Academic literature on the topic 'Multiphase Upscaling'

Summary Representing the complete spectrum of fine-scale stratigraphic details in full-field dynamic models of geologically complex clastic reservoirs is beyond the limits of existing computational capabilities. A quasiglobal multiphase upscaling method—the regional-scale multiphase upscaling (RMU) method—is developed, in which the dynamic effects of subgrid-scale (typically subseismic) nonlocal stratigraphic reservoir elements (e.g., channels, lobes, sand bars, and shale drapes) are captured by means of pseudofunctions for flow simulation. Unlike conventional dynamic multiphase upscaling methods, the RMU method does not require fine-resolution reservoir-scale simulations. Rather, it relies on intermediate-scale sector-model simulations for pseudoization. The intermediate scale, also referred to as the regional scale, is defined as the spatial scale at which the global multiphase flow effects of nonlocal stratigraphic elements can be approximated by fine-resolution flow simulations with reasonable accuracy. During the pseudoization process, dynamic multiphase flow responses of coarse regional-scale sector models are calibrated against those stemming from their corresponding fine-resolution parent models. Each regional-scale sector model is simulated only once at the fine geologic resolution. The process involves automatic determination and subsequent modification of the parameters that describe rock relative permeability and capillary pressure functions. Coarse regional-scale models are simulated a few times until a reasonable match between their coarse- and fine-resolution dynamic responses can be attained. The parameter-estimation step of the pseudoization process is performed by use of a very efficient constrained nonlinear optimization algorithm. The RMU method is evaluated in two proof-of-concept numerical examples involving a plethora of turbidite stratigraphic architectures. The method yields simulation results that are always more accurate than conventionally upscaled coarse-resolution model predictions. Incorporating geologically based pseudofunctions into otherwise simple coarse-resolution full-field reservoir models reduces the simulation cycle time significantly and improves the accuracy of production forecasts. The RMU method typically delivers two to three orders of magnitude in speed up of flow simulations.

Summary Carbonate fractured reservoirs introduce a tremendous challenge to the upscaling of both single- and multiphase flow. The complexity comes from both heterogeneous matrix and fracture systems in which the separation of scales is very difficult. The mathematical upscaling techniques, derived from representative elementary volume (REV), must therefore be replaced by a more realistic geology-based approach. In the case of multiphase flow, an evaluation of the main forces acting during oil recovery must also be performed. A matrix-sector model from a highly heterogeneous carbonate reservoir is linked to different fracture realizations in dual-continuum simulations. An integrated iterative workflow between the geology-based static modeling and the dynamic simulations is used to investigate the effect of fracture heterogeneity on multiphase fluid flow. Heterogeneities at various scales (i.e., diffuse fractures and subseismic faults) are considered. The diffuse-fracture model is built on the basis of facies and porosity from the matrix model together with core data, image-log data, and data from outcrop-analogs. Because of poor seismic data, the subseismic-fault model is mainly conceptual and is based on the analysis of outcrop-analog data. Fluid-flow simulations are run for both single-phase and multiphase flow and gas and water injections. A better understanding of fractured-reservoirs behavior is achieved by incorporating realistic fracture heterogeneity into the geological model and analyzing the dynamic impact of fractures at various scales. In the case of diffuse fractures, the heterogeneity effect can be captured in the upscaled model. The subseismic faults, however, must be explicitly represented, unless the sigma (shape) factor is included in the upscaling process. A local grid-refinement approach is applied to demonstrate explicit fractures in large-scale simulation grids. This study provides guidelines on how to effectively scale up a heterogeneous fracture model and still capture the heterogeneous flow behavior.

