共查询到20条相似文献，搜索用时 652 毫秒
1.
Oilfield development involves several key decisions, including the number, type (injection/production), location, drilling schedule, and operating control trajectories of the wells. Without considering the coupling between these decision variables, any optimization problem formulation is bound to find suboptimal solutions. This paper presents a unified formulation for oilfield development optimization that seeks to simultaneously optimize these decision variables. We show that the source/sink term of the governing multiphase flow equations includes all the above decision variables. This insight leads to a novel and unified formulation of the field development optimization problem that considers the source/sink term in reservoir simulation equations as optimization decision variables. Therefore, a single optimization problem is formulated to simultaneously search for optimal decision variables by determining the complete dynamic form of the source/sink terms. The optimization objective function is the project net present value (NPV), which involves discounted revenue from oil production, operating costs (e.g. water injection and recycling), and capital costs (e.g., cost of drilling wells). A major difficulty after formulating the generalized field development optimization problem is finding an efficient solution approach. Since the total number of cells in a reservoir model far exceeds the number of cells that are intersected by wells, the source/sink terms tend to be sparse. In fact, the drilling cost in the NPV objective function serves as a sparsity-promoting penalty to minimize the number of wells while maximizing the NPV. Inspired by this insight, we solve the optimization problem using an efficient gradient-based method based on recent algorithmic developments in sparse reconstruction literature. The gradients of the NPV function with respect to the source/sink terms is readily computed using well-established adjoint methods. Numerical experiments are presented to evaluate the feasibility and performance of the generalized field development formulation for simultaneous optimization of the number, location, type, controls, and drilling schedule of the wells. 相似文献
2.
In a recent paper, we developed a physics-based data-driven model referred to as INSIM-FT and showed that it can be used for history matching and future reservoir performance predictions even when no prior geological model is available. The model requires no prior knowledge of petrophysical properties. In this work, we explore the possibility of using INSIM-FT in place of a reservoir simulation model when estimating the well controls that optimize water flooding performance where we use the net present value (NPV) of life-cycle production as our cost (objective) function. The well controls are either the flowing bottom-hole pressure (BHP) or total liquid rates at injectors and producers on the time intervals which represent the prescribed control steps. The optimal well controls that maximize NPV are estimated with an ensemble-based optimization algorithm using the history-matched INSIM-FT model as the forward model. We compare the optimal NPV obtained using INSIM-FT as the forward model with the estimate of the optimal NPV obtained using the correct full-scale reservoir simulation model when performing waterflooding optimization. 相似文献
3.
Andrea Capolei Eka Suwartadi Bjarne Foss John Bagterp Jørgensen 《Computational Geosciences》2013,17(6):991-1013
In conventional waterflooding of an oil field, feedback based optimal control technologies may enable higher oil recovery than with a conventional reactive strategy in which producers are closed based on water breakthrough. To compensate for the inherent geological uncertainties in an oil field, robust optimization has been suggested to improve and robustify optimal control strategies. In robust optimization of an oil reservoir, the water injection and production borehole pressures (bhp) are computed such that the predicted net present value (NPV) of an ensemble of permeability field realizations is maximized. In this paper, we both consider an open-loop optimization scenario, with no feedback, and a closed-loop optimization scenario. The closed-loop scenario is implemented in a moving horizon manner and feedback is obtained using an ensemble Kalman filter for estimation of the permeability field from the production data. For open-loop implementations, previous test case studies presented in the literature, show that a traditional robust optimization strategy (RO) gives a higher expected NPV with lower NPV standard deviation than a conventional reactive strategy. We present and study a test case where the opposite happen: The reactive strategy gives a higher expected NPV with a lower NPV standard deviation than the RO strategy. To improve the RO strategy, we propose a modified robust optimization strategy (modified RO) that can shut in uneconomical producer wells. This strategy inherits the features of both the reactive and the RO strategy. Simulations reveal that the modified RO strategy results in operations with larger returns and less risk than the reactive strategy, the RO strategy, and the certainty equivalent strategy. The returns are measured by the expected NPV and the risk is measured by the standard deviation of the NPV. In closed-loop optimization, we investigate and compare the performance of the RO strategy, the reactive strategy, and the certainty equivalent strategy. The certainty equivalent strategy is based on a single realization of the permeability field. It uses the mean of the ensemble as its permeability field. Simulations reveal that the RO strategy and the certainty equivalent strategy give a higher NPV compared to the reactive strategy. Surprisingly, the RO strategy and the certainty equivalent strategy give similar NPVs. Consequently, the certainty equivalent strategy is preferable in the closed-loop situation as it requires significantly less computational resources than the robust optimization strategy. The similarity of the certainty equivalent and the robust optimization based strategies for the closed-loop situation challenges the intuition of most reservoir engineers. Feedback reduces the uncertainty and this is the reason for the similar performance of the two strategies. 相似文献
4.
