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**Industry**

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A new methodology for the joint optimization of economic project life and time-varying well controls is introduced. The procedure enables the maximization of net present value (NPV) subject to satisfaction of a specified modified internal rate of return. Use of this framework allows an operator to avoid situations where NPV continues to increase in time, but the late-time cash flows are negligible (in terms of an appropriate financial metric) relative to the capital invested in the project. The optimization is formulated as a nested procedure in which economic project life is optimized in the outer loop, and the associated well settings (time-varying bottomhole pressures in the cases considered) are optimized in the inner loop. The inner-loop optimization is accomplished by use of an adjointgradient-based approach, while the outer-loop optimization entails an interpolation technique. We demonstrate the successful application of this framework for production optimization for two-and three-dimensional reservoir models under waterflood. The tradeoff between maximized NPV and rate of return is assessed, as is the impact of discount rate on optimal operations. We believe this to be the first production optimization formulation that explicitly incorporates both NPV and rate of return. As such, this approach may represent an alternative to existing treatments that entail the bi-objective optimization of long-and short-term NPV.

annular pressure drilling, Artificial Intelligence, blowout flow modeling, cash flow, day, evolutionary algorithm, example, formation evaluation, machine learning, mirr, NPV, optimal, optimization, optimization problem, production control, production monitoring, production optimization, project, project life, rate, reservoir simulation, return, simulator development, value, waterflooding, well control

SPE Disciplines:

Hui, Mun-Hong Robin (Chevron Energy Technology Co) | Karimi-Fard, Mohammad (Stanford University) | Mallison, Bradley (Chevron Energy Technology Co) | Durlofsky, Louis J. (Stanford University)

A comprehensive methodology for gridding, discretizing, coarsening, and simulating discrete-fracture-matrix models of naturally fractured reservoirs is described and applied. The model representation considered here can be used to define the grid and transmissibilities, at either the original fine scale or at coarser scales, for any connectivity-list-based finite-volume flow simulator. For our fine-scale mesh, we use a polyhedral gridding technique to construct a conforming matrix grid with adaptive refinement near fractures, which are represented as faces of grid cells. The algorithm uses a single input parameter to obtain a suitable compromise between fine-grid cell quality and the fidelity of the fracture representation. Discretization using a two-point flux approximation is accomplished with an existing procedure that treats fractures as lower-dimensional entities (i.e., resolution in the transverse direction is not required). The upscaling method is an aggregation-based technique in which coarse control volumes are aggregates of fine-scale cells, and coarse transmissibilities are computed using a general flow-based procedure. Numerical results are presented for waterflood, sour gas injection, and gas condensate primary production. Coarse-model accuracy is shown to generally decrease with increasing levels of coarsening, as would be expected. We demonstrate, however, that by using our methodology, two orders of magnitude of speedup can be achieved with models that introduce less than about 10% error (with error appropriately defined). This suggests that the overall framework may be very useful for the simulation of realistic discrete-fracture-matrix models.

artificial lift system, cell, condensate reservoir, Durlofsky, example, fine, flow in porous media, Fluid Dynamics, formation evaluation, fracture, gas injection method, gas lift, geologic modeling, GeoModel, grid, H2S management, matrix, model, oilfield chemistry, pressure, produced water, production control, production monitoring, PVT measurement, reservoir simulation, resolution, result, scaling method, shale gas, simulator development, transmissibility, waterflooding

Oilfield Places:

- North America > Canada > British Columbia > Horn River Basin > Horn River Shale (0.99)
- North America > Canada > Alberta > Western Canada Sedimentary Basin > Duvernay Shale Gas Field > Durvernay Shale (0.98)

Li, Hangyu (Stanford University) | Durlofsky, Louis J. (Stanford University)

Compositional flow simulation, which is required for modeling enhanced-oil-recovery (EOR) operations, can be very expensive computationally, particularly when the geological model is highly resolved. It is therefore difficult to apply computational procedures that require large numbers of flow simulations, such as optimization, for EOR processes. In this paper, we develop an accurate and robust upscaling procedure for oil/gas compositional flow simulation. The method requires a global fine-scale compositional simulation, from which we compute the required upscaled parameters and functions associated with each coarse-scale interface or wellblock. These include coarse-scale transmissibilities, upscaled relative permeability functions, and so-called *α*-factors, which act to capture component flow rates in the oil and gas phases. Specialized near-well treatments for both injection and production wells are introduced. An iterative procedure for optimizing the *α*-factors is incorporated to further improve coarse-model accuracy. The upscaling methodology is applied to two example cases, a 2D model with eight components and a 3D model with four components, with flow in both cases driven by wells arranged in a five-spot pattern. Numerical results demonstrate that the global compositional upscaling procedure consistently provides very accurate coarse results for both phase and component production rates, at both the field and well level. The robustness of the compositionally upscaled models is assessed by simulating cases with time-varying well bottomhole pressures that are significantly different from those used when the coarse model was constructed. The coarse models are shown to provide accurate predictions in these tests, indicating that the upscaled model is robust with respect to well settings. This suggests that one can use upscaled models generated from our procedure to mitigate computational demands in important applications such as well-control optimization.

