K-Values-Based Upscaling of Compositional Simulation

SPE Journal ◽  
2019 ◽  
Vol 24 (02) ◽  
pp. 579-595 ◽  
Author(s):  
Amir Salehi ◽  
Denis V. Voskov ◽  
Hamdi A. Tchelepi
Keyword(s):  
Phase Space ◽  
Phase Behavior ◽  
Thermodynamic Functions ◽  
Equilibrium Phase ◽  
Absolute Permeability ◽  
Fine Scale ◽  
Compositional Simulation ◽  
Coarse Scale ◽  
K Value ◽  
Tie Lines

Summary Enhanced-oil-recovery (EOR) processes involve complex flow, transport, and thermodynamic interactions; as a result, compositional simulation is necessary for accurate representation of the physics. Flow simulation of compositional systems with high-resolution reservoir models is computationally intensive because of the large number of unknowns and the strong nonlinear interactions. Thus, there is a great need for upscaling methods of compositional processes. The complex multiscale interactions between the phase behavior and the heterogeneities lie at the core of the difficulty in constructing consistent upscaling procedures. We use a mass-conservative formulation and introduce upscaled phase-molar-mobility functions for coarse-scale modeling of multiphase flow. These upscaled flow functions account for the subgrid effects caused by the absolute permeability and relative permeability variations, as well as the effects of compressibility. Upscaling of the phase behavior is performed as follows. We assume that instantaneous thermodynamic equilibrium is valid on the fine scale, and we derive coarse-scale equations in which the phase behavior may not necessarily be at equilibrium. The upscaled thermodynamic functions, which represent differences in the component fugacities, are used to account for the nonequilibrium effects on the coarse scale. We demonstrate that the upscaled phase-behavior functions transform the equilibrium phase space on the fine scale to a region of similar shape, but with tilted tie-lines on the coarse space. The numerical framework uses K-values that depend on the orientation of the tie-lines in the new nonequilibrium phase space and the sign of upscaled thermodynamic functions. The proposed methodology is applied to challenging gas-injection problems with large numbers of components and highly heterogeneous permeability fields. The K-value-based coarse-scale operator produces results that are in good agreement with the fine-scale solutions for the quantities of interest, including the component overall compositions and saturation distributions.

Nonlinear Formulation Based on an Equation-of-State Free Method for Compositional Flow Simulation

SPE Journal ◽  
2012 ◽  
Vol 18 (02) ◽  
pp. 264-273 ◽  
Author(s):  
R.. Zaydullin ◽  
D.V.. V. Voskov ◽  
H.A.. A. Tchelepi
Keyword(s):  
Multiphase Flow ◽  
Phase Behavior ◽  
Oil Recovery ◽  
Equilibrium Phase ◽  
Computational Cost ◽  
Practical Interest ◽  
Flow Simulation ◽  
Flow In Porous Media ◽  
Compositional Simulation ◽  
Tie Lines

Summary Compositional simulation is necessary for modeling complex enhanced oil recovery (EOR) processes. For accurate simulation of compositional processes, we need to resolve the coupling of the nonlinear conservation laws, which describe multiphase flow and transport, with the equilibrium phase behavior constraints. The complexity of the problem requires extensive computations and consumes significant time. This paper presents a new framework for the general compositional problem associated with multicomponent multiphase flow in porous media. Here, adaptive construction and interpolation using the supporting tie lines are used to obtain the phase state and the phase compositions. For the parameterization of the full solution of a complex compositional problem, we need only a limited number of supporting tie lines in the compositional space. The parameterized tie lines are triangulated using Delaunay tessellation, and natural-neighbor interpolation is used inside the simplexes. Then, the computation of the phase behavior in the course of a simulation becomes an iteration-free, table look-up procedure. The treatment of nonlinearities associated with complex thermodynamic behavior of the fluid is based on the new set of unknowns—tie-line parameters that allow for efficient representation of the subcritical region. For the supercritical region, we use the standard compositional variable set based on the overall composition. The efficiency and accuracy of the method are demonstrated for several multidimensional compositional problems of practical interest. In terms of the computational cost of the thermodynamic calculations, the proposed method shows results comparable to those of state-of-the-art techniques. Moreover, the method shows better nonlinear convergence in the case of near-miscible gas-injection simulation.

