A large proportion of gas and oil resources are trapped in carbonate reservoirs. Efficient development of these formations is crucial for world energy supply. Recently, a novel hybrid volume stimulation (HVS) technique has been proposed and enhanced carbonate reservoir production in the Bohai Bay Basin and the Ordos Basin of China (Cai et al., 2015; Chu, 2017). This technique involves three stages, including pad-fluid fracturing (primary fracture and fracture branch initiation), massive acid fracturing (acid etching and connection of natural and induced fractures), and proppant injection (conductivity maintenance). Compared with conventional acid fracturing, HVS generates a more complex fracture system by taking the advantage of both hydraulic fracturing and acid fracturing, mitigating high-temperature effects, and increasing the acid penetration distance. Currently, no existing models can predict the pressure and rate behavior of wells after HVS treatments due to the complex fracture geometry and the complicated flow pattern.

This study presents a multi-region linear flow model to facilitate evaluating well performance of carbonate reservoirs after HVS and obtaining a better understanding of key factors that control well responses. The model incorporates the fundamental characteristics of the complex fracture system generated by HVS. The primary hydraulic fracture is characterized by two flow regions. One is for the propped primary fracture segment (region 1), while the other represents the unpropped but acid-etched primary fracture tip (region 2). The region adjacent to the primary fracture (region 3) denotes acid-etched fracture branches. Because the acid usually cannot fully penetrate the hydraulic-fracturing-induced branches, the fractal theory is employed to depict the properties of the small fracture branches beyond the acid-etched sections. Finally, the unstimulated reservoir is described by a dual-porosity region (region 4) with vug and matrix systems. Specifically, triple-porosity region 3 contains two possible flow scenarios: one is from vugs to matrices, to fracture branches, and to the primary fracture, while the other is from vugs to matrices, and to the primary fracture. Two weighting factors are utilized to describe the proportion of reservoir volume that is involved in the two fluid flow scenarios. These flow regions are coupled through flux and pressure continuity conditions.

The degenerated form of this model is verified against a published analytical model. A good agreement has been achieved between the results of the two models. Analysis results show that four flow regimes can be identified in the log-log type curve. Compared with classical type curves of fractured wells, there is a distinctive fracture-branch-affected transient regime in the pressure derivative curve with a slope between one-half and unity. The HVS generated complex fracture system enhances well productivity from the inter-porosity flow regime to the late fracture-branch-affected transient regime. The impacts of various fracture and reservoir properties on pressure and rate behavior are also documented.

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