History-matched Reservoir Models Research Articles

History Matching Reservoir Models With Many Objective Bayesian Optimization

ABSTRACTReservoir models for predicting subsurface fluid and rock behaviors can now include upwards of billions (and potentially trillions) of grid cells and are pushing the limits of computational resources. History matching, where models are updated to match existing historical data more closely, is conducted to reduce the number of simulation runs and is one of the primary time‐consuming tasks. As models get larger the number of parameters to match increases, and the number of objective functions increases, and traditional methods start to reach their limitations. To solve this, we propose the use of Bayesian optimization (BO) in a hybrid cloud framework. BO iteratively searches for an optimal solution in the simulations campaign through the refinement of a set of priors initialized with a set of simulation results. The current simulation platform implements grid management and a suite of linear solvers to perform the simulation on large scale distributed‐memory systems. Our early results using the hybrid cloud implementation shown here are encouraging on tasks requiring over 100 objective functions, and we propose integrating BO as a built‐in module to efficiently iterate to find an optimal history match of production data in a single package platform. This paper reports on the development of the hybrid cloud BO based history matching framework and the initial results of the application to reservoir history matching.

AI, Data Analytics Enable Approach to History Matching in Geologically Complex Field

This article, written by JPT Technology Editor Judy Feder, contains highlights of paper SPE 202460, “History Matching of Production Performance for Highly Faulted, Multilayered, Clastic Oil Reservoirs Using Artificial Intelligence and Data Analytics: A Novel Approach,” by Nis Ilyani Mohmad and Dipak Mandal, SPE, Petronas, and Hadi Amat, Petroliam Nasional, et al., prepared for the 2020 SPE Asia Pacific Oil and Gas Conference and Exhibition, originally scheduled to be held in Perth, Australia, 20-22 October. The paper has not been peer reviewed. History matching is a critical step for dynamic reservoir modeling to establish a reliable, predictive model. Numerous approaches have emerged over decades to accomplish a robust history-matched reservoir model. As geological and completion complexity of oil and gas fields increase, building a fully representative predictive reservoir model can be arduous to almost impossible. The complete paper outlines an approach to history matching that uses artificial intelligence (AI) with an artificial neural network (ANN) and data-driven analytics. The new approach has been used to mitigate history-matching challenges in a mature, highly geologically complex field offshore Malaysia. Overview The complete paper describes a step-by-step methodology for building a reservoir model and a history-matching process using ANN. The paper discusses data preparation and quality assurance and control (QA/QC), spatiotemporal database formulation, reservoir model design, ANN architecture design, model training, and history-matching strategy. A case study of implementation in an offshore Malaysian field is presented, wherein good-to-fair history-matching quality was obtained for all production parameters. Field A is a highly geologically complex, 25×75-km oil sandstone reservoir with more than 200 major and minor faults and more than 30 reservoir layers. It has been producing for more than 25 years. The challenges of history matching this field lie not only in its geologically complex structure and corresponding subsurface uncertainties, but also in a production strategy that has involved commingled dual-string production with several integrity issues that exacerbate the field’s complexities. To date, Field A has no fieldwide history-matched reservoir model because the complexity of history matching has precluded using conventional numerical simulation methods. This challenge has been mitigated by implementing an AI-based reservoir model and data analytics. The new approach is estimated to be more time- and cost-efficient than the conventional method. The complete paper compares the AI-based and conventional numerical reservoir modeling approaches and highlights the advantages, limitations, and areas of improvement of the new methodology. The authors present their case for AI-based reservoir modeling as a complement or alternative to conventional numerical modeling to create time-efficient reservoir models while reducing risk in field-development plans.

