A Practical Approach to Select Representative Deterministic Models Using Multiobjective Optimization from an Integrated Uncertainty Quantification Workflow

Simulation models for large complex reservoirs with a long production history are traditionally used in the framework of deterministic forecasts. The estimation of prediction uncertainties based on reservoir models with long run times is often impractical due to limited statistical data generated from direct full field reservoir simulation runs. Here, we use surrogate models to capture key performance indicators as a function of reservoir uncertainties. Monte Carlo sampling processes are applied for generating key parameter distributions and to identify representative simulation models for field development planning. Transparent workflow steps and a thorough validation exercise of the predictability of surrogate models is a prerequisite for obtaining prediction uncertainties based on proxy modeling results. In this work we present a case study for estimating prediction uncertainties including history data of a large mature offshore oil field. A workflow is designed for a limited number of simulation runs which is expected to affect the stability of statistical reservoir performance indicators. Proxy models are introduced in that framework for analyzing sensitivities and to prepare a basis for extensive data sampling. Alternative proxy modeling techniques are used to cross validate results. To assure an acceptable quality of the history match simulated field oil production rate and gas oil ratio as well as water cut and shut-in pressures in several wells are compared to their historical data. A quantitative measure for the simulation error is calculated for each case. Filtering techniques are applied for discriminating cases with a poor match quality. Sensitivities and correlation effects between field wide uncertainties and reservoir performance indicators are calculated. Representative full field simulation models representing P10, P50 and P90 for oil reserves are identified. The uncertainty quantification workflow was validated for a mature field case study and serves as a basis for field development planning scenarios.

Full-physics models in history matching and optimization can be computationally expensive since these problems usually require hundreds of simulations or more. We have previously implemented a physics-based data-driven network model with a commercial simulator that serves as a surrogate without the need to build the 3-D geological model. In this paper, we reconstruct the network model to account for complex reservoir conditions of mature fields and successfully apply it to a diatomite reservoir in the San Joaquin Valley (SJV) for rapid history matching and optimization. The reservoir is simplified into a network of 1-D connections between well perforations. These connections are discretized into grid blocks and the grid properties are calibrated to historical production data. Elevation change, saturation distribution, capillary pressure, and relative permeability are accounted for to best represent the mature field conditions. To simulate this physics-based network model through a commercial simulator, an equivalent 2-D Cartesian model is designed where rows correspond to the above-mentioned connections. Thereafter, the history matching can be performed with the Ensemble Smoother with Multiple Data Assimilation (ESMDA) algorithm under a sequential iterative process. A representative model after history matching is then employed for well control optimization. The network model methodology has been successfully applied to the waterflood optimization for a 56-well sector model of a diatomite reservoir in the SJV. History matching result shows that the network model honors field-level production history and gives reasonable matches for most of the wells, including pressure and flow rate. The calibrated ensemble from the last iteration of history matching yields a satisfactory production prediction, which is verified by the remaining historical data. For well control optimization, we select the P50 model to maximize the Net Present Value (NPV) in 5 years under provided well/field constraints. This confirms that the calibrated network model is accurate enough for production forecasts and optimization. The use of a commercial simulator in the network model provided flexibility to account for complex physics, such as elevation difference between wells, saturation non-equilibrium, and strong capillary pressure. Unlike traditional big-loop workflow that relies on a detailed characterization of geological models, the proposed network model only requires production data and can be built and updated rapidly. The model also runs much faster (tens of seconds) than a full-physics model due to the employment of much fewer grid blocks. To our knowledge, this is the first time this physics-based data-driven network model is applied with a commercial simulator on a field waterflood case. Unlike approaches developed with analytic solutions, the use of commercial simulator makes it feasible to be further extended for complex processes, e.g., thermal or compositional flow. It serves as an useful surrogate model for both fast and reliable decision-making in reservoir management.