Summary Although numerous upscaling techniques are reported in the literature, efficiently computing reasonably accurate equivalent rock properties from geological data at fine scale remains difficult. This is especially true for facies with multiple lithologies under multiphase-flow conditions. Because of the nature of multiscale heterogeneity inherent in petroleum reservoirs, the equivalent rock and flow properties will vary with the scales of heterogeneity. Therefore, upscaled properties under multiphase-flow conditions cannot be estimated without reference to the absolute scales of heterogeneity. Wavelet analysis is a multiresolution framework; thus, it is well suited for upscaling rock and flow properties in a multiscale heterogeneous reservoir. The compact support property of the wavelet transform assures efficient computation. Choice of regularity provides a flexible way to control the smoothness of the resulting upscaling properties. In this study, we developed a new procedure to improve significantly the computational efficiency and accuracy of upscaling for generating equivalent rock and rock-fluid properties under various geological and flow conditions based on multiresolution analysis of wavelet transforms. Additionally, we explored a wavelet reconstruction method to provide a basis for downsampling fine-scale rock property fields from information at various levels of coarser scale. The beauty of the method is that because the equivalent properties at different length scales are computed recursively, the interdependent influences of the heterogeneities on the scales are included effectively. We demonstrate the method by successfully applying it to upscale interbedset and interfacies reservoir properties of Almond formation outcrops under multiphase-flow conditions. Introduction It is well known that petroleum reservoirs are inherently heterogeneous, flow performance of reservoirs is controlled by variability in reservoir properties at various scales, and the dominant scale effects will vary with the production processes involved. Limited by the computational power or based on the consideration of the dominant scale on the production scheme involved, the flow simulation is usually carried on a scale that is much coarser than the scale of the direct or indirect measurements. Therefore, one needs first to reconstruct adequately the fine-scale variability mapping of the reservoir properties from sparsely distributed, multiscale samples, and then properly coarsen, or upscale the fine-scale variability. Roughly speaking, upscaling is considered a procedure to transfer the rock and rock-fluid properties carried in the finer scale to appropriate coarser scale. Upscaling reservoir properties is complicated and challenging, especially for multiple lithologies and multiphase-flow conditions. Unlike the case of single-phase flow, where only absolute permeability affects the steady-state flow, where only absolute permeability affects the steady-state flow behavior, the flow properties for each phase and phase pressure differ within each geological facies, and, probably more important, the rock-fluid property contrasts between the facies also play a vital role for multiple lithologies and multiphase-flow situations. Therefore, besides effective absolute permeability, as in the case of single-phase flow, one needs to determine two additional equivalent properties: effective relative permeabilities and effective capillary pressure for the coarse-scale grid model. Such equivalent properties are flow-regime sensitive, making the problem more complicated. It is well known that flow regime in a multiphase flow is determined by the relative ratio among three major driving forces: viscous force, gravitational force, and capillary pressure. Such a relative ratio among various driving forces will depend on flow velocity, scale of heterogeneity, size of gridblock, and fluid properties. Considering that flow velocity and heterogeneity in a reservoir are spatially and/or temporally varying the equivalent relative permeability and capillary pressure generally will be spatially and temporally dependent and cannot be constructed without reference to geological structure and dominant flow regime. Although the literature reports numerous upscaling techniques,1–5 efficiently computing reasonably accurate equivalent rock properties from the data at finer scale remains challenging. We lack a method that can be used consistently for both single and multiphase-flow conditions. With multiresolution analysis properties, compact support, orthogonality, and localized transforms in both space and frequency domains, wavelet analysis provides a consistent, efficient, and accurate way for upscaling reservoir properties. In this study, we developed a decomposition and reconstruction procedure for rock property fields in light of Mallat's work.6 Application of the developed procedure to absolute permeability fields presents promising results. When coarsening fine-grid permeability to more accessible scales, although the number of grids are reduced substantially, the main trends or characters of the permeability fields are reasonably well preserved. The flow behavior from the original fine-grid permeability field is reproduced perfectly by the upscaled permeability field. The developed method also can reconstruct the fine-scale properties adequately from coarser-scale information. To check the consistency of the proposed procedure, the same framework was extended further to upscale rock-fluid properties under multiple lithologies and multiphase-flow conditions in addition to rock properties. To verify the applicability of the newly developed upscaling procedure within a realistic geological context, we constructed testing problems with measurements from the Almond formation. Theoretical Background Wavelet Transforms. Wavelet transforms, like the extensively used Fourier transform, are kinds of linear integral transforms that are represented as a convolution of a given function, f(x), with a kernel function,Equation 1 Here, ? is a scale parameter, x is a location parameter, and the family of functions, ? ?x(u), are called wavelet functions. There are two major differences between the Fourier transform and Wavelet transforms. First of all, instead of one parameter transforms, as Eq. 1 shows. In this way, Wavelet transforms give not only information about the content of a function in the frequency domain, but also information about the location of these frequencies in the spatial domain. Wavelet Transforms. Wavelet transforms, like the extensively used Fourier transform, are kinds of linear integral transforms that are represented as a convolution of a given function, f(x), with a kernel function,Equation 1 Here, ? is a scale parameter, x is a location parameter, and the family of functions, ? ?x(u), are called wavelet functions. There are two major differences between the Fourier transform and Wavelet transforms. First of all, instead of one parameter transforms, as Eq. 1 shows. In this way, Wavelet transforms give not only information about the content of a function in the frequency domain, but also information about the location of these frequencies in the spatial domain.