Robust Isenthalpic Flash for Multiphase Water/Hydrocarbon Mixtures

SPE Journal ◽  
2015 ◽  
Vol 20 (06) ◽  
pp. 1350-1365 ◽  
Author(s):  
Di Zhu ◽  
Ryosuke Okuno
Keyword(s):  
Elevated Temperatures ◽  
Equilibrium Phase ◽  
Steam Injection ◽  
Iteration Step ◽  
Compositional Simulation ◽  
Hydrocarbon Mixtures ◽  
K Value ◽  
Total Enthalpy ◽  
Bisection Algorithm ◽  
Three Phases

Summary Robust isenthalpic flash is important in compositional simulation of steam injection, which involves at least three phases—oleic, gaseous, and aqueous. However, multiphase isenthalpic flash is challenging because the total enthalpy can be substantially nonlinear, or even discontinuous, with respect to temperature. This type of phase behavior is referred to as narrow-boiling behavior in the literature. This paper presents robust isenthalpic flash for multiphase water-containing hydrocarbon mixtures. The algorithm developed is based on the direct substitution (DS) presented in our previous research for two phases. A detailed analysis is given for narrow-boiling behavior and its effects on the DS algorithm. A new method is also presented for K-value estimates for three phases for water-hydrocarbon mixtures. The thermodynamic model used is the Peng-Robinson equation of state with the van der Waals mixing rules. The narrow-boiling behavior in isenthalpic flash occurs when a small temperature change yields significant changes of equilibrium-phase compositions relative to the overall composition. The system of equations used in the DS algorithm becomes degenerate for narrow-boiling fluids. The multiphase DS algorithm developed in this paper adaptively switches between Newton's iteration step and the bisection step depending on the Jacobian condition number. The bisection algorithm solves for temperature, based solely on the enthalpy constraint only when narrow-boiling behavior is identified. The algorithm is tested with a number of different isenthalpic flash calculations for three and four phases formed by water-containing hydrocarbon mixtures at elevated temperatures. Results show the robustness of the algorithm for narrow-boiling fluids, including the cases with one degree of freedom.

Two-Stage Upscaling of Two-Phase Flow: From Core to Simulation Scale

SPE Journal ◽  
2006 ◽  
Vol 11 (03) ◽  
pp. 304-316 ◽  
Author(s):  
Arild Lohne ◽  
George A. Virnovsky ◽  
Louis J. Durlofsky
Keyword(s):  
Capillary Pressure ◽  
Effective Properties ◽  
Absolute Permeability ◽  
Scale Model ◽  
Phase Flow ◽  
Fine Scale ◽  
Coarse Scale ◽  
Two Stage ◽  
Two Phase ◽  
Rate Dependent

Summary In the coarse-scale simulation of heterogeneous reservoirs, effective or upscaled flow functions (e.g., oil and water relative permeability and capillary pressure) can be used to represent heterogeneities at subgrid scales. The effective relative permeability is typically upscaled along with absolute permeability from a geocellular model. However, if no subgeocellular-scale information is included, the potentially important effects of smaller-scale heterogeneities (on the centimeter to meter scale) in both capillarity and absolute permeability will not be captured by this approach. In this paper, we present a two-stage upscaling procedure for two-phase flow. In the first stage, we upscale from the core (fine) scale to the geocellular (intermediate) scale, while in the second stage we upscale from the geocellular scale to the simulation (coarse) scale. The computational procedure includes numerical solution of the finite-difference equations describing steady-state flow over the local region to be upscaled, using either constant pressure or periodic boundary conditions. In contrast to most of the earlier investigations in this area, we first apply an iterative rate-dependent upscaling (iteration ensures that the properties are computed at the appropriate pressure gradient) rather than assume viscous or capillary dominance and, second, assess the accuracy of the two-stage upscaling procedure through comparison of flow results for the coarsened models against those of the finest-scale model. The two-stage method is applied to synthetic 2D reservoir models with strong variation in capillarity on the fine scale. Accurate reproduction of the fine-grid solutions (simulated on 500'500 grids) is achieved on coarse grids of 10'10 for different flow scenarios. It is shown that, although capillary forces are important on the fine scale, the assumption of capillary dominance in the first stage of upscaling is not always appropriate, and that the computation of rate-dependent effective properties in the upscaling can significantly improve the accuracy of the coarse-scale model. The assumption of viscous dominance in the second upscaling stage is found to be appropriate in all of the cases considered. Introduction Because of computational costs, field-simulation models may have very coarse cells with sizes up to 100 to 200 m in horizontal directions. The cells are typically populated with effective properties (porosity, absolute permeability, relative permeabilities, and capillary pressure) upscaled from a geocellular (or geostatistical) model. In this way, the effects of heterogeneity on the geocellular scale will be included in the large-scale flow calculations. The cell sizes in geocellular models may be on the order of 20 to 50 m in horizontal directions. However, heterogeneities on much smaller scales (cm- to m- scale) may have a significant influence on the reservoir flow (Coll et al. 2001; Honarpour et al. 1994), and this potential effect cannot be captured if the upscaling starts at the geocellular scale.

