Liu, Guoxiang (Baker Hughes a GE Company) | Stephenson, Hayley (Baker Hughes a GE Company) | Shahkarami, Alireza (Baker Hughes a GE Company) | Murrell, Glen (Baker Hughes a GE Company) | Klenner, Robert (Energy & Environmental Research Center, University of North Dakota) | Iyer, Naresh (GE Global Research) | Barr, Brian (GE Global Research) | Virani, Nurali (GE Global Research)
Optimization problems, such as optimal well-spacing or completion design, can be resolved rapidly via surrogate proxy models, and these models can be built using either data-based or physics-based methods. Each approach has its strengths and weaknesses with respect to management of uncertainty, data quality or validation. This paper explores how data- and physics-based proxy models can be used together to create a workflow that combines the strengths of each approach and delivers an improved representation of the overall system. This paper presents use cases that display reduced simulation computational costs and/or reduced uncertainty in the outcomes of the models. A Bayesian calibration technique is used to improve predictability by combining numerical simulations with data regressions. Discrepancies between observations and surrogate outcomes are then observed to calibrate the model and improve the prediction quality and further reduce uncertainty. Furthermore, Gaussian Process Regression is used to locate global minima/maxima, with a minimal number of samples. To demonstrate the methodology, a reservoir model involving two wells in a drill space unit (DSU) in the Bakken Formation was constructed using publicly available data. This reservoir model was tuned by history matching the production data for the two wells. A data-based regression model was constructed based on machine learning technologies using the same dataset. Both models were coupled in a system to build a hybrid model to test the proposed process of data and physics coupling for completion optimization and uncertainty reduction. Subsequently, Gaussian Process Model was used to explore optimization scenarios outside of the data region of confidence and to exploit the hybrid model to further reduce uncertainty and prediction. Overall, both the computation time to identify optimal completion scenarios and uncertainty were reduced. This technique creates a robust framework to improve operational efficiency and drive completion optimization in an optimal timeframe. The hybrid modeling workflow has also been piloted in other applications such as completion design, well placement and optimization, parent-child well interference analysis, and well performance analysis.
Gao, Guohua (Shell Global Solutions (US)) | Vink, Jeroen C. (Shell Global Solutions International) | Chen, Chaohui (Shell International Exploration and Production) | Araujo, Mariela (Shell Global Solutions (US)) | Ramirez, Benjamin A. (Shell International Exploration and Production) | Jennings, James W. (Shell International Exploration and Production) | El Khamra, Yaakoub (Shell Global Solutions (US)) | Ita, Joel (Shell Global Solutions (US))
Uncertainty quantification of production forecasts is crucially important for business planning of hydrocarbon-field developments. This is still a very challenging task, especially when subsurface uncertainties must be conditioned to production data. Many different approaches have been proposed, each with their strengths and weaknesses. In this work, we develop a robust uncertainty-quantification work flow by seamless integration of a distributed-Gauss-Newton (GN) (DGN) optimization method with a Gaussian mixture model (GMM) and parallelized sampling algorithms. Results are compared with those obtained from other approaches.
Multiple local maximum-a-posteriori (MAP) estimates are determined with the local-search DGN optimization method. A GMM is constructed to approximate the posterior probability-density function (PDF) by reusing simulation results generated during the DGN minimization process. The traditional acceptance/rejection (AR) algorithm is parallelized and applied to improve the quality of GMM samples by rejecting unqualified samples. AR-GMM samples are independent, identically distributed samples that can be directly used for uncertainty quantification of model parameters and production forecasts.
The proposed method is first validated with 1D nonlinear synthetic problems with multiple MAP points. The AR-GMM samples are better than the original GMM samples. The method is then tested with a synthetic history-matching problem using the SPE01 reservoir model (Odeh 1981; Islam and Sepehrnoori 2013) with eight uncertain parameters. The proposed method generates conditional samples that are better than or equivalent to those generated by other methods, such as Markov-chain Monte Carlo (MCMC) and global-search DGN combined with the randomized-maximum-likelihood (RML) approach, but have a much lower computational cost (by a factor of five to 100). Finally, it is applied to a real-field reservoir model with synthetic data, with 235 uncertain parameters. AGMM with 27 Gaussian components is constructed to approximate the actual posterior PDF. There are 105 AR-GMM samples accepted from the 1,000 original GMM samples, and they are used to quantify the uncertainty of production forecasts. The proposed method is further validated by the fact that production forecasts for all AR-GMM samples are quite consistent with the production data observed after the history-matching period.
