Prediction of Three-Phase Gravity Drainage from Two-Phase Capillary Pressure Curves

2010 ◽  
Author(s):  
Mohammad Mirzaei ◽  
David A. DiCarlo ◽  
Mandana Ashouripashaki ◽  
Hassan Dehghanpour ◽  
Behdad Aminzadeh
Keyword(s):  
Capillary Pressure ◽  
Gravity Drainage ◽  
Two Phase ◽  
Three Phase ◽  
Capillary Pressure Curves

scholarly journals Pore-Scale Modelling of Three-Phase Capillary Pressure Curves Directly in Uniformly Wet Rock Images

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Yingfang Zhou ◽  
Dimitrios Georgios Hatzignatiou ◽  
Johan Olav Helland ◽  
Yulong Zhao ◽  
Jianchao Cai
Keyword(s):  
Capillary Pressure ◽  
Water Saturation ◽  
Pore Space ◽  
Phase Region ◽  
Gas Oil ◽  
Two Phase ◽  
Sem Image ◽  
Three Phase ◽  
Scale Modelling ◽  
Capillary Pressure Curves

In this work, we developed a semianalytical model to compute three-phase capillary pressure curves and associated fluid configurations for gas invasion in uniformly wet rock images. The fluid configurations and favorable capillary entry pressures are determined based on free energy minimization by combining all physically allowed three-phase arc menisci. The model was first validated against analytical solutions developed in a star-shaped pore space and subsequently employed on an SEM image of Bentheim sandstone. The simulated fluid configurations show similar oil-layer behavior as previously imaged three-phase fluid configurations. The simulated saturation path indicates that the oil-water capillary pressure can be described as a function of the water saturation only. The gas-oil capillary pressure can be represented as a function of gas saturation in the majority part of the three-phase region, while the three-phase displacements slightly reduce the accuracy of such representation. At small oil saturations, the gas-oil capillary pressure depends strongly on two-phase saturations.

Rigorous Calculation of Miscible Displacement Using Immiscible Reservoir Simulators

1970 ◽  
Vol 10 (02) ◽  
pp. 192-202 ◽  
Author(s):  
R.B. Lantz
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Capillary Pressure ◽  
Truncation Error ◽  
Capillary Flow ◽  
Miscible Displacement ◽  
Partial Differential ◽  
Two Phase ◽  
Numerical Diffusion ◽  
Three Phase

Abstract In the past miscible displacement calculations have been approximated with two-phase reservoir simulators. Such calculations have neglected diffusional mixing between miscible components. In fact, no analog bas been proposed for rigorously treating miscible simulations with two-phase programs. This paper describes requirements that programs. This paper describes requirements that permit such a rigorous simulation. permit such a rigorous simulation. The sets of partial differential equations describing each of the displacement processes are shown to be exactly analogous if relative permeability and capillary pressure functions are permeability and capillary pressure functions are adjusted in a special manner. Application of the "miscible" analogy in a two-phase simulator, however, has several limitations, the most severe of which is the truncation error (numerical diffusion) typical of an immiscible formulation. Since this error is time-step and/or block-size dependent, numerical smearing can, in principle, be made as small as necessary. But this feature limits the practical applicability of the "miscible" analogy practical applicability of the "miscible" analogy to cases with rather large physical diffusion. The range of applicability and other limitations are outlined in the paper. Also, illustrative sample calculations are presented for linear, radial and layer-cake systems. Component densities and viscosities are varied in the linear model. Introduction In recent years, use of two- and three-phase reservoir simulators to calculate the performance of immiscible fluid displacement has become widespread. Reservoir simulators capable of calculating miscible displacement problems, however, have been limited to special use programs. The primary reason for this limitation has been the significant truncation error (numerical diffusion) typical of ordinary finite difference approximations to the miscible equations. The method of characteristics provided a means of making miscible displacement calculations without significant truncation error. A recently proposed second calculation technique, based on variational methods, also reduces numerical diffusion. Both of these calculational techniques can be used for immiscible calculations. Still, general miscible displacement applications such as gas cycling, enriched-gas injection, or tracer injection have historically required use of immiscible reservoir simulators for performance predictions. Larson et al. have reported an example of such use of a two-phase computer program. Displacement involving two components flowing within a single phase would appear to be analogous to a two-phase displacement. Yet, past miscible calculations using immiscible simulators made the two-phase saturation profile as near piston-like as possible and neglected component mixing due to possible and neglected component mixing due to diffusional processes. The capillary pressure function was chosen to minimize capillary flow. Also, in these miscible approximations, no provision had been made for viscosity variations provision had been made for viscosity variations with component concentration. Though mixing due to diffusional processes had been neglected, countercurrent diffusion due to component concentration differences in a miscible process should be essentially analogous to countercurrent capillary flow due to saturation differences in a two-phase system. This paper describes a method by which two- and three-phase reservoir simulators can be made to calculate miscible displacement rigorously. The only requirement of the method is that relative permeability and capillary pressure be special permeability and capillary pressure be special functions of saturation. With these properly chosen functions, the set of partial differential equations describing immiscible displacement becomes completely analogous to the partial differential equations describing miscible displacement. SPEJ P. 192