Field Applications of Constrained Multiwell Deconvolution

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 195516, “Field Applications of Constrained Multiwell Deconvolution,” by V. Jaffrezic, SPE, Total, K. Razminia, SPE, Imperial College, J. Cumming, Durham University, and A.C. Gringarten, SPE, Imperial College, prepared for the 2019 SPE Europec featured at the 81st EAGE Annual Conference and Exhibition, London, 3–6 June. The paper has not been peer reviewed. This paper applies a new constrained multiwell deconvolution algorithm to two field cases: a gas reservoir with two producers and an oil reservoir with three producers and one injector. Responses given by the constrained multiwell deconvolution are compared with simulations from history-matched reservoir models. By extraction of well and interwell reservoir signatures, multiwell deconvolution, the theoretical background of which is discussed in detail in the complete paper, allows identification of compartmentalization or unanticipated heterogeneities very early in field life, making adjustments possible for field-development plans and future well locations. Introduction Permanent downhole pressure gauges are installed routinely in most new wells. In theory, they provide invaluable data for monitoring well productivity and formation pressure in real time and for calibrating the reservoir-simulation model. In practice, however, the resulting large data sets are usually underexploited, mainly because extraction of meaningful information from interfering wells with conventional well-test-analysis techniques is nearly impossible. Field Case 1 A sandstone dry gas reservoir has been developed with two horizontal wells (Wells 9 and 10) with lengths of approximately 400 m that are 1.6 km apart. The production data set spans 19,800 hours (approximately 2 years and 3 months). No datum correction was applied because the vertical distance between the pressure gauges in the two wells was only 10 m and the correction would be negligible. Data Selection. Because the field case involves dry gas, pressure was converted into single-phase normalized pseudopressure using pressure/volume/temperature data. Depletion is moderate, so use of material balance pseudotime to account for changes in gas properties was unnecessary. Pressure data to be used for multiwell deconvolution had to be selected with care. Flowing pressures are usually too noisy, so buildup data are preferred. Linearity is enforced by only considering buildups with similar pressure derivatives. If these differ at early times, because of changing wellbore and skin effects, a buildup of reference is selected, with elimination of early-time data in all other buildups. Derivatives of the selected buildups, however, may also differ at late times because of interference between wells. These late-time data must be kept because they contain information on interwell connectivity and are necessary to recover constant rate interference responses from multi-well deconvolution. Multiwell Algorithm Setup. The following parameters were selected for the deconvolution process: The first nodes of the well main responses were set at 0.01 hours. The derivative slopes before that time were considered a regression parameter with no constraint applied. The same procedure was used for the interference derivatives except that the first nodes were set at 0.1 hours. All deconvolved derivatives were constrained to converge to a unit slope straight line at late times because the two wells are in communication and the reservoir is closed. The deconvolved derivatives were extended by 1.5 log cycles beyond the test duration, and the constraint of convergence was applied from 22,000 hours. The interference derivatives were constrained to remain below the deconvolved derivatives of the individual wells. The initial pressure was considered a regression parameter with no constraint applied. As a result, the algorithm returned different initial pressure estimates for each well. Default weight parameters were used except for the curvature, where a weight of 0.001 was applied to the main responses and 0.005 to the interferences. These values were selected by trial and error to limit the contribution of the curvature constraint.

Finite Element Numerical Simulation Research on Fractured Horizontal Well in Stress-dependent Tight Reservoirs Based on Heat Transfer Theory

We present an efficient numerical method to handle stress-dependent behavior for fractured wells in tight reservoirs using the large-scale general finite element software ANSYS as the platform. A new similarity criterion is deduced to describe the seepage flow based on the similarity principle. The similarity criterion is a key parameter to transfer unstable heat problems to well performances. Then a comparison between the numerical and history-matched results is made to validate the accuracy of the results, by which effective stress-dependent coefficient calculated by numerical simulation is in agreement with that from experiment. The result shows that it is feasible to apply the ANSYS function of temperature field analysis in the computation of the unstable seepage flow considering permeability change in stress-dependent tight reservoirs. Finally using a certain field data and history-matched reservoir model, the influence of the fractures on horizontal well is investigated, including fracture spacing, fracture length and parameters of fracture with included angle on the basis of the new method. The results from the model considering the stress-dependent factor are significantly different from that without considering the factor. This work provides reservoir engineers with a simple and feasible method for optimizing the fracture parameters of tight oil development.

