Determination of Arps' Decline Exponent From Gas Reservoir Properties, and the Efficacy of Arps' Equation in Forecasting Single-Layer, Single-Phase Gas Well Decline

Abstract

Abstract This paper presents conclusions as to the ability of Arps’ rate-time decline equation1 to predict boundary dominated gas well rate decline. A correlation of Arps equation parameters, to initial and boundary reservoir conditions, is also presented, enabling the equation to be used to forecast gas well production rates, prior to first production. The conclusions are derived from a numerical study, consisting of 39 radial flow simulations. The simulations predicted rate declines, against constant bottomhole well pressures, in a single-layer, single-phase, bounded, volumetric gas reservoir model. The 39 simulations include initial reservoir pressures ranging from 1000 to 10000 psia, flowing bottomhole well pressures from 100 to 7500 psia, and gas gravity from 0.56 to 0.8. The approach is semi-analytical in that the non-linear differential equation that describes the process, is linearized with a function that approximates the change in viscosity-compressibility product in dimensionless time. The function is integrable and thereby directly yields a closed form solution, of which the Arps equation is a particular case. The coefficients of the function, which are the Arps parameters, as well as coefficients in a generalized form of Arps’ equation, were optimized to generate rate declines that matched those from the simulation models. Correlation to reservoir and well conditions was then constructed. It is concluded that Arps’ equation adequately predicts constant pressure, gas well rate decline, over the entire range of conditions enumerated above. It was also found that Arps’ decline exponent is correlated to reservoir, well, and gas properties. The correlation is aided by Carter's Drawdown Parameter,2 and under certain conditions, the Arps decline exponent is a simple linear function of Carter's Drawdown Parameter. A determination of the decline exponent from initial reservoir and well conditions, allows the field engineer to forecast depletion (boundary dominated) gas well decline rates, for wells producing against constant bottomhole pressure, without historical decline. The closed form equation precludes the need for reservoir simulation, or specialized commercial software. The procedure for gas well forecasting using these results is demonstrated.