In recent years, more traditional history matching methods have been increasingly challenged by sequential data assimilation techniques such as the ensemble Kalman filter (EnKF). There are strong similarities between EnKF and the non-sequential method, randomized maximum likelihood (RML). For a linear forward model the two methods are equal, for a nonlinear forward model there arises some differences (in addition to sequential/batch data assimilation): RML can be iterative, while EnKF is not; RML uses realization-specific gradients/sensitivities to change a model realization while EnKF uses the same covariance for all realizations. We assess the sampling capabilities of RML and EnKF for a weakly nonlinear forward model. Results are compared to a Markov chain Monte Carlo (McMC) method, which samples correctly from the posterior. Our aim is to clarify which of the above mentioned differences between RML and EnKF has the biggest impact on the sampling capabilities. We apply the methods to a two-phase reservoir models small enough to be suitable for McMC. The assessment of RML and EnKF is performed by comparing history matching capabilities, and properties of their posterior distributions to those of the posterior distributions obtained with McMC.

Optimization of solar-coal hybridization for low solar augmentation

SummaryFull-physics models in history matching (HM) and optimization can be computationally expensive because these problems usually require hundreds of simulations or more. In a previous study, a physics-based data-driven network model was implemented with a commercial simulator that served as a surrogate without the need to build a 3D geological model. In this paper, the network model is reconstructed to account for complex reservoir conditions of mature fields and successfully apply it to a diatomite reservoir in the San Joaquin Valley, California, for rapid HM and optimization.The reservoir is simplified into a network of 1D connections between well perforations. These connections are discretized into gridblocks, and the grid properties are calibrated to historical production data. Elevation change, saturation distribution, capillary pressure, and relative permeability are accounted for to best represent the mature field conditions. To simulate this physics-based network model through a commercial simulator, an equivalent Cartesian model is designed where rows correspond to the previously mentioned connections. Thereafter, the HM can be performed with the ensemble smoother with multiple data assimilation (ESMDA) algorithm under a sequential iterative process. A representative model after HM is then used for well control optimization.The network model methodology has been successfully applied to the waterflood optimization for a 56-well sector model of a diatomite reservoir in the San Joaquin Valley. HM results show that the network model matches with field level production history and gives reasonable matches for most of the wells, including pressure and volumetric data. The calibrated posterior ensemble of HM yields a satisfactory production prediction that is verified by the remaining historical data. For well control optimization, the P50 model is selected to maximize the net present value (NPV) in 5 years under provided well/field constraints. This confirms that the calibrated network model is accurate enough for production forecasts and optimization. The use of a commercial simulator in the network model provided flexibility to account for complex physics, such as elevation difference between wells, saturation nonequilibrium, and strong capillary pressure. Unlike the traditional big-loop workflow that relies on a detailed characterization of geological models, the proposed network model only requires production data and can be built and updated rapidly. The model also runs much faster (tens of seconds) than a full-physics model because of the use of much fewer gridblocks.To our knowledge, this is the first time this physics-based data-driven network model is applied with a commercial simulator on a field waterflood case. Unlike approaches developed with analytic solutions, the use of a commercial simulator makes it feasible to be further extended for complex processes (e.g., thermal or compositional flow). It serves as a useful surrogate model for both fast and reliable decision-making in reservoir management.

Summary CO2-water-alternating-gas (CO2-WAG) is a reservoir development method that can simultaneously enhance oil recovery and achieve CO2 storage. However, improperly designed parameters for CO2 injection and oil production may significantly reduce the oil displacement efficiency and CO2 storage. Furthermore, optimizing the injection parameters is computationally expensive due to the high computational cost of the compositional simulation. This work aims to propose an efficient optimization method to obtain a series of well-control schemes that balance maximizing net present value (NPV) and CO2 storage for decision-makers. Given the number of CO2-WAG cycles and the duration of each cycle, we optimize the water injection rate, gas injection rate, and half-cycle for the injection well and the bottomhole pressure (BHP) for the production well. In this paper, a two-stage optimization strategy is proposed to enhance the optimization efficiency. The first stage performs the surrogate-assisted single-objective optimizations of each considered objective. It is designed to find the endpoints of the Pareto front that connect all solutions of the multiobjective optimization; this stage not only provides important search directions for the subsequent multiobjective optimization but also improves the accuracy of the surrogate model near the Pareto front. The second stage is the surrogate-assisted multiobjective optimization, which aims to find all the solutions along the Pareto front based on the Pareto endpoints obtained from the first stage. In addition, this study successfully combines the gradient of the objective functions with the meta-heuristic algorithm during the multiobjective optimization, which ensures a faster convergence to the global optimum. The proposed multiobjective optimization algorithm shows faster convergence than the conventional optimization methods when applied to the three multiobjective optimization test functions. Finally, a comparison with the conventional multiobjective optimization is conducted based on one test function and two benchmark reservoir simulation models to verify the correctness and efficiency of the proposed method. It is confirmed that the proposed method outperforms the conventional ones for the optimization of CO2-WAG injection.

