Browsing by Subject "Confidence interval"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Development of linear capacitance-resistance models for characterizing waterflooded reservoirs(2011-12) Kim, Jong Suk; Edgar, Thomas F.; Lake, Larry W.The capacitance-resistance model (CRM) has been continuously improved and tested on both synthetic and real fields. For a large waterflood, with hundreds of injectors and producers present in a reservoir, tens of thousands of model parameters (gains, time constants, and productivity indices) in a field must be determined to completely define the CRM. In this case obtaining a unique solution in history-matching large reservoirs by nonlinear regression is difficult. Moreover, this approach is more likely to produce parameters that are statistically insignificant. The nonlinear nature of the CRM also makes it difficult to quantify the uncertainty in model parameters. The analytical solutions of the two linear reservoir models, the linearly transformed CRM whose control volume is the drainage volume around each producer (ltCRMP) and integrated capacitance-resistance model (ICRM), are developed in this work. Both models are derived from the governing differential equation of the producer-based representation of CRM (CRMP) that represents an in-situ material balance over the effective pore volume of a producer. The proposed methods use a constrained linear multivariate regression (LMR) to provide information about preferential permeability trends and fractures in a reservoir. The two models’ capabilities are validated with simulated data in several synthetic case studies. The ltCRMP and ICRM have the following advantages over the nonlinear waterflood model (CRMP): (1) convex objective functions, (2) elimination of the use of solver when constraints are ignored, and (3) faster computation time in optimization. In both methods, a unique solution can always be obtained regardless of the number of parameters as long as the number of data points is greater than the number of unknowns (parameters). The methods of establishing the confidence limits on CRMP gains and ICRM parameters are demonstrated in this work. This research also presents a method that uses the ICRM to estimate the gains between newly introduced injectors and existing producers for a homogeneous reservoir without having to do additional simulations or regression on newly simulated data. This procedure can guide geoscientists to decide where to drill new injectors to increase future oil recovery and provide rapid solutions without having to run reservoir simulations for each scenario.Item Statistical Inference for Costs and Incremental Cost-Effectiveness Ratios with Censored Data(2012-07-16) Chen, ShuaiCost-effectiveness analysis is widely conducted in the economic evaluation of new treatment options. In many clinical and observational studies of costs, data are often censored. Censoring brings challenges to both medical cost estimation and cost-effectiveness analysis. Although methods have been proposed for estimating the mean costs with censored data, they are often derived from theory and it is not always easy to understand how these methods work. We provide an alternative method for estimating the mean cost more efficiently based on a replace-from-the-right algorithm, and show that this estimator is equivalent to an existing estimator based on the inverse probability weighting principle and semiparametric efficiency theory. Therefore, we provide an intuitive explanation to a theoretically derived mean cost estimator. In many applications, it is also important to estimate the survival function of costs. We propose a generalized redistribute-to-the right algorithm for estimating the survival function of costs with censored data, and show that it is equivalent to a simple weighted survival estimator of costs based on inverse probability weighting techniques. Motivated by this redistribute-to-the-right principle, we also develop a more efficient survival estimator for costs, which has the desirable property of being monotone, and more efficient, although not always consistent. We conduct simulation to compare our method with some existing survival estimators for costs, and find the bias seems quite small. Thus, it may be considered as a candidate for survival estimator for costs in a real setting when the censoring is heavy and cost history information is available. Finally, we consider one special situation in conducting cost-effectiveness analysis, when the terminating events for survival time and costs are different. Traditional methods for statistical inference cannot deal with such data. We propose a new method for deriving the confidence interval for the incremental cost-effectiveness ratio under this situation, based on counting process and the general theory for missing data process. The simulation studies show that our method performs very well for some practical settings. Our proposed method has a great potential of being applied to a real setting when different terminating events exist for survival time and costs.