Simulation of Block-to-Block Processes in Naturally Fractured Reservoirs
- Larry S.K. Fung (Computer Modelling Group)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- November 1991
- Document Type
- Journal Paper
- 477 - 484
- 1991. Society of Petroleum Engineers
- 5.8.6 Naturally Fractured Reservoir, 4.1.2 Separation and Treating, 5.5 Reservoir Simulation, 5.3.2 Multiphase Flow, 5.2.1 Phase Behavior and PVT Measurements, 5.4.3 Gas Cycling, 4.3.4 Scale, 4.6 Natural Gas, 5.4.2 Gas Injection Methods
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Simulation of fractured reservoirs with the dual-porosity/dual-permeabilityapproach involves discretization of the solution domain into two collocatedcontinua called the matrix and the fracture. The original idealized modelassumes that the matrix acts essentially as a source or sink to the fracture,which is the primary conduit for fluid flow. In multiphase flow situations,this idealization was found to be inadequate. Enhancements are needed torepresent the local matrix/fracture and matrix/matrix drainage and imbibitionprocesses. Attempts to represent these processes include the gravity-segregatedmodel, the subdomain model, the pseudofunction method, and thedual-permeability model. This work examines the mechanisms involved in gas/oilgravity drainage in terms of the block-to-block process. Current methods fortreating this problem are reviewed to identify deficiencies. A new approach isproposed in which these mechanisms can he represented properly in thefield-scale simulation of these reservoirs. The method involves the calculationof pseudo capillary potentials, which in an average sense (on a computationalblock basis) give the correct flow behaviors. These pseudos can be calculated apriori if a vertical equilibrium (VE) assumption can be made about the fluiddistribution in the matrix blocks. When the VE assumption is not valid, thepseudos can be determined from fine-grid simulations.
The development of simulation tools that can capture the dominant flowprocesses and recovery mechanisms of naturally fractured reservoirs has beenthe subject of much attention and controversy over the last 15 years. Since theinception of the dual-porosity con-cept, many research papers on models thatuse the concept have appeared in the literature. The dual-porosity approachassumes that the fissured porous media can be represented by two overlappingcontinua called the fracture and the matrix. The fracture continuum consists ofthe interconnected network of fractures and/or so-lution vugs that constitutethe primary conduits for fluid flow. The matrix continuum consists of theintergranular pore space of the rock, which comprises the majority of thestorage in the pore space of the rock, which comprises the majority of thestorage in the reservoir. Early dual-porosity models include those of Kazemi etal. and Saidi. Saidi modeled a fractured reservoir by dividing it into sectorsin which the fracture was assumed to have infinite transmissi-bility. Thematrix was represented by several cylindrical matrix blocks that were suitablydistributed vertically and horizontally. These matrix blocks were gridded withboundary conditions imposed on them by the fracture, which was under thegravity-segregation assumption. Kazemi et al. discretized the fracturecon-tinuum into gridblocks and simulated fluid flow by a set of fracturemass-balance equations. The matrix was assumed to act as a source or sink tothe fracture, and the flow between the two continua was represented by a singlematrix/fracture transfer term. With the assumption that the matrix blocks wereisolated, the transfer term was constructed from a representative matrix blocklocated at the center of the gridblock. The total transfer rate for thegrid-block was thus the transfer rate for the representative matrix blockmultiplied by the total number of matrix blocks within the gridblock. Becausethe representative matrix blocks and the fracture were at the same depth,gravity effect on recovery from the matrix was not included in the transfercalculation. Most state-of-the-art dual-porosity simulators discretize thefracture continuum but with additional enhancements to handle the effects ofgravity on the transfer.
Saidi et al. discussed the gas/oil gravity-drainage process in fracturedreservoirs in Iran. Because of the low viscous gradient in the fracture,liberated gas tends to percolate to form a secondary gas cap. As the gas zoneadvances, matrix blocks become surrounded by gas. The density differencebetween the gas in the fracture and the oil in the matrix becomes the maindriving force for oil recovery, which is limited by the capillary pressurebetween the two phases. The ultimate recovery from a single matrix block undergravity drainage depends on the balance between two forces: gravity, which is adirect function of the matrix block height and the density difference betweenthe two phases, and capillarity, which depends on the gas/oil interfacialtension (IFT).
The two important phenomena associated with the gravity-drainage processesare reimbibition and matrix continuity. Reim-bibition refers to processes arereimbibition and matrix continuity. Reim-bibition refers to the re-entering ofdrained matrix oil into other matrix blocks, also known as the block-to-blockprocess. Matrix continuity describes the situation where the fractureseparating the matrix blocks is incomplete, resulting in some degree ofcontinuity of flow paths and potentials between them. These phenomena, as wewill see, have significant implications for the modeling phenomena, as we willsee, have significant implications for the modeling of gravity drainage withthe dual-porosity concept.
Much of the more recent literature on dual-porosity modeling is devoted todeveloping enhancements for modeling the gravity effects in the transfercalculation. These can be roughly classified into four groups:gravity-segregated, subdomain, pseudofunction, and dual-permeability models.Ref. 15 discusses these models. Essentially, all the models try to account forgravity effects, with varying degrees of accuracy and complexity. None of themethods treats the reimbibition phenomenon, although the concept ofreimbibition is rather irrelevant to phenomenon, although the concept ofreimbibition is rather irrelevant to the dual-permeability model. All themodels except the dual-permeability model neglect capillary continuity. In thedual-permeability model, the matrix is assumed to be completely continuous. Thematrix oil recovery under gravity drainage reflects the gravity/capillarybal-ance for the entire matrix column and has nothing to do with the matrixblock height.
This work examines the gravity-drainage process and associated phenomena,such as capillary continuity and reimbibition. A new method is then introducedthat can handle block-to-block interaction and is efficient for use in thefield-scale simulation of these reservoirs. The method involves the calculationof pseudo capillary potentials, which give the correct flow behaviors on acomputational block basis. Accuracy of the technique is verified by comparingits results with results from fine-grid simulations. Some comparisons withexisting models are also made.
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