A Negative-Flash Tie-Simplex Approach for Multiphase Reservoir Simulation

SPE Journal ◽  
2013 ◽  
Vol 18 (06) ◽  
pp. 1140-1149 ◽  
Author(s):  
Alireza Iranshahr ◽  
Denis V. Voskov ◽  
Hamdi A. Tchelepi
Keyword(s):  
Phase Behavior ◽  
Oil Recovery ◽  
Large Scale ◽  
Flow Simulation ◽  
Steam Injection ◽  
Compositional Simulation ◽  
Reservoir Flow ◽  
Wide Range ◽  
Tie Lines ◽  
Eor Processes

Summary Enhanced Oil Recovery (EOR) processes usually involve complex phase behavior between the injected fluid (e.g., steam, hydrocarbon, CO2, sour gas) and the in-situ rock-fluid system. Several fundamental questions remain regarding Equation-of-State (EOS) computations for mixtures that can form three, or more, phases at equilibrium. In addition, numerical and computational issues related to the proper coupling of the thermodynamic phase behavior with multi-component transport must be resolved to accurately and efficiently model the behavior of large-scale EOR processes. Previous work has shown that the adaptive tabulation of tie-simplexes in the course of a compositional simulation is a reliable alternative to the conventional EOS-based compositional simulation. In this paper, we present the numerical results of reservoir flow simulation with adaptive tie-simplex parameterization of the compositional space. We study the behavior of thermal-compositional reservoir displacement processes across a wide range of fluid mixtures, pressures, and temperatures. We show that our approach rigorously accounts for tie-simplex degeneration across phase boundaries. We also focus on the complex behavior of the tie-triangles and tie-lines associated with three-phase, steam injection problems in heterogeneous formations. Our studies indicate that the tie-simplex based simulation is a potential approach for fast EOS modeling of complex EOR processes.

A Unified Algorithm for Phase-Stability/Split Calculation for Multiphase Isobaric-Isothermal Flash

SPE Journal ◽  
2017 ◽  
Vol 23 (02) ◽  
pp. 498-521 ◽  
Author(s):  
Di Zhu ◽  
Sara Eghbali ◽  
Chandra Shekhar ◽  
Ryosuke Okuno
Keyword(s):  
Free Energy ◽  
Phase Behavior ◽  
Gibbs Free Energy ◽  
Conventional Method ◽  
Phase Stability ◽  
Equilibrium Phase ◽  
Stationary Points ◽  
Simple Formulation ◽  
Complex Phase ◽  
K Value

Summary The conventional method for multiphase flash is the sequential usage of phase-stability and phase-split calculations. Multiphase flash requires the conventional method to obtain multiple false solutions in phase-split calculations and correct them in phase-stability analysis. Improvement of the robustness and efficiency of multiphase flash is important for compositional flow simulation with complex phase behavior. This paper presents a new algorithm that solves for stationary points of the tangent-plane-distance (TPD) function defined at an equilibrium-phase composition for isobaric-isothermal (PT) flash. A solution from the new algorithm consists of two groups of stationary points: tangent and nontangent stationary points of the TPD function. Hence, equilibrium phases, at which the Gibbs free energy is tangent to the TPD function, are found as a subset of the solution. Unlike the conventional method, the new algorithm does not require finding false solutions for robust multiphase flash. The advantage of the new algorithm in terms of robustness is more pronounced for more-complex phase behavior, for which multiple local minima of the Gibbs free energy are present. Case studies show that the new algorithm converges to a lower Gibbs free energy compared with the conventional method for the complex fluids tested. It is straightforward to implement the algorithm because of the simple formulation, which also allows for an arbitrary number of iterative compositions. It can be robustly initialized even when no K value correlation is available for the fluid of interest. Although the main focus of this paper is on robust solution of multiphase flash, the new algorithm can be used to initialize a second-order convergent method in the vicinity of a solution.

