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Abstract Capacitance–resistance model (CRM) is a nonlinear signal processing approach that provides information about interwell communication and reservoir heterogeneity. Several forms of CRM have been introduced; however, they would deliver erroneous model parameters if production history involves shut-in period. To address this issue, this study presents a dynamic capacitance–resistance model (D-CRMP), a comprehensive formulation that is capable of handling multiple shut-in periods in different producers. CRM model parameters are representative of the geological information. Accordingly, two geologically identical synthetic examples are used to validate D-CRMP; one including shut-in periods in historical production data of some producers and the other one with all continuously operating wells. Obtaining the same model parameters and the high quality of fitting in both cases proved the reliability of D-CRMP, which allows the utilization of historical data to characterize the reservoir behavior in real cases. Investigation of uncertainty on the fitted model parameters was also performed to demonstrate that confidence intervals are affected mostly by two aspects; permeability distribution and interwell distance. It is shown that though the confidence intervals in the heterogeneous fields are relatively higher than the homogeneous examples, higher permeability and lower producer–injector distance reduce the uncertainty of model parameters in both cases. This study also applies the proposed model in reservoirs with horizontal wells and further examines the impact of well direction and length of the productive interval on the connectivities between wells.

Abstract History matching is the process of modifying a numerical model (representing a reservoir) in the light of observed production data. In the oil and gas industry, production data are employed during a history matching exercise in order to reduce the uncertainty in associated reservoir models. However, production data, normally measured using commercial flowmeters that may or may not be accurate depending on factors such as maintenance schedules, or estimated using mathematical equations, inevitably has inherent errors. In other words, the data which are used to reduce the uncertainty of the model may have considerable uncertainty in itself. This problem is exacerbated for gas condensate and wet gas reservoirs as there are even greater errors associated with measuring small fractions of liquid. The influence of this uncertainty in the production data on history matching has not been addressed in the literature so far. In this paper, the effect of systematic and random flow measurement errors on history matching is investigated. Initially, 14 production data sets with different ranges of systematic and random errors, from 0 to 10%, have been employed in a history matching exercise for an oil reservoir and the results have later been evaluated based on a reference model. Subsequently, 23 data sets with errors ranging from 0 to 20% have been employed in the same process for a wet gas reservoir. The results show that for both cases systematic errors considerably affect history matching, while the effect of random errors on the considered scenarios is seen to be insignificant. Although reservoir model parameters in the wet gas reservoir were not as sensitive to the flow measurement errors as in the oil reservoir, for both cases, the future production forecast was significantly affected by the errors. Permeability was seen to be the most sensitive history matching parameter to the flow measurement errors in the oil reservoir, while for the wet gas reservoir, the most sensitive parameter was the forecast of future oil and gas production. Finally, considering the noticeable effect of systematic errors on both cases, it is suggested that flowmeter calibration and regular maintenance is prioritised, although the subsequent economic cost needs to be considered.

Abstract Evaluation of the economic benefit of field development projects in the oil and gas industry is naturally subject to subsurface uncertainties and risks. While high economic returns from produced volumes compensated for the lack of robust uncertainty estimates in the past, lower margins in tight market conditions and more complex project designs require increased efforts in delivering reliable uncertainty estimates for improving reservoir management decision support in times to come. An increasing number of field development projects include rigorous uncertainty quantification workflows based on parameterized subsurface uncertainties. Estimation and reduction of prediction uncertainty has no value unless it can potentially influence a decision process. This requires an integrated workflow design across disciplines and a proper risk mitigation plan. This work presents the implementation of an uncertainty workflow in reservoir management with a focus on reservoir modeling and simulation. Practical workflow design steps and intermediate milestones are discussed for generating alternative reservoir model realizations including historical production data. Calibrated model realizations define the basis for prediction estimates of a predefined field development plan. Practical steps are discussed with application to a complex oil rim development for an existing reservoir with long production history. This study aimed at an uncertainty assessment of a field development plan and a proposal for optimized relocations of infill wells considering multiple geological realizations. In conclusion, this work describes examples, experiences, and recommendations for an industry implementation for a risk assessment of a field development plan under subsurface uncertainties.

Iterative ensemble smoothers (IES) are among the state-of-the-art approaches to solving history matching problems. From an optimization-theoretic point of view, these algorithms can be derived by solving certain stochastic nonlinear-least-squares problems. In a broader picture, history matching is essentially an inverse problem, which is often ill-posed and may not possess a unique solution. To mitigate the ill-posedness, in the course of solving an inverse problem, prior knowledge and domain experience are often incorporated, as a regularization term, into a suitable cost function within a respective optimization problem. Whereas in the inverse theory there is a rich class of inversion algorithms resulting from various choices of regularized cost functions, there are few ensemble data assimilation algorithms (including IES) which in their practical uses are implemented in a form beyond nonlinear-least-squares. This work aims to narrow this noticed gap. Specifically, we consider a class of more generalized cost functions, and establish a unified formula that can be used to construct a corresponding group of novel ensemble data assimilation algorithms, called generalized IES (GIES), in a principled and systematic way. For demonstration, we choose a subset (up to 30 +) of the GIES algorithms derived from the unified formula, and apply them to two history matching problems. Experiment results indicate that many of the tested GIES algorithms exhibit superior performance to that of an original IES developed in a previous work, showcasing the potential benefit of designing new ensemble data assimilation algorithms through the proposed framework. [ABSTRACT FROM AUTHOR]