annular pressure drilling, Artificial Intelligence, blowout flow modeling, case, comp upsc, component, Computation, Durlofsky, flow in porous media, Fluid Dynamics, formation evaluation, function, geologic modeling, interface, machine learning, miscible method, oil, Phase, procedure, production control, production logging, production monitoring, rate, reservoir, reservoir simulation, result, scaling method, simulator development, well control

In this work, we develop and apply a general methodology for optimal closed-loop field development (CLFD) under geological uncertainty. CLFD involves three major steps: optimizing the field-development plan on the basis of current geological knowledge; drilling new wells, and collecting hard data and production data; and updating multiple geological models on the basis of all the available data. In the optimization step, the number, type, locations, and controls for new wells (and future controls for existing wells) are optimized with a hybrid particle swarm optimization-mesh adaptive direct search algorithm. The objective here is to maximize expected (over multiple realizations) net present value (NPV) of the overall project. History matching is accomplished with an adjoint-gradient-based "randomized maximum likelihood" procedure. Because the CLFD history-matching component is fast relative to the optimization component, we generate a relatively large number of history-matched models. Optimization is then performed with a set of "representative" realizations selected from the full set of history-matched models. We introduce a systematic optimization with sample validation (OSV) procedure, in which the number of realizations used for optimization is increased if an appropriate validation criterion is not satisfied. The CLFD methodology is applied to 2D and 3D example cases. Results show that the use of CLFD increases the NPV for the "true" (synthetic) model by 10 to 70% relative to that achieved by optimizing over a large number of prior realizations. We also compare the results for CLFD with OSV to results that use a fixed number of geological realizations. These comparisons show that the use of too few realizations in the CLFD optimization step can result in lower true-model NPVs, whereas OSV provides a systematic approach for determining the proper number of realizations.

Artificial Intelligence, CLFD, CLFD step, computational, data, evolutionary algorithm, example, formation evaluation, geologic modeling, history matching, location, machine learning, NPV, number, optimal, optimization problem, procedure, production control, production monitoring, realization, representative, representative realization, reservoir simulation, simulator development, STEP, waterflooding, well

SPE Disciplines:

Mishra, Srikanta (Battelle Memorial Institute) | Ganesh, Priya Ravi (Battelle Memorial Institute) | Schuetter, Jared (Battelle Memorial Institute) | He, Jincong (Stanford University) | Jin, Zhaoyang (Stanford University) | Durlofsky, Louis J. (Stanford University)

CO_{2} sequestration in deep saline formations is increasingly being considered as a viable strategy for the mitigation of greenhouse gas emissions from anthropogenic sources. In this context, full-physics compositional simulations are routinely used to understand key processes and parameters affecting pressure propagation and buoyant plume migration. As these models are data and computation intensive, the development of computationally-efficient alternatives to conventional numerical simulators has become an active area of research. Such simplified models can be valuable assets during preliminary CO_{2} injection project screening, serve as a key element of probabilistic system assessment modeling tools, and assist regulators in quickly evaluating geological storage projects. We present three strategies for the development and validation of simplified modeling approaches for CO_{2}sequestration in deep saline formations: (1) simplified physics-based modeling, (2) statistical-learning based modeling, and (3) reduced-order method based modeling.

In the first category, a set of well-designed full-physics compositional simulations is used to develop correlations for dimensionless injectivity as a function of the slope of the CO_{2} fractional-flow curve, variance of layer permeability values, and the nature of vertical permeability arrangement. The same variables, along with a modified gravity number, can be used to develop a correlation for the total storage efficiency within the CO_{2} plume footprint. Furthermore, the dimensionless average pressure buildup after the onset of boundary effects can be correlated to dimensionless time, CO_{2} plume footprint, and storativity contrast between the reservoir and caprock.

In the second category, statistical "proxy models" are developed using the simulation domain described previously with two different approaches: (a) classical Box-Behnken experimental design with a quadratic response surface, and (b) maximin Latin Hypercube sampling (LHS) based design with a multidimensional kriging metamodel fit. For roughly the same number of simulations, the LHS-based metamodel yields a more robust predictive model, as verified by a

In the third category, a reduced-order modeling procedure is utilized that combines proper orthogonal decomposition (POD) for reducing problem dimensionality with trajectory-piecewise linearization (TPWL) in order to represent system response at new control settings from a limited number of training runs. Significant savings in computational time are observed with reasonable accuracy from the POD-TPWL reduced-order model for both vertical and horizontal well problems – which could be important in the context of history matching, uncertainty quantification and optimization problems.