The newly proposed approach for history matching and uncertainty quantification is quite efficient and robust. The DGN optimization method can efficiently identify multiple local MAP points in parallel. The GMM yields proposal candidates with sufficiently high acceptance ratios for the AR algorithm. Parallelization makes the AR algorithm much more efficient, which further enhances the efficiency of the integrated work flow.
A well-designed pilot is instrumental in reducing uncertainty for the full-field implementation of improved oil recovery (IOR) operations. Traditional model-based approaches for brown-field pilot analysis can be computationally expensive as it involves probabilistic history matching first to historical field data and then to probabilistic pilot data. This paper proposes a practical approach that combines reservoir simulations and data analytics to quantify the effectiveness of brown-field pilot projects.
In our approach, an ensemble of simulations are first performed on models based on prior distributions of subsurface uncertainties and then results for simulated historical data, simulated pilot data and ob jective functions are assembled into a database. The distribution of simulated pilot data and ob jective functions are then conditioned to actual field data using the Data-Space Inversion (DSI) technique, which circumvents the difficulties of traditional history matching. The samples from DSI, conditioned to the observed historical data, are next processed using the Ensemble Variance Analysis (EVA) method to quantify the expected uncertainty reduction of ob jective functions given the pilot data, which provides a metric to ob jectively measure the effectiveness of the pilot and compare the effectiveness of different pilot measurements and designs. Finally, the conditioned samples from DSI can also be used with the classification and regression tree (CART) method to construct signpost trees, which provides an intuitive interpretation of pilot data in terms of implications for ob jective functions.
We demonstrate the practical usefulness of the proposed approach through an application to a brown-field naturally fractured reservoir (NFR) to quantify the expected uncertainty reduction and Value of Information (VOI) of a waterflood pilot following more than 10 years of primary depletion. NFRs are notoriously hard to history match due to their extreme heterogeneity and difficult parameterization; the additional need for pilot analysis in this case further compounds the problem. Using the proposed approach, the effectiveness of a pilot can be evaluated, and signposts can be constructed without explicitly history matching the simulation model. This allows ob jective and efficient comparison of different pilot design alternatives and intuitive interpretation of pilot outcomes. We stress that the only input to the workflow is a reasonably sized ensemble of prior simulations runs (about 200 in this case), i.e., the difficult and tedious task of creating history-matched models is avoided. Once the simulation database is assembled, the data analytics workflow, which entails DSI, EVA, and CART, can be completed within minutes.
To the best of our knowledge, this is the first time the DSI-EVA-CART workflow is proposed and applied to a field case. It is one of the few pilot-evaluation methods that is computationally efficient for practical cases. We expect it to be useful for engineers designing IOR pilot for brown fields with complex reservoir models.
Calibrating production and economic forecasts (objective functions) to observed data is a key component in oil and gas reservoir management. Traditional model-based data assimilation (history matching) entails first calibrating models to the data and then using the calibrated models for probabilistic forecast, which is often ill-posed and time-consuming. In this study, we present an efficient regression-based approach that directly predicts the objectives conditioned to observed data without model calibration.
In the proposed workflow, a set of samples is drawn from the prior distribution of the uncertainty parameter space, and simulations are performed on these samples. The simulated data and values of the objective functions are then assembled into a database, and a functional relationship between the perturbed simulated data (simulated data plus error) and the objective function is established through nonlinear regression methods such as nonlinear partial least square (NPLS) with automatic parameter selection. The prediction from this regression model provides estimates for the mean of the posterior distribution. The posterior variance is estimated by a localization technique.
