A new analytical model for non-uniformly distributed multi-fractured system in shale gas reservoirs

• We propose a new analytical model for multiple fractured horizontal wells in shale gas reservoirs which can be applied to interpret more complex cases in the well test interpretation.
• Adsorption, desorption, and viscous flow were considered in the new model.
• More practical physical conditions (different models in SRV region, non-uniform distribution of fractures and stimulated or un-stimulated region, and distinct respective properties in each region) were introduced in the new model.
• The effect of relevant parameters on pressure transients was modeled and analyzed.

Recently, many kinds of linear flow models, such as tri-linear flow model and five-region model, have been introduced to simulate the flow in shale gas reservoirs with multiple fractured horizontal wells (MFHWs) due to their conciseness and effectiveness. However, most of the existing linear flow models are based on many ideal assumptions that may not always be true in practice. Based on the five-region model, this paper establishes a new analytical model (enhanced five-region model) of MFHWs in shale gas reservoirs considering desorption, different models in stimulated reservoir volume (SRV) region, non-uniform distribution of fractures and stimulated or un-stimulated region, and distinct respective properties in each region. Laplace transformation and Duhamel's theorem are employed to solve this new model. The pseudo-pressure transient responses are inverted into time space using Stehfest algorithm. Type curves of pressure transients are plotted. The main flow regimes for two situations (homogenous and dual-porosity) in SRV region are identified. The sensitivity analysis in terms of the size of SRV region, property of SRV region, fracture number, fracture intervals, dimensionless fracture conductivity coefficient, inter-porosity flow coefficient, storativity ratio and adsorption coefficient on type curves are presented. Type curves calculated by the simplified present model and existing models match well. This also indicates the validity of the proposed new model. Compared with the existing linear flow models, more factors (different relevant parameters in non-uniformly or uniformly distributed multi-fractured systems) are considered in the new model. So the new model can be applied to interpret more complex cases.