Traditional reconciliation of geomodels with production data is one of the most laborious tasks in reservoir engineering. The uncertainty associated with the great majority of model variables only adds to the overall complexity. This paper describes the conceptualization, implementation, and visualization characteristics of the multilevel assisted history matching (AHM) technique that captures inherent model uncertainty and allows for better quantification of production forecasts. The workflow is applied to history matching of the pilot area in a major, structurally complex Middle East (ME) carbonate reservoir. The simulation model combines 49 wells in five waterflood patterns to match 50 years of oil production and 12 years of water injection and to predict eight years of production. Initially, the reservoir model was calibrated to match oil production by modifying permeability and/or porosity at well locations and by fine-tuning rock-type properties and water saturation. The second level history match implemented two-stage Markov chain Monte Carlo (McMC) stochastic optimization to minimize the misfit in water cut on a well-by-well basis. The inversion process is dramatically accelerated by the efficient parameterization of permeability, constraining the proxy model using streamline-based sensitivities and using parallel and cluster computing. The optimal number of representative history-matched models was identified to capture the uncertainty in reservoir spatial connectivity using rigorous optimization and dynamic model ranking based on forecasted oil recovery factors (ORFs). The reduced set of models minimized the computational load for forecast-based analysis, while retaining the knowledge of the uncertainty in the recovery factor. The comprehensive probabilistic AHM workflow was implemented at the operator's North Kuwait Integrated Digital Oilfield (KwIDF) collaboration center. It delivers an optimized reservoir model for waterflood management and automatically updates the model quarterly with geological, production, and completion information. This allows engineers to improve the reservoir characterization and identify the areas that require more data capture.

