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SPE Members Abstract Published imbibition experiments of an advancing fracture water level surrounding a single matrix block are simulated using a fine grid single porosity model and various double porosity models. The fine grid simulations show that a stationary water saturation profile quickly develops and advances in the matrix at the same rate as the fracture water level. A new double porosity transfer function for imbibition dominated matrix/fracture fluid exchange is presented based on stationary profile solutions of the fractional flow equation. This transfer function models the imbibition recovery for these advancing water level experiments better than the conventional double porosity imbibition formulations. It is shown that the stationary profile transfer function is best suited to systems where the time to develop the stationary profile is short relative to the length of the waterflood. The experimental data was also simulated using a diffusion equation with a nonlinear diffusion coefficient in combination with a moving boundary condition as the imbibition model. A constant diffusion coefficient based upon water relative permeability and capillary pressure gradient values at 1 - Sor matched the experimental results as well as the nonlinear diffusion coefficient, but required much less computer time. From analyzing two different diffusion type equations as imbibition models, we show that countercurrent imbibition is not a likely recovery mechanism for this type of advancing water level imbibition experiment. Introduction Naturally fractured reservoirs present one of the most difficult problems in reservoir simulation. The fracture network may be spatially difficult to define while the transfer of fluids from the matrix blocks to the fracture network may be qualitatively described by many different physical mechanisms. This paper will discuss the exchange of fluids via capillary imbibition in a matrix domain of regular, dispersed parallelepipeds within a continuous fracture domain. We will present fine grid simulation of the experimental work of Kleppe and Morsel and present a transfer function that models their single block waterflood better than existing double porosity formulations. The double porosity approach formulated by Barenblatt et al. for single phase flow considered the naturally fractured reservoir to be composed of two superimposed continua, a continuous fracture system and a discontinuous system of matrix blocks. The fracture system has a low storativity and high conductivity while the majority of the oil resides in a matrix block system of low conductivity. The transfer of fluids between these two systems, as described by Barenblatt, assumes pseudosteady-state flow between the matrix blocks and the fracture system. The matrix/fracture transfer function can then be expressed as Darcy's Law with an appropriate geometrical factor that describes the characteristic length and flow area between the matrix blocks and the fracture system. Warren and Root" presented an analytical solution for single-phase, unsteady-state, radial flow in a naturally fractured reservoir and introduced the dual porosity concept to petroleum engineering. They also derived a formula for the shape factor for parallelepiped matrix blocks within an orthonormal fracture system of one, two or three dimensions. The formulation of Warren and Root was extended to a multiphase system by Kazemi et al., who numerically solved for flow in three dimensions. As with the Barenblatt formulation, Kazemi's transfer function assumes pseudosteady-state flow based on potential differences between the matrix node center and the fracture node center within a gridblock. In a later paper Kazemi and Merrill used their simulator to model water imbibition into artificially fractured cores. Most of their simulations involved gridding the matrix block into more than one computational unit, thereby improving the model's performance through enhanced matrix block definition. With a single matrix block per grid block, they presented simulations at two different water injection rates for cores initially saturated with 100 percent diesel oil and for cores with n-decane replacing diesel oil. P. 509^ |