Mathematical Simulation of Polymer Flooding in Complex Reservoirs

1972 ◽  
Vol 12 (05) ◽  
pp. 369-382 ◽  
Author(s):  
P.L. Bondor ◽  
G.J. Hirasaki ◽  
M.J. Tham
Keyword(s):  
Finite Difference ◽  
Aqueous Phase ◽  
Flow Behavior ◽  
Polymer Flooding ◽  
Gravity Drainage ◽  
Two Phase ◽  
Polymer Injection ◽  
Well Spacing ◽  
Three Phase ◽  
Polymer Flood

Abstract Simulation of polymer flooding in many complex reservoirs has requirements that preclude the use of either three-phase stream tube or two-phase finite-difference simulators. The development of a polymer flooding model used in a three-phase, polymer flooding model used in a three-phase, four-component, compressible, finite-difference reservoir simulator that allows the simulation of a variety of complex situations is discussed. The polymer model represents the polymer solution as a fourth component that is included in the aqueous phase and is fully miscible with it. Adsorption of polymer is represented, as is both (1) the resulting permeability reduction of the aqueous phase and (2) the resulting lag of the polymer injection front and generation of a stripped polymer injection front and generation of a stripped water bank. The effects of fingering between the water and polymer are taken into account using an empirical "mixing parameter" model. The resulting simulator is capable of modeling reservoirs with nonuniform dip, multiple zones, desaturated zones, gravity segregation, and irregular well spacing and reservoir shape. Two examples are presented. The first illustrates the polymer flooding of a multizone dipping reservoir with a desaturated zone due to gravity drainage. The second illustrates the flooding of a reservoir with a gas cap and an oil rim with polymer injection near the oil-water contact. In this example, the effects of nonuniform dip, irregular well spacing and field shape, and gravity segregation of the flow are all taken into account. The two examples presented illustrate the versatility of the simulator presented illustrate the versatility of the simulator and its applicability to a wide range of problems. Introduction The design of a polymer flood for a complex reservoir requires a model that represents the reservoir features that have a significant effect on the performance of the flood. These features may include the presence of a gas cap or a desaturated zone due to gravity drainage in a dipping formation, the presence of an aquifer, irregular well spacing and reservoir boundaries, multiple zones, reservoir heterogeneities, and a well performance that is limited by state proration, injectivity, and productivity. These reservoir features are being productivity. These reservoir features are being represented by most compressible, three-phase, three-dimensional simulators. However, to model polymer flood projects, it is necessary to include a polymer flood projects, it is necessary to include a conservation equation for the polymer, and to represent the adsorption of polymer, the reduction of be rock permeability to the aqueous phase after contact with the polymer, the dispersion of the polymer slug, and the non-Newtonian flow behavior polymer slug, and the non-Newtonian flow behavior of the polymer solution. PREVIOUS SIMULATOR DEVELOPMENT PREVIOUS SIMULATOR DEVELOPMENT Previous simulator development of polymer flooding has been reported in two different general categories: three-phase stream tube models and one- or two-phase, incompressible, finite-difference simulators. Jewett and Schurz developed a two-phase, multilayer Buckley-Leverett displacement simulator capable of modeling either linear or five-spot patterns. A mobile gas saturation also could be patterns. A mobile gas saturation also could be specified, but this was treated as void space and did not affect the flow characteristics of the system. Gravitational and capillarity effects were neglected. The residual resistance of the brine following a water slug was modeled as an increase in its viscosity; the viscous fingering of the brine through the polymer slug was treated by altering empirical relative permeability relationships to specify a more adverse mobility ratio. Slater and Farouq-Ali modeled five-spot patterns with a two-phase, two-dimensional, finite-difference simulator, neglecting gravity and capillarity. They obtained an empirical expression for the resistance factor of the porous medium as a function of a time-dependent mobility ratio. SPEJ P. 369

