Gravity Drainage and Oil Reinfiltration Modeling in Naturally Fractured Reservoir Simulation

Abstract

The gravity drainage and oil reinfiltration phenomena that occur in the gas cap zone of naturally fractured reservoirs are studied through single porosity refined grid simulations. A stack of initially oil-saturated matrix blocks in presence of connate water surrounded by gas-saturated fractures is considered; gas is provided at the top of the stack at a constant pressure under gravity-capillary dominated flow conditions. An in-house reservoir simulator, SIMPUMA-FRAC, and two other commercial simulators were used to run the numerical experiments; the three simulators gave basically the same results. Gravity drainage and oil reinfiltration rates, along with average fluid saturations, were computed in the stack of matrix blocks through time. Pseudo functions for oil reinfiltration and gravity drainage were developed and considered in a revised formulation of the dual-porosity flow equations used in fractured reservoir simulation. The modified dual-porosity equations were implemented in SIMPUMA-FRAC,1,18 and solutions were verified, with good results, against those obtained from the equivalent single porosity refined grid simulations. Same simulations, considering gravity drainage and oil reinfiltration phenomena, were attempted to run in the two other commercial simulators, in their dual-porosity mode and using available options. Results obtained were different among them and significantly different from those obtained from SIMPUMA-FRAC. Introduction One of the most important aspects in the numerical simulation of fractured reservoir is the description of the processes that occur during the rock matrix-fracture fluid exchange and the connection with the fractured network. This description was initially done in a simplified manner and therefore incomplete.2,3 Experiments, theoretical and numerical studies 3–6 have allowed to understand there are mechanisms and phenomena such as oil reinfiltritation or oil imbibition and capillary continuity between matrix blocks that were not taken into account with sufficient detail in the original dual porosity formulations to model them properly and that modify significantly the oil production forecast and the ultimate recovery in a naturally fractured reservoir. The main idea of this paper is to study in further detail the oil reinfiltration phenomenon that occur in the gas invaded zone (gas cap zone) in NFR and to evaluate its modeling to implement it in a dual porosity numerical simulator. Considering the reservoir to be a stack of matrix blocks (sugar cubes) according to the Warren and Root 7 conceptual dual porosity model, the oil reinfiltration occurs when the oil confined in the upper blocks is expelled out of matrix blocks thru fractures and it reinfiltrates in the blocks below. This block to block oil flow occurs mainly because of the competition of the capillary and viscous forces. The study was divided in two parts, firstly using a single porosity simulator a fine grid was built in the space occupied by the stack of matrix blocks and fractures allocating the particular characteristics and properties of each medium to the different portions that these systems occupy in the grid. The phenomena that occur during the numerical experiment were studied. The capillary forces act only on the matrix blocks being zero in the fractures and the viscous forces are canceled out through the introduction of a very low gas injection rate through the top face of the stack; a flow process driven by capillary and gravitational forces only is established in this fashion. 8,9 In the fine grid simulation average gas and oil saturations are computed as time goes by for each one of the matrix blocks in the stack. Drainage and reinfiltration rates are computed through each one of the matrix block faces and their dependencies on the matrix block average gas saturations are established. Then the pseudo functions that are required in the modified dual porosity formulation are calculated. Secondly, using the modified dual porosity simulator SIMPUMA-FRAC, a coarse grid is built of the same dimensions of the single porosity fine grid and the gravity drainage is simulated by using the matrix-fracture transfer pseudo functions that had been previously generated. Hence, the modified dual porosity simulator should reproduce the average behavior observed in the fine grid for the stack of blocks in the single porosity model.