Many hydraulically fractured shale gas horizontal wells in the shale gas reservoirs have been observed to exhibit transient linear behavior. This transient linear behavior is characterized by a one-half slope on a log-log plot of rate against time. This transient linear flow regime is believed to be caused by transient drainage of low permeability matrix blocks into adjoining fractures. This transient flow regime is the only flow regime available for analysis in many wells.
In this paper, a linear dual porosity model is used to approximate the shale gas completions with a horizontal well and multiple hydraulic fractures. Five flow regions are identified with this model. It seems that field production data exhibit Region 4 behavior which is primarily transient drainage from the matrix.
However, a skin effect for Region 4 is observed in many wells. This modifies the shape of the log-log rate plot and the square root of time plot. A new analytical equation is presented to model the effect of skin on linear flow behavior. The resulting curve shapes are somewhat surprising and tend to explain the early curve shapes of actual wells. A procedure is presented in this paper to analyze field data.
Shale gas reservoirs constitute a major source of the gas production in the United States. The Gas Technology Institute estimates that organic shale reservoirs in the United States contain up to 780 tcf of gas.1 In shales, natural fractures provide permeability and the matrix provides storage of most of the gas. Shale matrix permeabilities can be as low as 10−9 md.2
Shale reservoirs have been described by the dual porosity model comprising matrix blocks (storage of fluid) separated by fractures (permeability) first proposed by Warren and Root.3 Warren and Root3 presented well test analysis methods/interpretation for slightly compressible fluids. Traditional well test analysis methods were extended to shale gas reservoirs as demonstrated in the work by Kucuk and Sawyer4 who presented a transient matrix-fracture transfer model incorporating gas pseudopressure definitions.
Subsequently, methods of analyzing production data were investigated by different authors. Carlson and Mercer5 coupled Fick's law for diffusion within the matrix and desorption in their transient radial reservoir model for shale gas. Modifications include use of the pressure-squared forms valid for gas at low pressures to modify the diffusivity equation. They provide a Laplace space equation for the gas cumulative production from their model and use it to history match a sample well. They also show that semi-infinite behavior (portions of the matrix remain at initial pressure and is unaffected by production from the fractures) occurs in shale gas reservoirs regardless of matrix geometry.
Gatens et al.6 analyzed production data from about 898 Devonian shale wells in four areas. They present three methods of analyzing production data – type curves, analytical model (slab matrix model presented by Serra et al.7) and empirical equations. The analytical model is used along with an automatic history matching algorithm and a model selection procedure to determine statistically the best fit with actual data.
