Summary Accurate calculation of multiphase-fluid transfer between the fracture and matrix in naturally fractured reservoirs is a crucial issue. In this paper, we will present the viability of the use of simple transfer functions to account accurately for fluid exchange resulting from capillary, gravity, and diffusion mass transfer for immiscible flow between fracture and matrix in dual-porosity numerical models. The transfer functions are designed for sugar-cube or match-stick idealizations of matrix blocks. The study relies on numerical experiments involving fine-grid simulation of oil recovery from a typical matrix block by water or gas in an adjacent fracture. The fine-grid results for water/oil and gas/oil systems were compared with results obtained with transfer functions. In both water and gas injection, the simulations emphasize the interaction of capillary and gravity forces to produce oil, depending on the wettability of the matrix. In gas injection, the thermodynamic phase equilibrium, aided by gravity/capillary interaction and, to a lesser extent, by molecular diffusion, is a major contributor to interphase mass transfer. For miscible flow, the fracture/matrix mass transfer is less complicated because there are no capillary forces associated with solvent and oil; nevertheless, gravity contrast between solvent in the fracture and oil in the matrix creates convective mass transfer and drainage of oil. Using the transfer functions presented in this paper, fracture- and matrix-flow calculations can be decoupled and solved sequentially--reducing the complexity of the computation. Furthermore, the transfer-function equations can be used independently to calculate oil recovery from a matrix block.

This paper continues the work presented in Ramirez et al. (2009). In Part I, we discussed the viability of the use of simple transfer functions to accurately account for fluid exchange as the result of capillary, gravity, and diffusion mass transfer for immiscible flow between fracture and matrix in dual-porosity numerical models.Here, we show additional information on several relevant topics, which include (1) flow of a low-concentration water-soluble surfactant in the fracture and the extent to which the surfactant is transported into the matrix; (2) an adjustment to the transfer function to account for the early slow mass transfer into the matrix before the invading fluid establishes full connectivity with the matrix; and (3) an analytical approximation to the differential equation of mass transfer from the fracture to the matrix and a method of solution to predict oil-drainage performance.Numerical experiments were performed involving singleporosity, fine-grid simulation of immiscible oil recovery from a typical matrix block by water, gas, or surfactant-augmented water in an adjacent fracture. Results emphasize the viability of the transfer-function formulations and their accuracy in quantifying the interaction of capillary and gravity forces to produce oil depending on the wettability of the matrix. For miscible flow, the fracture/matrix mass transfer is less complicated because the interfacial tension (IFT) between solvent and oil is zero; nevertheless, the gravity contrast between solvent in the fracture and oil in the matrix creates convective mass transfer and drainage of the oil.

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Accurate calculation of multiphase-fluid transfer between the fracture and matrix in naturally fractured reservoirs is a crucial issue. In this paper, we will present the viability of the use of simple transfer functions to account accurately for fluid exchange resulting from capillary, gravity, and diffusion mass transfer for immiscible flow between fracture and matrix in dual-porosity numerical models. The transfer functions are designed for sugarcube or match-stick idealizations of matrix blocks. The study relies on numerical experiments involving fine-grid simulation of oil recovery from a typical matrix block by water or gas in an adjacent fracture. The fine-grid results for water/oil and gas/oil systems were compared with results obtained with transfer functions. In both water and gas injection, the simulations emphasize the interaction of capillary and gravity forces to produce oil, depending on the wettability of the matrix. In gas injection, the thermodynamic phase equilibrium, aided by gravity/capillary interaction and, to a lesser extent, by molecular diffusion, is a major contributor to interphase mass transfer. For miscible flow, the fracture/matrix mass transfer is less complicated because there are no capillary forces associated with solvent and oil; nevertheless, gravity contrast between solvent in the fracture and oil in the matrix creates convective mass transfer and drainage of oil. Using the transfer functions presented in this paper, fractureand matrix-flow calculations can be decoupled and solved sequentially-reducing the complexity of the computation. Furthermore, the transfer-function equations can be used independently to calculate oil recovery from a matrix block. *Now with Marathon Oil Corporation.

fax 01-972-952-9435. AbstractAccurate calculation of multi-phase fluid transfer between the fracture and matrix in naturally fractured reservoirs is a crucial issue. In this paper, we will present the viability of the use of simple transfer functions to accurately account for fluid exchange resulting from capillary, gravity and diffusion mass transfer for immiscible flow between fracture and matrix in dual-porosity numerical models. The transfer functions are designed for sugar-cube or match-stick idealizations of matrix blocks.The study relies on numerical experiments involving finegrid simulation of oil recovery from a typical matrix block by water or gas in an adjacent fracture. The fine-grid results for water-oil and gas-oil systems were compared with results obtained with transfer functions. Both in water and gas injection, the simulations emphasize the interaction of capillary and gravity forces to produce oil depending on the wettability of the matrix.In gas injection, the thermodynamic phase-equilibrium, aided by gravity-capillary interaction and to a lesser extent by molecular diffusion, is a major contributor to interphase mass transfer. For miscible flow the fracture-matrix mass transfer is less complicated because there is no capillary forces associated with solvent and oil; nevertheless, gravity contrast between solvent in the fracture and oil in the matrix creates convective mass transfer and drainage of oil.Using the transfer functions presented in this paper, fracture and matrix flow calculations can be decoupled and solved sequentially-reducing the complexity of the computation. Furthermore, the transfer function equations can be used independently to calculate oil recovery from a matrix block. x k p D J J y k p D J J w k p D J J q z v t p D x k J J p D y k J J p D w k J J