Waterflooding strategy design using optimal control theory

Virnovsky, G.A.

doi:10.3997/2214-4609.201411270

Cited by 30 publications

(21 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In these studies, the optimal rates were computed using a gradient-based optimization routine where the derivative information was obtained through the use of an adjoint equation. These results are in line with those from earlier studies that addressed the optimization of waterflooding using optimal control of conventional wells [3,23,24]. For a review of other applications of optimal control in reservoir simulation, we refer to [5].…”

Section: Introductionsupporting

confidence: 92%

Waterflooding using closed-loop control

2006

View full text Add to dashboard Cite

To fully exploit the possibilities of Bsmart^wells containing both measurement and control equipment, one can envision a system where the measurements are used for frequent updating of a reservoir model, and an optimal control strategy is computed based on this continuously updated model. We developed such a closed-loop control approach using an ensemble Kalman filter to obtain frequent updates of a reservoir model. Based on the most recent update of the reservoir model, the optimal control strategy is computed with the aid of an adjoint formulation. The objective is to maximize the economic value over the life of the reservoir. We demonstrate the methodology on a simple waterflooding example using one injector and one producer, each equipped with several individually controllable inflow control valves (ICVs). The parameters (permeabilities) and dynamic states (pressures and saturations) of the reservoir model are updated from pressure measurements in the wells. The control of the ICVs is rate-constrained, but the methodology is also applicable to a pressureconstrained situation. Furthermore, the methodology is not restricted to use with Bsmartŵ ells with down-hole control, but could also be used for flooding control with conventional wells, provided the wells are equipped with controllable chokes and with sensors for measurement of (wellhead or down hole) pressures and total flow rates. As the ensemble Kalman filter is a Monte Carlo approach, the final results will vary for each run. We studied the robustness of the methodology, starting from different initial ensembles. Moreover, we made a comparison of a case with low measurement noise to one with significantly higher measurement noise. In all examples considered, the resulting ultimate recovery was significantly higher than for the case of waterflooding using conventional wells. Furthermore, the results obtained using closed-loop control, starting from an unknown permeability field, were almost as good as those obtained assuming a priori knowledge of the permeability field.

show abstract

Section: Introductionsupporting

confidence: 92%

Waterflooding using closed-loop control

2006

View full text Add to dashboard Cite

show abstract

“…Zakirov et al [13] applied adjoint models to optimize production from a thin oil rim. Optimization of water flooding using adjoints has been studied by many researchers including Asheim [14], Virnovsky [15], Sudaryanto and Yortsos [16], and recently by Brouwer and Jansen [17]. The use of adjoints for history matching was pioneered by Chen et al [18] and Chavent et al [19], who applied it to single-phase problems.…”

Section: Introductionmentioning

confidence: 98%

Efficient real-time reservoir management using adjoint-based optimal control and model updating

et al. 2006

View full text Add to dashboard Cite

The key ingredients to successful real-time reservoir management, also known as a Bclosed-loop^approach, include efficient optimization and model-updating (historymatching) algorithms, as well as techniques for efficient uncertainty propagation. This work discusses a simplified implementation of the closed-loop approach that combines efficient optimal control and model-updating algorithms for real-time production optimization. An adjoint model is applied to provide gradients of the objective function with respect to the well controls; these gradients are then used with standard optimization algorithms to determine optimum well settings. To enable efficient history matching, Bayesian inversion theory is used in combination with an optimal representation of the unknown parameter field in terms of a KarhunenYLoeve expansion. This representation allows for the direct application of adjoint techniques for the history match while assuring that the two-point geostatistics of the reservoir description are maintained. The benefits and efficiency of the overall closed-loop approach are demonstrated through real-time optimizations of net present value (NPV) for synthetic reservoirs under waterflood subject to production constraints and uncertain reservoir description. For two example cases, the closed-loop optimization methodology is shown to provide a substantial improvement in NPV over the base case, and the results are seen to be quite close to those obtained when the reservoir description is known a priori.

show abstract

“…This includes partial and sometimes heuristic approaches, valid for particular types of constraints [5,38,39,43], and more systematic approaches, valid for a broader range of constraint equations [9,14,22,33,37]. An important feature in simulations involving highly compressible fluids, which we have in the systems considered here since we inject gas, is the occurrence of transient peaks in the rate in response to changes in well bottom-hole pressure (bottom-hole pressure, or BHP, is the wellbore pressure at a specified depth within the reservoir).…”

Section: Nonlinear Constraintsmentioning

confidence: 99%

“…Much of the early work on their use for optimization of oil recovery was performed by Ramirez and coworkers, who considered the optimization of several different enhanced oil recovery (EOR) processes [25,26,32]. In subsequent work, the focus was on gradient-based optimization (and in some cases on the optimization of 'smart wells') for water flooding [1,5,34,36,39]. Recent studies have addressed the implementation of adjoint-based procedures into general purpose simulators, the treatment of general constraints, and regularization and other numerical issues [15,20,24,33].…”

Section: Introductionmentioning

confidence: 99%

Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow

et al. 2014

View full text Add to dashboard Cite

An adjoint formulation for the gradient-based optimization of oil-gas compositional reservoir simulation problems is presented. The method is implemented within an automatic differentiation-based compositional flow simulator (Stanford's AD-GPRS). The development of adjoint procedures for general compositional problems is much more challenging than for oil-water problems due to the increased complexity of the code and the underlying physics. The treatment of nonlinear constraints, an example of which is a maximum gas rate specification in injection or production wells, when the control variables are well bottom-hole pressures, poses a particular challenge. Two approaches for handling these constraints are presented -a formal treatment within the optimizer, and a simpler heuristic treatment in the forward model. The relationship between discrete and continuous adjoint formulations is also elucidated. duced) relative to reference solutions range from 4.2% to 11.6%. The heuristic treatment of nonlinear constraints is shown to offer a cost-effective means for obtaining feasible solutions, which are in some cases better than those obtained using the formal constraint handling procedure.

show abstract

Waterflooding strategy design using optimal control theory

Cited by 30 publications

References 0 publications

Waterflooding using closed-loop control

Waterflooding using closed-loop control

Efficient real-time reservoir management using adjoint-based optimal control and model updating

Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow

Contact Info

Product

Resources

About