5.
Large-scale history matching with quadratic interpolation models 总被引：2，自引：0，他引：2
6.
Theoretical connections between optimization algorithms based on an approximate gradient 总被引：1，自引：0，他引：1
Performing a line search method in the direction given by the simplex gradient is a well-known method in the mathematical optimization community. For reservoir engineering optimization problems, both a modification of the simultaneous perturbation stochastic approximation (SPSA) and ensemble-based optimization (EnOpt) have recently been applied for estimating optimal well controls in the production optimization step of closed-loop reservoir management. The modified SPSA algorithm has also been applied to assisted history-matching problems. A recent comparison of the performance of EnOpt and a SPSA-type algorithm (G-SPSA) for a set of production optimization test problems showed that the two algorithms resulted in similar estimates of the optimal net-present-value and required roughly the same amount of computational time to achieve these estimates. Here, we show that, theoretically, this result is not surprising. In fact, we show that both the simplex, preconditioned simplex, and EnOpt algorithms can be derived directly from a modified SPSA-type algorithm where the preconditioned simplex algorithm is presented for the first time in this paper. We also show that the expectation of all these preconditioned stochastic gradients is a first-order approximation of the preconditioning covariance matrix times the true gradient or a covariance matrix squared times the true gradient. 相似文献
7.
Dimitris Papadopoulos Michael Herty Volker Rath Marek Behr 《Computational Geosciences》2011,15(4):737-753
A shape reconstruction method for geophysical objects by temperature measurements is presented which uses adjoint equations
and a level set function approach. Temperature is measured on subdomains, e.g., representing boreholes. This information is
used to reconstruct the shape of the geophysical layers. For this purpose, shape optimization techniques are applied. The
method uses a representation of the layers by a so-called level set function. The evolution of this level set function is
then used to determine the optimal shape. The “speed” of the evolution is computed using adjoint equations. Synthetic examples
demonstrate the use of the inverse method and its behavior in different configurations. 相似文献
8.
Małgorzata P. Kaleta Remus G. Hanea Arnold W. Heemink Jan-Dirk Jansen 《Computational Geosciences》2011,15(1):135-153
Gradient-based history matching algorithms can be used to adapt the uncertain parameters in a reservoir model using production
data. They require, however, the implementation of an adjoint model to compute the gradients, which is usually an enormous
programming effort. We propose a new approach to gradient-based history matching which is based on model reduction, where
the original (nonlinear and high-order) forward model is replaced by a linear reduced-order forward model and, consequently,
the adjoint of the tangent linear approximation of the original forward model is replaced by the adjoint of a linear reduced-order
forward model. The reduced-order model is constructed with the aid of the proper orthogonal decomposition method. Due to the
linear character of the reduced model, the corresponding adjoint model is easily obtained. The gradient of the objective function
is approximated, and the minimization problem is solved in the reduced space; the procedure is iterated with the updated estimate
of the parameters if necessary. The proposed approach is adjoint-free and can be used with any reservoir simulator. The method
was evaluated for a waterflood reservoir with channelized permeability field. A comparison with an adjoint-based history matching
procedure shows that the model-reduced approach gives a comparable quality of history matches and predictions. The computational
efficiency of the model-reduced approach is lower than of an adjoint-based approach, but higher than of an approach where
the gradients are obtained with simple finite differences. 相似文献
9.
