A 6M digital twin for modeling and simulation in subsurface reservoirs

   Modeling and simulation of flow, transport and geomechanics in the subsurface porous media is an effective approach to help make decisions associated with the management of subsurface oil and gas reservoirs, as well as in other wide application areas including groundwater contamination and carbon sequestration. Accurate modeling and efficient, robust simulation have always been the main purposes of reservoir researches, and a 6M digital twin (multi-scale, multi-domain, multi-physics and multi-numerics numerical modeling and simulation of multi-component and multi-phase fluid flow in porous media) is designed, equipped with the following six pronounced features, to better digitally model and simulate the engineering processes and procedures in physical reality and further control and optimize such processes and procedures: 1. Efficient and reliable flash calculation: An accurate estimation on the phase equilibrium conditions is essentially needed prior to multi-phase flow and transport simulation for multi-component fluid mixtures in complex porous geometry and thermodynamic conditions. A remarkable progress was recognized in 2018, when a thermodynamically stable multi-phase equilibrium calculation algorithm of hydrocarbon mix- tures based on realistic equation of state (e.g., Peng-Robinson Equation of State) at specified moles, volume and temperature (NVT-flash) was generated and proposed (Kou and Sun, 2018a, 2018b; Sun, 2019). Robustness of this algorithm is preserved by proved consistency with the first and second laws of thermodynamics and capillarity can be incorporated in this algorithm to extend the application into unconventional reservoirs (e.g., shale gas reservoirs and tight oil reservoirs) and carbon dioxide sequestration (with cubic-plus-association type of equation of states) (Zhang et al., 2019a, 2019b; Li et al., 2020). Sparse grids method and parallel computing techniques have been involved in further studies to accelerate the phase equilibrium estimation  on parallel computers (Wu et al., 2015a). Recently, deep learning algorithms have been successfully developed to significantly speed up the multi-component flash calculations in complex thermodynamic conditions at the same time of ensuring stability and self-adaptivity (Li et al., 2019a, 2019b; Zhang et al., 2019c, 2020a).2. Advanced phase interface modeling: In multiphase flow simulation in porous media, modeling of the thin interface, usually in nanoscale thickness, is recognized as the key issue in order to simulate macroscale  fluid  behaviors  containing the formation and motion of interphase. The multi-component multi-phase flow can be investigated using a diffuse interface model based on realistic equations of state (typically Peng-Robinson equation of state), and bulk phase properties as well as interfacial properties could be modeled accurately and efficiently, where partial immiscibility can be considered to cover more engineering applications like carbon dioxide in oil (Qiao and Sun, 2014; Kou et al., 2018). Based on that, a new momentum balance equation was proposed in Kou and Sun (2018c) to identify the correlation associating the gradients of temperature and chemical potential and the pressure gradient, which further indicates that the gradient of the temperature and chemical potential has been found as the primary driving force of the macroscale fluid motions. Later, phase field modeling was incorporated with the moving contact line method to study the motion of soluble surfactants using two Chan-Hilliard type of equations, which are designed to govern the surfactant concentration and interface evolution respectively (Zhu et al., 2019). Recently, a semi-implicit scheme was proposed in Kou et al. (2020) to generate for the first time a scheme  that inherits the original energy dissipation law, using a delicate novel energy factorization (EF) approach to factorize an energy function into a product of several factors. Application of phase field modeling has been extended to a wider range in the whole process of petroleum engineering. An exploratory phase-field model was presented in Zhang et al. (2020b) to simulate the multiphase flow in  injection  pipeline  investigating  the  effect of injection salinity on pipeline scaling.3. Fully conservative bound-preserving