Coarse Scale Simulation in Tight Gas Reservoirs

Abstract It is common for field models of tight gas reservoirs to include several wells with hydraulic fractures. These hydraulic fractures can be very long, extending for more than a thousand feet. A hydraulic fracture width is usually no more than about 0.02 ft. The combination of the above factors leads to the conclusion that there is a need to model hydraulic fractures in coarse grid blocks for these field models since it may be impractical to simulate these models using fine grids. In this paper, a method was developed to simulate a reservoir model with a single hydraulic fracture that passes through several coarse gridblocks. This method was tested and a numerical error was quantified that occurs at early time due to the use of coarse grid blocks. Introduction A single hydraulic fracture is conventionally modeled for research purposes using fine grids. In actual field models of tight gas reservoirs, there can be several wells with hydraulic fractures. These hydraulic fractures are usually very long. They can extend in length to be more than a thousand feet. These long hydraulic fractures extend for several gridblocks in a simulation model (Fig. 1). Therefore, it is very difficult to use fine grids to simulate these actual field models. Many authors1,2 suggested the replacement of the hydraulic fracture by an effective wellbore radius but this technique is only valid when the hydraulic fracture does not extend beyond the boundaries of one gridblock. There were also attempts by some authors3–5 to modify transmissiblities of the gridblocks, which contain hydraulic fractures however these attempts were done for hydraulically fractured horizontal wells. In addition, these attempts had several rules of thumb that had no basic theory behind them. In this paper, ways are showed to model hydraulic fractures in coarse gridblocks. Pseudo-permeability values were used to account for the hydraulic fracture passing through the coarse gridblock. An alternative way that was also shown in this chapter was to modify the transmissibilities of the gridblocks that contain the hydraulic fracture. WELL MODELS In radial flow, the calculated pressures in gridblocks containing wells pwb must be corrected to formation face pressure pwf. This correction is done using Peaceman's1 equation. Peaceman's6,7 equations are programmed into any conventional reservoir simulator for the case of radial flow. Elahmady8 repeated the same numerical experiments reported by Peaceman1 for the case of linear flow and reached a result that pwf=pwb for the case of linear flow. MODELING HYDRAULIC FRACTURES IN COARSE BLOCKS USING PSEUDOPERMEABILITIES Our objective in this section was to show how to model a single hydraulic fracture that passes through coarse gridblocks as shown in Fig. 2. The formulas shown below in Eq. 1 and Eq. 3 were derived by Elahmady8 for the pseudo-permeability in the x-direction (direction along the fracture) and in the y-direction (direction perpendicular to the fracture) respectively for the coarse gridblocks that have hydraulic fractures passing through them. Equation (1) (Available in full paper)

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