Pressure and rate transient analysis of composite shale gas reservoirs considering multiple mechanisms

Based on multiple mechanisms, including adsorption/desorption, viscous flow, diffusive flow in shale matrix and stress sensitivity of natural fractures, a new semi-analytical composite model is presented for multi-stage fractured horizontal well (MFHW) in shale gas reservoirs. The simplified composite model of an actual gas reservoir is composed of an inner and an outer region. Inner region represents stimulated reservoir volume (SRV) and contains natural fractures and matrix. Matrix-natural fracture transfer flow is assumed to be pseudo-steady state (PSS) or transient state (TS) which are described by the Warren & Root and the De Swan models respectively. Outer region is un-stimulated reservoir volume (USRV), which is described by single porosity medium model. First, transient flow model for continuous line source in composite shale gas reservoir is established. Perturbation method is applied to linearize the model. Then the line source solution is solved by Laplace transformation. Pressure responses of multi-stage fractured horizontal well is obtained using principle of superposition. The model is verified with the available field data from the Barnett Shale. In addition, transient pressure and production rate of MFHW in shale gas reservoirs with consideration of multiple mechanisms and SRV are analyzed and five typical regimes are identified: radial flow in SRV, interporosity flow, region pseudo-steady flow, diffusive flow and late pseudo-radial flow. In PSS transfer model, type curve has two cavities: the early one is caused by pseudo-steady interporosity flow between natural fractures and matrix and the late one is caused by diffusive flow in the matrix. But in TS transfer model, there is no obvious cavity in interporosity flow period due to subtle pressure fluctuation. The effects of relevant parameters on transient pressure and production rate are analyzed, including SRV radius, stress sensitivity coefficient, adsorption index, storability ratio, interporosity coefficient and diffusivity coefficient. The results demonstrate that larger SRV can reduce formation energy depletion and improve production rate. Stress sensitivity causes more pressure depletion, while desorption and diffusion can compensate for the pressure loss in the formation. The production rate increases as adsorption index σ rises. Storability ratio of natural fractures ωf and interporosity coefficient λ1 mainly affect interporosity flow period while storability ratio of matrix ωm and diffusivity coefficient λ2 mainly have effects on diffusive flow period. The larger the value of these four parameters, the larger the production rate in corresponding periods.