Darcys scale flow simulation: Fully mass-conservative (both globally and locally, for wetting phase and non-wetting phase) IMPES (IMplicit Pressure Explicit Saturation) schemes for the simulation of incompressible and immiscible two-phase flow in porous media were generated in (Chen et al., 2019), which deserves a merit that a new treatment of capillarity was introduced and the unbiased and the bound-preserving property can provide a much larger time step choice. Furthermore, a nonlinear complementarity problem was reformulated and the resultant non-smooth nonlinear system of equations arising at  each time step  are  solved  fully  implicitly  by  a  parallel,  scalable, and nonlinearly preconditioned semi-smooth Newton algorithm (Yang et al., 2019a). Later, a new scheme containing up to three continuity equations were generated in Yang et al. (2020) so that mass conservation holds for all present phases. By using a variational inequality formulation with box inequality constraints, boundedness requirement on pressure and saturations can be preserved well and then the problem is solved using a well-designed nonlinear solver consisting of the nonlinear elimination preconditioning technique and active-set reduced-space  method.4. Reactive flow and transport in porous media: Reactive dissolution of carbonates by the action of the injected acid, also known as wormhole propagation, is a widely practiced technique in the product enhancement of petroleum industry. A semi-analytic scheme was proposed with a reconstruction of analytical porosity functions to analyze the time error of the porosity, and a coupled analysis approach was employed to achieve the estimates of pressure, velocity and solute concentration on the basis of porosity error estimation (Wu et al., 2015b; Kou et al., 2019). Meanwhile, various primal discontinuous Galerkin schemes, including NIPG, SIPG and IIPG have been investigated deeply for solving multi-component reactive transport and coupled with multiphase flow simulation in porous media (Sun and Wheeler, 2005, 2006).5. Molecular simulation of microscopic mechanisms: As an effective approach to investigate the microscopic mechanisms affecting macroscopic flow and transport behaviors as well as to obtain the value of key parameters in numerical modeling, molecular simulation has attracted increasing attentions. The diffusion and sorption behaviors of carbon dioxide and methane as well as the structural features were studied using molecular dynamics and hybrid Monte Carlo approaches (Kadoura et al., 2017; Yang et al., 2017a, 2019b). The intercalation behavior of carbon dioxide in various brines were studied using grand canonical Monte Carlo methods to study the molecular mechanisms indicating that the intercalation of carbon dioxide strongly depends on the relative humidity (Li et al., 2019c).6. High-performance computation based on fully-Implicit and bound-preserving algorithms: Bound-preserving discretization and solvers for subsurface flow models based on a fully implicit framework is the future of parallel reservoir simulation (Yang et al., 2019a, 2020). A family of mixed finite element methods have been used to discretize various model equations in porous media flow for the spatial terms, and the implicit backward Euler scheme with adaptive time stepping for the temporal integration. The resultant nonlinear system arising at each time step was  then  solved  in  a  monolithic way by using a Newton–Krylov type method, where the resultant nonlinear system was solved by a generalized Newton method, i.e., active-set reduced-space method, and then the ill-conditioned linear Jacobian systems were solved with an effective preconditioned Krylov subspace method. The used nonlinear preconditioner was built by applying overlapping additive Schwarz type domain decomposition and nonlinear elimination. Numerical results on parallel computers indicated that the nonlinear solver overcomes the severe limits on the time step associated with conventional methods, and it results in superior convergence performance, often reducing the total computing time by more than one order of magnitude (Yang et al., 2016, 2017b, 2018).Cited as: Sun, S., Zhang, T. A 6M digital twin for modeling and simulation in subsurface reservoirs. Advances in Geo-Energy Research, 2020, 4(4): 349-351, doi: 10.46690/ager.2020.04.0

