Mm Muhammad Siraj

Risk management in oil reservoir water-flooding under economic uncertainty

Model-based economic optimization of the water-flooding process in oil reservoirs suffers from high levels of uncertainty. The achievable economic objective is highly uncertain due to the varying economic conditions and the limited knowledge of the reservoir model parameters. For improving robustness, different approaches, e.g., mean or mean-variance optimization have been proposed. One of the drawbacks of the mean-variance approach is the symmetric nature of the variance and hence the reduction of the best cases. In this work, we focus only on the lower tail, i.e., the worst-case(s) and aims to maximize the lower tail of the economic objective function without heavily compromising the best cases. Concepts from robust optimization (max-min approach) and the theory of risk (a risk averse mean-CVaR approach) are considered to offer an asymmetric shaping of the objective function distribution with respect to the given uncertainty. A scenario-based approach is used, where an ensemble of oil price scenarios characterizes the economic uncertainty.

Model and Economic Uncertainties in Balancing Short-Term and Long-Term Objectives in Water-Flooding Optimization

Model-based optimization of oil production has a significant scope to increase ultimate recovery or financial life-cycle performance. The Net Present Value (NPV) objective in such an optimization framework, because of its nature, focuses on the long-term gains while the short-term production is not explicitly addressed. At the same time the achievable NPV is highly uncertain due to the limited knowledge of reservoir model parameters and varying economic conditions. Different (ad-hoc) methods have been proposed to introduce short-term considerations to balance short-term and long-term objectives in a model-based approach. In this work, we address the question whether through an explicit handling of model and economic uncertainties in NPV (robust) optimization, an appropriate balance between these economic objectives is naturally obtained. A set (ensemble) of possible realizations of the reservoir models is considered as a discretized approximation of the uncertainty space, while different oil price scenarios are considered to characterize the economic uncertainty. A gradient-based optimization procedure is used where the gradient information is computed by solving adjoint equations. A robust optimization framework with an average NPV with respect to the ensemble of models and the oil price scenarios is formulated and the NPV build-up over time is studied. As robust optimization (RO) does not attempt to reduce the sensitivity of the solution to uncertainty, a mean-variance optimization (MVO) approach is implemented which maximizes the average NPV and minimizes the variance of the NPV distribution. It is shown by simulation examples that with RO, the average NPV is increased compared to the reactive strategy, with both forms of uncertainty. However, an NPV build-up over time that is considerably slower than for a reactive strategy is obtained. A faster NPV build-up compared to RO is achieved in MVO by choosing different weightings on variance in the mean-variance objective, at the price of slightly compromising on the long-term gains.

Joint order and dependency reduction for LPV state-space models

In the reduction of Linear Parameter-Varying (LPV) models, decreasing model complexity is not only limited to model order reduction (state reduction), but also to the simplification of the dependency of the model on the scheduling variable. This is due to the fact that the concept of minimality is strongly connected to both types of complexities. While order reduction of LPV models has been deeply studied in the literature resulting in the extension of various reduction approaches of the LTI system theory, reduction of the scheduling dependency still remains to be a largely open problem. In this paper, a model reduction method for LPV state-space models is proposed which achieves both state-order and scheduling dependency reduction. The introduced approach is based on an LPV Ho-Kalman algorithm via imposing a sparsity expectation on the extended Hankel matrix of the model to be reduced. This sparsity is realized by an L1-norm based minimization of a priori selected set of dependencies associated sub-Markov parameters. The performance of the proposed method is demonstrated via a representative simulation example.

Handling Geological and Economic Uncertainties in Balancing Short-Term and Long-Term Objectives in Waterflooding Optimization

Model-based economic optimization of oil production has a significant scope to increase financial life-cycle performance. The net-present-value (NPV) objective in this optimization, because of its nature, focuses on long-term gains, whereas short-term production is not explicitly addressed. At the same time, the achievable NPV is highly uncertain because of strongly varying economic conditions and limited knowledge of the reservoir-model parameters. The prime focus of this work is to develop optimization strategies that balance both long-term and short-term economic objectives and also offer robustness to the long-term NPV. An earlier robust hierarchical optimization method honoring geological uncertainty with robust long-term and short-term NPV objectives serves as a starting base of this work. We address the issue of extending this approach to include economic uncertainty and aim to analyze how the optimal solution reduces the uncertainty in the achieved average NPV. An ensemble of varying oil prices is used to model economic uncertainty with average NPVs as robust objectives in the hierarchical approach. A weighted-sum approach is used with the same objectives to quantify the effect of uncertainty. To reduce uncertainty, a mean-variance-optimization (MVO) objective is then considered to maximize the mean and also minimize the variance. A reduced effect of uncertainty on the long-term NPV is obtained compared with the uncertainty in the mean-optimization (MO) objectives. Last, it is investigated whether, because of the better handling of uncertainty in MVO, a balance between short-term and long-term gains can be naturally obtained by solving a single-objective MVO. Simulation examples show that a faster NPV buildup is naturally achieved by choosing appropriate weighting of the variance term in the MVO objective. Copyright [2017], Society of Petroleum Engineers.