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Geological carbon storage represents a new and substantial challenge for the subsurface geosciences. To increase understanding and make good engineering decisions, containment processes and large-scale storage operations must be simulated in a thousand year perspective. A hierarchy of models of increasing computational complexity for analysis and s...
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... obtain a practical method, we have there- fore implemented different approximations in MRST-co2lab to speed up the evaluation of effective properties and generally make the S-formulation of VE models more computationally tractable. Table 2 summarizes some cases where simplified models can be obtained. We have found the sharp-interface model (first row) and the capillary fringe approximation (third row) to be particularly important. ...
Citations
... This approach helps to reduce the computational cost by solving on the lower dimension and visualizing on the larger dimension. Concepts of the VE fine scale reconstruction are also laid out in [20]. ...
... Concurrently, the computation of n requires P n which in turn is dependent on z p . One could either solve a system of non-linear equations to compute n and z p or simply compute n by using P w instead of P n as suggested by [20]. Although this simplification leads to an error in n , the deviation should not be significant given the large absolute values for the pressures in aquifers and also small relative differences in phase pressures compared to their absolute values. ...
... The following simulations were run on a laptop with an AMD Ryzen 7 4700U CPU using eight cores with a maximum clock speed of 2000MHz and 14.8GiB of RAM at disposal. It is also worth mentioning that a code base developed for solving the full-dimensional equations can be adapted to solve the VE model [20] as for both models the same equations with identical structure are utilized. However, direct access to the source code of the FD implementation is required. ...
Vertical equilibrium models have proven to be well suited for simulating fluid flow in subsurface porous media such as saline aquifers with caprocks. However, in most cases the dimensionally reduced model lacks the accuracy to capture the dynamics of a system. While conventional full-dimensional models have the ability to represent dynamics, they come at the cost of high computational effort. We aim to combine the efficiency of the vertical equilibrium model and the accuracy of the full-dimensional model by coupling the two models adaptively in a unified framework and solving the emerging system of equations in a monolithic, fully-implicit approach. The model domains are coupled via mass-conserving fluxes while the model adaptivity is ruled by adaptive criteria. Overall, the adaptive model shows an excellent behaviour both in terms of accuracy as well as efficiency, especially for elongated geometries of storage systems with large aspect ratios.
... There has been much research effort to expedite this process such as using analytical equations for fluid flow (Nordbotten et al., 2005;Okwen et al., 2010) or sketch-based reservoir models (Jackson et al., 2022). As a compromise between full physics simulations and analytical expressions, Vertical Equilibrium (VE) models have emerged as effective tools for representing CO 2 plume behavior (Gasda et al., 2009;Nilsen et al., 2011Nilsen et al., , 2016Nordbotten and Celia, 2011;Lie et al., 2016). By simplifying the governing equations into a lower-dimensional system, VE models significantly reduce computational complexity while still providing valuable insights into storage behavior. ...
Carbon capture and storage is vital for reducing greenhouse gas emissions and mitigating climate change. Most projects involve the permanent geological storage of CO2 within deep sedimentary rock formations, but accurately constraining storage capacity usually involves detailed and computationally demanding reservoir modeling and simulation. Efficiency factors can also be used but these often lead to capacity overestimations. To address this, a workflow is proposed harnessing various existing, reduced complexity models that account for the surface topography and dynamic fluid behavior in a computationally efficient manner. This workflow was tested in an area of the Malay Basin mapped from 3D seismic data but with illustrative reservoir parameters. A static analysis was first undertaken using algorithms within MRST-co2lab. Structural traps, spill paths and spill regions were identified using the reservoir topography. This provided initial indications into optimal well placement and led to refinement of the total capacity of the area into the capacity available within structural traps. This was followed with a dynamic analysis, also within MRST-co2lab, using computationally efficient Vertical Equilibrium models. Hundreds of simulations were undertaken and the optimal well placement was determined based on the maximum storage efficiency achieved. The results indicated that the amount that can be contained within this area is 15 times less than equivalent predictions using static storage efficiency factors. The advantage of such a light approach is that sensitivity and uncertainty analysis can be carried out at speed, before targeting certain parameters/areas for more detailed study.
... Concurrently, the computation of ̺ n requires P n which in turn is dependent on z p . One could either solve a system of non-linear equations to compute ̺ n and z p or simply compute ̺ n by using P w instead of P n as suggested by [17]. Although this simplification leads to an error in ̺ n , the deviation should not be significant given the large absolute values for the pressures in aquifers and also small relative differences in phase pressures compared to their absolute values. ...