Advancing Carbon Sequestration through Smart Proxy Modeling: Leveraging Domain Expertise and Machine Learning for Efficient Reservoir Simulation

Geological carbon sequestration (GCS) offers a promising solution to effectively manage extra carbon, mitigating the impact of climate change. This doctoral research introduces a cutting-edge Smart Proxy Modeling-based framework, integrating artificial neural networks (ANNs) and domain expertise, to re-engineer and empower numerical reservoir simulation for efficient modeling of CO2 sequestration and demonstrate predictive conformance and replicative capabilities of smart proxy modeling. Creating well-performing proxy models requires extensive human intervention and trial-and-error processes. Additionally, a large training database is essential to ANN model for complex tasks such as deep saline aquifer CO2 sequestration since it is used as the neural network\u27s input and output data. One major limitation in CCS programs is the lack of real field data due to a lack of field applications and issues with confidentiality. Considering these drawbacks, and due to high-dimensional nonlinearity, heterogeneity, and coupling of multiple physical processes associated with numerical reservoir simulation, novel research to handle these complexities as it allows for the creation of possible CO2 sequestration scenarios that may be used as a training set. This study addresses several types of static and dynamic realistic and practical field-base data augmentation techniques ranging from spatial complexity, spatio-temporal complexity, and heterogeneity of reservoir characteristics. By incorporating domain-expertise-based feature generation, this framework honors precise representation of reservoir overcoming computational challenges associated with numerical reservoir tools. The developed ANN accurately replicated fluid flow behavior, resulting in significant computational savings compared to traditional numerical simulation models. The results showed that all the ML models achieved very good accuracies and high efficiency. The findings revealed that the quality of the path between the focal cell and injection wells emerged as the most crucial factor in both CO2 saturation and pressure estimation models. These insights significantly contribute to our understanding of CO2 plume monitoring, paving the way for breakthroughs in investigating reservoir behavior at a minimal computational cost. The study\u27s commitment to replicating numerical reservoir simulation results underscores the model\u27s potential to contribute valuable insights into the behavior and performance of CO2 sequestration systems, as a complimentary tool to numerical reservoir simulation when there is no measured data available from the field. The transformative nature of this research has vast implications for advancing carbon storage modeling technologies. By addressing the computational limitations of traditional numerical reservoir models and harnessing the synergy between machine learning and domain expertise, this work provides a practical workflow for efficient decision-making in sequestration projects

Tracing back the source of contamination

From the time a contaminant is detected in an observation well, the question of where and when the contaminant was introduced in the aquifer needs an answer. Many techniques have been proposed to answer this question, but virtually all of them assume that the aquifer and its dynamics are perfectly known. This work discusses a new approach for the simultaneous identification of the contaminant source location and the spatial variability of hydraulic conductivity in an aquifer which has been validated on synthetic and laboratory experiments and which is in the process of being validated on a real aquifer

Hydrogeological challenges in a low carbon economy

Hydrogeology has traditionally been regarded as the province of the water industry, but it is increasingly finding novel applications in the energy sector. Hydrogeology has a longstanding role in geothermal energy exploration and management. Although aquifer management methods can be directly applied to most high-enthalpy geothermal reservoirs, hydrogeochemical inference techniques differ somewhat owing to peculiarities of high-temperature processes. Hydrogeological involvement in the development of ground-coupled heating and cooling systems using heat pumps has led to the emergence of the sub-discipline now known as thermogeology. The patterns of groundwater flow and heat transport are closely analogous and can thus be analysed using very similar techniques. Without resort to heat pumps, groundwater is increasingly being pumped to provide cooling for large buildings; the renewability of such systems relies on accurate prediction and management of thermal breakthrough from reinjection to production boreholes. Hydrogeological analysis can contribute to quantification of accidental carbon emissions arising from disturbance of groundwater-fed peatland ecosystems during wind farm construction. Beyond renewables, key applications of hydrogeology are to be found in the nuclear sector, and in the sunrise industries of unconventional gas and carbon capture and storage, with high temperatures attained during underground coal gasification requiring geothermal technology transfer

Leveraging Artificial Intelligence and Geomechanical Data for Accurate Shear Stress Prediction in CO2 Sequestration within Saline Aquifers (Smart Proxy Modeling)

This research builds upon the success of a previous project that used a Smart Proxy Model (SPM) to predict pressure and saturation in Carbon Capture and Storage (CCS) operations into saline aquifers. The Smart Proxy Model is a data-driven machine learning model that can replicate the output of a sophisticated numerical simulation model for each time step in a short amount of time, using Artificial Intelligence (AI) and large volumes of subsurface data. This study aims to develop the Smart Proxy Model further by incorporating geomechanical datadriven techniques to predict shear stress by using a neural network, specifically through supervised learning, to construct Smart Proxy Models, which are critical to ensuring the safety and effectiveness of Carbon Capture and Storage operations. By training the Smart Proxy Model with reservoir simulations that incorporate varying geological properties and geomechanical data, we will be able to predict the distribution of shear stress. The ability to accurately predict shear stress is crucial to mitigating the potential risks associated with Carbon Capture and Storage operations. The development of a geomechanical Smart Proxy Model will enable more efficient and reliable subsurface modeling decisions in Carbon Capture and Storage operations, ultimately contributing to the safe and effective storage of CO2 and the global effort to combat climate change