Best Practices of Assisted History Matching Using Design of Experiments

SummaryAssisted history matching (AHM) using design of experiments (DOE) is one of the most commonly applied history-matching techniques in the oil and gas industry. When applied properly, this stochastic method finds a representative ensemble of history-matched reservoir models for probabilistic uncertainty analysis of production forecasts. Although DOE-based AHM is straightforward in concept, it can be misused in practice because the work flow involves many statistical and modeling principles that should be followed rigorously.In this paper, the entire DOE-based AHM work flow is demonstrated in a coherent and comprehensive case study that is divided into seven key stages: problem framing, sensitivity analysis, proxy building, Monte Carlo simulation, history-match filtering, production forecasting, and representative model selection. The best practices of each stage are summarized to help reservoir-management engineers understand and apply this powerful work flow for reliable history matching and probabilistic production forecasting.One major difficulty in any history-matching method is to define the history-match tolerance, which reflects the engineer's comfort level of calling a reservoir model “history matched” even though the difference between simulated and observed production data is not zero. It is a compromise to the intrinsic and unavoidable imperfectness of reservoir-model construction, data measurement, and proxy creation. A practical procedure is provided to help engineers define the history-match tolerance considering the model, data-measurement, and proxy errors.

A robust adaptive iterative ensemble smoother scheme for practical history matching applications

Much of the recent work on history matching reservoir models has focused on the iterative Ensemble Smoother (iES) method. This is well suited for practical applications because it avoids frequent simulation restarts which can be expensive for traditional Ensemble Kalman Filter (EnKF) approaches. In this paper, we derive a novel, adaptive iES method (ES-LM) based on the Levenberg-Marquardt algorithm for nonlinear least squares optimization. We demonstrate that the solution of the linearized least squares subproblems from each iteration of ES-LM have a similar structure to those of the standard ensemble smoother update equation. This allows us to use the ensemble smoother as an approximate linear least squares solver and thus avoid expensive adjoint calculations. The proposed algorithm may therefore be seen as a variant of iES whose regularization parameter can be updated using the usual trust region method. The resulting parameter update equation is similar to those in existing iES methods, but our derivation provides new insights into iES that enable us to extend the adaptive ES-LM to two new formulations: (1) Auto ES-LM, where the measurement error has unknown variance that will be estimated by the algorithm; and (2) Robust ES-LM, where the measurement error follows a Cauchy distribution. Robust ES-LM, in particular, reduces the effect of outliers in the data, which can be critical for real-world applications. Although estimating measurement error and adding robustness are common for data assimilation with EnKF, they have not been incorporated into iES within the reservoir engineering community. The three resulting algorithms are easy for reservoir engineers to use for practical history matching applications without the need for deep understanding of the computational details. Finally, we demonstrate the effectiveness and robustness of these algorithms on two synthetic reservoir models.

4D Seismic With Reservoir Simulation Improves Reservoir Forecasting

This article, written by JPT Technology Editor Judy Feder, contains highlights of paper SPE 191521, “Quantitative Integration of 4D Seismic with Reservoir Simulation,” by Sarath Pavan Ketineni, SPE, Subhash Kalla, SPE, Shauna Oppert, SPE, and Travis Billiter, SPE, Chevron, prepared for the 2018 SPE Annual Technical Conference and Exhibition, Dallas, 24–26 September. The paper has not been peer reviewed. Standard history-matching work flows use qualitative 4D seismic observations in reservoir modeling and simulation. However, such work flows lack a robust framework for quantitatively integrating 4D seismic interpretations. Four-dimensional, or time-lapse, seismic interpretations provide valuable interwell saturation and pressure information. Quantitatively integrating these data can help constrain simulation parameters and improve the reliability of production modeling. This paper outlines the value of 4D for reducing uncertainty in the range of history-matched models and improving the production forecast. Introduction Reservoir-simulation models play an essential role in generating optimal field-development strategies, but they need to be history-matched before they can be used for reliable forecasting. Traditional history matching of a reservoir involves matching observed production and pressure data at well locations by changing the uncertain parameters in the reservoir model within the acceptable range. The parameters can be classified broadly as static and dynamic. Static parameters include permeability, porosity, and net to gross, among many others. Dynamic parameters may include oil/water contacts, fault transmissibilities, relative permeability curves, and flow pathways. Deterministic modeling focuses on a single scenario of the reservoir model, ignoring the effect of uncertainty in the parameters considered. Probabilistic history matching is the process of selecting non unique and multiple history-matched reservoir models by altering the uncertain static and dynamic parameters to obtain a range of possible forecasts. Typically, in probabilistic work flows, objective functions composed of a combination of differences in measured and simulated bottomhole pressure data and individual fluid-phase flow rates are used to identify significant factors or uncertainties. The functions are typically based on surveillance data obtained at well locations and therefore may not be sensitive to key reservoir uncertainty away from wells. A good match with production data for a given reservoir model does not ensure robustness in making performance forecasts. Reservoir heterogeneities—high-permeability pathways, barriers and baffles, or vertical connections forged from geologic erosion—can significantly affect drainage and swept patterns and well-production forecasts. Especially during early stages of field production, history matching to pressure and fluid-rate production data often lacks information necessary to resolve these critical heterogeneities fully, which may significantly affect production. Even a well-posed probabilistic history-matching approach cannot incorporate the variety and complexities of heterogeneities that are yet to have a strong imprint on future production because of insufficient data away from wells and the sheer number of static and dynamic uncertainties that can affect production.

