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Production forecasting using numerical simulation has become a standard in the oil and gas industry. The model construction process requires an explicit definition of multiple uncertain parameters; thus, the outcome of the modelling is also uncertain. For the reservoirs with production data, the uncertainty can be reduced by history-matching. However, the manual matching procedure is time-consuming and usually generates one deterministic realization. Due to the ill-posed nature of the calibration process, the uncertainty cannot be captured sufficiently with only one simulation model. In this paper, the uncertainty quantification process carried out for a gas-condensate reservoir is described. The ensemble-based uncertainty approach was used with the ES-MDA algorithm, conditioning the models to the observed data. Along with the results, the author described the solutions proposed to improve the algorithm's efficiency and to analyze the factors controlling modelling uncertainty. As a part of the calibration process, various geological hypotheses regarding the presence of an active aquifer were verified, leading to important observations about the drive mechanism of the analyzed reservoir. [ABSTRACT FROM AUTHOR]

Numerical models representing geological reservoirs can be used to forecast production and help engineers to design optimal development plans. These models should be as representative as possible of the true dynamic behavior and reproduce available static and dynamic data. However, identifying models constrained to production data can be very challenging and time consuming. Machine learning techniques can be considered to mimic and replace the fluid flow simulator in the process. However, the benefit of these approaches strongly depends on the simulation time required to train reliable predictors. Previous studies highlighted the potential of the multi-fidelity approach rooted in cokriging to efficiently provide accurate estimations of fluid flow simulator outputs. This technique consists in combining simulation results obtained on several levels of resolution for the reservoir model to predict the output properties on the finest level (the most accurate one). The degraded levels can correspond for instance to a coarser discretization in space or time, or to less complex physics. The idea behind is to take advantage of the coarse level low-cost information to limit the total simulation time required to train the meta-models. In this paper, we propose a new sequential design strategy for iteratively and automatically training (kriging and) cokriging based meta-models. As highlighted on two synthetic cases, this approach makes it possible to identify training sets leading to accurate estimations for the error between measured and simulated production data (objective function) while requiring limited simulation times. [ABSTRACT FROM AUTHOR]

Multi-stage hydraulic fracturing in horizontal wells has been proven an effective stimulation method to enhance well performances from extremely low permeable reservoirs by creating a complex fracture network. The concept of stimulated reservoir volume (SRV) was introduced to quantify the complex fracture network. Knowledge of the SRV is important for the evaluation of the hydraulic fracturing performance and the estimation of hydrocarbon recovery. However, it is still a challenging topic to model the evolution of the SRV and estimate its properties because of the presence of fluid–solid complex interactions during the fracturing process. Most current SRV estimation methods are complex and computationally expensive. The paper applied a simple modified dilation-recompaction model to simulate the evolution of the effective SRV without representing the fracture geometry explicitly. By history matching production data of a multi-stage fractured horizontal well in Chang 8 formation of the YanChang oilfield, China, the calibrated dilation-recompaction model can successfully characterize the evolution of the generated SRV and estimate the rock properties of the fractured zones. The simulation results show that the total effective stimulated reservoir volumes amount to 88,375 m3. The shape of a fracture zone is nearly elliptical about 54 m wide and 20 m high surrounding a well perforation. The permeability of the zone reaches as high as 28 mD, centering around the wellbore and decreasing gradually outward. [ABSTRACT FROM AUTHOR]

Production forecasting using numerical simulation has become a standard in the oil and gas industry. The model construction process requires an explicit definition of multiple uncertain parameters; thus, the outcome of the modelling is also uncertain. For the reservoirs with production data, the uncertainty can be reduced by history-matching. However, the manual matching procedure is time-consuming and usually generates one deterministic realization. Due to the ill-posed nature of the calibration process, the uncertainty cannot be captured sufficiently with only one simulation model. In this paper, the uncertainty quantification process carried out for a gas-condensate reservoir is described. The ensemble-based uncertainty approach was used with the ES-MDA algorithm, conditioning the models to the observed data. Along with the results, the author described the solutions proposed to improve the algorithm’s efficiency and to analyze the factors controlling modelling uncertainty. As a part of the calibration process, various geological hypotheses regarding the presence of an active aquifer were verified, leading to important observations about the drive mechanism of the analyzed reservoir.