Ensemble data assimilation methods, particularly iterative forms of ensemble smoother, are very useful assisted history matching techniques. One of the main challenges in the application of these methods is the excessive variance loss due to sampling errors occasioned by the limited size ensembles used in practical cases. The standard procedure to mitigate this problem is called distance-based localization. However, in this case, the data assimilation performance becomes highly dependent on the choice of the localization region. Moreover, there are several relevant examples of non-local model parameters and data types, in which cases, distance-based localization does not apply. This paper proposes a distance-free localization procedure that combines a least-squares support vector (LS-SVR) proxy with a non-isotropic tapering function proposed in the literature. We tested the proposed method in two versions of the PUNQ-S3 problem. In the first version, we tested the method to localize scalar (non-local) parameters. The results show relevant improvements, especially in terms of preserving the posterior variance of the ensemble compared to methods investigated in Lacerda et al. (J. Pet. Sci. Eng. 172,690–706, 2019). The second version considered the problem of localization of grid parameters. In this case, the proposed method outperformed a distance-based localization approach proposed in the literature. [ABSTRACT FROM AUTHOR]

Reservoir simulation is critically important for optimally managing petroleum reservoirs. Often, many of the parameters of the model are unknown and cannot be measured directly. These parameters must then be inferred from production data at the wells. This is an inverse problem which can be formulated within a Bayesian framework to integrate prior knowledge with observational data. Markov Chain Monte Carlo (MCMC) methods are commonly used to solve Bayesian inverse problems by generating a set of samples which can be used to characterize the posterior distribution. In this work, we present a novel MCMC algorithm which uses a sequential transition kernel designed to exploit the redundancy which is often present in time series data from reservoirs. This method can be used to efficiently generate samples from the Bayesian posterior for time-dependent models. While this method is general and could be useful for many different models. We consider a Bayesian inverse problem in which we wish to infer fault transmissibilities from measurements of pressure at wells using a two-phase flow model. We demonstrate how the sequential MCMC algorithm presented here can be more efficient than a standard Metropolis-Hastings MCMC approach for this inverse problem. We use integrated autocorrelation times along with mean-squared jump distances to determine the performance of each method for the inverse problem. [ABSTRACT FROM AUTHOR]

• Compositional model was developed to assess EOR performance of nanoemulsions. • Core-flood process was explained using mathematical model equations. • Oil saturation and relative permeability curves confirmed water-wet state of rock. • History-matched models were used to explain flooding behavior. • Emulsifier(s) composition within nanoemulsion has significant impact on recovery factor. Simulation plays a pivotal role in the design of enhanced oil recovery (EOR) processes based on reservoir and in-situ fluid conditions. A robust compositional model, using a complicated multi-component nanoemulsion injection fluid, was developed to describe the performance of nanoemulsion flooding to predict their feasibility for pilot oilfield projects. Gemini surfactant/polymer/nanoparticle stabilized Pickering nanoemulsions were prepared by high-energy method and characterized to assess core-flooding performance. During simulation, a Cartesian grid model with fixed bulk volume, injection flow rate, well completion parameters and rock-fluid properties was employed. Core-flooding experiments were performed in steps, involving ~2.16 pore volume (PV) brine injection, ~0.90 PV nanoemulsion injection and ~1.50 PV chase water injection. Oil saturation map and relative permeability data analyses showed that the wetting nature of sandstone core altered from intermediate-wet to strongly water-wet condition. Tertiary recoveries were obtained in the range of 21-27% of the original oil in place (OOIP) for different surfactant/polymer/nanoparticle (SPN) compositions of injected nanoemulsion fluids. Flooding simulation studies showed good history matching of production data within ± 6% between experimental and simulated results. In summary, the efficacy of SPN nanoemulsions as an EOR fluid was corroborated with the aid of numerical simulation analyses. [Display omitted] [ABSTRACT FROM AUTHOR]

A Bayesian method of inference known as "Stein variational gradient descent" was recently implemented for data assimilation problems, under the heading of "mapping particle filter". In this manuscript, the algorithm is applied to another type of geoscientific inversion problems, namely history matching of petroleum reservoirs. In order to combat the curse of dimensionality, the commonly used Gaussian kernel, which defines the solution space, is replaced by a p-kernel. In addition, the ensemble gradient approximation used in the mapping particle filter is rectified, and the data assimilation experiments are re-run with more relevant settings and comparisons. Our experimental results in data assimilation are rather disappointing. However, the results from the subsurface inverse problem show more promise, especially as regards the use of p-kernels. [ABSTRACT FROM AUTHOR]

Smurf is an open source modular system developed in Python for running and cycling data assimilation (DA) systems. It is organised around three super classes for numerical model management, assimilation schemes and observation instruments. Any new item can be easily plugged in by defining a child class that will override as many methods as necessary. Non intrusive, Smurf can be used in any applicative domain for numerical models written in any language.

How can one design a building that will be sufficiently protected against overheating and sufficiently energy efficient, whilst considering the expected increases in temperature due to climate change? We successfully manage to address this question—greatly reducing a large set of initial candidate building designs down to a small set of acceptable buildings. We do this using a complex computer model, statistical models of said computer model (emulators), and a modification to the history matching calibration technique. This modification tackles the problem of level‐set estimation (rather than calibration), where the goal is to find input settings which lead to the simulated output being below some threshold. The entire procedure allows us to present a practitioner with a set of acceptable building designs, with the final design chosen based on other requirements (subjective or otherwise). [ABSTRACT FROM AUTHOR]