Regional Scale Generalizations of Firn Thickness and Snow Accumulation in Southeast Alaska: an Applied Deep Learning Framework

High elevation mountain glaciers are referred to as the “water towers of the world” due to their ability to store water internally and release it later through melt and runoff. Much of the work to understand these complex environments has focused on cold based polar glaciers in high latitude regions, neglecting temperate glaciers and associated snowpack which are more responsive than polar systems to minor climatic changes. Advancements in the availability of open source data, deep learning theory, and computational efficiency has opened up new methods of “data hungry” modeling that may be well suited to the type of complex terrain-climate interactions common in these environments. Through the use of regression based deep neural networks (DNNs), this study explores the applicability of this method on a 400 MHz ground penetrating radar dataset collected on the Juneau Icefield between 2012 and 2021. The primary task of these networks is to find the statistical relationship between englacial layer thickness and a collection of topographic and climatological data with the goal of upscaling measurements from radar transects to the entire region. These models are separated into two primary tasks, the prediction of firn thickness, and the prediction of annual accumulation thickness. These tasks are approached using two different data structures, one that uses only a single year of data, and one that uses all available years of data. Models are validated using the standard “leave on glacier out (LOGO) and “leave one year out” (LOYO) holdout methods depending on the data structure. Results indicate that the available data for the Juneau Icefield is better suited for the prediction of annual accumulation thickness rather than firn thickness, with much better regional scale models produced by the multiyear data structure. Through this method, realistic simulations of icefield scale firn and snowpack distributions are generated and can be paired with existing models to output estimations of key environmental characteristics such as snow water equivalent and porosity

Uncertainty reduction in reservoir parameters prediction from multiscale data using machine learning in deep offshore reservoirs.

Developing a complete characterization of reservoir properties involved in subsurface multiphase flow is a very challenging task. In most cases, these properties - such as porosity, water saturation, permeability (and their variants), pressure, wettability, bulk modulus, Young modulus, shear modulus, fracture gradient - cannot be directly measured and, if measured, are available only at small number of well locations. The limited data are then combined with geological interpretation to generate a model. Also increasing the degree of this uncertainty is the fact that the reservoir properties from different data sources - like well logs, cores and well test - often produce different results, thus making predictions less accurate. The present study focussed on three reservoir parameters: porosity, fluid saturation and permeability. These were selected based on literature and sensitivity analysis, using Monte Carlo simulations on net present value, reserve estimates and pressure transients. Sandstone assets from the North Sea were used to establish the technique for uncertainty reduction, using machine learning as well as empirical models after data digitization and cleaning. These models were built (trained) with observed data using other variables as inputs, after which they were tested by then using the input variables (not used for the training) to predict their corresponding observed data. Root Mean Squared Error (RMSE) of the predicted and the actual observed data was calculated. Model tuning was done in order to optimize its key parameters to reduce RMSE. Appropriate log, core and test depth matching was also ensured including upscaling combined with Lorenz plot to identify the dominant flow interval. Nomographic approach involving a numerial simulation run iteratively on multiple non-linear regression model obtained from the dataset was also run. Sandstone reservoirs from the North Sea not used for developing the models were then used to validate the different techniques developed earlier. Based on the above, the degree of uncertainty associated with porosity, permeability and fluid saturation usage was demonstrated and reduced. For example, improved accuracies of 1-74%, 4-77% and 40% were achieved for Raymer, Wyllie and Modified Schlumberger, respectively. Raymer and Wyllie were also not suitable for unconsolidated sandstones while machine learning models were the most accurate. Evaluation of logs, core and test from several wells showed permeability to be different across the board, which also highlights the uncertainty in their interpretation. The gap between log, core and test was also closed using machine learning and nomographic methods. The machine learning model was then coded into a dashboard containing the inputs for its training. Their relationship provides the benchmark to calibrate one against the other, and also to create the platform for real-time reservoir properties prediction. The technology was applied to an independent dataset from the Central North Sea deep offshore sandstone reservoir for the validation of these models, with minimum tuning and thus effective for real-time reservoir and production management. While uncertainties in measurements are crucial, the focus of this work was on the intermediate models to get better final geological models, since the measured data were from the industry