Abstract Diagenesis is rarely accounted for in the standard modeling workflows for carbonate reservoirs, although it has a huge impact on both porosity and permeability. This can be explained by at least two reasons: first, it is difficult to quantify the influence of diagenetic overprints on porosity and permeability; second, the integration of the diagenetic effects in carbonate reservoir models makes history matching much more difficult. Herein, a modeling methodology is proposed, in which the diagenetic imprints are included in the reservoir model and calibrated with dynamic data. The key point consists in defining a parametrization technique able to capture these diagenetic imprints. We assume that distinct regions of occurrence of a given diagenetic phase can be identified within the reservoir. Therefore, restricting our attention to a facies, we may distinguish regions characterized by low, medium or high proportions of the targeted diagenetic phase. The advantage of this parametrization technique is that the proportions of these regions can be easily driven by a reduced number of proportionality coefficients. Then, the overall modeling approach is integrated in an optimization workflow making it possible to vary the proportions of the region with a given occurrence for a given diagenetic phase, the variograms characterizing the spatial distribution of the regions, or even the way they are spatially distributed. The optimization process is run to adjust these various unknown parameters in order to match production history. The potential of the proposed methodology is finally investigated through the study of a two-dimensional numerical example.

Diagenesis is rarely accounted for in the standard modeling workflows for carbonate reservoirs, although it has a huge impact on both porosity and permeability. This can be explained by at least two reasons: first, it is difficult to quantify the influence of diagenetic overprints on porosity and permeability; second, the integration of the diagenetic effects in carbonate reservoir models makes history matching much more difficult. Herein, a modeling methodology is proposed, in which the diagenetic imprints are included in the reservoir model and calibrated with dynamic data. The key point consists in defining a parametrization technique able to capture these diagenetic imprints. We assume that distinct regions of occurrence of a given diagenetic phase can be identified within the reservoir. Therefore, restricting our attention to a facies, we may distinguish regions characterized by low, medium or high proportions of the targeted diagenetic phase. The advantage of this parametrization technique is that the proportions of these regions can be easily driven by a reduced number of proportionality coefficients. Then, the overall modeling approach is integrated in an optimization workflow making it possible to vary the proportions of the region with a given occurrence for a given diagenetic phase, the variograms characterizing the spatial distribution of the regions, or even the way they are spatially distributed. The optimization process is run to adjust these various unknown parameters in order to match production history. The potential of the proposed methodology is finally investigated through the study of a two-dimensional numerical example. [ABSTRACT FROM AUTHOR]

Unlike conventional or tight gas reservoirs, shale gas or oil reservoirs have complex fracture networks that are often developed due to the interactions between natural and hydraulic fractures. Another major characteristic of shale reservoirs is that a good portion of shale gas can be in adsorbed state. In order to capture these characteristics of shale reservoirs numerically, PSU-SHALECOMP , a compositional dual-porosity, dual-permeability, multi-phase reservoir simulator is employed together with the implementation of stimulated reservoir volume ( SRV ) approach. In this approach, three of the reservoir parameters are altered to define hydraulic fractures in the form of SRV . These altered properties are SRV fracture permeability, SRV fracture porosity and SRV fracture spacing. In the validation phase of these computationally inexpensive SRV models, rock and fluid properties and reservoir conditions representative of a Marcellus shale reservoir and normalized field data from Marcellus shale wells to history-match the production performances were used. It is shown that the PSU-SHALECOMP simulator with the implementation of SRV model is capable of matching the historical data effectively and rapidly. In pursuit of successful validations of various production scenarios, several carbon dioxide injection scenarios were performed to see the performance of the PSU-SHALECOMP simulator in depleted Marcellus shale reservoirs. [ABSTRACT FROM AUTHOR]

Gravity drainage is one of the essential recovery mechanisms in naturally fractured reservoirs. Several mathematical formulas have been proposed to simulate the drainage process using the dual-porosity model. Nevertheless, they were varied in their abilities to capture the real saturation profiles and recovery speed in the reservoir. Therefore, understanding each mathematical model can help in deciding the best gravity model that suits each reservoir case. Real field data from a naturally fractured carbonate reservoir from the Middle East have used to examine the performance of various gravity equations. The reservoir represents a gas−oil system and has four decades of production history, which provided the required mean to evaluate the performance of each gravity model. The simulation outcomes demonstrated remarkable differences in the oil and gas saturation profile and in the oil recovery speed from the matrix blocks, which attributed to a different definition of the flow potential in the vertical direction. Moreover, a sensitivity study showed that some matrix parameters such as block height and vertical permeability exhibited a different behavior and effectiveness in each gravity model, which highlighted the associated uncertainty to the possible range that often used in the simulation. These parameters should be modelled accurately to avoid overestimation of the oil recovery from the matrix blocks, recovery speed, and to capture the advanced gas front in the oil zone.

