Multi-fractured (multi-frac) horizontal wells have emerged as an advanced mean for enhancing well productivity in low permeability reservoirs, being used to advance the development of shale oil and shale gas reservoirs. Fluid transport in the fracture domain is dominated by the fracture effect. In the non-fracture domain mainly representing the area of fluid flow from reservoir boundary to the fracture domain, there exists a threshold pressure gradient. The fluid in low permeability porous media is not able to flow until the reservoir pressure gradient is greater than a minimum value. Due to the complexity of reservoir simulations for multi-frac horizontal wells in low permeability shale reservoirs, a reliable mechanistic model is needed for production engineers. The analytical solution to well performance in multi-frac horizontal wells has been studied by different researchers. None of the models considered the effect of multiple phase fluid flow. These models were further weakened by using the constant fluid properties.

This paper presents a rigorous model used to predict multi-frac horizontal well performance for low permeability reservoirs, under the effects of reservoir threshold pressure gradient and non-constant fluid properties while also considering the impact of multiphase flow through non-fracture and fracture domains. The effect of pressure dependent reservoir properties was often overlooked in multi-frac horizontal well models. In general, the significant pressure difference across the reservoir boundary and at the wellbore results in the changes of fluid viscosity, and density. The existing single phase and constant fluid property models overestimate production rates, while that predicted by the new, multi-phase model better matches the field production rate.

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