Improved Decline Curve Analysis Equations – Integration of Reservoir Properties into Arps Equation
Authors: Keshinro Olalekan , Aladeitan Yetunde , Oni Olugbenga , Samuel Jemimah-Sandra , Adagogo Jaja 
Published: October 2018

Abstract
Arps in 1944 developed decline curve equations for analyzing reservoir/well production decline and the estimated decline rate constant is used for production forecast. In making reservoir production forecast, the Arps equations are usually calibrated to match the reservoir historical production decline by adjusting the decline rate constant value. The decline rate constant indirectly influences the reservoir properties responsible for production decline. However, the value assigned to the decline rate constant might either overestimate or underestimate the uncertainties in the reservoir rock and fluid properties responsible for reservoir production decline. The decline rate constant in the Arps equation has no equation relating it to the reservoir properties that are responsible for the reservoir production decline hence; the direction of uncertainty quantification on these reservoir parameters is not explicit, therefore undermining the predictive power of the Arps equations. The impact of reservoir properties uncertainties on the production rate decline and forecast by Arps equations cannot be examined due to the empirical nature of the Arps equations. Also, the decline rate constant is not explicitly related to reservoir rock and fluid properties responsible for production decline. However, the predictive power of the Arps model can be greatly improved if the decline constant can be expressed as a function of the reservoir rock and fluid properties responsible for production decline. Hence, the impact of uncertainty on the production forecast by Arps models can be examined. The objective of this work is to introduce reservoir rock and fluid properties into the Arps decline curve equations. This will enable the imposition of reservoir physics on the decline curve equations and the impact of uncertainties in these properties on matching historical production decline and forecast. In addition, a relationship between the decline rate constant in the Arps equations and the reservoir rock and fluid properties that influence reservoir production decline has been developed. A mechanistic approach using dimensional analysis was used to develop the relationship. The decline rate was assumed to be proportional to the various reservoir rock and fluid parameters, such as permeability, porosity, net-to-gross, drainage area, fluid density, and viscosity, that could influence production decline and by unit dimensional analysis, a relationship was developed between the decline constant and these reservoir rock and fluid properties. The decline rate constant was directly related to the product of reservoir permeability, fluid density, and the square of the pressure difference but inversely proportional to the cubic power of fluid viscosity. The relationship developed for the decline constant in this work will give the modified Arps model strong predictive power and allows for the impact of uncertainties on the production forecast to be evaluated. The results obtained from the modified Arps equations give better reservoir properties dependent outcomes than the traditional Arps equations and enable analysis of the effects of reservoir rock and fluid properties uncertainties on the production decline and forecast.