Data-space inversion (DSI) and related procedures represent a family of methods applicable for data assimilation in subsurface flow settings. These methods differ from usual model-based techniques in that they provide only posterior predictions for quantities (time series) of interest, not posterior models with calibrated parameters. DSI methods require a large number (O(500–1000)) of flow simulations to first be performed on prior geological realizations. Given observed data, posterior predictions for time series of interest, such as well injection or production rates, can then be generated directly. DSI operates in a Bayesian setting and provides posterior samples of the data vector. In this work, we develop and evaluate a new approach for data parameterization in DSI. Parameterization is useful in DSI as it reduces the number of variables to determine in the inversion, and it maintains the physical character of the data variables. The new parameterization uses a recurrent autoencoder (RAE) for dimension reduction, and a long short-term memory (LSTM) recurrent neural network architecture to represent flow-rate time series. The RAE-based parameterization is combined with an ensemble smoother with multiple data assimilation (ESMDA) for posterior data sample generation. Results are presented for two- and three-phase flows in a 2D channelized system and a 3D multi-Gaussian model. The new DSI RAE procedure, along with several existing DSI treatments, is assessed through detailed comparison to reference rejection sampling (RS) results. The new DSI methodology is shown to consistently outperform existing approaches, in terms of statistical (P10–P90 interval and Mahalanobis distance) agreement with RS results. The method is also shown to accurately capture derived quantities which are computed from variables considered directly in DSI. This requires correlation and covariance between variables to be properly captured, and accuracy in these relationships is demonstrated. The RAE-based parameterization developed here is clearly useful in DSI, and it may also find application in other subsurface flow problems. [ABSTRACT FROM AUTHOR]

Information on interwell connectivity is important in reservoir field dynamic analysis. However, all conventional methods, such as the tracer test, interference well test, and numerical simulation, have disadvantages. These disadvantages include the length of time taken, high costs, and the effect on oilfield production. Thus, research focus has been directed toward the development of approaches that use production and injection data to obtain interwell connectivity data. Prevailing interwell connectivity models are sensitive to shut-ins, and their corresponding inversion methods are unreliable. The improved interwell connectivity model presented in this study exhibits enhanced robustness to shut-ins. The application of seepage theories and numerical simulation methods enables the main model parameters to absorb prior geological knowledge to characterize the reservoir and improve the initial estimate of connectivity. Corresponding inverse methods for model parameters are implemented based on Bayesian inverse theory and the projection gradient method and obtain greater robustness for the model parameter, compared with those in previous studies. Testing of a heterogeneous synthetic reservoir and a Z16 reservoir block demonstrates that the methodology can precisely determine the interwell connectivity and can be used in real oilfields. [ABSTRACT FROM AUTHOR]

Smurf is an open source modular system developed in Python for running and cycling data assimilation (DA) systems. It is organised around three super classes for numerical model management, assimilation schemes and observation instruments. Any new item can be easily plugged in by defining a child class that will override as many methods as necessary. Non intrusive, Smurf can be used in any applicative domain for numerical models written in any language. [ABSTRACT FROM AUTHOR]

Abstract Most inverse reservoir modeling techniques require many forward simulations, and the posterior models cannot preserve geological features of prior models. This study proposes an iterative static modeling approach that utilizes dynamic data for rejecting an unsuitable training image (TI) among a set of TI candidates and for synthesizing history-matched pseudo-soft data. The proposed method is applied to two cases of channelized reservoirs, which have uncertainty in channel geometry such as direction, amplitude, and width. Distance-based clustering is applied to the initial models in total to select the qualified models efficiently. The mean of the qualified models is employed as a history-matched facies probability map in the next iteration of static models. Also, the most plausible TI is determined among TI candidates by rejecting other TIs during the iteration. The posterior models of the proposed method outperform updated models of ensemble Kalman filter (EnKF) and ensemble smoother (ES) because they describe the true facies connectivity with bimodal distribution and predict oil and water production with a reasonable range of uncertainty. In terms of simulation time, it requires 30 times of forward simulation in history matching, while the EnKF and ES need 9000 times and 200 times, respectively.

History matching is used to constrain flow simulations and reduce uncertainty in forecasts. In this work, we revisited some fundamental engineering tools for predicting waterflooding behavior to better understand the flaws in our simulation and thus find some models which are more accurate with better matching. The Craig-Geffen-Morse (CGM) analytical method was used to predict recovery performance calculations and it was simple enough which can be applied in a spreadsheet. In this study, the analytical approach of history matching was applied to a layered reservoir from a shallow marine deposit which was composed of different facies includes lower shoreface facies (LSF), middle shoreface facies (MSF) and upper shoreface facies (USF). Truncated Gaussian Simulation (TGS) is often used to stochastically distribute the facies in the geological model around a deterministic mean representation. The actual distribution is often hard to determine. Starting with the deterministic element of the facies distributions, corrections were made by matching the CGM method predictions to historical data. These corrections were amalgamated in the model and produced a much better history match. Further, the modifications were used to condition the stochastic simulator to provide a geologically more robust model that also matched history. The results showed that the variation of the total field production rate (FPR) between the deterministic model and history data was reduced by about 19.8% (from 21.52% to 1.73%) after applying history match analytically.

Abstract At present, chemical flooding is one of essential enhanced oil recovery methods. In this study, three core flooding experiments (brine flooding, Alkaline, and Alkaline + Ionic Liquid slug flooding) were selected for history matching using CMG-STARS. Depending on the composition of the chemical slug, two pore volumes were injected into the porous medium to enhance the RF of heavy oil (14° API). We observed that the most challenging part of building up the model was relative permeability curves. So, the relative permeability values were tuned to end up with a successful match of cumulatively produced oil and water cut. Finally, history matching is significant to apply a wide range of assumptions and upscale the experimental results.

