# Research

The research within the Stanford Smart Fields consortium targets the solving of many of the issues related to the practical implementation of the closed-loop reservoir management paradigm. These issues involve topics such as production optimization, model order reduction, uncertainty quantification and propagation, data assimilation and optimal decision making. Apart from production optimization, the Smart Fields concept can be useful also for optimal carbon dioxide sequestration.

### Research Areas:

#### Optimal Well Placement & Control

By the Smart Fields paradigm we aim at finding an optimal reservoir management. This typically means optimizing well location and control under different uncertainty sources. At the Stanford Smart Fields consortium we study a large variety of optimization strategies for an effective and efficient solving of computationally expensive optimization problems.

#### Model Order Reduction

The optimization problems dealt with in the Smart Fields paradigm usually yield a very time-consuming objective function (where a reservoir simulator is called). Reduced order modeling can be used to accelerate these optimization processes while keeping the quality of the optimal solution obtained.

#### Reservoir Inverse Modelling & Uncertainty Quantification

Reservoir management relies on a proper reservoir characterization. This characterization is accomplished in practice by solving inverse problems based on measurements. Since the number of measurements is smaller than the number of unknown parameters, inverse problems are in general ill-conditioned. Thus, multiple solutions that match the measure data within a certain level of accuracy (model uncertainty) can be found. At Stanford Smart Fields we dedicate some effort developing inverse modeling methodologies, together with means to quantify model uncertainty and to describe how it propagates along the reservoir management closed loop. Many of these methodologies consider measurements of disparate nature (e.g., production and time-lapse seismic data) in order to reduce model uncertainty.

#### Carbon Dioxide Sequestration

Carbon dioxide sequestration can be interpreted from the perspective of the Smart Fields paradigm. Based on that, many of the techniques developed for reservoir management can be applied to optimally store carbon dioxide away.

#### Data Assimilation and Integration

The amount of data generated in practical implementations of the Smart Fields paradigm is huge. A data assimilation/filtering stage in the closed loop is thus mandatory because it can have significant impact on the management strategies obtained.

#### Decision Analysis under Uncertainty

The closed-loop reservoir management paradigm can be used for making better decisions. At Stanford Smart Fields there is also research on integrating the decision making process with some of the other techniques needed in the loop.

#### Gradient-based History Matching

History matching production data is an important part of closed-loop reservoir management. Gradient-based optimization has proven to be significantly more efficient than gradient-free methods for history matching problems. As the adjoint is available in AD-GPRS, gradient-based history matching for both two-point and multi-point geostatistical models is an active research area in our group.

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