Field Scale Permeability Estimation Based on Microseismic Monitoring
Zhang, Xin 1987-
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The 3-dimension diffusion equation which describes fluid flow during hydraulic fracturing is interpreted in a statistical way. For all diffusing particles in a pumping procedure, the root-mean-square average of diffusing distance, which evaluates the fluctuation of diffusing particles as time evolves, is proportional to the square root of the product of diffusivity and elapsed time. The diffusivity is obtained from the spatial-temporal distribution of located microseismic events as a function of the distance between these events and pumping points, as well as elapsed time from injection inception. The upper-limit diffusivity of the original formation is characterized by the curve which fits the outermost located events on a distance-time plot. Similarly, diffusivity of the formation after hydraulic fracturing is obtained by curve fitting innermost located events induced by fluid flow back after injection stops. The theoretical expression between the diffusivity tensor and permeability tensor is obtained based on an isothermal condition and assumed incompressible slurry. The diffusivity tensor is found to be equal to the permeability tensor divided by a scalar which is the product of dynamic viscosity, connected formation porosity, and formation compressibility. Application of these equations to microseismic data acquired in the Barnett Shale Formation yields, with assumed hydraulic fracture geometry, initial permeability of 0.16 to 3.21 milliDarcy in the assumed dominant direction of fracturing and normal to it, with an increase to 12.1 milliDarcy along the dominant direction of fracturing after hydraulic fracturing. Numerical simulation results of fluid flow in synthetic media demonstrate: (1) If the flow domain size is not much larger than the part influenced by the entrance effect, the variables in Darcy’s law are inter-dependent. If so, the obtained permeability, no matter by experiment or simulation, cannot be upscaled, even under homogeneous condition. (2) The volume or area influenced by the entrance effect inside the flow domain depends on the geometry of the flow domain, fluid properties, and in-situ parameters. The more viscous fluid flow in a lower rate, the smaller volume or area influenced by entrance effect. (3) The flow field is difficult to be fully developed in a periodic domain. The wide throat zones store fluid as reservoirs.