A Fully Coupled Three-Phase Model for Capillary Pressure and Relative Permeability for Implicit Compositional Reservoir Simulation

SPE Journal ◽  
2010 ◽  
Vol 15 (04) ◽  
pp. 1003-1019 ◽  
Author(s):  
Odd Steve Hustad ◽  
David John Browning
Keyword(s):  
Capillary Pressure ◽  
Relative Permeability ◽  
Reservoir Simulation ◽  
Two Phase ◽  
Water Alternating Gas ◽  
Three Phase ◽  
Capillary Pressures ◽  
And Performance ◽  
Model Features ◽  
2D And 3D

Summary A coupled formulation for three-phase capillary pressure and relative permeability for implicit compositional reservoir simulation is presented. The formulation incorporates primary, secondary, and tertiary saturation functions. Hysteresis and miscibility are applied simultaneously to both capillary pressure and relative permeability. Two alternative three-phase capillary pressure formulations are presented: the first as described by Hustad (2002) and the second that incorporates six representative two-phase capillary pressures in a saturation-weighting scheme. Consistency is ensured for all three two-phase boundary conditions through the application of two-phase data and normalized saturations. Simulation examples of water-alternating-gas (WAG) injection are presented for water-wet and mixed-wet saturation functions. 1D homogeneous and 2D and 3D heterogeneous examples are employed to demonstrate some model features and performance.

scholarly journals A novel Shan and Chen type Lattice Boltzmann two phase method to study the capillary pressure curves of an oil water pair in a porous media

Petroleum ◽  
2018 ◽  
Vol 4 (3) ◽  
pp. 347-357 ◽  
Author(s):  
Sahand Nekoeian ◽  
Ataallah Soltani Goharrizi ◽  
Mohammad Jamialahmadi ◽  
Saeed Jafari ◽  
Fatemeh Sotoudeh
Keyword(s):  
Porous Media ◽  
Capillary Pressure ◽  
Lattice Boltzmann ◽  
Phase Method ◽  
Two Phase ◽  
Oil Water ◽  
Type Lattice ◽  
Capillary Pressure Curves

Computation of Three-Phase Capillary Pressure Curves and Fluid Configurations at Mixed-Wet Conditions in 2D Rock Images

SPE Journal ◽  
2016 ◽  
Vol 21 (01) ◽  
pp. 152-169 ◽  
Author(s):  
Y.. Zhou ◽  
J. O. Helland ◽  
D. G. Hatzignatiou
Keyword(s):  
Capillary Pressure ◽  
Cross Sections ◽  
Water Saturation ◽  
Gas Oil ◽  
Initial Water ◽  
Three Phase ◽  
Mixed Wettability ◽  
Oil Water ◽  
Simulation Results ◽  
Capillary Pressure Curves

Summary In this study, we present a three-phase, mixed-wet capillary bundle model with cross sections obtained from a segmented 2D rock image, and apply it to simulate gas-invasion processes directly on images of Bentheim sandstone after two-phase saturation histories consisting of primary drainage, wettability alteration, and imbibition. We calculate three-phase capillary pressure curves, corresponding fluid configurations, and saturation paths for the gas-invasion processes and study the effects of mixed wettability and saturation history by varying the initial water saturation after primary drainage and simulating gas invasion from different water saturations after imbibition. In this model, geometrically allowed gas/oil, oil/water, and gas/water interfaces are determined in the pore cross sections by moving two circles in opposite directions along the pore/solid boundary for each of the three fluid pairs separately. These circles form the contact angle with the pore walls at their front arcs. For each fluid pair, circle intersections determine the geometrically allowed interfaces. The physically valid three-phase fluid configurations are determined by combining these interfaces systematically in all permissible ways, and then the three-phase capillary entry pressures for each valid interface combination are calculated consistently on the basis of free-energy minimization. The valid configuration change is given by the displacement with the most favorable (the smallest) gas/oil capillary entry pressure. The simulation results show that three-phase oil/water and gas/oil capillary pressure curves are functions of two saturations at mixed wettability conditions. We also find that oil layers exist in a larger gas/oil capillary pressure range for mixed-wet conditions than for water-wet conditions, even though a nonspreading oil is considered. Simulation results obtained in sandstone rock sample images show that gas-invasion paths may cross each other at mixed-wet conditions. This is possible because the pores have different and highly complex, irregular shapes, in which simultaneous bulk-gas and oil-layer invasion into water-filled pores occur frequently. The initial water saturation at the end of primary drainage has a significant effect on the gas-invasion processes after imbibition. Small initial water saturations yield more-oil-wet behavior, whereas large initial water saturations show more-water-wet behavior. However, in both cases, the three-phase capillary pressure curves must be described by a function of two saturations. For mixed-wet conditions, in which some pores are water-wet and other pores are oil-wet, the gas/oil capillary pressure curves can be grouped into two curve bundles that represent the two wetting states. Finally, the results obtained in this work demonstrate that it is important to describe the pore geometry accurately when computing the three-phase capillary pressure and related saturation paths in mixed-wet rock.

