Coarse Scale Simulation in Tight Gas Reservoirs
Authors: Elahmady M. , Wattenbarger R.A. 
Published: March 2010

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 modelled for research purposes using fine grids. In actual field models of tight gas reservoirs, there are several wells with hydraulic fractures (see Figure 1). These hydraulic fractures are usually very long. They can extend in length to more than a thousand feet. These long hydraulic fractures extend for several gridblocks in a simulation model (Figure 1). Therefore, it is very difficult to use fine grids to simulate these actual field models. Some authors(1, 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 another group of authors(3–5) to modify transmissibility multipliers of the gridblocks, which contain hydraulic fractures. However, these attempts were done for hydraulically fractured horizontal wells. In addition, these attempts were based on empirical rules that had no basic theory behind them.
In this paper, the means to model hydraulic fractures in coarse gridblocks are demonstrated. Pseudo-permeability values were used to account for the hydraulic fracture passing through the coarse gridblock. Several simulated cases were shown in this paper and compared to rigorous analytical solutions to prove the validity of the method proposed. An alternative way to model hydraulic fractures in coarse gridblocks (also based on theory), developed by Elahmady(6) but not discussed in this paper, was to modify the transmissibility multipliers of the gridblocks that contain the hydraulic fracture. Elahmady(6) cautioned that there are different ways to use transmissibility multipliers depending on the kind of simulator that is used.
The authors would like to note that during the course of their study they were aware of the work by Peaceman(7, 8) where the calculated pressures in gridblocks containing wells, pwb must be corrected to formation face pressure, pwf. Peaceman's(7) equation is programmed into any conventional reservoir simulator for the case of radial flow. Elahmady(6) repeated Peaceman's(7) numerical experiments, but for linear flow (which is the focus of this paper) instead of radial flow, and reached a conclusion that pwf = pwb for the case of linear flow.