In this paper, we develop a simple, closed form approximation for the Laplace transform solution for the case of a well with a finite conductivity vertical fracture in an infinite-acting reservoir. Our hybrid solution is based on a coupling of the solution for a bilinear finite conductivity vertical fracture model (which does not model radial flow) and the solution for a uniform flux/infinite conductivity vertical fracture (which does model pseudoradial flow). These solutions are readily obtained from the literature.
Overall, we consider our solution to be valid for CfD≥0.5 and we show that our solution gives less than 1 percent error in both pD and p D’ for CfD>2. We suggest that our hybrid solution is not valid for CfD<0.5 and do not recommend its use for CfD<0.5 under any circumstances.
We have verified this solution against four different solutions given in the literature. Each comparison was excellent which suggests that our simplified solution is more than adequate for practical applications. In particular, we provide verification for constant rate and constant pressure production for values of CfD between 0.25 and 10,000. We also show that our solution is capable of producing very accurate derivative functions.
In addition, by reproducing the literature solutions so well, we also verified that individual flow regimes (formation/fracture bilinear flow, formation linear flow, and pseudoradial flow) are all modeled accurately by our new solution.