Evaluation of Scale-Up Laws for Two-Phase Flow Through Porous Media

1963 ◽  
Vol 3 (02) ◽  
pp. 164-176 ◽  
Author(s):  
Russell L. Nielsen ◽  
M.R. Tek
Keyword(s):  
Porous Media ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Scaling Laws ◽  
Laboratory Model ◽  
Gas Reservoir ◽  
Two Phase ◽  
Phase Saturation ◽  
Water Coning ◽  
Capillary Pressure Curves

The scaling laws as formulated by Rapport relate dynamically similar flow systems in porous media each involving two immiscible, incompressible fluids. A two-dimensional numerical technique for solving the differential equations describing systems of this type has been employed to assess the practical value of the scaling laws in light of the virtually unscalable nature of relative permeability and capillary pressure curves and boundary conditions.Two hypothetical systems - a gas reservoir subject to water drive and the laboratory scaled model of that reservoir - were investigated with emphasis placed on water coning near a production well. Comparison of the computed behavior of these particular systems shows that water coning in the reservoir would be more severe than one would expect from an experimental study of a laboratory model scaled within practical limits to the reservoir system.This paper also presents modifications of the scaling laws which are available for systems that can be described adequately in two-dimensional Cartesian coordinates. Introduction Present day digital computing equipment and methods of numerical analysis allow realistic and quantitative studies to be carried out for many two-phase flow systems in porous media. Before these tools became available the anticipated behavior of systems of this type could be inferred only from analytical solutions of simplified mathematical models or from experimental studies performed on laboratory models.To reproduce the behavior of a reservoir system on the laboratory scale, certain relationships must be satisfied between physical and geometric properties of the reservoir and laboratory systems. Where the reservoir fluids may be considered as two immiscible and incompressible phases, the necessary relationships have been formulated by Rapoport and others. Rapoport's scaling laws follow from inspectional analysis of the differential equation describing phase saturation distribution in such systems.It will be recalled that these scaling laws presuppose three conditions:the relative permeability curves must be identical for the model and prototype;the capillary pressure curve (function of phase saturation) for the model must be linearly related to that of the prototype; andboundary conditions imposed on the model must duplicate those existing at the boundaries of the prototype. These three requirements seldom if ever can be satisfied in scaling an actual reservoir to the laboratory system because:The laboratory medium normally will be unconsolidated (glass beads or sand) while the reservoir usually is consolidated. Relative permeability and capillary pressure curves are usually quite different for consolidated and unconsolidated porous media.The reservoir usually will be surrounded by a large aquifer which could be simulated in the laboratory only to a limited extent.Wells present in the reservoir would scale to microscopic dimensions in the laboratory if geometric similarity is to be maintained. In view of these considerations, rigorous scaling of even a totally defined reservoir probably would never be possible.The purpose of this paper is to assess the practical value of the scaling laws in the light of the unscalable variables. This has been done by carrying out numerical solutions in two dimensions to the differential equations describing the flow of two immiscible, incompressible fluids in porous media for a field scale reservoir and a laboratory model of that reservoir. While both the reservoir and the laboratory model were purely fictional, each has been made as realistic and representative as possible.The field problem selected as the basis for the investigation was an inhomogeneous, layered gas reservoir initially at capillary gravitational equilibrium and subsequently produced in the presence of water drive. The laboratory model of this reservoir was designed to utilize oil and water in a glass bead pack. SPEJ P. 164^

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