The main contribution of this paper is the development and validation of simplified modeling approaches that will enable rapid feasibility and risk assessment for CO_{2}sequestration in deep saline formations.

air emission, annular pressure drilling, approach, Artificial Intelligence, blowout flow modeling, case, data mining, design, Efficiency, flow in porous media, Fluid Dynamics, formation evaluation, geologic modeling, history matching, injection, machine learning, model, model-based reasoning, permeability, plume, production control, production monitoring, reservoir simulation, Response, result, risk and uncertainty assessment, scaling method, Sequestration, simulator development, subsurface storage, system, training, value, waterflooding, well control

Oilfield Places:

- North America > United States > Kentucky > Illinois Basin (0.99)
- North America > United States > Indiana > Illinois Basin (0.99)
- North America > United States > Illinois > Illinois Basin (0.99)
- North America > Canada (0.89)

In this work we develop and apply a general methodology for optimal closed-loop field development (CLFD) under geological uncertainty. CLFD involves three major steps: optimizing the field development plan based on current geological knowledge, drilling new wells and collecting hard data and production data, and updating multiple geological models based on all of the available data. In the optimization step, the number, type, locations and controls for new wells (and future controls for existing wells) are optimized using a hybrid Particle Swarm Optimization - Mesh Adaptive Direct Search algorithm. The objective here is to maximize expected (over multiple realizations) net present value (NPV) of the overall project. History matching is accomplished using an adjoint-gradient-based randomized maximum likelihood (RML) procedure. Because the CLFD history matching component is fast relative to the optimization component, we generate a relatively large number of history matched models. Optimization is then performed using a set of ‘representative’ realizations selected from the full set of history matched models. We introduce a systematic multilevel optimization with validation (MLOV) procedure, in which the number of realizations used for optimization is increased if an appropriate validation criterion is not satisfied. The CLFD methodology is applied to two- and three-dimensional example cases. Results show that the use of CLFD increases the NPV for the true model by 18% or more relative to that achieved by optimizing over prior realizations. We also compare the results for CLFD with MLOV to results that use a fixed number of geological realizations. These comparisons show that the use of too few realizations in the CLFD optimization step can result in lower true-model NPVs, while MLOV provides a systematic approach for determining the proper number of realizations.

Artificial Intelligence, CLFD, data, evolutionary algorithm, example, field development, formation evaluation, geologic modeling, history matching, location, machine learning, NPV, number, optimal, optimization problem, procedure, production control, production monitoring, realization, representative, representative realization, reservoir simulation, simulator development, STEP, waterflooding, well

SPE Disciplines:

Li, Hangyu (Stanford University) | Durlofsky, Louis J. (Stanford University)

Compositional flow simulation, which is required for modeling enhanced oil recovery (EOR) operations, can be very expensive computationally, particularly when the geological model is highly resolved. It is therefore difficult to apply computational procedures that require large numbers of flow simulations, such as optimization, for EOR processes. In this paper we develop an accurate and robust upscaling procedure for compositional flow simulation. The method requires a global fine-scale compositional simulation, from which we compute the required upscaled parameters and functions associated with each coarse-scale interface or well block. These include coarse-scale transmissibilities, upscaled relative permeability functions, and so-called a-factors, which act to capture component flow rates in the oil and gas phases. Specialized near-well treatments for both injection and production wells are introduced. An iterative procedure for optimizing the a-factors is incorporated to further improve coarse-model accuracy. The upscaling methodology is applied to two example cases, a two-dimensional model with eight components and a threedimensional model with four components, with flow in both cases driven by wells arranged in a five-spot pattern. Numerical results demonstrate that the global compositional upscaling procedure consistently provides very accurate coarse results for both phase and component production rates, at both the field and well level. The robustness of the compositionally upscaled models is assessed by simulating cases with time-varying well bottom-hole pressures that are significantly different from those used when the coarse model was constructed. The coarse models are shown to provide accurate predictions in these tests, indicating that the upscaled model is robust with respect to well settings. This suggests that upscaled models generated using our procedure can be used to mitigate computational demands in important applications such as well control optimization.

annular pressure drilling, block, blowout flow modeling, case, component, Computation, Durlofsky, field, flow in porous media, Fluid Dynamics, formation evaluation, function, geologic modeling, oil, permeability, Phase, procedure, production control, production logging, production monitoring, PVT measurement, rate, reservoir simulation, result, scaling method, simulator development, solution, well control