A post-fracturing evaluation is essential to optimize a fracturing design for a multi-stage fractured well located in unconventional reservoirs. To accomplish this task, a production logging tool (PLT) can be utilized to provide the oil production rate of each fracturing stage. In this research, a practical method is proposed to integrate PLT and surface production data into a reservoir model. It applies the ensemble smoother for history-matching to integrate various kinds of dynamic data. To investigate the validity of the proposedmethod, three cases are designed according to the frequency of PLT surveys. Each fracture half-length calibrated by PLT data is similar to the true value, and the dynamic behavior also has the same trend as true production behavior. Integration with PLT data can reduce error ratios for fracture half-length down to 48%. In addition, it presents the applicability of reserve prediction and uncertainty assessment. It has been proven that the more frequently PLTs are surveyed, the more accurate the results. By sensitivity analysis of PLT frequency--a cost-effective strategy--a combination of only one PLT survey and continuous surface production data is employed to demonstrate this proposed concept. [ABSTRACT FROM AUTHOR]

Parameterization of petroleum reservoirs is an important component of reservoir management. However, the process of reservoir parameterization is fraught with nonuniqueness of estimated parameters. Such nonuniqueness leads to large uncertainty and risks in reservoir management. One way to quantify and reduce the uncertainty in parameter estimation is to generate multiple realizations of the parameter field often through geostatistical simulations. Such realizations do not reproduce the production history and there is always a need to adjust such models to match the history data. Conditioning all geostatistically-simulated reservoir models to production data is often time-consuming, and the process does not usually produce maps that truly mimic the actual reservoir heterogeneity. This work presents a global-local optimization template (GLOCAL) that produces multiple estimates of the parameter field by history-matching production data. More fundamentally, the technique produces realizations of the parameter field at different scales of resolution. Two sample history-matching problems are presented to illustrate the effectiveness of the method. Results from these examples show that the method can produce several estimates that show some pattern of heterogeneity found in the true field. However, the resemblance to the true field varies across different scales of resolution of the parameter field in the global template. [ABSTRACT FROM AUTHOR]

The process of reservoir history-matching is a costly task. Many available history-matching algorithms either fail to perform such a task or they require a large number of simulation runs. To overcome such struggles, we apply the Gaussian Process (GP) modeling technique to approximate the costly objective functions and to expedite finding the global optima. A GP model is a proxy, which is employed to model the input-output relationships by assuming a multi-Gaussian distribution on the output values. An infill criterion is used in conjunction with a GP model to help sequentially add the samples with potentially lower outputs. The IC fault model is used to compare the efficiency of GP-based optimization method with other typical optimization methods for minimizing the objective function. In this paper, we present the applicability of using a GP modeling approach for reservoir history-matching problems, which is exemplified by numerical analysis of production data from a horizontal multi-stage fractured tight gas condensate well. The results for the case that is studied here show a quick convergence to the lowest objective values in less than 100 simulations for this 20-dimensional problem. This amounts to an almost 10 times faster performance compared to the Differential Evolution (DE) algorithm that is also known to be a powerful optimization technique. The sensitivities are conducted to explain the performance of the GP-based optimization technique with various correlation functions. [ABSTRACT FROM AUTHOR]

We determine the potential accuracy in estimating the size and location of leaks in the caprock by history-matching above-zone pressure monitoring data to leakage models. The number of monitoring wells and the total monitoring time is varied in order to determine minimum pressure-monitoring requirements for effective leak characterization. The history-matching procedure uses particle swarm optimization to minimize the error between leakage-model solutions and synthetic observation data by adjusting model parameters governing the size and location of the leak, as well as the heterogeneous permeability field throughout the model. The method applies to storage projects with uncertain heterogeneous geology that may be described by a variogram model. Results from several examples indicate that as little as 6–12 months of above-zone pressure monitoring data, collected from at least 3 or 4 wells, may be sufficient to locate and estimate the size of a leak to inform mitigation and remediation strategies. No significant benefit is seen when using multilevel monitoring wells versus single-level monitoring wells. We also find that adding white noise to the synthetic observation data, with magnitude consistent with current pressure monitoring techniques, generally reduces error in solutions, likely due to a regularization effect. Taken in total, the results and procedures introduced in this study should be of use in designing monitoring strategies in large-scale carbon storage projects. [ABSTRACT FROM AUTHOR]