The proposed methodology is applied to a data assimilation problem on a field-scale reservoir model. The posterior distributions from our approach are validated with reference solution from rejection sampling and then compared with a recently proposed method called ensemble variance analysis (EVA). It is shown that EVA, which is based on a linear-Gaussian assumption, is equivalent to simulation regression with linear regression function. It is also shown that the use of NPLS regression and localization in our proposed workflow eliminates the numerical artifact from the linear-Gaussian assumption and provides substantially better prediction results when strong nonlinearity exists. Systematic sensitivity studies have shown that the improvement is most dramatic when the number of training samples is large and the data errors are small.
The proposed nonlinear simulation-regression procedure naturally incorporates data error and enables the estimation of the posterior variance of objective quantities through an intuitive localization approach. The method provides an efficient alternative to traditional two-step approach (probabilistic history matching and then forecast) and offers improved performance over other existing methods. In addition, the sensitivity studies related to the number of training runs and measurement errors provide insights into the necessity of introducing nonlinear treatments in estimating the posterior distribution of various objective quantities.
The aim of this study is to determine to what extent the quality of a history matched model is a good predictor of future production. The background is the common assumption that the better a model matches the production data is the better it is for forecasting, or, at the very least, it leads to an improved estimate of the uncertainty in future production. We demonstrate that the validity of this assumption depends on the length of the history match period and that of the forecasting period. It also depends on how heterogeneous the reservoir is.
The correlation between the quality of history match and quality of forecast depends on various factors. For the same level of heterogeneity one of the strongest factors is the water breakthrough time for the base and compared cases.
Broadly if both the base and compared case have water breakthrough before the end of the history match period then the forecasts are reasonable. However, there appears to be a very rapid transition from a reasonably good history match leading to a good forecast to a moderately good history match leading to a very poor forecast. If water breakthrough has not occurred there is a very poor correlation between the quality of the history match and the quality of the forecast. So, the traditional belief that a good history matched model will also produce a good forecast is not always true.
Chemical enhanced oil recovery (EOR) methods have received increased attention in recent years since they have the ability to recover the capillary trapped oil. Successful chemical flooding application requires accurate numerical models and reliable forecast across multiple scales: core scale, pilot scale, and field scale. History matching and optimization are two key steps to achieve this goal.
For history matching chemical floods, we propose a general workflow for multi-stage model calibration using an Evolutionary Algorithm. A comprehensive chemical flooding simulator is used to model important physical mechanisms including phase behavior, cation exchange, chemical and polymer adsorption and capillary desaturation. First, we identify dominant reservoir and process parameters based on a sensitivity analysis. The history matching is then carried out in a stage-wise manner whereby the most dominant parameters are calibrated first and additional parameters are incorporated sequentially until a satisfactory data misfit is achieved. Next, a diverse subset of history matched models is selected for optimization using a Pareto-based multi-objective optimization approach. Based on the concept of dominance, Pareto optimal solutions are generated representing the trade-off between increasing oil recovery while improving the efficiency of chemical usage. These solutions are searched using a Non-dominated Sorting Genetic Algorithm (NSGA-II). Finally we implement a History Matching Quality Index (HMQI) with Moving Linear Regression Analysis to evaluate simulation results from history matching process. The HMQI provides normalized values for all objective functions having different magnitude and leads to a more consistent and robust approach to evaluate the updated models through model calibration.
An ensemble-based history-matching framework is proposed to enhance the characterization of petroleum reservoirs through the assimilation of crosswell electromagnetic (EM) data. As one of advanced technologies in reservoir surveillance, crosswell EM tomography can provide a cross-sectional conductivity map and hence saturation profile at an interwell scale by exploiting the sharp contrast in conductivity between hydrocarbons and saline water. Incorporating this new information into reservoir simulation in combination with other available observations is therefore expected to enhance the forecasting capability of reservoir models and to lead to better quantification of uncertainty.