On multistage hydraulic fracturing in tight gas reservoirs: Montney Formation, Alberta, Canada

The combination of horizontal drilling and multistage hydraulic fracturing technology has unlocked production of petroleum from tight/shale rock. Prediction of single or multistage hydraulic fracturing treatments along horizontal wells in tight formations remains a challenge and thus optimization of these stimulation treatments is difficult. Currently, there are few effective approaches to characterize multistage hydraulic fracturing in tight rock reservoirs. In this paper, we use a three-dimensional tight rock simulator based on the Unconventional Fracture Model (UFM) to understand multistage hydraulic fracturing in the Montney Formation in Alberta, Canada. We use geological and geomechanical properties, stress magnitude and orientation, completion and production data to history match and characterize fracture volume and conductivity in the Montney Formation. Predictions of fractures from the history-matched reservoir model reveal the strong connection between the fracture conductivity and reservoir permeability, elastic rock properties as well as stresses distributions. The field example demonstrates how stress maps and rock properties calculated from density and gamma logs are integrated to yield predictive hydraulic fracturing capability. This study illustrates the critical role of reservoir permeability on fracture extent and conductivity. This workflow can be used to develop strategies for (1) refracturing of existing wells, (2) design and number of perforations, and (3) prediction of fracture propagation in later stages.

Correlation-Based Adaptive Localization With Applications to Ensemble-Based 4D-Seismic History Matching

Summary Ensemble-based history-matching methods have received much attention in reservoir engineering. In real applications, small ensembles are often used in reservoir simulations to reduce the computational costs. A small ensemble size may lead to ensemble collapse, a phenomenon in which the spread of the ensemble of history-matched reservoir models becomes artificially small. Ensemble collapse is not desired for an ensemble-based history-matching method because it not only deteriorates the capacity in uncertainty quantification, but also forces the ensemble-based method to later stop updating reservoir models. In practice, distance-based localization is thus introduced to tackle ensemble collapse. Distance-based localization works well in many problems. However, one prerequisite in using distance-based localization is that the observations have associated physical locations. In certain circumstances with complex observations, this may not be true, and it thus becomes challenging to apply distance-based localization. In this work, we propose a correlation-based adaptive localization scheme that does not rely on the physical locations of the observations. Instead, we use the spatial distributions of the correlations between model variables and the corresponding simulated observations. In the course of history matching, we update model variables by only using the observations that have relatively high correlations with them, while excluding those that have relatively low correlations. This is equivalent to introducing a data-selection procedure to the history-matching algorithm. As a result, the threshold values for data selection play an essential role in the proposed adaptive localization scheme, and we develop both ideal and practical approaches to the choices of the threshold values. We demonstrate the efficacy of the proposed localization scheme using seismic history-matching problems—one 2D and one 3D—in which ensemble collapse is severe in the presence of large amounts of observational data, but distance-based localization may not be applicable because of the lack of physical locations of the seismic data in use. In contrast, correlation-based localization works well to prevent ensemble collapse and also renders good history-matching results. We also note some practical conveniences of the proposed localization scheme, including the applicability to nonlocal observations, the relative simplicity in implementation, the transferability of the same codes among different (either 2D or 3D) case studies, and the adaptivity to different types of observations and petrophysical parameters.

