Geothermal energy is the heat that can be extracted from the interior of the earth and considered as renewable energy. Energy resources like coal and petroleum are located at specific places. Renewable resources, like
Geothermal, are moving and are approximately site specific.
Regression analysis is one of statistical tools that frequently used in geothermal
data analysis. However,
nonlinear regression is rarely used in analyzing geothermal data. The combination of nonlinear regression and
bootstrap is used in extracting information from geothermal database. A random resampling of stochastic components in stochastic model is used to generate a large number of geothermal data to be used in evaluation of production performance. This resampling scheme, called bootstrap analysis, does not rely on the assumption of normality; i.e. nonparametric. The approach can be used to forecast the probability of specific outcomes such as the traveling time between injector and producer. Bootstrap was developed based on one-sample model where a single unknown distribution F produces the data by random sampling. Applications of bootstrap in decline curve analysis involve complicated data such as time series of steam flow rates. Bootstrap algorithm was developed for AR(1) process similar to bootstrapping regression residual. Moving blocks bootstrap, close to one-sample bootstrap, was developed to retain the correlation structure present in the observations. Markov bootstrap is based on nonparametric estimate of transition density. Since the generating process of dependent data is not specified, bootstrap algorithm for dependent data differ from iid sample. The resampling plan should be design such that the dependence structure should be preserved. Reinjections are an important part of geothermal steam production, and have been used extensively, but a comprehensive interpretation is limited.
Tracer test aims to determine the degree of connectivity between injections well and production well. Parameters of tracer profiles related to the parameter of the system and can be estimated using non-linear regression approach. The parameter confidence interval is based on assumption of normal distribution. This paper aims to explore the applicability of bootstrap nonlinear regression to estimate confidence interval of decline rate parameters and mean transit time of the tracer. Bootstrap mean, bootstrap regression and bootstrap nonlinear regression are reviewed and some examples will be given.
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