Microemulsion Phase Behavior Observations, Thermodynamic Essentials, Mathematical Simulation

1981 ◽  
Vol 21 (06) ◽  
pp. 747-762 ◽  
Author(s):  
Karl E. Bennett ◽  
Craig H.K. Phelps ◽  
H. Ted Davis ◽  
L.E. Scriven
Keyword(s):  
Experimental Data ◽  
Phase Behavior ◽  
Experimental Studies ◽  
Mathematical Framework ◽  
Alkyl Aryl Sulfonate ◽  
Phase Volume ◽  
Displacement Efficiency ◽  
Alkyl Aryl ◽  
Theoretical Understanding ◽  
Tie Lines

Abstract The phase behavior of microemulsions of brine, hydrocarbon, alcohol, and a pure alkyl aryl sulfonate-sodium 4-(1-heptylnonyl) benzenesulfonate (SHBS or Texas 1) was investigated as a function of the concentration of salt (NaCl, MgCl2, or CaCl2), the hydrocarbon (n-alkanes, octane to hexadecane), the alcohol (butyl and amyl isomers), the concentration of surfactant, and temperature. The phase behavior mimics that of similar systems with the commercial surfactant Witco TRS 10–80. The phase volumes follow published trends, though with exceptions.A mathematical framework is presented for modeling phase behavior in a manner consistent with the thermodynamically required critical tie lines and plait point progressions from the critical endpoints. Hand's scheme for modeling binodals and Pope and Nelson's approach to modeling the evolution of the surfactant-rich third phase are extended to satisfy these requirements.An examination of model-generated progressions of ternary phase diagrams enhances understanding of the experimental data and reveals correlations of relative phase volumes (volume uptakes) with location of the mixing point (overall composition) relative to the height of the three-phase region and the locations of the critical tie lines (critical endpoints and conjugate phases). The correlations account, on thermodynamic grounds, for cases in which the surfactant is present in more than one phase or the phase volumes change discontinuously, both cases being observed in the experimental study. Introduction The phase behavior of a surfactant-based micellar formulation is one of the major factors governing the displacement efficiency of any chemical flooding process employing that formulation. Knowledge of phase behavior is, thus, important for the interpretation of laboratory core floods, the design of flooding processes, and the evaluation of field tests. Phase behavior is connected intimately with other determinants of the flooding process, such as interfacial tension and viscosity. Since the number of equilibrium phases and their volumes and appearances are easier to measure and observe than phase compositions, viscosities, and interfacial tensions, there is great interest in understanding the phase-volume/phase-property relationships. Commercial surfactants, such as Witco TRS 10-80, are sulfonates of crude or partially refined oil. While they seem to be the most economically practicable surfactants for micellar flooding, their behavior, particularly with crude oils and reservoir brines, can be difficult to interpret, the phases varying with time and from batch to batch. Phase behavior studies with a small number of components, in conjunction with a theoretical understanding of phase behavior progressions, can aid in understanding more complex behavior. In particular, one can begin to appreciate which seemingly abnormal experimental observations (e.g., surfactant present in more than one phase or a discontinuity in phase volume trends) are merely features of certain regions of any phase diagram and which are peculiar to the specific crude oil or commercial surfactant used in the study.We report here experimental studies of the phase behavior of microemulsions of a pure sulfonate surfactant (Texas 1), a single normal alkane hydrocarbon, a simple brine, and a small amount of a suitable alcohol as cosurfactant or cosolvent. The controlled variables are hydrocarbon chain length, alcohol, salinity, salt type (NaCl, MgCl2, or CaCl2), surfactant purity, surfactant concentration, and temperature. Many of these experimental data were presented earlier. SPEJ P. 747^

scholarly journals Spatial Downscaling of TRMM Precipitation Using Geostatistics and Fine Scale Environmental Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
No-Wook Park
Keyword(s):  
Environmental Variables ◽  
Vegetation Index ◽  
Normalized Difference Vegetation Index ◽  
Tropical Rainfall Measuring Mission ◽  
Predictive Performance ◽  
Environmental Modeling ◽  
Fine Scale ◽  
Coarse Scale ◽  
Uncertainty Measures ◽  
Trmm Precipitation