Quantification of a maximum injection volume of CO2 to avert geomechanical perturbations using a compositional fluid flow reservoir simulator

Abstract Subsurface CO2 injection and storage alters formation pressure. Changes of pore pressure may result in fault reactivation and hydraulic fracturing if the pressure exceeds the corresponding thresholds. Most simulation models predict such thresholds utilizing relatively homogeneous reservoir rock models and do not account for CO2 dissolution in the brine phase to calculate pore pressure evolution. This study presents an estimation of reservoir capacity in terms of allowable injection volume and rate utilizing the Frio CO2 injection site in the coast of the Gulf of Mexico as a case study. The work includes laboratory core testing, well-logging data analyses, and reservoir numerical simulation. We built a fine-scale reservoir model of the Frio pilot test in our in-house reservoir simulator IPARS (Integrated Parallel Accurate Reservoir Simulator). We first performed history matching of the pressure transient data of the Frio pilot test, and then used this history-matched reservoir model to investigate the effect of the CO2 dissolution into brine and predict the implications of larger CO2 injection volumes. Our simulation results –including CO2 dissolution– exhibited 33% lower pressure build-up relative to the simulation excluding dissolution. Capillary heterogeneity helps spread the CO2 plume and facilitate early breakthrough. Formation expansivity helps alleviate pore pressure build-up. Simulation results suggest that the injection schedule adopted during the actual pilot test very likely did not affect the mechanical integrity of the storage complex. Fault reactivation requires injection volumes of at least about sixty times larger than the actual injected volume at the same injection rate. Hydraulic fracturing necessitates much larger injection rates than the ones used in the Frio pilot test. Tested rock samples exhibit ductile deformation at in-situ effective stresses. Hence, we do not expect an increase of fault permeability in the Frio sand even in the presence of fault reactivation.

Development of a robust multi-objective history matching for reliable well-based production forecasts

This article presents a dynamic reservoir characterization using a new multi-objective optimization algorithm to quantify the reservoir uncertainties in history matching. The proposed method formulated Pareto-optimality with preference-ordering to derive multiple trade-off history-matched reservoir models for probabilistic production estimation. The integration of linear programming with multi-objective genetic algorithm enhances the efficiency of a multi-directional search by prioritizing the reservoir models that satisfy the aspiration levels on the discrepancy between the observed and the calculated production data. The preference levels are automatically adjusted in correspondence to the quality of the reservoir models for facilitating the model update process during optimization. An oil-field application result indicates the method outperforms the conventional multi-objective optimization method in terms of the relative average error for the production data despite a small loss of diversity-preservation among the reservoir models.

Determination of lower and upper bounds of predicted production from history-matched models

We present a method to determine lower and upper bounds to the predicted production or any other economic objective from history-matched reservoir models. The method consists of two steps: 1) performing a traditional computer-assisted history match of a reservoir model with the objective to minimize the mismatch between predicted and observed production data through adjusting the grid block permeability values of the model. 2) performing two optimization exercises to minimize and maximize an economic objective over the remaining field life, for a fixed production strategy, by manipulating the same grid block permeabilities, however without significantly changing the mismatch obtained under step 1. This is accomplished through a hierarchical optimization procedure that limits the solution space of a secondary optimization problem to the (approximate) null space of the primary optimization problem. We applied this procedure to two different reservoir models. We performed a history match based on synthetic data, starting from a uniform prior and using a gradient-based minimization procedure. After history matching, minimization and maximization of the net present value (NPV), using a fixed control strategy, were executed as secondary optimization problems by changing the model parameters while staying close to the null space of the primary optimization problem. In other words, we optimized the secondary objective functions, while requiring that optimality of the primary objective (a good history match) was preserved. This method therefore provides a way to quantify the economic consequences of the well-known problem that history matching is a strongly ill-posed problem. We also investigated how this method can be used as a means to assess the cost-effectiveness of acquiring different data types to reduce the uncertainty in the expected NPV.

A Parallelized and Hybrid Data-Integration Algorithm for History Matching of Geologically Complex Reservoirs

