Three growth models (Richards, Gompertz, and Weibull) were estimated using a computer program employing a modified version of the Levenberg-Marquardt approach for solving non-linear regression models. With both small and high sample sizes, three data sets were collected. The most suitable model for growth studies was added by decomposing the growth models into their component parts: additive and multiplicative error factors. The analysis based on the mathematical properties was conducted using Gretl statistics software. Prior to using an iterative strategy, a third-order polynomial (cubic function) solves the issue of the initial parameters. The final estimate of the parameters, standard errors, p-values, and model adequacy standards used to choose the best growth model are included in the result. Out of the five growth models considered suitable for the agricultural data, this study was able to pinpoint the Weibull Growth Model with Multiplicative Error Term. The Hill Growth Model with Additive Error Term is the best growth model for the engineering data out of the five growth models. Among the Five Growth Models for Population Growth, the Weibull Growth Model with Additive Error Term is a viable growth model. Several growth models are suggested or recommended by this study for use in forecasting this growth behavior.
Fitting nonlinear models is not a single-step procedure but it involved a process that requires careful examination of each individual step. Depending on the objective and the application domain, different priorities are set when fitting nonlinear models; these include obtaining acceptable parameter estimates and a good model fit while meeting standard assumptions of statistical models. We propose steps in fitting nonlinear models in this research work. Two reciprocal power regression models were considered with a non-linear data set. Then, the following steps are considered (i) fit the models to the data collected using iterative steps, (ii) to develop a linear model to estimate the parameter β1 and β2 when the initial value (or growth rate β3) lies between -1.0 ≤ β3 ≤1.0 ); using the transform models of the reciprocal power regression model (iii) to find the “best” model between the two models using R2, AIC and BIC. The results show Model B is better than Model A, using the model selection criteria.
In pressure transient analysis, the derivative, typecurve and semi-log pressure curve is used to estimate wellbore and reservoir parameters. How accurate are this figures which solely depend on the extent of the transient period as interpreted by the derivative plot considered for reservoir characterization. Though this approach is universally accepted by welltest analysts, reservoir engineers and the academia in the oil and gas industry but the possibility of over or under estimating wellbore and reservoir parameter is not in doubt, hence there is need to checkmate such interpretation using alternative approach This paper focus on permeability and skin estimation using the statistical approach to checkmate the quantitative interpretation of the derivative method. Part 1 of this work focus on flow regime identification using the statistical method. Result from channel sand, low and high permeability reservoir, infinite acting and closed boundary indicates that the estimated permeability for both approach is much closed. Maximum difference of about 13% is notice in closed boundary model while the minimum difference is about 1% in infinite acting reservoir response. Generally, the best match for K and S estimate is seen in channel sand and high K, acidized model. Also in all cases considered, lower slope is obtained from the Statdev approach which is responsible for lower estimated permeability. Invariably the Statdev depict larger extent of transient flow regime as compare with the derivative, making it applicable even where data whose fingerprint for the transient period are insufficient for the analysis.
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