Pressure transient behavior of fractured wells in multilayered tight gas reservoirs with heterogeneous properties and limited fracture height

Hydraulic fracturing and commingle production of multiple layers are extensively adopted in unconventional tight gas reservoirs. Accurate determination of parameters of individual layers in multilayered tight gas reservoirs is essential for well performance evaluation and development strategy optimization. However, most analytical models for fractured vertical wells in stratified gas reservoirs focus on fully penetrated hydraulic fractures, neglecting the influence of partial penetration of hydraulic fractures. This paper presents a semi-analytical model to investigate the transient pressure behavior of vertically fractured wells in dual porosity multi-layered tight gas reservoirs. The partial penetration of hydraulic fracture, the vertical heterogeneities of layer properties, the differences between hydraulic fracture lengths in each layer and the stress sensitivity are all incorporated in the proposed model. The point-source solution, Laplace transformation, Fourier transformation, Pedrosa's transformation, perturbation technique, and the superposition principle are applied to obtain the analytical solution of transient pressure responses. The proposed model is validated against a commercial software, and the transient pressure behavior of vertically fractured wells in multi-layered tight gas reservoirs are analyzed. Based on the characteristics of the type curves, seven flow regimes can be identified, including wellbore storage, transitional flow period, reservoir linear flow period, vertical pseudo-radial flow in fracture system, inter-porosity flow period, late-time pseudo-radial flow period, and the boundary-dominated flow period. Sensitivity analyses reveal that the penetration ratio of hydraulic fracture has primary influence on early-time transient pressure behavior and production contribution, while the stress sensitivity mainly affects the late-time transient pressure behavior. Gas production at the initial stage is mainly contributed by the high-pressure/high-permeability layer, and gas backflow will occur during initial production stage for obviously unequal initial formation pressures. Finally, two field cases are conducted to illustrate the applicability of the proposed model. The model and corresponding conclusions can provide technical support for performance analysis of tight gas reservoirs.