Summary It is extremely challenging to design effective assisted-history-matching (AHM) methods for complex geological models with discrete-facies types. One of the difficulties is the irregular and nonsmooth nature of the data-mismatch function that needs to be minimized, because of either numerical noise on simulation results or nonsmooth reparameterization. In this paper, a parallelized direct-pattern-search (DPS) approach with auto-adaptive pattern-size updating is developed to guarantee the convergence of the data-mismatch minimization, even when the objective function is nonsmooth because of numerical noise. A trust-region variant of the Gauss-Newton (GN) or quasi-Newton (QN) method is effectively combined with the noise-insensitive DPS method to enhance its performance by exploiting any available smoothness features of the objective function. The new approach is first validated by a linear toy problem and a nonlinear toy problem where artificial numerical noise is introduced. Then, it is applied to a synthetic case and a real field case for history matching of channelized-turbidite reservoirs with three facies types. The model parameters subject to AHM include principal component analysis (PCA) coefficients, which automatically reconstruct the facies indicators and permeability, porosity, and net-to-gross maps. Other matching parameters such as aquifer strength and fault transmissibility are also included. Numerical tests indicate that the hybrid algorithms perform better than the traditional QN line-search algorithms and the original Hooke-Jeeves DPS algorithm (Hooke and Jeeves 1961). The hybrid algorithms either can converge to a satisfactory solution with the same accuracy using lower cost or find a better solution with the same cost, especially for cases where adjoint derivatives are unavailable and numerical noise is unavoidable from reservoir simulation. The GN-DPS algorithm performs the best among all tested algorithms. The history-matched reservoir models obtained with the new AHM approach (GN-DPS combined with pluri-PCA) honor the production measurements with good accuracy. For both the synthetic and real cases, the history-matched reservoir models preserve geological realism.

Produced-Water-Chemistry History Matching in the Janice Field

Summary Produced-water-chemistry (PWC) data are the main sources of information to monitor scale precipitation in oilfield operations. Chloride concentration is used to evaluate the seawater fraction of the total produced water per producing well and is included as an extra history-matching constraint to reevaluate a good conventionally history-matched (HM) reservoir model for the Janice field. Generally, PWC is not included in conventional history matching, and this approach shows the value of considering the nature of the seawater-injection front and the associated brine mixing between the distinctive formation water and injected seawater. Adding the extra constraint resulted in the reconceptualization of the reservoir geology between a key injector and two producers. The transmissibility of a shale layer is locally modified within a range of geologically consistent values. Also, a major lineament is identified which is interpreted as a northwest/southeast-trending fault, whereby the zero transmissibility of a secondary shale in the Middle Fulmar is locally adjusted to allow crossflow. Both uncertainties are consistent with the complex faulting known to exist in the region of the targeted wells. Other uncertainties that were carried forward to the assisted-history-matching phase included water allocation to the major seawater injectors; thermal fracture orientation of injectors; and the vertical and horizontal permeability ratio (Kv/Kh) of the Fulmar formation. Finally, a stochastic particle-swarm-optimization (PSO) algorithm is used to generate an ensemble of HM models with seawater fraction as an extra constraint in the misfit definition. Use of additional data in history matching has improved the original good HM solution. Field oil-production rate is interpreted as improved over a key period, and although no obvious improvement was observed in field water-production rate, seawater fraction in a number of wells was improved.

Conformity assessment of monitoring and simulation of CO2 storage: A case study from the Ketzin pilot site

Demonstrating conformity between observed and simulated plume behaviour is one of the main high-level requirements, which have to be fulfilled by an operator of a CO2 storage site in order to assure safe storage operations and to be able to transfer liability to the public after site closure. The observed plume behaviour is derived from geophysical and/or geochemical monitoring. Repeated 3D seismic observations have proven to provide the most comprehensive image of a CO2 plume in various projects such as Sleipner, Weyburn, or Ketzin. The simulated plume behaviour is derived from reservoir simulation using a model calibrated with monitoring results. Plume observations using any monitoring method are always affected by limited resolution and detection ability, and reservoir simulations will only be able to provide an approximated representation of the occurring reservoir processes. Therefore, full conformity between observed and simulated plume behaviour is difficult to achieve, if it is at all. It is therefore of crucial importance for each storage site to understand to what degree conformity can be achieved under realistic conditions, comprising noise affected monitoring data and reservoir models based on geological uncertainties. We applied performance criteria (plume footprint area, lateral migration distance, plume volume, and similarity index) for a comparison between monitoring results (4D seismic measurements) and reservoir simulations, considering a range of seismic amplitude values as noise threshold and a range of minimum thickness of the simulated CO2 plume. Relating the performance criteria to the noise and thickness threshold values allows assessing the quality of conformance between simulated and observed behaviour of a CO2 plume. The Ketzin site is provided with a comprehensive monitoring data set and a history-matched reservoir model. Considering the relatively high noise level, which is inherent for land geophysical monitoring data, a reasonable conformance between the observed and simulated plume behaviour is demonstrated.