Reduced-order optimal control of water flooding using proper orthogonal decomposition 总被引：1，自引：0，他引：1
Jorn F. M. van Doren Renato Markovinović Jan-Dirk Jansen 《Computational Geosciences》2006,10(1):137-158
Model-based optimal control of water flooding generally involves multiple reservoir simulations, which makes it into a time-consuming
process. Furthermore, if the optimization is combined with inversion, i.e., with updating of the reservoir model using production
data, some form of regularization is required to cope with the ill-posedness of the inversion problem. A potential way to
address these issues is through the use of proper orthogonal decomposition (POD), also known as principal component analysis,
Karhunen–Loève decomposition or the method of empirical orthogonal functions. POD is a model reduction technique to generate
low-order models using ‘snapshots’ from a forward simulation with the original high-order model. In this work, we addressed
the scope to speed up optimization of water-flooding a heterogeneous reservoir with multiple injectors and producers. We used
an adjoint-based optimal control methodology that requires multiple passes of forward simulation of the reservoir model and
backward simulation of an adjoint system of equations. We developed a nested approach in which POD was first used to reduce
the state space dimensions of both the forward model and the adjoint system. After obtaining an optimized injection and production
strategy using the reduced-order system, we verified the results using the original, high-order model. If necessary, we repeated
the optimization cycle using new reduced-order systems based on snapshots from the verification run. We tested the methodology
on a reservoir model with 4050 states (2025 pressures, 2025 saturations) and an adjoint model of 4050 states (Lagrange multipliers).
We obtained reduced-order models with 20–100 states only, which produced almost identical optimized flooding strategies as
compared to those obtained using the high-order models. The maximum achieved reduction in computing time was 35%. 相似文献
10.
Waterflooding using closed-loop control 总被引：2，自引：0，他引：2
To fully exploit the possibilities of “smart” 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 pressure-constrained situation. Furthermore,
the methodology is not restricted to use with “smart” wells 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. 相似文献
11.
Dmitry Eydinov Sigurd Ivar Aanonsen Jarle Haukås Ivar Aavatsmark 《Computational Geosciences》2008,12(2):209-225
A method for history matching of an in-house petroleum reservoir compositional simulator with multipoint flux approximation
is presented. This method is used for the estimation of unknown reservoir parameters, such as permeability and porosity, based
on production data and inverted seismic data. The limited-memory Broyden–Fletcher–Goldfarb–Shanno method is employed for minimization
of the objective function, which represents the difference between simulated and observed data. In this work, we present the
key features of the algorithm for calculations of the gradients of the objective function based on adjoint variables. The
test example shows that the method is applicable to cases with anisotropic permeability fields, multipoint flux approximation,
and arbitrary fluid compositions. 相似文献
12.
In a previous paper, we developed a theoretical basis for parameterization of reservoir model parameters based on truncated
singular value decomposition (SVD) of the dimensionless sensitivity matrix. Two gradient-based algorithms based on truncated
SVD were developed for history matching. In general, the best of these “SVD” algorithms requires on the order of 1/2 the number
of equivalent reservoir simulation runs that are required by the limited memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) algorithm.
In this work, we show that when combining SVD parameterization with the randomized maximum likelihood method, we can achieve
significant additional computational savings by history matching all models simultaneously using a SVD parameterization based
on a particular sensitivity matrix at each iteration. We present two new algorithms based on this idea, one which relies only
on updating the SVD parameterization at each iteration and one which combines an inner iteration based on an adjoint gradient
where during the inner iteration the truncated SVD parameterization does not vary. Results generated with our algorithms are
compared with results obtained from the ensemble Kalman filter (EnKF). Finally, we show that by combining EnKF with the SVD-algorithm,
we can improve the reliability of EnKF estimates. 相似文献
13.
Multiobjective optimization deals with mathematical optimization problems where two or more objective functions (cost functions) are to be optimized (maximized or minimized) simultaneously. In most cases of interest, the objective functions are in conflict, i.e., there does not exist a decision (design) vector (vector of optimization variables) at which every objective function takes on its optimal value. The solution of a multiobjective problem is commonly defined as a Pareto front, and any decision vector which maps to a point on the Pareto front is said to be Pareto optimal. We present an original derivation of an analytical expression for the steepest descent direction for multiobjective optimization for the case of two objectives. This leads to an algorithm which can be applied to obtain Pareto optimal points or, equivalently, points on the Pareto front when the problem is the minimization of two conflicting objectives. The method is in effect a generalization of the steepest descent algorithm for minimizing a single objective function. The steepest-descent multiobjective optimization algorithm is applied to obtain optimal well controls for two example problems where the two conflicting objectives are the maximization of the life-cycle (long-term) net-present-value (NPV) and the maximization of the short-term NPV. The results strongly suggest the multiobjective steepest-descent (MOSD) algorithm is more efficient than competing multiobjective optimization algorithms. 相似文献
14.