Summary Geologists often generate highly heterogeneous descriptions of reservoirs, containing complex structures which are likely to give rise to very tortuous flow paths. However, these models contain too many grid cells for multiphase flow simulation, and the number of cells must be reduced by upscaling for reservoir simulation. Conventional upscaling methods often have difficulty in the representation of tortuous flow paths, mainly because of the inappropriate assumptions concerning the boundary conditions. An accurate and practical upscaling method is therefore required to preserve the flow features caused by highly heterogeneous fine scale geological description. In this paper, the problems encountered in routinely used upscaling approaches are outlined, and a more accurate and practical way of performing upscaling is proposed. The new upscaling method, Well Drive Upscaling (WDU), employs the wells and the actual reservoir boundary conditions (e.g., faults and physical boundaries of the geological model). The main advantage of this method is that the dominant flow paths can be preserved, and thus the geological knowledge can be assimilated appropriately. The new method has firstly been applied to a synthetic model with a tortuous channel, and is shown to have significant improvement over the traditional approach. The sensitivity study on the scale-up factor using a benchmark model shows the advantage of the method with various scale-up factors. The method was then applied to a model of a field in the central North Sea, which involves three-phase flow. In the cases studied, the WDU method produced a comparable result to the dynamic Pore Volume Weighted approach, which involves running the fine grid simulation and computing appropriate relative permeabilities and interblock transmissibilities. The new method makes the upscaling process practical, and our tests show it to be more accurate than traditional methods. Introduction The heterogeneity observed in a field is generally high and the geological structures therein can be complex. From a geological point of view, it would be ideal to represent each facies boundary, both vertically and horizontally, by a gridblock boundary (Mallet 1997; Deutsch and Tran 2002). Also, if distinct layering exists within a genetic unit, a further split into subunits is also desirable. In practice, reservoir models are usually created at the scale of meters or less vertically and 100 meters or less areally [and each block itself may have involved small-scale upscaling (Pickup et al. 2005)]. In many cases, detailed reservoir modeling for a highly heterogeneous reservoir may result in a large number of grid cells (e.g., 106 grid cells or more). This large number of grid cells prohibits direct simulation of the reservoir, especially for a very heterogeneous reservoir model. This is because, apart from the limitation of computational power, the high level of heterogeneity often makes it difficult to obtain a converged solution. The problem becomes more severe when simulations involve three-phase flow. In order to perform reservoir simulation on a highly heterogeneous geological model within a reasonable time frame, we have to apply appropriate upscaling techniques to reduce the number of grid cells so as to speed up the reservoir simulation and thus field development planning process. Although a number of upscaling methods have been developed in the past a few decades (Pickup et al. 2005; Christie 1996, 2001), they are often not satisfactory and have been discussed in a number of critical reviews (Barker and Thibeau 1997; Farmer 2002). The main conflict in the application of the current upscaling techniques lies in the balance of the accuracy and practicality of the methods. There are two main problems that cause the conflict. The first is the problem of using inappropriate boundary conditions in single-phase upscaling, which is likely to reduce the accuracy, and the second problem is the impracticality of the dynamic two-phase upscaling which should (in theory) be more accurate. Details of the these methods have been discussed in a number of reviews on upscaling (Christie 1996, 2001; Barker and Thibeau 1997; Farmer 2002; Renard and de Marsily 1997), so a complete review of upscaling methods will not be presented here. However, we outline one of the commonly used methods: the pressure solution method for upscaling single-phase flow. In this method, a single-phase pressure solve is carried out in each coarse cell in turn, and Darcy's law is used to calculate the effective permeability tensor (Christie 1996). In order to solve the pressure equation, boundary conditions must be applied to each cell. (This is referred to as the local upscaling method.) A typical example is the no-flow, or constant pressure boundary condition, where the pressure is fixed at either end of the region of a coarse block, and no flow is allowed through the sides. Other boundary conditions include linear pressure and periodic boundary conditions (Farmer 2002). Such boundary conditions, however, may differ significantly from the actual boundary conditions within a heterogeneous fine-scale model (Chen et al. 2003; Zhang 2006). A highly heterogeneous reservoir model often produces tortuous flow paths, and it is difficult to generalize a flow pattern on the boundaries of a coarse block and apply to all the coarse blocks in a reservoir model. The flow paths for a coarse model may be completely different from the original fine-scale geological model response when inappropriate boundary conditions are applied (i.e., the effect of geological structure may be lost). A multiphase flow simulation from such a coarse model will not honor the small-scale geological structure either, even if we ignore the error caused by multiphase flow effects in the upscaling process.

