During hydraulic fracturing process, different hydraulic loading and stress status of formations result in hydraulic fractures with various geometries and properties. Several propagation models including PKN and KGD have been widely applied in fracturing design and implementation. However, in the process of post-stimulation modeling, fractures are usually simplified with uniform geometries and conductivity distribution; therefore the effects of actual fracture geometry and proppant properties on the well transient pressure and production performance remain unclear. This study intends to comprehensively study the fractured wells with 2-D and 3-D non-uniform geometry and conductivity distribution.

In the development of shale gas reservoirs and tight oil formations, horizontal well multistage fracturing is the key technology. The modeling results presented in this paper can help offer valuable information of reservoir properties, evaluate the conductivity distribution of propped fractures, simulate more realistic fracture configurations, and help optimize fracture treatment process and fractured wells’ performances with improved accuracy.

A semi-analytical approach coupling fluid flow in reservoir and fractures existed in more realistic shape with non-uniform conductivity distribution has been developed to obtain well transient pressure and production responses. Source and sink function method is utilized to solve unsteady state flow problems of fluid flowing from reservoir to non-uniform fractures with geometries that are well defined in PKN, KGD and other generally ideal models. The effect of fracture conductivity with linear and stepwise distribution, and elliptic fracture shape variations has been investigated. Comparison study has been highlighted to illustrate effects of fracture geometry and conductivity distributions. Realistic hydraulic fractured wells with non-uniform fracture geometry and conductivity have been studied to showcase a consistent workflow of entering fracture properties from hydraulic fracturing models and outputting fractured well performance prediction in post-stimulation reservoirs.

Instead of assuming pseudo-steady state flow status between reservoir and fracture, unsteady state flow problems related to non-uniform fracture geometric have been solved in a semi-analytical manner with solution of near analytical accuracy. More realistic fracture geometries estimated from fracture propagation models can be entered into post-stimulation models without idealized simplification; thus the gap between fracture propagation and post-stimulation modeling has been fulfilled.

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