This paper proposes an augmented Lagrangian method for production optimization in which the cost function to be maximized
is defined as an augmented Lagrangian function consisting of the net present value (NPV) and all the equality and inequality
constraints except the bound constraints. The bound constraints are dealt with using a trust-region gradient projection method.
The paper also presents a way to eliminate the need to convert the inequality constraints to equality constraints with slack
variables in the augmented Lagrangian function, which greatly reduces the size of the optimization problem when the number
of inequality constraints is large. The proposed method is tested in the context of closed-loop reservoir management benchmark
problem based on the Brugge reservoir setup by TNO. In the test, we used the ensemble Kalman filter (EnKF) with covariance
localization for data assimilation. Production optimization is done on the updated ensemble mean model from EnKF. The production
optimization resulted in a substantial increase in the NPV for the expected reservoir life compared to the base case with
reactive control. 相似文献
15.
Well placement optimization with the covariance matrix adaptation evolution strategy and meta-models
The amount of hydrocarbon recovered can be considerably increased by finding optimal placement of non-conventional wells.
For that purpose, the use of optimization algorithms, where the objective function is evaluated using a reservoir simulator,
is needed. Furthermore, for complex reservoir geologies with high heterogeneities, the optimization problem requires algorithms
able to cope with the non-regularity of the objective function. In this paper, we propose an optimization methodology for
determining optimal well locations and trajectories based on the covariance matrix adaptation evolution strategy (CMA-ES)
which is recognized as one of the most powerful derivative-free optimizers for continuous optimization. In addition, to improve
the optimization procedure, two new techniques are proposed: (a) adaptive penalization with rejection in order to handle well
placement constraints and (b) incorporation of a meta-model, based on locally weighted regression, into CMA-ES, using an approximate
stochastic ranking procedure, in order to reduce the number of reservoir simulations required to evaluate the objective function.
The approach is applied to the PUNQ-S3 case and compared with a genetic algorithm (GA) incorporating the Genocop III technique
for handling constraints. To allow a fair comparison, both algorithms are used without parameter tuning on the problem, and
standard settings are used for the GA and default settings for CMA-ES. It is shown that our new approach outperforms the genetic
algorithm: It leads in general to both a higher net present value and a significant reduction in the number of reservoir simulations
needed to reach a good well configuration. Moreover, coupling CMA-ES with a meta-model leads to further improvement, which
was around 20% for the synthetic case in this study. 相似文献
16.
Large-scale flow models constructed using standard coarsening procedures may not accurately resolve detailed near-well effects.
Such effects are often important to capture, however, as the interaction of the well with the formation can have a dominant
impact on process performance. In this work, a near-well upscaling procedure, which provides three-phase well-block properties,
is developed and tested. The overall approach represents an extension of a recently developed oil–gas upscaling procedure
and entails the use of local well computations (over a region referred to as the local well model (LWM)) along with a gradient-based
optimization procedure to minimize the mismatch between fine and coarse-scale well rates, for oil, gas, and water, over the
LWM. The gradients required for the minimization are computed efficiently through solution of adjoint equations. The LWM boundary
conditions are determined using an iterative local-global procedure. With this approach, pressures and saturations computed
during a global coarse-scale simulation are interpolated onto LWM boundaries and then used as boundary conditions for the
fine-scale LWM computations. In addition to extending the overall approach to the three-phase case, this work also introduces
new treatments that provide improved accuracy in cases with significant flux from the gas cap into the well block. The near-well
multiphase upscaling method is applied to heterogeneous reservoir models, with production from vertical and horizontal wells.
Simulation results illustrate that the method is able to accurately capture key near-well effects and to provide predictions
for component production rates that are in close agreement with reference fine-scale results. The level of accuracy of the
procedure is shown to be significantly higher than that of a standard approach which uses only upscaled single-phase flow
parameters. 相似文献
17.
