# 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 also be also useful for optimal carbon dioxide sequestration.

#### Production Optimization Using Gradient-Free Methods

The determination of optimum well controls represents a challenging optimization problem which is an integral component of the more general closed-loop approach to reservoir management. A very efficient technique that has been used to address this problem is the adjoint method, which provides gradients of the objective function (cumulative oil production, net present value, etc.) with respect to the well controls. Having these gradients, an appropriate gradient-based optimization algorithm can be used to maximize the objective function. A limitation of this technique...

#### A Well Pattern Optimization Algorithm for Large-Scale Field Development

Large-scale field development optimization entails the optimization of the number, type, locations and trajectories drilling schedule, and wells rates, of many wells to maximize an objective function. Optimization algorithms are employed to address this problem, with recent applications requiring several hundred wells. The most common solution representation technique in well placement optimization is to consider a series of wells, and to concatenate the well-by-well optimization parameters. For problems with many wells, however...

#### Retrospective Optimization of Well Location under Uncertainty

Optimizing well locations is challenging due to discreteness, large solution space and expensive simulation. In oil production, the reservoir is often subject to different types of geological uncertainties. Optimization of well location under uncertainty becomes more challenging since it involves the variability of simulation observations.

#### Reservoir Management Optimization based on Approximate Dynamic Programming

In general, petroleum reservoir management problem could be modeled as a large-scale, dynamic optimization problem. Dynamic Programming (DP) is an optimization algorithm that theoretically achieves the global optimum of dynamic optimization problem. However, in practice, when computing cost-to-go function, DP suffers from computational difficulty, known as "curse of dimensionality". Approximate Dynamic Programming (ADP) is proposed to overcome this computational difficulty, by...

#### Linear Programming in Streamline Model

Streamline models provide a linear approximation of the reservoir state at a time instance. Such a linear approximation can be useful in approximating the optimal rates of the wells.</p><p>In streamline-based simulation, it is assumed that there are direct links between injector wells and producer wells. For a link between an injector well and a producer well two quantities are defined: efficiency and rate. Efficiency of the link is ratio of the oil produced in the link to total fluid in the link. Rate of the link is the ratio between fluid in the link and total fluid injected in the injector well. For example,...

#### Efficient Field Development Optimization Using Upscaled Models

Field development optimization in heterogeneous reservoirs to maximize cumulative oil production or net present value (NPV) is a challenging reservoir management problem. The problem gets computationally more expensive by including subsurface geological uncertainty because to represent subsurface geological uncertainty many geological realizations are considered...

#### Water Flood Management and Optimization (Past Project)

With 70% of oil production coming from fields that are 30 years or older, the optimal management of reservoir floods, and of water floods in particular, is a specially important topic. Despite many advances in reservoir simulation and management, reservoir engineers still struggle in setting optimal injection/production target rates for such fields...

#### Reduced-order Models for Nonlinear Optimization

Production of unconventional oil resources, such as oil sands in the province of Alberta, Canada, may contribute significantly to the future energy supply of the planet. It is indeed estimated that several trillions of oil barrels remain under the ground along the Athabasca River only. This extremely viscous oil however, cannot be recovered using traditional production techniques. One approach that has been developed consists in using in-situ electrical heaters in order to upgrade the oil sands directly within the subsurface. Such a technique shall however...

#### Theory and Applications of Reduced Order Models for Reservoir Simulation

Reservoir simulation can be very demanding computationally as a result of the potentially large number of system unknowns and the intrinsic nonlinearity of typical problems. A black-oil or compositional simulation for a reservoir model with 104 - 106 grid blocks can take hours or even days to run. Furthermore, In applications such as production optimization or history matching, the simulation will need to be run hundreds of times. This makes the traditional full order simulator very computational expensive for such applications.

#### Reduced Order Models for Production Optimization (Past Project)

Progress in seismic and well log tools over the last decade resulted in exceptionally detailed geological models and, as a consequence, more complex reservoir flow models (with an elevated number of grid blocks, typically in the order of tens of thousands to millions). Maximizing the hydrocarbon production or the Net Present Value (NPV) of a reservoir in a Smart Field can be accomplished by applying Optimal Control Theory. This usually requires many simulations of the reservoir model. The time needed...

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