The proposed approach applies ensemble-based data-assimilation methods to build a robust and flexible framework under which various sources of available measurements can be readily integrated. Because the assimilation of crosswell EM data can be implemented in different ways (e.g., components of EM fields or inverted conductivity), a comparative study is conducted. The first approach integrates crosswell EM data in its original form which entails establishing a forward model simulating observed EM responses. In this work, the forward model is based on Archie's law that provides a link between fluid properties and formation conductivity, and Maxwell’s equations that describe how EM fields behave given the spatial distribution of conductivity. Alternatively, formation conductivity can be used for history matching, which is obtained from the original EM data through inversion using an adjoint gradient-based optimization method. Because the inverted conductivity is usually of high dimension and very noisy, an image-oriented distance parameterization utilizing fluid front information is applied aiming to assimilate the conductivity field efficiently and robustly. Numerical experiments for different test cases with increasing complexity are carried out to examine the performance of the proposed integration schemes and potential of crosswell EM data for improving the estimation of relevant model parameters. The results demonstrate the efficiency of the developed history-matching workflow and added value of crosswell EM data in enhancing the characterization of reservoir models and reliability of model forecasts.
Important decisions in the oil industry rely on reservoir simulation predictions. Unfortunately, most of the information available to build the necessary reservoir simulation models are uncertain, and one must quantify how this uncertainty propagates to the reservoir predictions. Recently, ensemble methods based on the Kalman filter have become very popular due to its relatively easy implementation and computational efficiency. However, ensemble methods based on the Kalman filter are developed based on an assumption of a linear relationship between reservoir parameters and reservoir simulation predictions as well as the assumption that the reservoir parameters follows a Gaussian distribution, and these assumptions do not hold for most practical applications. When these assumptions do not hold, ensemble methods only provide a rough approximation of the posterior probability density functions (pdf's) for model parameters and predictions of future reservoir performance. However, in cases where the posterior pdf for the reservoir model parameters conditioned to dynamic observed data can be constructed from Bayes' theorem, uncertainty quantification can be accomplished by sampling the posterior pdf. The Markov chain Monte Carlos (MCMC) method provides the means to sample the posterior pdf, although with an extremely high computational cost because, for each new state proposed in the Markov chain, the evaluation of the acceptance probability requires one reservoir simulation run. The primary objective of this work is to obtain a reliable least-squares support vector regression (LS-SVR) proxy to replace the reservoir simulator as the forward model when MCMC is used for sampling the posterior pdf of reservoir model parameters in order to characterize the uncertainty in reservoir parameters and future reservoir performance predictions using a practically feasible number of reservoir simulation runs. Application of LS-SVR to history-matching is also investigated.
In this work, we investigate different approaches for history matching of imperfect reservoir models while accounting for model error. The first approach (base case scenario) relies on direct Bayesian inversion using iterative ensemble smoothing with annealing schedules without accounting for model error. In the second approach the residual, obtained after calibration, is used to iteratively update the covariance matrix of the total error, that is a combination of model error and data error. In the third approach, PCA-based error model is used to represent the model discrepancy during history matching. However, the prior for the PCA weights is quite subjective and is generally hard to define. Here the prior statistics of model error parameters are estimated using pairs of accurate and inaccurate models. The fourth approach, inspired from
We present a novel sampling algorithm for characterization and uncertainty quantification of heterogeneous multiple facies reservoirs. The method implements a Bayesian inversion framework to estimate physically plausible porosity distributions. This inversion process incorporates data matching at the well locations and constrains the model space by adding
The proposed workflow uses an ensemble-based Markov Chain Monte Carlo approach combined with sampling probability distributions that are physically meaningful. Moreover, the method targets geostatistical modeling to specific zones in the reservoir. Accordingly, it improves fulfilling the inherent stationarity assumption in geostatistical simulation techniques. Parameter sampling and geostatistical simulations are calculated through an inversion process. In other words, the models fit the known porosity field at the well locations and are structurally consistent within main reservoir compartments, zones, and layers obtained from the seismic impedance volume. The new sampling algorithm ensures that the automated history matching algorithm maintains diversity among ensemble members avoiding underestimation of the uncertainty in the posterior probability distribution.
We evaluate the efficiency of the sampling methodology on a synthetic model of a waterflooding field. The predictive capability of the assimilated ensemble is assessed by using production data and dynamic measurements. Also, the qualities of the results are examined by comparing the geological realism of the assimilated ensemble with the reference probability distribution of the model parameters and computing the predicted dynamic data mismatch. Our numerical examples show that incorporating the seismically constrained models as prior information results in an efficient model update scheme and favorable history matching.