Hydraulic fracturing has been used extensively over the past fifteen years to stimulate low permeability oil and gas wells. A considerable permeability oil and gas wells. A considerable amount of fractured well performance theory has accumulated during this period. Transient drawdown solutions for vertically fractured liquid wells based on numerical simulation were published in 1964. These solutions established the influence of vertical fractures on transient pressure buildup and drawdown testing. Others have investigated well tests of vertically fractured gas wells using both analytical and numerical models. Recent studies have provided new information for type-curve matching of pressure data obtained from fractured (vertical and horizontal) wells. The objective of this paper is to illustrate the application of numerical simulation in evaluation of fracture stimulation of gas wells. The previously published interpretation methods, such as pressure buildup and drawdown analyses and type-curve pressure buildup and drawdown analyses and type-curve matching, form an extremely important part of the complete analysis. Better and more comprehensive well test interpretation can often be obtained by using the so-called conventional methods and numerical modeling together.
Prats, et.al., originally developed analytical solutions for the performance of vertically fractured reservoirs for the compressible fluid case. They considered both the constant terminal pressure and constant terminal rate cases. In the case of constant rate, however, the early-time pressure transient solutions were not investigated. In 1964, Russell and Truitt published transient pressure solutions for vertically-fractured oil or water wells based on numerical simulation. From their solutions they developed methods of analyzing pressure buildup and drawdown tests with conventional plotting techniques. Clark later applied the Russell-Truitt results in analysis of water-injection well falloff data. Analytical solutions and example applications for vertically fractured wells which produce slightly compressible fluids also were presented by van Everdingen and Meyer.
More recently Gringarten, et.al., have reviewed the work of previous authors and published new solutions especially useful for published new solutions especially useful for type-curve analysis. They illustrated the use of their results (for wells with either vertical or horizontal fractures) in a companion papers.