Document Type : Research Paper


1 Professor, Department of Instrumentation and Industrial Automation, Petroleum University of Technology, Ahwaz, Iran

2 M.S. Student, Department of Instrumentation and Industrial Automation, Petroleum University of Technology, Ahwaz, Iran


The model-based optimization of the waterflooding process has found significant scope for improving the economic life-cycle performance of oil fields due to geological and economic uncertainties compared to conventional reactive strategies. This paper proposes a new frequency-based system identification method to identify a robust multi-input, multi-output (MIMO) surrogate model for an oil reservoir under waterflooding process so as to describe all the injector-producer relationships. In contrast to the conventional modeling methods, the proposed data-driven modeling approach uses the available injection and production rates as the reservoir input–output data. Meanwhile, it includes a structured-bounded uncertainty model in the form of norm-bounded state-space function blocks to account for uncertainties, facilitating the identified model employed in robust control methodology using linear matrix inequality (LMI) problem formulation so as to eliminate the effect of model uncertainty. The identified MIMO surrogate model is integrated with a desired nonlinear net present value (NPV) objective function in a multi-input, single-output (MISO) system configuration to synthesize a model-based optimization prediction for economical operation and production of oil from oil reservoirs under both geological and economic uncertainties. The introduced approach is implemented on the “EGG model” as a well-recognized three-dimensional synthetic oil reservoir with eight water injection wells and four oil production wells. The results demonstrate that economic performance prediction of the oil reservoir, having an uncertain permeability field, lies in the evaluated bound of the uncertainty model. Waterflooding is a well-known method for increasing oil production. A significant amount of time and effort is required even for high-performance processors to numerically simulate a reservoir with thousands of grid blocks. On the other hand, there is a high uncertainty level in oil reservoir model-based economic optimization due to limited information about geological model parameters. Employing robust control methods can provide robustness for the performance and stability of the control system against model norm-bounded uncertainty. However, in all standard identification methods, it is assumed that the uncertainties in the model can be accommodated in the form of noise. Therefore, the challenge of using the models estimated from the standard identification approach in robust control methods can mainly be considered an essential subject. This paper presents a new frequency-based modeling approach to identify a surrogate model and uncertainty modeling for the waterflooding process with the ease of being employed in robust control methods. A desirable relationship is obtained between the injection rate and the economic production function to model the dynamics of the reservoir using the identification of the surrogate model. Then, the concept of structure bounded uncertainty modeling is presented to describe the model geological uncertainty.


• A framework system theory-based approach modeling for waterflooding process in oil reservoirs is proposed;

• The effect of geological uncertainties on hydrocarbon recovery efficiency is modeled and measured;

• Reservoir management goals can be pursued in the presence of uncertainty based on the obtained model;

• The developed approach has been assessed by being implemented in MRST on the EGG reservoir model.


Main Subjects

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