Analytical Production Modeling for Hydraulically Fractured Gas Reservoirs

: This article presents a complete analytical method to efficiently generate gas production profiles from hydraulically fractured reservoirs. Equations for production rates are first developed incorporating fracture parameters in the diffusivity-based drawdown solutions for transient as well as pseudo steady-state flow conditions. Some important considerations for modeling the key propped-fracture parameter—dimensionless fracture conductivity—are detailed for realistic production prediction. A time-step algorithm is then discussed to apply the rate equations to generate production profiles over a period of time. Analytical equations are presented to update declining reservoir pressure and resulting rock and gas properties in every time-step as functions of cumulative gas productions. Finally, a simple new equation is developed through a series of parametric applications of the two rate equations, to determine the time to switch from the transient rate equation to the pseudo steady-state equation, particularly in low-permeability reservoirs. To establish confidence in the predictability of the model, results are verified by a numerical reservoir simulator. Thus, the model is a high potential for efficient repetitive computation in early-stage design optimization of hydraulic fracture treatments for gas reservoirs.