A geostatistical downscaling scheme is presented and can generate fine scale precipitation information from coarse scale Tropical Rainfall Measuring Mission (TRMM) data by incorporating auxiliary fine scale environmental variables. Within the geostatistical framework, the TRMM precipitation data are first decomposed into trend and residual components. Quantitative relationships between coarse scale TRMM data and environmental variables are then estimated via regression analysis and used to derive trend components at a fine scale. Next, the residual components, which are the differences between the trend components and the original TRMM data, are then downscaled at a target fine scale via area-to-point kriging. The trend and residual components are finally added to generate fine scale precipitation estimates. Stochastic simulation is also applied to the residual components in order to generate multiple alternative realizations and to compute uncertainty measures. From an experiment using a digital elevation model (DEM) and normalized difference vegetation index (NDVI), the geostatistical downscaling scheme generated the downscaling results that reflected detailed characteristics with better predictive performance, when compared with downscaling without the environmental variables. Multiple realizations and uncertainty measures from simulation also provided useful information for interpretations and further environmental modeling.

Numerical Calculation of Equivalent Permeability Tensor for Fractured Vuggy Porous Media Based on Homogenization Theory

2011 ◽  
Vol 9 (1) ◽  
pp. 180-204 ◽  
Author(s):  
Zhaoqin Huang ◽  
Jun Yao ◽  
Yajun Li ◽  
Chenchen Wang ◽  
Xinrui Lv
Keyword(s):  
Porous Media ◽  
Network Model ◽  
Darcy's Law ◽  
Permeability Tensor ◽  
Homogenization Theory ◽  
Fine Scale ◽  
Porous Rock ◽  
Coarse Scale ◽  
Equivalent Permeability ◽  
Discrete Fracture

AbstractA numerical procedure for the evaluation of equivalent permeability tensor for fractured vuggy porous media is presented. At first we proposed a new conceptual model, i.e., discrete fracture-vug network model, to model the realistic fluid flow in fractured vuggy porous medium on fine scale. This new model consists of three systems: rock matrix system, fractures system, and vugs system. The fractures and vugs are embedded in porous rock, and the isolated vugs could be connected via discrete fracture network. The flow in porous rock and fractures follows Darcy’s law, and the vugs system is free fluid region. Based on two-scale homogenization theory, we obtained an equivalent macroscopic Darcy’s law on coarse scale from fine-scale discrete fracture-vug network model. A finite element numerical formulation for homogenization equations is developed. The method is verified through application to a periodic model problem and then is applied to the calculation of equivalent permeability tensor of porous media with complex fracture-vug networks. The applicability and validity of the method for these more general fractured vuggy systems are assessed through a simple test of the coarse-scale model.

scholarly journals Thermodynamic Analysis of Relaxation Model for Non-Equilibrium Phase Behavior of Hydrocarbon Mixtures

2021 ◽  
Vol 2090 (1) ◽  
pp. 012138
Author(s):  
I M Indrupskiy ◽  
P A Chageeva
Keyword(s):  
Relaxation Time ◽  
Phase Behavior ◽  
Relaxation Process ◽  
Thermodynamic Analysis ◽  
Balance Equation ◽  
Equilibrium Phase ◽  
Characteristic Relaxation Time ◽  
Relaxation Model ◽  
Entropy Balance ◽  
Non Equilibrium

Abstract Mathematical models of phase behavior are widely used to describe multiphase oil and gas-condensate systems during hydrocarbon recovery from natural petroleum reservoirs. Previously a non-equilibrium phase behavior model was proposed as an extension over generally adopted equilibrium models. It is based on relaxation of component chemical potentials difference between phases and provides accurate calculations in some typical situations when non-instantaneous changing of phase fractions and compositions in response to variations of pressure or total composition is to be considered. In this paper we present a thermodynamic analysis of the relaxation model. General equations of non-equilibrium thermodynamics for multiphase flows in porous media are considered, and reduced entropy balance equation for the relaxation process is obtained. Isotropic relaxation process is simulated for a real multicomponent hydrocarbon system with different values of characteristic relaxation time using the non-equilibrium model implemented in the PVT Designer module of the RFD tNavigator simulation software. The results are processed with a special algorithm implemented in Matlab to calculate graphs of the total entropy time derivative and its constituents in the entropy balance equation. It is shown that the constituents have different signs, and the greatest influence on the entropy is associated with the interphase flow of the major component of the mixture and the change of the total system volume in the isotropic process. The characteristic relaxation time affects the rate at which the entropy is approaching its maximum value.

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