Use of Tracers To Evaluate and Optimize Scale-Squeeze-Treatment Design in the Norne Field

Summary When squeezing scale inhibitors (SIs) into oil-production wells, the inhibitor should usually be uniformly placed in the open intervals to optimize squeeze lifetime. In wells with varying reservoir quality and/or significant crossflow, however, uniform placement is difficult to obtain. Flow diverters are frequently used to improve the chemical placement. In many cases, it is of great interest to evaluate the squeeze performance and assess the actual placement and back production of inhibitor to gather well information and thereby optimize future squeeze designs. This can be particularly interesting in subsea wells in which other types of data collection, such as production logging, are not feasible because of high intervention costs and high operational risk. This study suggests the use of tracers during squeeze treatments to evaluate the placement as an alternative to running production-logging tools (PLTs). The main purpose of this paper is to demonstrate the applicability of tracers [in this particular study, the injection of a potassium chloride (KCl) slug in a producer well in the Norne field] to evaluate the layer flow-rate profile along the completion interval, which depends on the pressure and geological properties of each layer. The study consists of verifying the layer flow-rate profile predicted by a history-matched reservoir model. On the basis of this layer flow-rate profile, a tracer-injection program is designed, which includes two production stages at different rates. Finally, on the basis of the reservoir-model predictions, it is identified that each layer is at different pressures, which leads to a distinctive return profile. To evaluate the match between the observed data and the simulation data, the layer flow-rate profile from the reservoir model was used to populate a specialized near-wellbore model for scale-squeeze treatments. The match between the observed data and the simulated data was good. However, the near-wellbore model, in particular the layer flow-rate profile, was fine-tuned further. Finally, the fine-tuned near-wellbore model was used to optimize future treatments more accurately with the fine-tuned layer flow-rate profile.

Estimating Scale Deposition Through Reservoir History Matching in the Janice Field

Summary Inorganic-scale precipitation and deposition in production wells can be a significant impediment to effective reservoir management. In extreme cases, scale can cause the well to be abandoned as a result of reservoir-formation damage in the near-wellbore region and the narrowing of the production-tubing annulus, thus preventing fluid flow. The prediction of the time and location of scale formation is therefore essential for scale management. This study is focused on sulfate scales, which form when sulfate-rich seawater mixes with formation brines that are rich in barium, calcium, and strontium, and which are among the most difficult types of scale to prevent and remove. Formation brines in reservoirs with a tendency for sulfate-scale deposition can have a very different makeup when compared with seawater, which may be injected for pressure support. Having such different chemistries allows seawater and formation brine to be tracked. In this study, two different types of water are considered: formation brine and injected seawater. The objective of this work is to predict uncertainty in sulfate-scale deposition from multiple history-matched reservoir models by tracking injected seawater in the Janice field. There are many examples in the literature in which conventional reservoir history matching (namely, gas rate, oil rate, and bottomhole pressure) are used to generate an ensemble of good history-matched models that will estimate uncertainty of a hydrocarbon-reservoir production. In this study, the same approach will be adopted, but including produced-water chemistry—in particular, seawater breakthrough. This approach provides a methodology to predict the uncertainty of the formation-brine/injected-seawater mixing zone within the reservoir formation. The methodology provides a Bayesian confidence interval (P10/P50/P90) in time and space for the injected seawater, identifying which wells will be at risk on the basis of seawater breakthrough and in which zones of the reservoir mixing is more likely to occur.

Estimation of Distribution Algorithms Applied to History Matching

Summary The topic of automatically history-matched reservoir models has seen much research activity in recent years. History matching is an example of an inverse problem, and there is significant active research on inverse problems in many other scientific and engineering areas. While many techniques from other fields, such as genetic algorithms, evolutionary strategies, differential evolution, particle swarm optimization, and the ensemble Kalman filter have been tried in the oil industry, more recent and effective ideas have yet to be tested. One of these relatively untested ideas is a class of algorithms known as estimation of distribution algorithms (EDAs). EDAs are population-based algorithms that use probability models to estimate the probability distribution of promising solutions, and then to generate new candidate solutions. EDAs have been shown to be very efficient in very complex high-dimensional problems. An example of a state-of-the-art EDA is the Bayesian optimization algorithm (BOA), which is a multivariate EDA employing Bayesian networks for modeling the relationships between good solutions. The use of a Bayesian network leads to relatively fast convergence as well as high diversity in the matched models. Given the relatively limited number of reservoir simulations used in history matching, EDA-BOA offers the promise of high-quality history matches with a fast convergence rate. In this paper, we introduce EDAs and describe BOA in detail. We show results of the EDA-BOA algorithm on two history-matching problems. First, we tune the algorithm, demonstrate convergence speed, and search diversity on the PUNQ-S3 synthetic case. Second, we apply the algorithm to a real North Sea turbidite field with multiple wells. In both examples, we show improvements in performance over traditional population-based algorithms.

