**An Analytical Model for Production Analysis of Hydraulically Fractured Shale Gas Reservoirs Considering Irregular Stimulated Regions**

#### **Kaixuan Qiu 1 and Heng Li 2,3,4,\***


Received: 23 September 2020; Accepted: 6 November 2020; Published: 12 November 2020

**Abstract:** Shale gas reservoirs are typically developed by multistage, propped hydraulic fractures. The induced fractures have a complex geometry and can be represented by a high permeability region near each fracture, also called stimulated region. In this paper, a new integrative analytical solution coupled with gas adsorption, non-Darcy flow effect is derived for shale gas reservoirs. The modified pseudo-pressure and pseudo-time are defined to linearize the nonlinear partial differential equations (PDEs) and thus the governing PDEs are transformed into ordinary differential equations (ODEs) by integration, instead of the Laplace transform. The rate vs. pseudo-time solution in real-time space can be obtained, instead of using the numerical inversion for Laplace transform. The analytical model is validated by comparison with the numerical model. According to the fitting results, the calculation accuracy of analytic solution is almost 99%. Besides the computational convenience, another advantage of the model is that it has been validated to be feasible to estimate the pore volume of hydraulic region, stimulated region, and matrix region, and even the shape of regions is irregular and asymmetrical for multifractured horizontal wells. The relative error between calculated volume and given volume is less than 10%, which meets the engineering requirements. The model is finally applied to field production data for history matching and forecasting.

**Keywords:** shale gas; multifractured horizontal wells; production analysis; irregular stimulated region