This paper presents a procedure to estimate relative permeability curves together with gridblock porosities and permeabilities by automatic history matching three-phase flow production data using the LBFGS algorithm for optimization and the adjoint method for generating sensitivity coefficients. Both power law and B-splines are considered for the representation of relative permeability curves. Power law is a simple representation; however, B-splines have the advantage of being able to accurately represent any set of relative permeability curves. In the B-spline representation, we provide a simple procedure based on a transformation of parameters (control points) defining the B-splines to ensure that monotonic curves are obtained. Without this transformation, the automatic history-matching process fails. If endpoint saturations are included as parameters, we show how to modify the adjoint procedure to account for the fact that initial conditions are sensitive to endpoint saturations. While the history-matching process is inherently non-unique, we show that reasonable estimates of relative permeability curves and porosity/ permeability fields can be obtained for a synthetic reservoir example. We also show the uncertainty quantification of the model parameters and reservoir performance prediction using the Randomized Maximum Likelihood (RML) method. Introduction Relative permeabilities are important parameters in reservoir performance calculations. Usually the relative permeability curves are obtained from labs through core flood tests. They can also be incorporated into the history matching procedure as model parameters. ARCHER and WONG (1973), and YANG and WATSON (1991) were among the early researchers to consider the estimation of relative permeability curves by history matching laboratory core flood data. A detailed literature review is given in REYNOLDS et al. (2004). REYNOLDS et al. (2004) also discussed the estimation of three-phase relative permeabilities by history matching roduction data. The current work is a natural extension of REYNOLDS et al. (2004). In this paper, we provide an alternative method for relative permeability estimation based on B-spline approximation. Compared to power law representation, Bsplines ave the advantage of being able to accurately represent any set of relative permeability curves. In the B-spline representation, we provide a simple procedure based on logtransformation of parameters (control points) defining the Bsplines to ensure the B-spline curves are monotonic or convex as used in CHEN et al. (2005). Since a reservoir simulator requires monotonic relative permeability curves, without this transformation, the automatic history-matching process may generate non-monotonic relative permeability curves and result in failed reservoir simulation run. A prior model for porosity and absolute permeability and relative permeability parameters is assumed to provide regularization, i.e., Bayesian estimation is applied to generate estimates. Model parameters, which are estimated by automatic history matching of production data, consist of gridblock porosties, gridblock absolute logpermeabilities and the parameters defining the relative permeability curves. We do not assume the endpoint saturations (i.e. irreducible water saturation, critical gas saturation and residual oil saturation) to be known and consider them as independent model parameters in history matching procedure.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 171671, “Understanding Waterflood Response in Tight Oil Formations: A Case Study of the Lower Shaunavon,” by Adrian Thomas, SPE, Anjani Kumar, SPE, and Kenny Rodrigues, SPE, Computer Modelling Group, and Ryan Sinclair, SPE, Colin Lackie, Angela Galipeault, and Mike Blair, Crescent Point Energy, prepared for the 2014 SPE/CSUR Unconventional Resources Conference—Canada, Calgary, 30 September–2 October. The paper has not been peer reviewed. An 18-well numerical-simulation model was built to represent an operator’s Lower Shaunavon waterfloodpilot area. Numerical simulation was used, and a history match on the pilot area was performed. By use of parameters obtained from the history match, a representative model was built and a sensitivity study was performed on hydraulic-fracture spacing and well spacing in both primary-depletion and waterflood scenarios. Modeling-Work-Flow Description The Shaunavon is partitioned into lower and upper members. The lower member is an authigenic carbonate shelf, while the upper member has a strong clastic influence from the west. Oil is trapped hydrodynamically; the oil fairway crosses both stratigraphic and structural trends. The Lower Shaunavon is divided into four intervals in the study area. The lowest interval is a calcareous cryptocrystalline mudstone. Sitting above this interval is the B Marker, which is a slightly more energetic environment. The A Marker marks a regressive lag as a result of a sea-level drop. It consists of wackestone to some packstone rock and is bounded above and below by mudstones. The uppermost interval represents a high-energy environment. A geological model was developed for the lower Shaunavon pilot area on the basis of well logs, petrophysical data, and surface maps. The model was developed further into a dynamic simulation model by incorporating pressure/volume/temperature data, relative permeability, well trajectory, well completion, and historical well-production and -injection information for all wells located within the pilot area. A history match was performed on a single-well submodel to obtain improved values of reservoir hydraulic-fracture properties in the surrounding region. These values were applied to the full pilot area, and the model was simulated in an attempt to achieve a history match. Once the pilot area was history matched, forecast runs of an additional 50 years were performed to gauge future production along with future drilling scenarios. By use of the properties obtained through history matching, a new generalized model was built and different forecast scenarios were run to determine well spacing under both primary depletion and waterflood. For a discussion of reservoir-parameter selection and simulation-model setup, please see the complete paper.

Steam allocation for SAGD: Multi-pad multi-criteria short and long-term real-time performance management

A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems

The objective of this paper is to integrate "Big Data" concept with petroleum engineering knowledge for the prediction of recovery factor in Deepwater Gulf of Mexico (dGOM) oilfields. Recovery factor is affected by many geological and engineering factors; as a result, there is no explicit approach to accurately calculate the recovery factor. This is particularly true for deepwater development as the parameters associated with the recovery factor estimation have significant uncertainties and usually extremely costly to obtain. Typically, the recovery factor of a field is estimated using analogs, material balance, decline curve or numerical simulation. These deterministic approaches requires representative geological models. However, enough information is often not available to capture the realistic flow. In addition, the estimated recovery factor can be very different using different methods. Reservoir engineers are faced with the challenging task of estimating recovery factor by optimizing a large number of parameters with limited, sometime inaccurate information. This dilemma calls for an alternative approach in handling the noisy data. Data mining and classification identify hidden patterns in unstructured data and tend to be fairly robost in the presence of noisy data. Using a database of 395 Deepwater Gulf of Mexico (dGOM) oilfields with 84 attributes, a set of dimensionless numbers are calculated for 59 oilfields with water drive. This helps in dimensionality reduction and scaling of reservoir models for comparison. Based on the distribution of dimensionless numbers, data mining techniques like K-means clustering followed by principal component analysis (PCA) are used for classifying oilfields into four categories. Subsequently, partial least square (PLS) regression is used for relating dimensionless numbers to recovery factor from sparse data in dGOM, which gives good coefficient of correlation for some clusters. This paper shows that dimensionless numbers together with data mining techniques provides a new, easy to implement method for predicting recovery factor for large datasets where application of other methods are limited due to requirement of high computational cost and time.

