observed among liquid properties. Of these relationships, the linear response of liquid density to changes in temperature is one of the simplest and most nearly universal. At low pressures, plots of saturated liquid density vs. temperature are linear over a substantial temperature range. This behavior has been observed for liquids as diverse as monoatomic elements, small organics, molten salts and metals, and polymers. Water and liquid helium are the only known exceptions to this low pressure linearity. This observation is extended to liquid isobars at elevated pressure and to liquid mixtures. To capture fluid relationships through easily implemented, analytical equations, a model using a Scaled Particle Theory (SPT) for mixtures of hard spheres in a mean-field approximation is developed. Thermodynamic properties are derived from the random insertion of a hard sphere (HS) chain into an HS mixture and invoking random mixing to calculate energetics. The SPT model completely characterizes pure fluids with three independent parameters that can be calculated from pure component properties. Binary mixtures require only one additional interaction parameter, which can be approximated using a geometric mean combining rule or treated as an adjustable parameter. This SPT chain model is comparable to other thermodynamic models with mean-field configurational energies for mixtures of small, similarly-sized molecules, but yields unsatisfactory results when applied to polymer/solvent systems. The approximations the SPT model makes for the HS chain are investigated as a potential source of error. To improve on the SPT configurational energy approximation, a Quasi-Chemical Square Well (QCSW) model is developed that limits both the attractive range of a given molecular segment and the number of other segments with which it can interact. Though the SPT and QCSW models do not explicitly reduce to a simple isobaric density/temperature relationship, the QCSW model predicts a linear-like regime for saturated liquids at low pressure over an extended temperature range, and introduces promising concepts for modeling liquids.Show more Item Time-resolved lattice measurements of shock-induced phase transitions in polycrystalline materials(2010-05) Milathianaki, Despina; Ditmire, Todd R.; Bengtson, Roger; Downer, Michael; Marder, Michael; Taleff, EricShow more The response of materials under extreme temperature and pressure conditions is a topic of great significance because of its relevance in astrophysics, geophysics, and inertial confinement fusion. In recent years, environments exceeding several hundred gigapascals in pressure have been produced in the laboratory via laser-based dynamic loading techniques. Shock-loading is of particular interest as the shock provides a fiducial for measuring time-dependent processes in the lattice such as phase transitions. Time-resolved x-ray diffraction is the only technique that offers an insight into these shock-induced processes at the relevant spatial (atomic) and temporal scales. In this study, nanosecond resolution x-ray diffraction techniques were developed and implemented towards the study of shock-induced phase transitions in polycrystalline materials. More specifically, the capability of a focusing x-ray diffraction geometry in high-resolution in situ lattice measurements was demonstrated by probing shock-compressed Cu and amorphous metallic glass samples. In addition, simultaneous lattice and free surface velocity measurements of shock-compressed Mg in the ambient hexagonal close packed (hcp) and shock-induced body centered cubic (bcc) phases between 12 and 45 GPa were performed. These measurements revealed x-ray diffraction signals consistent with a compressed bcc lattice above a shock pressure of 26.2±1.3 GPa, thus capturing for the first time direct lattice evidence of a shock-induced hcp to bcc phase transition in Mg. Our measurement of the hcp-bcc phase boundary in Mg was found to be consistent with the calculated boundary from generalized pseudopotential theory in the pressure and temperature region intersected by the principal shock Hugoniot. Furthermore, the subnanosecond timescale of the phase transition implied by the shock-loading conditions was in agreement with the kinetics of a martensitic transformation. In conclusion, we report on the progress and future work towards time-resolved x-ray diffraction measurements probing solid-liquid phase transitions in high Z polycrystalline materials, specifically Bi.Show more