Increasing hydrocarbon recovery from tight reservoirs is an essential goal of oil industry in the recent years. Building real dynamic simulation models and selecting and designing suitable development strategies for such reservoirs need basically to construct accurate structural static model construction. The uncertainties in building 3-D reservoir models are a real challenge for such micro to nano pore scale structure. Based on data from 24 wells distributed throughout the Sadi tight formation. An application of building a 3-D static model for a tight limestone oil reservoir in Iraq is presented in this study. The most common uncertainties confronted while building the model were illustrated. Such as accurate estimations of cut-off permeability and porosity values. These values directly affect the calculation of net pay thickness for each layer in the reservoir and consequently affect the target of estimating reservoir initial oil in place (IOIP). Also, the main challenge to the static modeling of such reservoirs is dealing with tight reservoir characteristics which cause major reservoir heterogeneity and complexities that are problematic to the process of modeling reservoir simulation. Twenty seven porosity and permeability measurements from Sadi/Tanuma reservoir were used to validate log interpretation data for model construction. The results of the history matching process of the constructed dynamic model is also presented in this paper, including data related to oil production, reservoir pressure, and well flowing pressure due to available production. [ABSTRACT FROM AUTHOR]

Geological carbon storage is a promising solution to reduce the CO2 concentration in the atmosphere to ameliorate the effects of global warming from the greenhouse effect. Among feasible storage options, deep saline aquifers are believed to have the largest storage capacity for the gas collected from industrial processes. The first CO2 storage project at a commercial scale in a saline aquifer is in the Sleipner field of the Utsira storage formation in Norway. The long ongoing storage operation in the Sleipner field has been the subject of several past studies attempting to recreate the observed injected CO2 plume migration behaviour. History matching is a method to adjust the input parameters of the model in a way to minimise the mismatch between the simulated and the actual production data in reservoir engineering and applicable to carbon sequestration. Typical parameters adjusted in history matching are porosity, absolute and relative permeability data. In this study, we used an adjoint‐based optimisation tool and showed the importance of caprock morphology in finding an accurate plume match. Using a set of synthetic models, we initially minimised the mismatch between the observed and simulated CO2 plume outline by modifying the caprock topographical details. After testing the optimisation tool on the synthetic models, we applied the methodology to the Sleipner benchmark 2019 model and improved the plume match by locally adjusting caprock elevation within seismic detection limits. We subsequently improved the match by calibrating porosity, permeability, CO2 density and injection rate together in an experiment in which we calibrated all the parameters, including the caprock morphology, to find a better match. The results showed an improvement of around 8% (compared with the original model) in the plume match resulting from an average absolute elevation change of 3.23 m in the model while keeping the other parameters constant. Calibrating the porosity, permeability, CO2 density and injection rate resulted in a 5% improvement in the match, and once caprock morphology was included in the optimisation process, the match improvement increased by 16%. We changed the caprock elevation within a range lower than the seismic detection limit, and results showed that even a few metres variations in the elevation have significant impacts on the plume migration and trapping mechanism in the Sleipner model. The method presented in this work results in a better match than the original seismic data for the Sleipner model. © 2020 The Authors. Greenhouse Gases: Science and Technology published by Society of Chemical Industry and John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Carbonate reservoirs in the Middle East hold a significant proportion of the remaining conventional oil reserves, which most of them were classified as naturally fractured. These reservoirs are well known for their low recoveries compared with their counterpart clastic unfractured reservoirs. Therefore, boosting their recoveries can assure to sustain the energy supply to the global oil markets. In this work, an example from the Middle East has been used to evaluate the impact of the fracture characteristics on the reservoir performance using four decades of production history. The characteristics of natural fractures have a remarkable impact on fluid flow behaviour in fractured reservoirs. Besides, these characteristics, such as fracture intensity, determines the matrix block dimensions, which in turn, influence the matrix recovery. However, it is challenging to estimate the fracture characteristics accurately due to the scarcity of the fracture data from subsurface measurements. Therefore, outcrop analogue data can be utilised to enhance the fracture modelling in fractured reservoirs and to fill the data gap between the seismic scale and well scale. In this work, we have integrated the outcrop fracture data with the core observations to improve the fracture modelling in the studied reservoir. Furthermore, a sensitivity study was carried out to investigate the impact of flow curves, gravity drainage mechanism, and its parameters, as well as the fracture storativity on the history matching in fractured reservoirs. Excellent matching results were obtained for the majority of the wells, as indicated by the low mismatch values. The obtained results highlighted the importance of fractures on the fluid flow behaviour, and hence the reservoir performance. Therefore, fracture properties should not be abusively modified using multipliers and local adjustment to avoid nullifying the reservoir characterisation efforts and degrade the simulation model capability for a future prediction. [ABSTRACT FROM AUTHOR]

Cardiac contraction is the result of integrated cellular, tissue and organ function. Biophysical in silico cardiac models offer a systematic approach for studying these multi-scale interactions. The computational cost of such models is high, due to their multi-parametric and nonlinear nature. This has so far made it difficult to perform model fitting and prevented global sensitivity analysis (GSA) studies. We propose a machine learning approach based on Gaussian process emulation of model simulations using probabilistic surrogate models, which enables model parameter inference via a Bayesian history matching (HM) technique and GSA on whole-organ mechanics. This framework is applied to model healthy and aortic-banded hypertensive rats, a commonly used animal model of heart failure disease. The obtained probabilistic surrogate models accurately predicted the left ventricular pump function (R2 =0.92 for ejection fraction). The HM technique allowed us to fit both the control and diseased virtual bi-ventricular rat heart models to magnetic resonance imaging and literature data, with model outputs from the constrained parameter space falling within 2 SD of the respective experimental values. The GSA identified Troponin C and cross-bridge kinetics as key parameters in determining both systolic and diastolic ventricular function. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'. [ABSTRACT FROM AUTHOR]

Reservoir engineers use large-scale numerical models to predict the production performance in oil and gas fields. However, these models are constructed based on scarce and often inaccurate data, making their predictions highly uncertain. On the other hand, measurements of pressure and flow rates are constantly collected during the operation of the field. The assimilation of these data into the reservoir models (history matching) helps to mitigate uncertainty and improve their predictive capacity. History matching is a nonlinear inverse problem, which is typically handled using optimization and Monte Carlo methods. In practice, however, generating a set of properly history-matched models that preserve the geological realism is very challenging, especially in cases with intricate prior description, such as models with fractures and complex facies distributions. Recently, a new data-space inversion (DSI) approach was introduced in the literature as an alternative to the model-space inversion used in history matching. The essential idea is to update directly the predictions from a prior ensemble of models to account for the observed production history without updating the corresponding models. The present paper introduces a DSI implementation based on the use of an iterative ensemble smoother and demonstrates with examples that the new implementation is computationally faster and more robust than the earlier method based on principal component analysis and gradient-driven optimization. The new DSI is also applied to estimate the production forecast in a real field with long production history and a large number of wells. For this field problem, the new DSI obtained forecasts comparable with a more traditional ensemble-based history matching. [ABSTRACT FROM AUTHOR]

The Ensemble Kalman Filter (EnKF), as the most popular sequential data assimilation algorithm for history matching, has the intrinsic problem of high computational cost and the potential inconsistency of state variables updated at each loop of data assimilation and its corresponding reservoir simulated result. This problem forbids the reservoir engineers to make the best use of the 4D seismic data, which provides valuable information about the fluid change inside the reservoir. Moreover, only matching the production data in the past is not enough to accurately forecast the future, and the development plan based on the false forecast is very likely to be suboptimal. To solve this problem, we developed a workflow for geophysical and production data history matching by modifying ensemble smoother with multiple data assimilation (ESMDA). In this work, we derived the mathematical expressions of ESMDA and discussed its scope of applications. The geophysical data we used is P-wave impedance, which is typically included in a basic seismic interpretation, and it directly reflects the saturation change in the reservoir. Full resolution of the seismic data is not necessary, we subsampled the P-wave impedance data to further reduce the computational cost. With our case studies on a benchmark synthetic reservoir model, we also showed the supremacy of matching both geophysical and production data, than the traditional reservoir history matching merely on the production data: the overall percentage error of the observed data is halved, and the variances of the updated forecasts are reduced by two orders of the magnitude. [ABSTRACT FROM AUTHOR]

Automatic history matching using production and seismic data is still challenging due to the size of seismic datasets. The most severe problem, when applying ensemble-based methods for assimilating large datasets, is that the uncertainty is usually underestimated due to the limited number of models in the ensemble compared with the dimension of the data, which inevitably leads to an ensemble collapse. Localization and data reduction methods are promising approaches mitigating this problem. In this paper, we present a new robust and flexible workflow for assimilating seismic attributes and production data. The methodology is based on sparse representation of the seismic data, using methods developed for image denoising. We propose to assimilate production and seismic data simultaneously, and to ensure equal weight on these data types, we apply scaling based on the initial data match. Further, a newly developed flexible correlation-based localization technique is used for both data types. The workflow is successfully implemented for the released Norne benchmark dataset, and an iterative ensemble smoother is used for the simultaneous assimilation of production and seismic data. We show that the methodology is robust and ensemble collapse is avoided. Furthermore, the proposed workflow is flexible, as it can be applied to seismic data or inverted seismic properties, and the methodology requires only moderate computer memory. The results show that through this method, we can successfully reduce the data mismatch for both production data and seismic data. [ABSTRACT FROM AUTHOR]

Data-space inversion (DSI) methods provide posterior (history-matched) predictions for quantities of interest, along with uncertainty quantification, without constructing posterior models. Rather, predictions are generated directly from a large set of prior model simulations and observed data. In this work, we develop a data-space inversion with variable control (DSIVC) procedure that enables forecasting with user-specified well controls in the post-history-match prediction period. In DSIVC, flow simulations on all prior realizations, with randomly sampled well controls, are first performed. User-specified controls are treated as additional observations to be matched in posterior predictions. Posterior data samples are generated using a randomized maximum likelihood procedure with a gradient-based optimizer. For prescribed post-history-match well control settings, posterior predictions can be generated in seconds or minutes. Results are presented for a channelized system, and posterior predictions from DSIVC are compared with those from the standard DSI method. Standard DSI requires prior models to be re-simulated using the specified controls, while DSIVC requires only one set of prior simulations. Substantial uncertainty reduction is achieved through data-space inversion, and reasonable agreement between DSIVC and DSI results is generally observed. DSIVC is then applied for data assimilation combined with production optimization under uncertainty, as well as for closed-loop reservoir management, which entails a sequence of data assimilation and optimization steps. Clear improvement in the objective function is attained in these examples. [ABSTRACT FROM AUTHOR]

Data assimilation methods often assume perfect models and uncorrelated observation error. The assumption of a perfect model is probably always wrong for applications to real systems, and since model error is known to generally induce correlated effective observation errors, then the common assumption of uncorrelated observation errors is probably almost always wrong, too. The standard approach to dealing with correlated observation errors, which simply ignores the correlation, leads to suboptimal assimilation of observations. In this paper, we examine the consequences of model errors on assimilation of seismic data. We show how to recognize the existence of correlated error through model diagnostics modified for large numbers of data, how to estimate the correlation in the error, and how to use a model with correlated errors in a perturbed observation form of an iterative ensemble smoother to improve the quantification of a posteriori uncertainty. The methodologies for each of these aspects have been developed to allow application to problems with very large number of model parameters and large amounts of data with correlated observation error. We applied the methodologies to a small toy problem with linear relationship between data and model parameters, and to synthetic seismic data from the Norne Field model. To provide a controlled investigation in the seismic example, we investigate an application of data assimilation with two sources of model error—errors in seismic resolution and errors in the petro-elastic model. Both types of model errors result in effectively correlated observation errors, which must be accounted for in the data assimilation scheme. Although the data are synthetic, parameters of the seismic resolution and the observation noise are estimated from the actual inverted acoustic impedance data. Using a structured approach, we are able to assimilate approximately 115,000 observations with correlated total observation error efficiently without neglecting correlations. We show that the application of this methodology leads to less overfitting to the observations, and results in an ensemble estimate with smaller spread than the initial ensemble of predictions, but that the final estimate of uncertainty is consistent with the truth. [ABSTRACT FROM AUTHOR]

