Ensemble-based Methods for Well Drilling Sequence and Time Optimization under Uncertainty

Leeuwenburgh, O.; Chitu, Alin; Nair, R.; Egberts, P.J.P.; Ghazaryan, L.; Feng, Tao; Hustoft, L.

doi:10.3997/2214-4609.201601871

Cited by 15 publications

(6 citation statements)

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“…The model is the same as was used in Evensen et al [12], and we will not describe the model at length here but rather focus on the impact of introducing correlated measurement errors for a reservoir case. The model was previously used also by Leeuwenburgh et al [18],Hanea et al [14], and Wang and Oliver [26], and we refer to these papers for a detailed presentation.…”

Section: Reservoir Experimentsmentioning

confidence: 99%

Formulating the history matching problem with consistent error statistics

Evensen

2021

Comput Geosci

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It is common to formulate the history-matching problem using Bayes’ theorem. From Bayes’, the conditional probability density function (pdf) of the uncertain model parameters is proportional to the prior pdf of the model parameters, multiplied by the likelihood of the measurements. The static model parameters are random variables characterizing the reservoir model while the observations include, e.g., historical rates of oil, gas, and water produced from the wells. The reservoir prediction model is assumed perfect, and there are no errors besides those in the static parameters. However, this formulation is flawed. The historical rate data only approximately represent the real production of the reservoir and contain errors. History-matching methods usually take these errors into account in the conditioning but neglect them when forcing the simulation model by the observed rates during the historical integration. Thus, the model prediction depends on some of the same data used in the conditioning. The paper presents a formulation of Bayes’ theorem that considers the data dependency of the simulation model. In the new formulation, one must update both the poorly known model parameters and the rate-data errors. The result is an improved posterior ensemble of prediction models that better cover the observations with more substantial and realistic uncertainty. The implementation accounts correctly for correlated measurement errors and demonstrates the critical role of these correlations in reducing the update’s magnitude. The paper also shows the consistency of the subspace inversion scheme by Evensen (Ocean Dyn. 54, 539–560 2004) in the case with correlated measurement errors and demonstrates its accuracy when using a “larger” ensemble of perturbations to represent the measurement error covariance matrix.

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Section: Reservoir Experimentsmentioning

confidence: 99%

Formulating the history matching problem with consistent error statistics

Evensen

2021

Comput Geosci

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“…Assuming that a trajectory is available for each well that is nominated to be drilled, the drilling schedule (order and timing for all wells) needs to be determined. Different options to represent the drilling schedule in combination with other development options such as well location and type were briefly reviewed by Leeuwenburgh et al [25]. In particular, Isebor et al [21] use an approach that uses a list of possible wells with a fixed drilling order, and the position and type, as well as a binary control to indicate if the well is to be drilled or not, are optimized to arrive at the final drilling schedule.…”

Section: Drilling Schedule Parameterizationmentioning

confidence: 99%

“…In this approach, if the drilling order for a producer and an injector, which are drilled one after the other, is to be reversed, both the well type and locations need to be switched. An alternative approach suitable for approximate gradients that does not require the use of binary controls was proposed by Leeuwenburgh et al [25]. They suggested a more direct parameterization of the drilling order by means of so-called priority controls.…”

Section: Drilling Schedule Parameterizationmentioning

confidence: 99%

“…Furthermore, the connections between each proposed well trajectory and the reservoir are computed using an open-source tool [28], and simulations are performed with an open-source reservoir simulator (Open Porous Media [29]), which enables application of the workflow on computing clusters without requirement for interaction with a geological modeling tool. The drilling schedule will be optimized in a separate step using so-called priority controls (Leeuwenburgh et al [25]).…”

Section: Introductionmentioning

confidence: 99%

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Ensemble-based well trajectory and drilling schedule optimization—application to the Olympus benchmark model

2020

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The general field development optimization problem is complex due to the potentially large number of controls of mixed type and discontinuities in the objective function related to varying numbers and types of wells being placed in a discretized grid. This may make the problem challenging or even unsuitable for certain types of optimization methods that rely on, e.g., the availability of (adjoint) gradients. It is not yet clear which alternative approaches will be most useful. Here we investigate the application of stochastic gradient-based optimization techniques to field development optimization. Since their initial application to large-scale well rate and pressure control problems, such techniques have been shown to produce useful results of practical value also for other types of reservoir optimization problems such vertical well placement, well drilling scheduling, and water-alternating-gas strategy optimization. Here we introduce an efficient parameterization for well trajectory optimization and discuss a simple way to handle the number of wells that is placed. The full field development problem is split into subproblems that are addressed sequentially. The sequential workflow is applied to the Olympus benchmark model which represents a complex green field development optimization challenge. Initial experiments show that the proposed approach based on stochastic gradient methods is able to find much improved development strategies, as defined by the number and trajectories of wells, a platform location and a drilling sequence, at relatively low computational cost. We additionally identify a number of possible improvements to the applied workflow that are expected to make it applicable to other field cases of intermediate complexity.

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“…In this example, we design a set of experiments to study the bias properties of the drilling-order problem applied to the synthetic REEK Field model [18,29,40], and the performances of various methods for estimating the bias for both complete and heuristic sequences by using the information from distinct controls and individual realizations. The objective of the robust optimization problem is maximization of the 10-year expected NPV with respect to the drilling schedule of wells.…”

Section: Reservoir Modelmentioning

confidence: 99%

Fast robust optimization using bias correction applied to the mean model

Wang

Oliver

2020

Comput Geosci

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Ensemble methods are remarkably powerful for quantifying geological uncertainty. However, the use of the ensemble of reservoir models for robust optimization (RO) can be computationally demanding. The straightforward computation of the expected net present value (NPV) requires many expensive simulations. To reduce the computational burden without sacrificing accuracy, we present a fast and effective approach that requires only simulation of the mean reservoir model with a bias correction factor. Information from distinct controls and model realizations can be used to estimate bias for different controls. The effectiveness of various bias-correction methods and a linear or quadratic approximation is illustrated by two applications: flow optimization in a one-dimensional model and the drilling-order problem in a synthetic field model. The results show that the approximation of the expected NPV from the mean model is significantly improved by estimating the bias correction factor, and that RO with mean model bias correction is superior to both RO performed using a Taylor series representation of uncertainty and deterministic optimization from a single realization. Use of the bias-corrected mean model to account for model uncertainty allows the application of fairly general optimization methods. In this paper, we apply a nonparametric online learning methodology (learned heuristic search) for efficiently computing an optimal or near-optimal robust drilling sequence on the REEK Field example. This methodology can be used either to optimize a complete drilling sequence or to optimize only the first few wells at a reduced cost by limiting the search depths.

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Ensemble-based Methods for Well Drilling Sequence and Time Optimization under Uncertainty

Cited by 15 publications

References 0 publications

Formulating the history matching problem with consistent error statistics

Formulating the history matching problem with consistent error statistics

Ensemble-based well trajectory and drilling schedule optimization—application to the Olympus benchmark model

Fast robust optimization using bias correction applied to the mean model

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