An approximate analytical model for unconventional reservoir considering variable matrix blocks and simultaneous matrix depletion

In regard to unconventional oil reservoirs, the transient dual-porosity and triple-porosity models have been adopted to describe the fluid flow in the complex fracture network. It has been proven to cause inaccurate production evaluations because of the absence of matrix–macrofracture communication. In addition, most of the existing models are solved analytically based on Laplace transform and numerical inversion. Hence, an approximate analytical solution is derived directly in real-time space considering variable matrix blocks and simultaneous matrix depletion.

To simplify the derivation, the simultaneous matrix depletion is divided into two parts: one part feeding the macrofractures and the other part feeding the microfractures. Then, a series of partial differential equations (PDEs) describing the transient flow and boundary conditions are constructed and solved analytically by integration. Finally, a relationship between oil rate and production time in real-time space is obtained.

The new model is verified against classical analytical models. When the microfracture system and matrix–macrofracture communication is neglected, the result of the new model agrees with those obtained with the dual-porosity and triple-porosity model, respectively. Certainly, the new model also has an excellent agreement with the numerical model. The model is then applied to two actual tight oil wells completed in western Canada sedimentary basin. After identifying the flow regime, the solution suitably matches the field production data, and the model parameters are determined. Through these output parameters, we can accurately forecast the production and even estimate the petrophysical properties.