Broad application of hydraulic fracturing techniques in oil industry since the 1950s led to the emergence of a large number of studies devoted to both production forecast methods and reservoir performance evaluation techniques to interpret the results of various well testing procedures. It is remarkable that analytical investigations devoted to the postfracturing analysis are focused primarily on the early-time unsteady flow regime, while for the production forecast it is commonly used the approximation of steady-state or pseudosteady-state flow models. The focus in oil engineering has recently turned towards unconventional reserves. Unsteady-state flow plays crucial role for reservoirs with low-mobility oil by making a major contribution to the cumulative oil production. With the appearance of the available computational techniques, the emphasis has shifted to the numerical simulation of flows, and the search for analytic approximations gone by the wayside.
A number of articles is devoted to discussing the critical issues associated with numerical simulations. Among others, it should be noted that the large-scale grid cannot adequately simulate transient flow regime of the fluids with low mobility owing to the fact that the cell size is much larger than the characteristic scale of the variations of physical parameters, particularly pressure. Changing the sizes of cells, including local refinement, always results in time-consuming model and adversely affect the convergence of the numerical scheme.
The study presents an approach to the analytical modeling of the production rate of the fractured vertical well during the unsteady flow regime. Asymptotic Laplace space solution based on trilinear flow model is developed to describe the flow at early times. The authors propose an asymptotic solution, which describes the flow rate towards vertical fracture under the assumption of an infinite reservoir, using the desuperposition concept to couple the trilinear and pseudoradial flow solutions.
Verification of the proposed model was carried out by comparison with the solution given by the finite-difference hydrodynamic commercial simulator. The model allows for quick and accurate assessment of the hydraulically fractured well production, avoiding errors associated with the convergence of numerical methods at the early times, as well as significantly reducing the time of calculation.References
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