The significant oil reserves related to karst reservoirs in Brazilian pre-salt field adds new frontiers to the development of upscaling procedures to reduce time on numerical simulations. This work aims to represent karst reservoirs in reservoir simulators based on special connections between matrix and karst mediums, both modeled in different grid domains of a single porosity flow model. This representation intends to provide a good relationship between accuracy and simulation time.
The concept follows the Embedded Discrete Fracture Model (EDFM) developed by Moinfar, 2013; however, this work extends the approach for karst reservoirs (Embedded Discrete Karst Model - EDKM) by adding a representative volume through grid blocks to represent karst geometries and porosity. For the extension of EDFM approach in a karst reservoir, we adapt the methodology to four stages: (a) construction of a single porosity model with two grid domains, (b) geomodeling of karst and matrix properties for the corresponding grid domain, (c) application of special connections through the conventional reservoir simulator to represent the transmissibility between matrix and karst medium, (d) calculation of transmissibility between karst and matrix medium.
For a proper validation, we applied the EDKM methodology in a carbonate reservoir with mega-karst structures, which consists of non-well-connected enlarged conduits and above 300 mm of aperture. The reference model was a refined grid with karst features explicitly combined with matrix facies, including coquinas interbedded with mudstones and shales. The grid block of the reference model measures approximately 10 × 10 × 1 meters. For the simulation model, the matrix grid domain has a grid block size of approximately 100 × 100 × 5 meters. The karst grid domain had the same block size as the refined grid. Flow in the individual karst grid domain or matrix grid domain is governed by Darcy's equation, implicitly solved by simulator. However, the transmissibility for the special connections between karst and matrix blocks is calculated as a function of open area to flow, matrix permeability and block center distance. The matrix properties were upscaled through conventional analytical methods. The results show that EDKM had a considerable performance regarding a dynamic matching response with reference model, within a reduced simulation time while maintaining a higher dynamic resolution in the karst grid domain without using an unconstructed grid.
This work aims to contribute to the extension of EDFM approach for karst reservoirs, which can be applied to commercial finite-difference reservoir simulators and it presents itself as a solution to reduce simulation time without disregarding the explicit representation of karst features in structured grids.
Classical fracture upscaling techniques are usually based on numerical or analytical solutions which can present some problems to capture the near-well flow behavior, leading to wrong well productivity index. In addition, grid cell size must be chosen carefully to maintain both connectivity and permeability tensor of fracture network in a reasonable simulation computational time. This paper proposes a near-well refinement in conjunction with a classic fracture upscaling technique in order to improve the accuracy of well productivity. The matrix porous media is respected to a microbial carbonate reservoir where discrete fractured network is composed by diffuse fracture pattern (small-scale fractures) and sub-seismic conductive fractures that strongly affect fluid flow. Fracture network density was defined using lithology as control driver. In this work, a dual-porosity system with a block cell size smaller than diffuse fractures was used as reference model (fine grid) for the upscaling method due to its quality to reproduce properly the connectivity between diffuse and sub-seismic fractures. The fracture upscaling method based on Oda´s solution (Oda, 1985) was applied to a coarser model defined by near-well refinements, which capture the fine grid fracture properties near-well. Homogeneous petrophysical matrix is applied in order to isolate the matrix heterogeneity effects. It was possible to adjust the main reservoir parameters (field average pressure, oil recovery factor and water cut) and advanced water front. The fine grid simulation time was drastically reduced using the proposed procedure.
The best way to analyze the sensitivity of dual porosity (DP) or dual permeability (DK) systems is his interaction with small and large scale petrophysical features using a fine grid, since in a coarser scale, small scale heterogeneities are always integrate in an upscaled background matrix. Two significant petrophysical features in carbonate reservoirs were applied over a background matrix, defined by, low permeability but with separate vugs (SV) randomly distributed with high porosity and permeability: (1) tectonic fractures (nearly vertical) and (2) touching vugs (nearly horizontal), were defined as large scale fractures, with high permeability and low porosity. These features are combined and tested in two cases. In the first case, the flow is controlled by touching vugs and tectonic fractures. In the second case, the flow is controlled only by touching vugs. The two cases were tested with and without SV in the background matrix. In both cases, oil recovery factor (ORF) is higher in presence of SV. ORF in DK system is also higher than in DP system. In Case 1A, the ORF for the DP system is nearly equal to the case 1B, showing that the flow rate between matrix blocks is highly important in the presence of SV, leading to the necessity of a DK system application. Without SV, ORF is nearly equal for DP and DK systems thus disregarding the necessity of a DK system, given the higher flow simulation time. The front of injected water in second case is nearly horizontal and homogeneous in fracture component resulting in a higher flow rate between SV to fracture network. The heterogeneous front of injected water in first case reduces the significance presence of SV. This work gives a valuable sensitivity of DP/DK systems in the study of small and large scale heterogeneities.
The purpose of this study is to develop an upscaling technique, applied to naturally fractured carbonate reservoirs, adjusting fracture blocks components and well indices according to our small scale fracture behavior using mini-models. Two significant petrophysical features of carbonate reservoirs were applied over a background matrix, defined by low permeability but with separate vugs (SV) randomly distributed with high porosity and permeability: (1) tectonic fractures (nearly vertical) and (2) touching vugs (nearly horizontal), were defined as large scale fractures , with high permeability and low porosity. These features are combined and tested in three cases, with the same background matrix. In the first case, the flow is controlled by high permeability thin facies and tectonic fractures; in the second case, the flow is controlled by touching vugs and tectonic fractures and in the third case the flow is controlled only by touching vugs. A fine grid cell size of 0.8x0.8x0.4 meters is used as reference for the upscaling method. All fracture grid blocks in coarser cell size (3x3x2 meters) were adjusted in order to calibrate the fracture direction according to our fine grid fracture behavior, combined with a well index adjustment. In order to isolate the matrix heterogeneities effects, the same fracture calibration procedure is applied to a homogeneous matrix using the same fracture network in order to validate the fracture upscaling. It was possible to adjust all reservoir parameters (field average and well pressure, oil recovery factor, etc.) and reduce the flow simulation time from days to a few seconds. With this methodology we can transfer small scale heterogeneities from different sources to a coarser scale without losing information.