Accurate representation of static fractures (i.e., fractures created by hydraulic fracturing treatments) is of importance in full field reservoir modeling, as well as in single well analysis. The common practice of using the skin factors is very approximate, and with the trend to finer-gridded models, it is often necessary to represent fractures which are not contained is a single block. This work formulates and compares different methods of representing a hydraulic fracture in a single-phase and multi-phase reservoir simulator, assuming that the fracture will extend over several grid blocks from the well. For singlephase flow, the methods based on the transmissibility modification (Settari et al., SPE PE, February 1990), and on the superposition of analytical fracture (Nghiem et al., SPEJ, 1983) both model accurately the fracture. However, in multiphase flow the method of Nghiem et al. produces less realistic saturation distribution for the case of fractured water injector. The methods were tested for conditions typical forinjection wells as well as for drawdown-buildup situations. The paper also addresses the issues of implementation of the algorithms in commercial simulators and the capability of extension to more complex physics such as turbulence in the fracture and geomechanical effects, and dynamic (propagating) fractures. In conclusion the method based on transmissibility modification appears to be the most accurate, flexible, and it is recommended for implementation in simulators.


Hydraulic fracturing, as one of important stimulation methods to increase well productivity or injectivity, has been applied widely for gas and oil wells and reservoirs. Producing or injecting performance of hydraulically fractured well is important not only in fracture design, evaluation, and single well analysis, but also in full field reservoir modeling. Usually a few analytical and numerical methods are available to study the effect of fracture on well performance.

The classical analytical methods for single well analysis are to represent the effect of fracture as the ratio of productivity index after and before fracturing. Prats1 first developed a simple equation to calculate the steady-state productivity-index ratio of a fractured well in a cylindrical drainage area, based on assumptions such as incompressible fluid flow, infinite fracture conductivity, and propped fracture height equal to formation height. Prats1 treated hydraulic fracture as enlarging well radius, the effective well radius equal to half of the half-length of the infinite-conductivity fracture.

Tinsley et al. 2 used electrolytic model studies to generate Productivity-Index Ratio in graphical form. The figures are based on assumptions including steady-state flow, cylindrical reservoir geometry, and incompressible fluid.

McGuire and Sikora3 also developed a chart for estimating productivity-index ratio, based on assumptions including pseudo steady-state flow, square drainage area, compressible fluid flow, and a fracture propped throughout the entire productive interval. Tannich and Nierode4 developed a method similar to the McGuire-Sikora charts for gas wells.

Gringarten and Ramey5 developed an analytical method to analyze the effect of fracture on transient pressure distribution in well test. Their analytical solution is applicable for infinite conductivity vertical fractures. And Cinco-Ley and Samaniego6 developed an analytical method to study the transient pressure behavior for a well with a finite conductivity vertical fracture

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