Ensemble-based optimization methods are of- ten efficiently applied to history-matching problems. Although satisfactory matches can be obtained, the updated realizations, affected by spurious correlations, generally fail to preserve prior information when using a small ensemble, even when localization is applied. In this work, we propose a multi-scale approach based on grid-adaptive second-generation wavelets. These wavelets can be applied on irregular reservoir grids of any dimensions containing dead or flat cells. The proposed method starts by modifying a few low frequency parameters (coarse scales) and then progressively allows more important updates on a limited number of sensitive parameters of higher resolution (fine scales). The Levenberg-Marquardt ensemble randomized maximum likelihood (LM-enRML) is used as optimization method with a new space-frequency distance-based localization of the Kalman gain, specifically designed for the multi-scale scheme. The algorithm is evaluated on two test cases. The first test is a 2D synthetic case in which several inversions are run using independent ensembles. The second test is the Brugge benchmark case with 10 years of history. The efficiency and quality of results of the multi-scale approach are compared with the grid-block-based LM-enRML with distance-based localization. We observe that the final realizations better preserve the spatial contrasts of the prior models and are less noisy than the realizations updated using a standard grid-block method, while matching the production data equally well. [ABSTRACT FROM AUTHOR]

The primary focus of the majority of current, and foreseeable, natural gas drilling within North America is low-permeability liquid-rich gas and gas condensate reservoirs, where the liquid fraction is now a major source of revenue. Development of these liquid-rich resources is aided by the use of multi-fractured horizontal wells (MFHWs), and is at an early stage; further research is required to appropriately manage the resource for optimal hydrocarbon recovery. The appropriate forecasting methodologies to apply to these tight liquid-rich plays are a focus of current research. While numerical simulation is the most rigorous forecasting methodology, practitioners have turned to simple analytical and empirical methods because of their ease-of-use and requirement of less data. However, these analytical and empirical approaches have limitations that limit their applicability for unconventional resevoirs with complex reservoir, hydraulic fracture and fluid properties. In this study, the workflow of Clarkson (2013b) is applied to address the limitations of existing empirical and analytical methods for forecasting MFHWs producing from liquid-rich tight gas/shale. The workflow calls for constraint of analytical models by linking inputs to rate-transient analysis-derived reservoir and hydraulic fracture properties, and constraining empirical model forecasts to be consistent with analytical model forecasts. In order to address the range in reservoir/fracture properties observed in shales, a suite of analytical models is proposed. Similarly, a suite of empirical methods is used, and the models yielding the most accurate matches to the analytical models are selected for forecasting. Lastly, in order to bridge the gap between analytical and empirical methods, the semi-analytical method introduced by Clarkson and Qanbari (2015), which has as its basis the contacted gas-in-place calculations of Agarwal (2010), is also used for forecasting. An important contribution of this work is the demonstration of the applicability of the analytical and semi-analytical models used in this work for tight gas/shale gas condensate MFHWs exhibiting multi-phase flow in the reservoir. As demonstrated in this study using simulation cases, constant condensate gas ratios can occur for tight/shale gas condensate wells exhibiting transient linear flow and flowing at near constant flowing bottomhole pressure, even for relatively rich gas cases, rendering the single-phase forecasting methods useful for forecasting gas and condensate phases. The accuracy of these methods is tested using simulated cases, and practicality of the workflow demonstrated using an actual field example of a liquid-rich shale MFHW. This study will be of interest to those petroleum engineers who are faced with forecasting a large number of liquid-rich shale wells, and desire methods that can be simply applied to constrain forecasts and improve accuracy. [ABSTRACT FROM AUTHOR]