A multilevel optimization procedure, in which optimization is performed over a sequence of upscaled models, is developed for use in combined well placement and control problems. The multilevel framework, which can be incorporated with any type of optimization algorithm, is implemented here with a derivative-free Particle Swarm Optimization – Mesh Adaptive Direct Search (PSO–MADS) hybrid technique. An accurate global transmissibility upscaling procedure is applied to generate the coarse-model parameters required at each grid level. Distinct upscaled models are constructed using this approach for each candidate solution evaluated by the optimization algorithm. We demonstrate that the coarse models are able to capture the basic ranking of the candidate well location and control scenarios, in terms of objective function, relative to the ranking that would be computed using fine-scale simulations. This enables the optimization algorithm to appropriately select and discard candidate solutions. Two- and three-dimensional example cases are presented, one of which involves optimization over multiple geological realizations. The multilevel procedure is shown to provide optimal solutions that are comparable, and in some cases better, than those from the conventional (single-level) approach, but with computational speedups of about an order of magnitude.

approach, Artificial Intelligence, case, constraint, evolutionary algorithm, Figure, formation evaluation, function, function evaluation, geologic modeling, grid, iteration, level, location, machine learning, optimization problem, procedure, produced water, production control, production monitoring, reservoir simulation, scaling method, shale gas, simulator development, solution, waterflooding, well

SPE Disciplines:

Compositional simulation can be very demanding computationally as a result of the potentially large number of system unknowns and the intrinsic nonlinearity of typical problems. In this work, we develop a reduced-order modeling procedure for compositional simulation. The technique combines trajectory piecewise linearization (TPWL) and proper orthogonal decomposition (POD) to provide a highly efficient surrogate model. The compositional POD-TPWL method expresses new solutions in terms of linearizations around states generated (and saved) during previously simulated "training" runs. High-dimensional states are projected (optimally) into a low-dimensional subspace by use of POD. The compositional POD-TPWL model is based on a molar formulation that uses pressure and overall component mole fractions as the primary unknowns. Several new POD-TPWL treatments, including the use of a Petrov-Galerkin projection to reduce the number of equations (rather than the Galerkin projection, which was applied previously), and a new procedure for determining which saved state to use for linearization are incorporated into the method. Results are presented for heterogeneous 3D reservoir models containing oil and gas phases with up to six hydrocarbon components. Reasonably close agreement between full-order reference solutions and compositional POD-TPWL simulations is demonstrated for the cases considered. Construction of the POD-TPWL model requires preprocessing overhead computations equivalent to approximately three or four full-order runs. Runtime speedups by use of POD-TPWL are, however, very significant—up to a factor of 800 for the cases considered. The POD-TPWL model is thus well suited for use in computational optimization, in which many simulations must be performed, and we present an example demonstrating its application for such a problem.

approach, Artificial Intelligence, case, component, flow in porous media, Fluid Dynamics, formation evaluation, gas injection method, geologic modeling, history matching, matrix, optimization problem, pressure, procedure, producer, production control, production logging, production monitoring, reservoir simulation, result, scaling method, Simulation, simulator development, solution, State, test, time, training, training simulation, use, well

Oilfield Places:

- North America > Canada > Saskatchewan > Williston Basin > Midale Field > Midale Reservoir (0.99)
- North America > Canada > Saskatchewan > Williston Basin > Midale Field > Charles Formation (0.99)
- North America > United States > Louisiana > University Oil Field (0.98)

SPE Disciplines:

The optimization of general oilfield development problems is considered. Techniques are presented to simultaneously determine the optimal number and type of new wells, the sequence in which they should be drilled, and their corresponding locations and (time-varying) controls. The optimization is posed as a mixed-integer nonlinear programming (MINLP) problem and involves categorical, integer-valued, and real-valued variables. The formulation handles bound, linear, and nonlinear constraints, with the latter treated with filter-based techniques. Noninvasive derivative-free approaches are applied for the optimizations. Methods considered include branch and bound (B&B), a rigorous global-search procedure that requires relaxation of the categorical variables; mesh adaptive direct search (MADS), a local pattern-search method; particle swarm optimization (PSO), a heuristic global-search method; and a PSO-MADS hybrid. Four example cases involving channelized-reservoir models are presented. The recently developed PSO-MADS hybrid is shown to consistently outperform the standalone MADS and PSO procedures. In the two cases in which B&B is applied, the heuristic PSO-MADS approach is shown to give comparable solutions but at much lower computational cost. This is significant since B&B provides a systematic search in the categorical variables. We conclude that, although it is demanding in terms of computation, the methodology presented here, with PSO-MADS as the core optimization method, appears to be applicable for realistic reservoir development and management.

Artificial Intelligence, case, constraint, evolutionary algorithm, formation evaluation, injection, iteration, location, machine learning, method, number, optimization problem, production control, production monitoring, PSO, relaxation, reservoir simulation, Run, simulator development, Software Engineering, solution, variable, waterflooding, well

SPE Disciplines: