ECMOR 2022

With the development of horizontal well and volume fracturing technologies as well as the conventional oil reserves depleting, the vast tight oil discovered in the world play a important role in source of energy supply. However, it is challenge to effectively forecast the recovery efficiency and the traditional knowledge and methodologies are not suitable for tight oil reservoirs.

To better forecast the recovery efficiency and exploit the tight oil reservoirs with lower expense, a variable weight combination model of XGBoost-SVR has been proposed based on data mining in this paper. It can be acquired by combining the Limit Gradient Climbing (XGBoost) and Support Vector Regression (SVR) and using the method of residual analysis. This model establishes the relationship between recovery efficiency and essential parameters including geography, formation and engineering by machine learning analysis.

The predictive results have shown that the cluster number of fracture, horizontal length sand intensity and permeability play a significant role in recovery efficiency. However, the well spacing, liquid intensity and reservoir temperature have an weak effect on recovery efficiency. The accuracy in predicting recovery efficiency for combination model of XGBoost-SVR can reach as high as 94.63%, which is higher than those of single XGBoost model and SVR model. Therefor, the predictive model based on XGBoost-SVR can be used as a feasible tool for economic evaluation.

The methodology, predictive model and predictive results demonstrated in this paper will have a great and novel effect on development of tight oil. This study gives an insight on the production mechanism for tight oil reservoir from a big data mining perspective, as well as a feasible and accurate method to forecast recovery efficiency. The methodology and model established in this paper can be easily applied to other unconventional oil reservoirs.

We have developed a support vector regression (SVR) accelerated variant of the distributed derivative-free optimization (DFO) method using the limited-memory BFGS Hessian updating formulation (LBFGS) for subsurface field-development optimization problems. The SVR enhanced distributed LBFGS (D-LBFGS) optimizer is designed to effectively locate multiple local optima of highly nonlinear optimization problems subject to numerical noise. It operates both on single- and multiple-objective field-development optimization problems. The basic D-LBFGS DFO optimizer runs multiple optimization threads in parallel and uses the linear interpolation method to approximate the sensitivity matrix of simulated responses with respect to optimized model parameters. However, this approach is less accurate and slows down convergence. In this paper, we implement an effective variant of the SVR method, namely ε-SVR, and integrate it into the D-LBFGS engine in synchronous mode within the framework of a versatile optimization library inside a next-generation reservoir simulation platform. Because ε-SVR has a closed-form of predictive formulation, we analytically calculate the approximated objective function and its gradients with respect to input model variables subject to optimization We investigate two different methods to propose a new search point for each optimization thread in each iteration through seamless integration of SVR with the D-LBFGS optimizer. The first method estimates the sensitivity matrix and the gradients directly using the analytical ε-SVR surrogate and then solves a LBFGS trust-region subproblem (TRS). The second method applies a trust-region search LBFGS method to optimize the approximated objective function using the analytical ε-SVR surrogate within a box-shaped trust region.

We first show that ε-SVR provides accurate estimates of gradient vectors on a set of nonlinear analytical test problems. We then report the results of numerical experiments conducted using the newly proposed SVR-enhanced D-LBFGS algorithms on both synthetic and realistic field-development optimization problems. We demonstrate that these algorithms operate effectively on realistic nonlinear optimization problems subject to numerical noise. We show that both SVR-enhanced D-LBFGS variants converge faster and thereby provide a significant acceleration over the basic implementation of D-LBFGS with linear interpolation

In the past decade, machine learning and deep learning have been popular tools for well production forecasting since these black-box approaches can bypass the incomplete understanding of physics while obtaining satisfactory prediction results given a considerable amount of data. However, due to their large data requirements, inability to produce physically consistent results, and their lack of generalizability to out-of-sample scenarios, pure machine learning approaches cannot meet the requirements for predictive performance and generalization ability in complex production forecasting problems.

Especially in tight oil and shale gas fields, the post-fracture production mechanisms of oil and gas wells have been challenging because of the application of horizontal drilling and hydraulic fracturing techniques. Typical deep learning models are generally scenario-specific and they may fail to capture relationships behind post-fracture production directly from limited observation data, leading to their failure to generalize to scenarios not encountered in training data.

In this work, we propose a new workflow for post-fracture production profile forecasting that could constrain production prediction profiles within known physics laws for more robust results, even beyond the training set. To this end, we use a state-of-the-art deep learning method called Physics-informed Long Short-Term Memory (PI-LSTM) networks. In this approach, PI-LSTM models are trained with additional production physics constraints of decline curve analysis incorporated into the loss function.

Our goal is to impose appropriate physics constraints on the LSTM networks and also explore the mathematical constraint patterns. In this way, we can take advantage of the complementary strengths of machine learning and corresponding physics equations to obtain more reliable and robust prediction results. Furthermore, this grey-box approach may provide us with more insights into the production behavior of fractured wells that cannot be simply described by simplified physics or empirical equations.

We conduct comparison experiments on two cases to show the forecasting ability of the proposed PI-LSTM approach, conventional decline curve analysis methods and deep learning models (i.e. RNN and LSTM). The results show that the PI-LSTM model has the smallest prediction errors both in the simulated case and in the actual field case.

The Ravn oilfield is located in licences 5/06 and 2/16 in the Central Graben of the Danish Offshore. It is a low permeable Upper Jurassic HP/HT oil reservoir which is developed using long horizontal wells with multiple hydraulic fractures. The Ravn oil is a light oil however with asphaltene in it. SARA analysis of the oil sample from one of the exploratory wells showed 3.3 wt% of asphaltene. The asphaltene inhibitor was injected downhole to mitigate potential asphaltene issues in the well tubing and surface facilities. The reservoir aquifer support was deemed very weak due to the low reservoir permeability and reservoir compartmentalization Pressure maintenance, i.e., water injection, was considered not viable for the same reasons. When reservoir pressure drops below Asphaltene Onset Pressure (AOP), asphaltene will precipitate and likely cause formation plugging, especially when a reservoir has a low permeability sand with small pore throats. The lab AOP measurements were deemed suspicious due to the unrepresentative oil samples from the production well. The modelled AOP was estimated instead after the field was brought in production with the help of surface oil sampling data and production well pressure response.

In order to simulate the asphaltene formation damage which occurred in the reservoir, a characterized fluid was developed in the PVT modelling software PVTsim. The Equation of State (EOS) parameters were calibrated with the PVT experiments performed on the oil sample from one of the exploratory wells. The AOP and asphaltene solution with pressure variation were modelled with the characterized fluid model in PVTsim. Thereafter the characterized fluid model was exported to the dynamic reservoir modelling software tNavigator which utilized relevant asphaltene formation damage keywords together with the exported compositional model to simulate the asphaltene precipitation, deposition and reservoir permeability impairment. Single parameter analysis showed flocculation rate and permeability reduction versus asphaltene deposits saturation table were the most sensitive parameters in achieving a good history match.

So far, there has been no sufficient production data to pinpoint the location of the asphaltene formation damage. Two alternative scenarios were simulated: (1) asphaltene formation damage happened in both reservoir and hydraulic fractures; (2) asphaltene formation damage happened only in the reservoir. Dynamic models based on the two scenarios could both match the well production history quite well, however the production forecasts based on the two scenarios were different and indicated a range of uncertainty.

Polymer flooding is one efficient EOR technology by overcoming non-uniform and unstable displacement caused by water injection. Polymer flooding in reservoirs is a complicated process that involves strongly nonlinear physics, e.g., non-Newtonian rheology in porous media with retention and adsorption. In the presence of multi-scale heterogeneity, high-fidelity simulations are usually required to capture such nonlinear behavior, which is a time-consuming process for conventional reservoir modelling.

In this study, we extend an advanced linearization strategy, called the Operator-Based Linearization (OBL) approach, to simulate non-Newtonian polymer flooding with retention and adsorption mechanisms using the fully implicit method. A velocity-dependent viscosity multiplier compliments the operator form of governing equations to represent the non-Newtonian rheology of the high-molecular-compound polymer. The retention of polymer, reducing the porosity, is represented by a Langmuir-type adsorption model. Several simplified models have been used for validation of the developed numerical framework. The numerical results show good agreement with both the analytical solutions and the coreflood experimental data though some negligible discrepancies can be observed in simulation results.

A highly resolved near-well model is used to test the performance of polymer flooding in realistic reservoir conditions. Both shear-thinning and thickening regimes, depending on the injection velocity and polymer concentration, are recognized in the near-wellbore zone. The injected polymer concentration and brine salinity significantly affect the shear viscosity, and consequently, polymer injectivity. Polymer retention and adsorption have a substantial effect on the rate of polymer propagation through porous media. Overall, polymer flooding shows its advantages to mitigate water fingering in field-scale operations and improves the ultimate sweep of the reservoir. However, optimal injectivity is one essential factor that affects the performance of polymer flooding. The computational superiority of the proposed model allows us to optimize the parameters of polymer flooding in realistic reservoirs and operational settings.

The uncertainties and risks related to the complex environments of deepwater oil and gas reservoirs require interdisciplinary workflows and advanced reservoir monitoring techniques to surveil reservoir performance during production activities. An example of the latter is a Permanent Reservoir Monitoring (PRM) system, which provides 4D seismic data on demand. A challenge of such approach to reservoir monitoring is the rapid assimilation of frequently acquired high-quality 4D seismic data into fast-track information. Delays and limitations in the interpretation and integration of 4D seismic data reduce the benefits of such approach to impact the decision-making processes, despite obtaining data on demand. This work presents an integrated workflow of 4D seismic and reservoir engineering data to harvest hidden dynamic reservoir insights over short periods of time. This information provides novel inputs to update reservoir models to improve model-based reservoir management. Our workflow illustrates the importance of multiple 4D seismic datasets in the field management strategy. This study was carried out in a Brazilian deepwater turbidite field, where a PRM system recorded a baseline survey at the start of production in 2013 and 5 monitor surveys up to 2020. We obtain an enhancement in the interpretive capability of the dynamic reservoir behavior such as identifying regions of possible pushed oil by injectors and revealing a hidden channel of aquifer movement.

Calculating the effective permeability entails considerable computation, even with local upscaling techniques. This study proposes a convolutional neural network architecture that estimates effective permeability. The network’s input is the permeability maps of those layers of the fine-scale model that are intended to be upscaled into a single layer with horizontally coarsened cells. It treats each layer of the fine-scale permeability maps as a channel of a high-resolution image. The output is a 3 -channel lower-resolution image where each channel presents the upscaled permeability map in one major direction. The proposed architecture is simple and robust. It consists of two 2D convolutional hidden layers with small kernels and a 2D MaxPooling layer.

The network was tested using two different datasets, (1)- a binary-facie fluvial model and (2)- a continuous Gaussian model. For each dataset, 500 geological realisations were created and upscaled using a pressure-solver with periodic boundary conditions. 50% of the realisations were used for training and the remaining for testing. The network captured the nonlinear behaviour very promisingly with no overfitting signs. The results were not only visually acceptable, but also the mean of the L2 norms was negligible (below 0.05 mD in the first dataset and below 0.01 mD in the second dataset). Two-phase simulation results also verified the accuracy of the estimated permeabilities. The proposed method can reduce the upscaling computation significantly. The training time was considerably less than the computation time needed for upscaling using the pressure-solver method. The proposed method can be a step towards more computationally efficient extended-local and quasi-global permeability upscaling methods.

This work investigates an ensemble-based workflow to simultaneously handle generic (possibly nonlinear) equality and inequality constraints in reservoir data assimilation problems. The proposed workflow is built upon a recently proposed umbrella algorithm, called the generalized iterative ensemble smoother (GIES), and inherits the benefits of ensemble-based data assimilation algorithms in geoscience applications. Unlike the traditional ensemble assimilation algorithms, the proposed workflow admits cost functions beyond the form of nonlinear-least-squares, and has the potential to develop an infinite number of constrained assimilation algorithms. In the proposed workflow, we treat data assimilation with constraints as a constrained optimization problem. Instead of relying on a general-purpose numerical optimization algorithm to solve the constrained optimization problem, we derive an (approximate) closed form to iteratively update model variables, but without the need to explicitly linearize the (possibly nonlinear) constraint systems. The established model update formula bears similarities to that of an iterative ensemble smoother (IES). Therefore, in terms of theoretical analysis, it becomes relatively easy to transit from an ordinary IES to the proposed constrained assimilation algorithms, and in terms of practical implementation, it is also relatively straightforward to implement the proposed workflow for users who are familiar with the IES, or other conventional ensemble data assimilation algorithms like the ensemble Kalman filter (EnKF). Apart from the aforementioned features, we also develop efficient methods to handle two noticed issues that would be of practical importance for ensemble-based constrained assimilation algorithms. These issues include localization in the presence of constraints, and the (possible) high dimensionality induced by the constraint systems. We use one 2D and one 3D case studies to demonstrate the performance of the proposed workflow. In particular, the 3D example contains experiment settings close to those of real field case studies. In both case studies, the proposed workflow achieves better data assimilation performance in comparison to the choice of using an original IES algorithm. As such, the proposed workflow has the potential to further improve the efficacy of ensemble-based data assimilation in practical reservoir data assimilation problems.

The geological storage of CO2 into depleted reservoirs represents a potential strategy for large-scale greenhouse gas mitigation. An evaluation of the storable volume and of the behaviour of the injected fluid considering the uncertainty is essential to mitigate the associated geo-mechanical risks and the potential CO2 leakage.

The accurate estimation of the quantity of CO2 that can be injected into a depleted reservoir is usually carried out after the calibration of the reservoir model. This model calibration can be addressed via a history matching process, by assimilating production and pressure data collected during the field production history. The prior uncertainties represented by an ensemble of reservoir model realizations are thus reduced, by solving a nonlinear inverse problem with computationally demanding methods such as iterative ensemble data assimilation. The history matching phase is crucial for the forecast simulation under realistic conditions of carbon capture and storage applications, but it can be time consuming especially in presence of a long historical time.

In the present work, we propose an innovative method to significantly reduce the computational impact of the calibration process, adopting a direct forecasting approach based on the ensemble data space inversion (DSI) introduced by Lima et al. [ 1 ]. With this approach, a direct prior ensemble prediction update is performed to account for the historical data, without modifying the models themselves. The Posterior (history-matched) geological models are not explicitly obtained as in standard model-space inversion methods and as consequence the requirements in term of computational resources and CPU time are strongly reduced.

The DSI approach is here implemented adopting an iterative ensemble smoother formulation tailored to quantify the uncertainty on the total volume of CO2 that can be stored into the depleted reservoir. Moreover, the method can be used to assess the uncertainty of the subsurface fluid flow. The application examples show that a calibration process via the DSI algorithm can produce accurate forecast predictions and can consistently reduce uncertainty. The results are comparable to the ones that are obtained by standard model-space inversion approaches.

In Bayesian approaches to subsurface inference, the prior model specifies the model parameters that are uncertain and the joint probability of those parameters before incorporating production-related data. A good prior model is generally complex enough to capture the future reservoir behaviour in the long term, realistic enough to be plausible, consistent with geologic knowledge, and simple enough to allow calibration for data matching. Model complexity is often associated with the number of model parameters, thus the focus on finding the sufficient number of parameters needed for history matching and to quantify uncertainty in the future. This work explores model selection based on concepts of complexity and informativeness of models for subsurface reservoir models. It focuses on the effect of misspecification of prior models for assimilating flow data and their predictive accuracy. Using concepts of mutual information, entropy and information criteria, we investigate the suitability of various types of prior models with different level of complexity, ranging from a highly simplified bilinear trends to realistic multipoint statistical models and complex hierarchical Gaussian models and explore the effect of level of model complexity on robustness of forecasting. We perform experiments with different combinations of data type, prior informativeness, forecast type and model type to compare the effect of different prior models on robustness of the results. For each model simulation, we analyse the effective number of parameters, entropy, time required for calibration and evaluate their predictive accuracy.

We show that information content and the number of parameters are useful measures for selection of prior models for history matching. We observe that model selection according to the “widely applicable information criterion” (WAIC) gives the same results as Bayesian leave-one-out cross validation (LOO-CV) for hierarchical Gaussian priors. Experiments indicate that penalizing model complexity could be useful for models that contain parameters without physical meaning. Moreover, hierarchical Bayesian models are useful when uncertainty in prior hyper-parameters is reasonable. In addition, we suggest a workflow for model development depending on forecast objectives and data availability.