Distributed Gauss-Newton (DGN) optimization method has been proved very efficient and robust for history matching and uncertainty quantification (HM&UQ). The major bottleneck for performance enhancement is the expensive computational cost of solving hundreds of Gauss-Newton trust-region (GNTR) subproblems in each iteration. The original GNTR solver applies the less efficient iterative Newton-Raphson (NR) method using a derivative which requires solving a large-scale linear system twice in each NR iteration. Instead of using a less accurate linear proxy as in the iterative NR method, the nonlinear GNTR equation is first approximated with an inverse-quadratic (IQ) or a cubic-spline (CS) model, by fitting points generated in previous iterations without using any derivative. Then, the analytical (or numerical) solution of the IQ (or CS) model is used as the new proposal for the next iteration. The performances of the two new GNTR solvers are benchmarked against different methods on different sets of test problems with different numbers of uncertain parameters (ranging from 500 to 100,000) and different numbers of observed data (ranging from 100 to 100,000). In terms of efficiency and robustness, the two new GNTR solvers have comparable performance, and they outperform other methods we tested, including the well-known direct and iterative trust-region solvers of the GALAHAD optimization library. Finally, the proposed GNTR solvers have been implemented in our in-house distributed HM&UQ system. Our numerical experiments indicate that the DGN optimizer using the newly proposed GNTR solver performs quite stable and is effective when applied to real-field history matching problems. [ABSTRACT FROM AUTHOR]

For most history matching problems, the posterior probability density function (PDF) may have multiple local maxima, and it is extremely challenging to quantify uncertainty of model parameters and production forecasts by conditioning to production data. In this paper, a novel method is proposed to improve the accuracy of Gaussian mixture model (GMM) approximation of the complex posterior PDF by adding more Gaussian components. Simulation results of all reservoir models generated during the history matching process, e.g., using the distributed Gauss-Newton (DGN) optimizer, are used as training data points for GMM fitting. The distance between the GMM approximation and the actual posterior PDF is estimated by summing up the errors calculated at all training data points. The distance is an analytical function of unknown GMM parameters such as covariance matrix and weighting factor for each Gaussian component. These unknown GMM parameters are determined by minimizing the distance function. A GMM is accepted if the distance is reasonably small. Otherwise, new Gaussian components will be added iteratively to further reduce the distance until convergence. Finally, high-quality conditional realizations are generated by sampling from each Gaussian component in the mixture, with the appropriate relative probability. The proposed method is first validated using nonlinear toy problems and then applied to a history-matching example. GMM generates better samples with a computational cost comparable to or less than other methods we tested. GMM samples yield production forecasts that match production data reasonably well in the history-matching period and are consistent with production data observed in the blind test period. [ABSTRACT FROM AUTHOR]

A major challenge in plant developmental biology is to understand how plant growth is coordinated by interacting hormones and genes. To meet this challenge, it is important to not only use experimental data, but also formulate a mathematical model. For the mathematical model to best describe the true biological system, it is necessary to understand the parameter space of the model, along with the links between the model, the parameter space and experimental observations. We develop sequential history matching methodology, using Bayesian emulation, to gain substantial insight into biological model parameter spaces. This is achieved by finding sets of acceptable parameters in accordance with successive sets of physical observations. These methods are then applied to a complex hormonal crosstalk model for Arabidopsis root growth. In this application, we demonstrate how an initial set of 22 observed trends reduce the volume of the set of acceptable inputs to a proportion of 6.1 × 10−7 of the original space. Additional sets of biologically relevant experimental data, each of size 5, reduce the size of this space by a further three and two orders of magnitude respectively. Hence, we provide insight into the constraints placed upon the model structure by, and the biological consequences of, measuring subsets of observations. [ABSTRACT FROM AUTHOR]

Using artificial intelligence (AI) and machine learning (ML) techniques, we developed and validated the smart proxy models for history matching of reservoir simulation, sensitivity analysis, and uncertainty assessment by artificial neural network (ANN). The smart proxy models were applied on two cases, the first case study investigated the application of a proxy model for calibrating a reservoir simulation model based on historical data and predicting well production while the second case study investigated the application of an ANN-based proxy model for fast-track modeling of CO 2 enhanced oil recovery, aiming at the prediction of the reservoir pressure and phase saturation distribution at injection stage and post-injection stage. The prediction effects for both cases are promising. While a single run of basic numerical simulation model takes hours to days, the smart proxy model runs in a matter of seconds, saving 98.9% of calculating time. The results of these case studies demonstrate the advantage of the proposed workflow for addressing the high run-time, computational time and computational cost of numerical simulation models. In addition, these proxy models predict the outputs of reservoir simulation models with high accuracy. [ABSTRACT FROM AUTHOR]