A real-time operation optimization model for flood management in river-reservoir systems 总被引：1，自引：1，他引：0
In this paper, a new methodology has been developed for real-time flood management in river-reservoir systems. This methodology
is based upon combining a Genetic Algorithm (GA) reservoir operation optimization model for a cascade of two reservoirs, a
hydraulic-based flood routing simulation model in downstream river system, a Geographical Information System (GIS) based database,
and application of K-Nearest Neighbor (K-NN) algorithm for development of optimal operating rules. The GA optimization model
estimates the optimal hourly reservoirs’ releases to minimize the flood damages in the downstream river. GIS tools have also
been used for specifying different land-uses and damage functions in the downstream floodplain and it has been linked to the
unsteady module of HEC-RAS flood routing model using Hec-GeoRAS module. An innovative approach has also been developed using
K-NN algorithm to formulate the optimal operating rules for a system of two cascade reservoirs based on optimal releases obtained
from the optimization model. During a flood event, the K-NN algorithm searches through the historical flood hydrographs and
optimal reservoir storages determined by the optimization model to find similar situations. The similarity between the hydrographs
is quantified based on the slopes of rising and falling limbs of inflow hydrographs and reservoir storages at the beginning
of each hourly time step during the flood events for two cascade reservoirs. The developed methodology have been applied to
the Bakhtiari and Dez River-Reservoir systems in southwest of Iran. The results show that the proposed models can be effectively
used for flood management and real-time operation of cascade river-reservoir systems. 相似文献
18.
In geosciences, complex forward problems met in geophysics, petroleum system analysis, and reservoir engineering problems often require replacing these forward problems by proxies, and these proxies are used for optimizations problems. For instance, history matching of observed field data requires a so large number of reservoir simulation runs (especially when using geostatistical geological models) that it is often impossible to use the full reservoir simulator. Therefore, several techniques have been proposed to mimic the reservoir simulations using proxies. Due to the use of experimental approach, most authors propose to use second-order polynomials. In this paper, we demonstrate that (1) neural networks can also be second-order polynomials. Therefore, the use of a neural network as a proxy is much more flexible and adaptable to the nonlinearity of the problem to be solved; (2) first-order and second-order derivatives of the neural network can be obtained providing gradients and Hessian for optimizers. For inverse problems met in seismic inversion, well by well production data, optimal well locations, source rock generation, etc., most of the time, gradient methods are used for finding an optimal solution. The paper will describe how to calculate these gradients from a neural network built as a proxy. When needed, the Hessian can also be obtained from the neural network approach. On a real case study, the ability of neural networks to reproduce complex phenomena (water cuts, production rates, etc.) is shown. Comparisons with second polynomials (and kriging methods) will be done demonstrating the superiority of the neural network approach as soon as nonlinearity behaviors are present in the responses of the simulator. The gradients and the Hessian of the neural network will be compared to those of the real response function. 相似文献
19.
W. Bangerth H. Klie M. F. Wheeler P. L. Stoffa M. K. Sen 《Computational Geosciences》2006,10(3):303-319
Determining optimal locations and operation parameters for wells in oil and gas reservoirs has a potentially high economic impact. Finding these optima depends on a complex combination of geological, petrophysical, flow regimen, and economical parameters that are hard to grasp intuitively. On the other hand, automatic approaches have in the past been hampered by the overwhelming computational cost of running thousands of potential cases using reservoir simulators, given that each of these runs can take on the order of hours. Therefore, the key issue to such automatic optimization is the development of algorithms that find good solutions with a minimum number of function evaluations. In this work, we compare and analyze the efficiency, effectiveness, and reliability of several optimization algorithms for the well placement problem. In particular, we consider the simultaneous perturbation stochastic approximation (SPSA), finite difference gradient (FDG), and very fast simulated annealing (VFSA) algorithms. None of these algorithms guarantees to find the optimal solution, but we show that both SPSA and VFSA are very efficient in finding nearly optimal solutions with a high probability. We illustrate this with a set of numerical experiments based on real data for single and multiple well placement problems. 相似文献
20.
Mathias C. Bellout David Echeverría Ciaurri Louis J. Durlofsky Bjarne Foss Jon Kleppe 《Computational Geosciences》2012,16(4):1061-1079
Well placement and control optimization in oil field development are commonly performed in a sequential manner. In this work, we propose a joint approach that embeds well control optimization within the search for optimum well placement configurations. We solve for well placement using derivative-free methods based on pattern search. Control optimization is solved by sequential quadratic programming using gradients efficiently computed through adjoints. Joint optimization yields a significant increase, of up to 20% in net present value, when compared to reasonable sequential approaches. The joint approach does, however, require about an order of magnitude increase in the number of objective function evaluations compared to sequential procedures. This increase is somewhat mitigated by the parallel implementation of some of the pattern-search algorithms used in this work. Two pattern-search algorithms using eight and 20 computing cores yield speedup factors of 4.1 and 6.4, respectively. A third pattern-search procedure based on a serial evaluation of the objective function is less efficient in terms of clock time, but the optimized cost function value obtained with this scheme is marginally better. 相似文献