Abstract: Perturbing facies proportions can provide significant flexibility to assisted history-matching processes since facies strongly impact fluid dynamics. In this paper, we develop a new parameterization technique for varying facies proportions and matching dynamic data. It involves both the definition of proportion ratios and co-kriging estimations. This method allows for changing facies proportions over all or part of the reservoir model while other parameterization techniques can still be applied to modify heterogeneity distribution. It is also appropriate whatever the technique used to generate the facies realizations, which populate the reservoir model. Overall, it takes advantage of the two following features: it induces continuous variations in facies proportions and it allows for driving these variations from a reduced number of parameters. Therefore, this method is well-suited for history-matching: an optimization algorithm is used to modify uncertain parameters until the numerical responses simulated for this parameter set reproduce the reference production data. Last, a numerical application is presented, which stresses the potential of the proposed parameterization technique for varying facies proportions when performing history-matching. [ABSTRACT FROM AUTHOR]

Abstract: The increase in computer power and the recent developments in history-matching can motivate the reexamination of previously built reservoir models. To save the time of engineers and the CPU time, four distinct algorithms, which allow for rebuilding an existing reservoir model without restarting the reservoir study from scratch, were formulated. The algorithms involve techniques such as optimization, relaxation, Wiener filtering, or sequential reconstruction. They are used to identify a stochastic function and a set of random numbers. Given the stochastic function, the random numbers yield a realization that is close to the existing reservoir model. Once the random numbers are known, the existing reservoir model can be submitted to a new history-matching process to improve the data fit or to account for newly collected data. A practical implementation is presented within the context of facies reservoirs. This article focuses on a previously built facies reservoir model. Although the simulation procedure is unknown to the authors, a set of random numbers are identified so that when provided to a multiple-point statistics simulator, a realization very close to the existing reservoir model is obtained. A new history-matching procedure is then run to update the existing reservoir model and to integrate the fractional flow rates measured in two producing wells drilled after the building of the existing reservoir model. [Copyright &y& Elsevier]

Four-dimensional seismic (4DS) contains spatial information that provides insights into the location, shape, and movement of fluids (oil, gas, water). It helps engineers to adjust reservoir simulation models and increase their capability of providing reliable production forecasts. Recent probabilistic approaches consider hundreds of numerical simulation model scenarios, which require automated methods to evaluate this large number of numerical models based on observed 4D seismic data. Comparing spatial information of seismic and numerical simulation data is difficult as, usually, these data are converted to maps with different properties. We propose a novel approach to compare 4D seismic data and simulation models using a three-way deep neural network that is trained using a reference image (4D seismic data) with two simulation model candidates. It learns to find the simulation models that best characterize the reference. Our method is underpinned by more than a thousand pairs of simulation models and reference maps evaluated by human specialists for training. For testing, we compare the inter-rater agreement among different specialist groups and generate a reliable test set considering examples in which there was agreement among at least two specialists. We observed that the group with best-trained specialists agree more in their answers and have a considerably higher inter-rater agreement than the less trained groups. When we evaluate our method with the answers from this specialized group, we observe that the simulation model chosen by our method is the one agreed by the specialists in almost 90% of the cases. We also discuss the impact of different noise levels in the input and show that our method outperforms other approaches in the literature if noise is present both in the training and test sets. [Display omitted] • Novel strategy to compare simulated data from observed four-dimensional seismic (4DS) data. • Three-way deep neural network to obtain image representations. • 4D seismic and simulation data represented by a vector of main features. • Method robust to different scales, various domains, and noisy setups. [ABSTRACT FROM AUTHOR]

Gravity drainage is one of the essential recovery mechanisms in naturally fractured reservoirs. Several mathematical formulas have been proposed to simulate the drainage process using the dual-porosity model. Nevertheless, they were varied in their abilities to capture the real saturation profiles and recovery speed in the reservoir. Therefore, understanding each mathematical model can help in deciding the best gravity model that suits each reservoir case. Real field data from a naturally fractured carbonate reservoir from the Middle East have used to examine the performance of various gravity equations. The reservoir represents a gas–oil system and has four decades of production history, which provided the required mean to evaluate the performance of each gravity model. The simulation outcomes demonstrated remarkable differences in the oil and gas saturation profile and in the oil recovery speed from the matrix blocks, which attributed to a different definition of the flow potential in the vertical direction. Moreover, a sensitivity study showed that some matrix parameters such as block height and vertical permeability exhibited a different behavior and effectiveness in each gravity model, which highlighted the associated uncertainty to the possible range that often used in the simulation. These parameters should be modelled accurately to avoid overestimation of the oil recovery from the matrix blocks, recovery speed, and to capture the advanced gas front in the oil zone. [ABSTRACT FROM AUTHOR]