This paper develops a reliable workflow for multi-objective history matching coupled with a distance-based model selection and ensemble-based data assimilation at a clastic channel reservoir with uncertain geological scenarios. The distance map allocated to each producer determines the probabilities of training images which assess the uncertainty of geological scenarios. K-medoids clustering selects the reservoir models within the ensemble set applied with some training images with less error. These geo-models play as initial ensembles suitable to explain the geological scenarios and ensemble Kalman filter recursively assimilates the oil rates of each producer. The developed workflow, updating reliable reservoir models suitable for well-performance-based history matching, more accurately forecasts water breakthrough and improves the predictability of unknown oil rates with a lower error than those of the conventional ensemble Kalman filter. This framework is able to preserve the spatial characteristics of facies models and reservoir properties without interpreting one fixed scenario. The proposed method can contribute to a reasonable design for data analytics with uncertain geological scenarios and for matching different-scaled well production histories. [ABSTRACT FROM AUTHOR]

The exploitation of subsurface hydrocarbon reservoirs is achieved through the control of production and injection wells (i.e., by prescribing time-varying pressures and flow rates) to create conditions that make the hydrocarbons trapped in the pores of the rock formation flow to the surface. The design of production strategies to exploit these reservoirs in the most efficient way requires an optimization framework that reflects the nature of the operational decisions and geological uncertainties involved. This paper introduces a new approach for production optimization in the context of closed-loop reservoir management (CLRM) by considering the impact of future measurements within the optimization framework. CLRM enables instrumented oil fields to be operated more efficiently through the systematic use of life-cycle production optimization and computer-assisted history matching. Recently, we have proposed a methodology to assess the value of information (VOI) of measurements in such a CLRM approach a-priori, i.e. during the field development planning phase, to improve the planned history matching component of CLRM. The reasoning behind the a-priori VOI analysis unveils an opportunity to also improve our approach to the production optimization problem by anticipating the fact that additional information (e.g., production measurements) will become available in the future. Here, we show how the more conventional optimization approach can be combined with VOI considerations to come up with a novel workflow, which we refer to as informed production optimization. We illustrate the concept with a simple water flooding problem in a two-dimensional five-spot reservoir and the results obtained confirm that this new approach can lead to significantly better decisions in some cases. [ABSTRACT FROM AUTHOR]

Ensemble-based analyses are useful to compare equiprobable scenarios of the reservoir models. However, they require a large suite of reservoir models to cover high uncertainty in heterogeneous and complex reservoir models. For stable convergence in ensemble Kalman filter (EnKF), increasing ensemble size can be one of the solutions, but it causes high computational cost in large-scale reservoir systems. In this paper, we propose a preprocessing of good initial model selection to reduce the ensemble size, and then, EnKF is utilized to predict production performances stochastically. In the model selection scheme, representative models are chosen by using principal component analysis (PCA) and clustering analysis. The dimension of initial models is reduced using PCA, and the reduced models are grouped by clustering. Then, we choose and simulate representative models from the cluster groups to compare errors of production predictions with historical observation data. One representative model with the minimum error is considered as the best model, and we use the ensemble members near the best model in the cluster plane for applying EnKF. We demonstrate the proposed scheme for two 3D models that EnKF provides reliable assimilation results with much reduced computation time. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel method for the automatic history matching of 3D reservoirs with two lithofacies. The method simultaneously estimates distributed geological reservoir properties and facies boundaries by combining the general Ensemble Kalman Filter (EnKF) strategy with the level set method for shape propagation in 3D. Each iteration of this novel Ensemble Kalman Filter-Level Set (EnKF-LS) scheme combines the update of the boundaries of two lithofacies, represented by associated level set functions, with an update of the corresponding parameter fields, namely porosity and permeability. A narrow band technique is employed for restricting the shape motion to a neighbourhood of the current interfaces. The proposed algorithm is tested on a synthetic 3D reservoir model which is a modification of the popular SPE10 model. We use an initial ensemble of porosity and permeability fields created by a multiple-point statistics-based algorithm for a channelized test case. We compared the proposed method with an implementation of the standard EnKF algorithm and showed that the proposed EnKF-LS scheme not only provides more adequate results for such a channelized structure, but also produces a better data fit than the standard EnKF approach. [ABSTRACT FROM AUTHOR]

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Production prediction has been playing an essential role in reservoir development and management. Reservoir history matching, typically involving time-consuming numerical simulations for model calibration and parameter estimation, is most applied to catch several reliable reservoir models for reservoir production prediction. This research introduces the proxy model, mainly based on the convolutional neural network (CNN), to accelerate the forward computation process and improve the history-matching efficiency. Firstly, numerous embedded discrete fracture models designed via Latin Hypercube Sampling and constructed by MATLAB Reservoir Simulation Toolbox are conducted to generate training and testing datasets with high complexity and diversity. Then, we introduced the concept of a tier system consisting of multiple cubes that record reservoir and fracture information in the form of channels in spatial space. Six channels were utilized to record fracture information, including fracture shape, time, matrix porosity, matrix permeability, fracture porosity, and fracture permeability. The cube data of the tier system served as input to our proxy model, whereas oil and water production rates served as output. Finally, we trained and tested the CNN-based proxy model to predict oil and water production accurately. We performed assisted history matching by the genetic algorithm using this artificial intelligence-based proxy model. The results indicate that the CNN-based proxy model can completely match the numerical simulation with an accuracy of 99% on synthetic production data, and the genetic algorithm-based-proxy model can accelerate the history-matching progress more efficiently than that using the traditional method. • Fracture information is stored in highly structured data, termed as tier system. • Multiple prolongable channels are used to characterize one fracture. • Production prediction is carried out at fracture scale with less computational cost. [ABSTRACT FROM AUTHOR]

