Modeling and Analysis of Reservoir Response to Stimulation by Water Injection
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The distributions of pore pressure and stresses around a fracture are of interest in conventional hydraulic fracturing operations, fracturing during water-flooding of petroleum reservoirs, shale gas, and injection/extraction operations in a geothermal reservoir. During the operations, the pore pressure will increase with fluid injection into the fracture and leak off to surround the formation. The pore pressure increase will induce the stress variations around the fracture surface. This can cause the slip of weakness planes in the formation and cause the variation of the permeability in the reservoir. Therefore, the investigation on the pore pressure and stress variations around a hydraulic fracture in petroleum and geothermal reservoirs has practical applications. The stress and pore pressure fields around a fracture are affected by: poroelastic, thermoelastic phenomena as well as by fracture opening under the combined action of applied pressure and in-situ stress. In our study, we built up two models. One is a model (WFPSD model) of water-flood induced fracturing from a single well in an infinite reservoir. WFPSD model calculates the length of a water flood fracture and the extent of the cooled and flooded zones. The second model (FracJStim model) calculates the stress and pore pressure distribution around a fracture of a given length under the action of applied internal pressure and in-situ stresses as well as their variation due to cooling and pore pressure changes. In our FracJStim model, the Structural Permeability Diagram is used to estimate the required additional pore pressure to reactivate the joints in the rock formations of the reservoir. By estimating the failed reservoir volume and comparing with the actual stimulated reservoir volume, the enhanced reservoir permeability in the stimulated zone can be estimated. In our research, the traditional two dimensional hydraulic fracturing propagation models are reviewed, the propagation and recession of a poroelastic PKN hydraulic fracturing model are studied, and the pore pressure and stress distributions around a hydraulically induced fracture are calculated and plotted at a specific time. The pore pressure and stress distributions are used to estimate the failure potentials of the joints in rock formations around the hydraulic fracture. The joint slips and rock failure result in permeability change which can be calculated under certain conditions. As a case study and verification step, the failure of rock mass around a hydraulic fracture for the stimulation of Barnett Shale is considered. With the simulations using our models, the pore pressure and poro-induced stresses around a hydraulic fracture are elliptically distributed near the fracture. From the case study on Barnett Shale, the required additional pore pressure is about 0.06 psi/ft. With the given treatment pressure, the enhanced permeability after the stimulation of hydraulic fracture is calculated and plotted. And the results can be verified by previous work by Palmer, Moschovidis and Cameron in 2007.