Summary Upscaling is often applied to coarsen detailed geological reservoir descriptions to sizes that can be accommodated by flow simulators. Adaptive local-global upscaling is a new and accurate methodology that incorporates global coarse-scale flow information into the boundary conditions used to compute upscaled quantities (e.g., coarse-scale transmissibilities). The procedure is iterated until a self-consistent solution is obtained. In this work, we extend this approach to 3D systems and introduce and evaluate procedures to decrease the computational demands of the method. This includes the use of purely local upscaling calculations for the initial estimation of coarse-scale transmissibilities and the use of reduced border regions during the iterations. This is shown to decrease the computational requirements of the reduced procedure significantly relative to the full methodology, while impacting the accuracy very little. The performance of the adaptive local-global upscaling technique is evaluated for three different heterogeneous reservoir descriptions. The method is shown to provide a high degree of accuracy for relevant flow quantities. In addition, it is shown to be less computationally demanding and significantly more accurate than some existing extended local upscaling procedures. Introduction Fine-scale heterogeneity can have a significant impact on reservoir performance. Because it is usually not feasible to simulate directly on the detailed geocellular model, some type of upscaling is often applied to generate the simulation model from the geological description. Here, we focus on the upscaling of single-phase flow parameters, particularly absolute permeability. The algorithms we consider can provide either coarse-scale permeability, designated k*, or coarse-scale transmissibility, designated T* . It is important to emphasize that the accurate upscaling of permeability (which can be studied within the context of single-phase flow) is essential for the development of accurate coarse models of two-phase or multiphase flow. Thus the applicability of the methods developed here is very broad and includes all types of displacement processes.

Fractured reservoirs are distributed widely over the world, and describing fluid flow in fractures is an important and challenging topic in research. Discrete fracture modeling (DFM) and equivalent continuum modeling are two principal methods used to model fluid flow through fractured rocks. In this paper, a novel method, embedded discrete fracture modeling (EDFM), is developed to compute equivalent permeability in fractured reservoirs. This paper begins with an introduction on EDFM. Then, the paper describes an upscaling procedure to calculate equivalent permeability. Following this, the paper carries out a series of simulations to compare the computation cost between DFM and EDFM. In addition, the method is verified by embedded discrete fracture modeling and fine grid methods, and grid-block and multiphase flow are studied to prove the feasibility of the method. Finally, the upscaling procedure is applied to a three-dimensional case in order to study performance for a gas injection problem. This study is the first to use embedded discrete fracture modeling to compute equivalent permeability for fractured reservoirs. This paper also provides a detailed comparison and discussion on embedded discrete fracture modeling and discrete fracture modeling in the context of equivalent permeability computation with a single-phase model. Most importantly, this study addresses whether this novel method can be used in multiphase flow in a reservoir with fractures.

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.

