Recursive estimation of states and parameters in oil reservoir

Akter, Farhana (2023) Recursive estimation of states and parameters in oil reservoir. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

A reservoir model is built with the initial guesses of reservoir parameters, which has high degree of uncertainty that may make the prediction unreliable. Appropriate assessment of the reservoir parameters’ uncertainty provides dependability on the reservoir model. Among several reservoir parameters, porosity and permeability are the two key parameters that affect reserves estimation, field development, future prediction, and development of alternative oil recovery scenarios. In this regard, an extensive study is required on reservoir model to estimate dynamic states and static parameters correctly along with uncertainty assessment. However, due to the presence of large number of variables in the geophysical model, nonlinearity in the multiphase fluid flow equations and assumptions toward linearization make the reservoir model more uncertain and non-unique. Therefore, correct estimation of the unknown or poorly known states and parameters becomes very difficult. In this regard, application of ensemble Kalman filter provides realistic solution as this tool is able to deal with large scale nonlinear system. In this approach, a set of reservoir models/realizations are generated considering the reference reservoir data and data assimilation is done for all the realizations incorporating available observations. After data assimilation, a range of forecasts are generated from the updated realizations on which the uncertainty in the reservoir performance predictions is evaluated. In this work, some key phenomena such as excitation in the reservoir due to production through injection, dynamic error in the reservoir model, non-Gaussianity effect in the water flooding case in heterogeneous reservoir, and dynamic change of parameters in asphaltic oil reservoir are investigated while estimating reservoir parameters. Investigation is conducted considering different production scenarios in reservoirs. To improve parameter estimation under these varying conditions, modifications are introduced into the traditional EnKF methodology to address these key factors. Dynamic model error has been mostly ignored for the cases of multiphase flow in porous media for estimating parameters. Therefore, a dynamic model error along with measurement error is added in water flooding oil reservoir model. Also to capture the change happened in the reservoir due to water injection, artificial perturbation of inputs is introduced in EnKF methodology. With these modifications, about 9% improvement in history matching is observed when mismatch between model and true system, and uncertainty in measurement are high. Next, the aspect of non-Gaussianity in state and parameter estimation is investigated in five spot oil-water reservoir by applying EnKF along with particle filter (PF). From the analysis, it is found that the performance of EnKF is comparable with PF where the non-Gaussianity is weak. However, in the presence of strong non-Gaussianity, EnKF shows four times higher error than PF. Also, the performance of particle filter is improved by incorporating “ensemble covariance” during resampling stage. This research work includes the analysis of formation damage due to asphaltene precipitation/deposition and its impact on reservoir properties such as permeability and porosity. In this work, a modification is introduced in the pure solid model regarding explicit estimation of the asphaltene precipitation, resulting in a reduced computation time. To calculate the amount of asphaltene precipitation, the modification brings the iteration steps from five to one with a difference of 9.945% between the pure solid model and modified solid model. In addition, the simulation of wellbore region of production well in a two-dimensional oil reservoir is conducted considering four-phase black oil model. The simulation results reveal that around the wellbore, the suspended asphaltene saturation reaches to its maximum value at the bubble point pressure; the maximum reduction in permeability (8%) and porosity (9.1%) occurs around the wellbore. Finally, EnKF is applied to an asphaltic oil reservoir for estimation of reservoir parameters considering their inherent uncertainty and dynamic change due to asphaltene precipitation. Due to continued production, dynamic state change from ‘pressure to saturation’ of gas and asphaltene phase happens. To capture this state change, a methodology is developed while applying EnKF. History matching is done by matching the results of bottomhole flowing pressure, fluid flow rate, suspended asphaltene saturation, gas saturation obtained from the filter and model. It is found that porosity and permeability are estimated with less than 2% error.

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