Summary The objective of this paper is to compare the performance of the ensemble Kalman filter (EnKF) to the performance of a gradient-based minimization method for the problem of estimation of facies boundaries in history matching. The EnKF is a Monte Carlo method for data assimilation that uses an ensemble of reservoir models to represent and update the covariance of variables. In several published studies, it outperforms traditional history-matching algorithms in adaptability and efficiency. Because of the approximate nature of the EnKF, the realizations from one ensemble tend to underestimate uncertainty, especially for problems that are highly nonlinear. In this paper, the distributions of reservoir-model realizations from 20 independent ensembles are compared with the distributions from 20 random-ized-maximum-likelihood (RML) realizations for a 2D waterflood model with one injector and four producers. RML is a gradient-based sampling method that generates one reservoir realization in each minimization of the objective function. It is an approximate sampling method, but its sampling properties are similar to the Markov-chain Monte Carlo (McMC) method on highly nonlinear problems and are relatively more efficient than McMC. Despite the nonlinear relationship between the data (such as production rates and facies observations) and the model variables, the EnKF was effective at history matching the production data. We find that the computational effort to generate 20 independent realizations was similar for the two methods, although the complexity of the code is substantially less for the EnKF.

SummaryIn this paper we demonstrate how key geological uncertainties in a giant onshore carbonate reservoir in the Middle East, most notably fracture permeability and saturation distributions, impact the quality of the history match and change the performance forecasts of a planned miscible water alternating gas (MWAG) injection process.Different geological models for the reservoir were designed by integrating static and dynamic data. These data indicated the need to consider fault-related fractures using effective medium theory (EMT) and to update the saturation distribution by integrating special core analysis and log-derived J-functions in the reservoir model during the history matching. Afterward, multiobjective optimization (MOO) was applied for each history-matched model to identify well controls that optimally balanced the need to maximize the time on the plateau rate while adhering to the field's gas production constraints.Our results clearly show that including low-intensity fault-controlled fractures in the reservoir model improved the quality of the history match for the gas/oil ratio (GOR), BHP and water cut (WC). This is especially true for wells located near faults, which were difficult to match in the past. Moreover, our results further show that the updated saturation model improved the quality of the history match for the WC, and honored water saturation from the log with high accuracy, particularly for wells located in the transition zone.Applying MOO for each history-matched model then allowed us to identify well controls for the MWAG injection that could extend the time at which the reservoir would be produced at the plateau rate for up to 11 years and the risk of losing production plateau down to 2 years, while always adhering to the current field operational constraints.We demonstrate how the integration of MOO with an innovative workflow for fracture and saturation modeling impacts the prediction of a planned MWAG injection in a giant onshore carbonate reservoir. Our work clearly illustrates the potential of integrating MOO with new reservoir characterization methods to improve the quantification of uncertainties in reservoir performance predictions in carbonate reservoirs.

The disassembly line is the best choice for automated disassembly of disposal products. Therefore, disassembly line should be designed and balanced so that it can work as efficiently as possible. In this paper, a mathematical model for the multi-objective disassembly line balancing problem is formalized firstly. Then, a novel multi-objective ant colony optimization (MOACO) algorithm is proposed for solving this multi-objective optimization problem. Taking into account the problem constraints, a solution construction mechanism based on the method of tasks assignment is utilized in the algorithm. Additionally, niche technology is used to embed in the updating operation to search the Pareto optimal solutions. Moreover, in order to find the Pareto optimal set, the MOACO algorithm uses the concept of Pareto dominance to dynamically filter the obtained non-dominated solution set. To validate the performance of algorithm, the proposed algorithm is measured over published results obtained from single-objective optimization approaches and compared with multi-objective ACO algorithm based on uniform design. The experimental results show that the proposed MOACO is well suited to multi-objective optimization in disassembly line balancing.