In the past decades, considerable effort has been put into developing high resolution geological models for oil and gas reservoirs. Although the growth of computational power is rapid, the static model size still exceeds the model size for routine reservoir simulation. We develop and apply a variety of grid coarsening and refinement algorithms and single and multiphase upscaling approaches, applied to tight gas and conventional reservoir models. The proposed research is organized into three areas. First the upgridding of detailed three dimensional geologic models is studied. We propose an improved layer design algorithm with considerations of accuracy and efficiency. This involves developing measures of reservoir heterogeneity and using these measures to design an optimal grouping of geologic model layers for flow simulation. The optimal design is shown to be a tradeoff between the desire to preserve the reservoir heterogeneity and a desire to minimize the simulation time. The statistical analysis is validated by comparison with flow simulation results. Accurate upgridding/upscaling of single-phase parameters is necessary. However, it does not always satisfy the accuracy requirements, especially for the model which is aggressively coarsened. We introduce a pseudoization method with total mobility and effective fractional flow as the major targets. This pseudoization method helps to push upgridding/coarsening degree to the limit but still be able to reproduce the fine scale field performance. In practice, it is common to not use a different set of pseudos for every coarse cell; only a limited number of pseudo functions should be generated for different “rock types” or geological zones. For similar well patterns and well control conditions, applying pseudo is able to reproduce the fine scale performance for different simulation runs. This is the second proposed research area. Finally, it is necessary to increase flow resolution for precise field history matching and forecasting. This has received increasing attention, especially when studying hydraulically fractured wells in unconventional reservoirs. We propose a multiscale reservoir simulation model combining local grid refinement (LGR) and pillar-based upscaling for tight gas reservoir performance prediction. Pillar-based coarsening away from the wells is designed for tight gas reservoirs. It compensates for the extra computational cost from LGR, which is used to represent hydraulic fractures. Overall reservoir performances, including the accuracy and efficiency, are evaluated.

A growing demand for more detailed modeling of subsurface physics as ever more challenging reservoirs - often unconventional, with significant geomechanical particularities - become production targets has moti-vated research in coupled flow and geomechanics. Reservoir rock deforms to given stress conditions, so the simplified approach of using a scalar value of the rock compressibility factor in the fluid mass balance equation to describe the geomechanical system response cannot correctly estimate multi-dimensional rock deformation. A coupled flow and geomechanics model considers flow physics and rock physics simultaneously by cou-pling different types of partial differential equations through primary variables. A number of coupled flow and geomechanics simulators have been developed and applied to describe fluid flow in deformable po-rous media but the majority of these coupled flow and geomechanics simulators have limited capabilities in modeling multiphase flow and geomechanical deformation in a heterogeneous and fractured reservoir. In addition, most simulators do not have the capability to simulate both coarse and fine scale multiphysics. In this study I developed a new, fully implicit multiphysics simulator (TAM-CFGM: Texas A&M Coupled Flow and Geomechanics simulator) that can be applied to simulate a 2D or 3D multiphase flow and rock deformation in a heterogeneous and/or fractured reservoir system. I derived a mixed finite element formu-lation that satisfies local mass conservation and provides a more accurate estimation of the velocity solu-tion in the fluid flow equations. I used a continuous Galerkin formulation to solve the geomechanics equa-tion. These formulations allowed me to use unstructured meshes, a full-tensor permeability, and elastic stiffness. I proposed a numerical upscaling of the permeability and of the elastic stiffness tensors to gener-ate a coarse-scale description of the fine-scale grid in the model, and I implemented the methodology in the simulator. I applied the code I developed to the simulation of the problem of multiphase flow in a fractured tight gas system. As a result, I observed unique phenomena (not reported before) that could not have been deter-mined without coupling. I demonstrated the importance and advantages of using unstructured meshes to effectively and realistically model a reservoir. In particular, high resolution discrete fracture models al-lowed me to obtain more detailed physics that could not be resolved with a structured grid. I performed numerical upscaling of a very heterogeneous geologic model and observed that the coarse-scale numerical solution matched the fine scale reference solution well. As a result, I believed I developed a method that can capture important physics of the fine-scale model with a reasonable computation cost.