Bootstrapping Nonlinear Regression Applied to Arps Hyperbolic Decline Curve

Geothermal energy is actually the heat that can be extracted from the interior of the earth and considered as an alternative renewable energy. Regression analysis is one of statistical tools that are frequently used in geothermal data analysis. However, nonlinear regression is rarely used in analyzing steam mass flow data due to its tricky computational and inferential problems. A probabilistic method in reserve estimation suggests the use of nonlinear regression and bootstrap method for the estimation of the potential recovery of a geothermal field. A random resampling of stochastic components is used to generate a large number of mass flow data to be used in evaluation of production performance. This resampling scheme, called bootstrap method, does not rely on the assumption of normality. Bootstrap was developed based on one-sample model where a single unknown distribution F produces the data by random sampling. Development of bootstrap method in decline curve analysis involves nonlinear regression of steam mass flow, and bootstrap nonlinear least squares algorithm was developed similar to bootstrapping residual linear regression. Tracer modeling aims to determine the degree of connectivity between injection and production wells, and non-linear regression was developed to estimate the parameter of tracer model. This paper aims to report the development of bootstrap nonlinear least squares regression to hyperbolic decline curve analysis. The main contribution is to show that (a) the simulation of Arps hyperbolic decline curve leads us to consider a modification of Arps equations by introducing a new parameter which represents the randomness adjustment and (b) bootstrap method can be used to estimate the distribution of hyperbolic decline curve parameters.