Population-Based Optimization Algorithms for History Matching and Uncertainty Quantification: PUNQ-S3

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 136861, ’Comparative Study of Novel Population-Based Op timization Algorithms for History Matching and Uncertainty Quantification: PUNQ-S3 Revisited,’ by Yasin Hajizadeh, SPE, Mike Christie, SPE, and Vasily Demyanov, Institute of Petroleum En gineering, Heriot-Watt University, prepared for the 2010 Abu Dhabi International Petroleum Exhibition & Conference, Abu Dhabi, UAE, 1-4 November. The paper has not been peer reviewed. Multiple history-matched models are essential for a realistic uncertainty estimate of the field’s future behavior. This study compared application of ant-colony optimization (ACO), differential evolution (DE), and neighborhood algorithms (NAs) for history matching and uncertainty quantification of the PUNQ-S3 reservoir, a synthetic benchmark case with challenging parameterization, history-matching, and uncertainty-quantification steps. Introduction History matching of reservoir models and uncertainty quantification of the predictions are two important steps in any field-management process. In the history-matching phase, simulation models are calibrated on the basis of the observed production history of the reservoir. Parameters of the reservoir model are perturbed, and the model’s output is compared with available fluid-production rates or pressure measurements. This procedure is repeated with new parameter values until good agreement is obtained between output of the simulation and observations. History matching is an inverse problem with nonunique solutions. Multiple combinations of reservoir properties can provide a good match to observed field behavior. To quantify the uncertainty of predictions realistically, multiple history-matched reservoir models are required. Diverse models are likely to show different production behavior in the future because of different reservoir parameters. Recently, ACO and DE algorithms have been applied to history matching of a simple reservoir model with a small number of unknowns (eight). The subject methods for history matching were applied to a more-complex reservoir with 45 uncertain parameters, and the results were compared to those from NA. Originally, ACO was proposed for problems with discrete parameter space, and it later was adopted to handle continuous-optimization problems. DE is a powerful global-optimization algorithm that is a parallel-population-based search algorithm. The NA is a recent stochastic-optimization method that uses simple geometrical constructs called Voronoi cells to find good-fitting regions of the search space. Voronoi cell is a method to decompose the search space into n cells around n points by centering on the generated points. Each of these cells is the nearest neighborhood region of the points. Case Study The PUNQ-S3 reservoir-simulation model is a five-layer model. The top depth of PUNQ-S3 reservoir is 2430 m. It has a 1.5° dip angle and is bounded by faults to the east and south. A relatively strong aquifer on the north and west provides pressure support. Because of this pressure support, no injection wells have been drilled in this reservoir. There also is a small gas cap in the reservoir in Layer 1, and no wells are completed in this layer because of the effect of free-gas production on recovery from the reservoir. There are six production wells, all near the initial gas/oil contact. Three producers are perforated in Layers 4 and 5. Two producers are completed in Layers 3 and 4, and one producer is perforated only in Layer 4. One of the producers is completed near the aquifer, and water breakthrough was observed in the seventh year. Free-gas production starts in Years 4 and 5 in two of the producers. There also are positions for five infill wells.

Recent progress on reservoir history matching: a review

History matching is a type of inverse problem in which observed reservoir behavior is used to estimate reservoir model variables that caused the behavior. Obtaining even a single history-matched reservoir model requires a substantial amount of effort, but the past decade has seen remarkable progress in the ability to generate reservoir simulation models that match large amounts of production data. Progress can be partially attributed to an increase in computational power, but the widespread adoption of geostatistics and Monte Carlo methods has also contributed indirectly. In this review paper, we will summarize key developments in history matching and then review many of the accomplishments of the past decade, including developments in reparameterization of the model variables, methods for computation of the sensitivity coefficients, and methods for quantifying uncertainty. An attempt has been made to compare representative procedures and to identify possible limitations of each.