A generalized analytical model for hydrocarbon production using multi-fractured horizontal well with non-uniform permeability distributions

The multi-fractured horizontal well (MFHW) has significantly facilitated the exploitation of unconventional hydrogen-carbon compound reservoirs, which is an abundant source of fossil hydrogen energy. The composite linear flow models were frequently adopted to analytically evaluate the hydrocarbon production using MFHW. Most of the existing composite linear flow models assume uniform permeability in the primary fractures and the Stimulated Reservoir Volume (SRV) region. However, due to the non-uniform proppant distribution in the primary fractures and the heterogeneity in the density of the secondary fractures in SRV region, the permeability field in both regions are non-uniform. For the first time, a generalized analytical model incorporating continuous permeability heterogeneity in both the primary fractures and SRV region is proposed for the hydrocarbon production of MFHW. Any arbitrary permeability distribution functions can be treated as inputs to the proposed model. The mathematical model is solved using the perturbation technique and the Laplace transform method.The good match with the numerical solution verifies the accuracy of the proposed analytical model. Subsequently, the proposed solution is assigned with different modes of permeability heterogeneity to investigate their impacts on well production performances, i.e., cumulative hydrocarbon production and transient bottom-hole pressure (BHP). The results reveal that the incorporation of permeability heterogeneity will enhance the production rate and lower the BHP drawdown compared to the homogeneous case with the same average permeability. Besides, a field case is presented to demonstrate the applicability of the proposed model.