In this study, we present an efficient and flexible adjoint-based framework for history matching and forecasting geothermal energy extraction at a large scale. In this framework, we applied the Principal Component Analysis to reduce the parameter space for representing the complex geological model. The adjoint method is implemented for gradient calculation to speed up the history-matching iteration process. Operator-based linearization (OBL) used in this framework makes the calculation of the physical state and its derivatives very efficient and facilitates the matrix assembly in the adjoint method. This study primarily focuses on history matching based on combined observation of well production and in-situ electromagnetic measurements to predict the temperature front. However, different types of misfit terms can be added to the objective function based on practical considerations. For example, our history-matching case studies include model misfit terms applied for regularization purposes. The measurement data is extracted from the true model, and realistic measurement errors are considered. Also, in this work, we propose an optimal weighting strategy for the terms of the objective function to balance their sensitivity with respect to the model control variables. The high efficiency of the framework is demonstrated for the geothermal doublet model implemented at the heterogeneous reservoir with multiple realizations. The framework allows for generating posterior Randomized Maximum Likelihood (RML) estimates of the entire ensemble of the realizations with a reasonable computational cost. Results show that the framework can achieve reliable history-matching results based on the doublets production data and the reservoir electromagnetic measurement. • An efficient and flexible adjoint-based history matching framework for geothermal reservoir is developed. • Reservoir temperature interpreted from electromagnetic data are included in the proposed framework. • The adjoint method is implemented in this framework to significantly improve the efficiency of the history matching. • The adjoint-based framework shows the potential to effectively characterize the reservoir geological features using electromagnetic data. • The space reduction technique like Principal Component Analysis is utilized in this study. [ABSTRACT FROM AUTHOR]

The current practice for multi-fractured horizontal well development in low-permeability reservoirs is to complete the full length of the well with evenly spaced fracture stages. Given methods to evaluate along-well variability in reservoir quality and to predict stage-by-stage performance, it may be possible to reduce the number of stages completed in a well without a significant sacrifice in well performance. Provision and demonstration of these methods is the goal of the current two-part study. In Part 1 of this study, reservoir and completion quality were evaluated along the length of a horizontal well in the Montney Formation in western Canada. In the current (Part 2) study, the along-well reservoir property estimates are first used to forecast per-stage production variability, and then used to evaluate production performance of the well when fewer stages are completed in higher quality reservoir. A rigorous and fast semi-analytical model was used for forecasting, with constraints on fracture geometry obtained from numerical model history matching of the studied Montney well flowback data. It is concluded that a significant reduction in the number of stages from 50 (what was implemented) to less than 40 could have yielded most of the oil production obtained over the forecast period.

Abstract Accurate fluid flow simulation in geologically complex reservoirs is of particular importance in construction of reservoir simulators. General approaches in naturally fractured reservoir simulation involve use of unstructured grids or a structured grid coupled with locally unstructured grids and discrete fracture models. These methods suffer from drawbacks such as lack of flexibility and of ease of updating. In this study, I combined fracture modeling by elastic gridding which improves flexibility, especially in complex reservoirs. The proposed model revises conventional modeling fractures by hard rigid planes that do not change through production. This is a dubious assumption, especially in reservoirs with a high production rate in the beginning. The proposed elastic fracture modeling considers changes in fracture properties, shape and aperture through the simulation. This strategy is only reliable for naturally fractured reservoirs with high fracture permeability and less permeable matrix and parallel fractures with less cross-connections. Comparison of elastic fracture modeling results with conventional modeling showed that these assumptions will cause production pressure to enlarge fracture apertures and change fracture shapes, which consequently results in lower production compared with what was previously assumed. It is concluded that an elastic gridded model could better simulate reservoir performance.

Raanes et al. [1] revised the iterative ensemble smoother of Chen and Oliver [2, 3], denoted Ensemble Randomized Maximum Likelihood (EnRML), using the property that the EnRML solution is contained in the ensemble subspace. They analyzed EnRML and demonstrated how to implement the method without the use of expensive pseudo inversions of the low-rank state covariance matrix or the ensemble-anomaly matrix. The new algorithm produces the same result, realization by realization, as the original EnRML method. However, the new formulation is simpler to implement, numerically stable, and computationally more efficient. The purpose of this document is to present a simple derivation of the new algorithm and demonstrate its practical implementation and use for reservoir history matching. An additional focus is to customize the algorithm to be suitable for big-data assimilation of measurements with correlated errors. The computational cost of the resulting “ensemble sub-space” algorithm is linear in both the dimension of the state space and the number of measurements, also when the measurements have correlated errors. The final algorithm is implemented in the Ensemble Reservoir Tool (ERT) for running and conditioning ensembles of reservoir models. Several verification experiments are presented.

Production forecasting is the basis for decision making in the oil and gas industry, and can be quite challenging, especially in terms of complex geological modeling of the subsurface. To help solve this problem, assisted history matching built on ensemble-based analysis such as the ensemble smoother and ensemble Kalman filter is useful in estimating models that preserve geological realism and have predictive capabilities. These methods tend, however, to be computationally demanding, as they require a large ensemble size for stable convergence. In this paper, we propose a novel method of uncertainty quantification and reservoir model calibration with much-reduced computation time. This approach is based on a sequential combination of nonlinear dimensionality reduction techniques: t-distributed stochastic neighbor embedding or the Gaussian process latent variable model and clustering K-means, along with the data assimilation method ensemble smoother with multiple data assimilation. The cluster analysis with t-distributed stochastic neighbor embedding and Gaussian process latent variable model is used to reduce the number of initial geostatistical realizations and select a set of optimal reservoir models that have similar production performance to the reference model. We then apply ensemble smoother with multiple data assimilation for providing reliable assimilation results. Experimental results based on the Brugge field case data verify the efficiency of the proposed approach.