... Furthermore, a memory of 14.8GiB was at disposal. It is also worth mentioning that a code base developed for solving the full-dimensional equations can easily be adapted to solve the VE model [17]. Specifically, only the computation of the porosities, sink/source terms, permeabilities, mobilities and boundary conditions needs to be modified to obtain a source code which solves the VE equations. ...
... In general, the adaptive method shines in scenarios with a large ratio of the number of horizontal cells to vertical cells, meaning settings for which the computational effort is less dominated by the cost of the coupling scheme. The speedup over the FD model should be even more impactful for a 3D computational domain [17], as the ratio of full-dimensional elements to VE elements significantly decreases in a 3D setting. However, the extension to three dimensions was not the focus of this work and will be addressed in a future project. ...
Vertical equilibrium models have proven to be well suited for simulating fluid flow in subsurface porous media such as saline aquifers with caprocks. However, in most cases the dimensionally reduced model lacks the accuracy to capture the dynamics of a system. While conventional full-dimensional models have the ability to represent dynamics, they come at the cost of high computational effort. We aim to combine the efficiency of the vertical equilibrium model and the accuracy of the full-dimensional model by coupling the two models adaptively in a unified framework and solving the emerging system of equations in a monolithic, fully-implicit approach. The model domains are coupled via mass-conserving fluxes while the model adaptivity is ruled by adaption criteria. Overall, the adaptive model shows an excellent behaviour both in terms of accuracy as well as efficiency, especially for elongated geometries of storage systems with large aspect ratios.
... Additionally, the changes in hydrodynamic conditions also caused fluctuations in the CF, affecting the contaminants' transport to the water table. For example, Nilsen et al. [6] noted that increased rainfall intensity diminishes the CF's capacity to impede pollutants, and Slavich et al. [7] found that irrigation resulting in a rising water table contributed to salt enrichment in the CF. Furthermore, contaminant transport in the CF is affected not only by porous media and hydrodynamic conditions but also by contaminant properties. ...
... Currently, MRST has a vertical equilibrium model (i.e., MRST-CO2Lab) tailored for large scale simulation of CO 2 storage . Vertical equilibrium model has been well studied and is promising for regional scale simulation of multi-phase flow during GCS, because it can offer fast prediction of the storage capacity of a reservoir Nilsen et al., 2016). However, it has limitation in simulating reactive multi-component multi-phase flow at Darcian scale (Gasda et al., 2012, and references therein). ...
We present a reactive multi-component multi-phase flow program for simulating Geological Carbon Sequestration (GCS), an approach that reduces carbon emissions by storing CO2
in deep subsurface formations. The program, called MRST_CO2, is implemented in the library Matlab Reservoir Simulation Toolbox (MRST). It can simulate multi-phase flow and transport of species undergoing chemical reactions and mass exchanges among gas, liquid and solid phases. Equations for flow, mass transport and chemical reactions are solved with a sequential iteration approach. The program was tested with a 1D benchmark. It has also been applied to heterogeneous 2D and 3D cases with a structured or unstructured grid.
... Energies 2023, 16, 1684 2 of 16 trapping [7,8,17,18]. As the free CO 2 phase percolates upward through the formation, a significant amount of CO 2 can be entrapped by capillary forces, which is referred to as residual trapping [19][20][21]. ...
... One practical approach to mitigating global climate change and reducing CO 2 emissions is CO 2 capture and storage (CCS) in the Earth's subsurface and storing it permanently in an underground geological formation [5,6]. CO 2 geological storage sites include deep saline aquifers, depleted oil and gas reservoirs, coal beds, and mineralization in reactive formations such as basalt [3,5,[7][8][9][10][11][12][13]. CO 2 utilization for enhanced oil recovery and sequestration into aquifers has been practiced for several decades [3], where the focus has been on deep saline aquifers due to their superior storage capacity [14]. ...
... Therefore, a high vertical resolution is needed to capture the plume shape and resolve the vertical segregation within. Therefore, using standard 3D simulation tools for largescale, long-term CO 2 migration can be challenging and computationally expensive [8,45]. For instance, 3D simulators tend to underestimate CO 2 migration velocities in simple conceptual models [45]. ...
Geological CO2 sequestration (GCS) has been proposed as an effective approach to mitigate carbon emissions in the atmosphere. Uncertainty and sensitivity analysis of the fate of CO2 dynamics and storage are essential aspects of large-scale reservoir simulations. This work presents a rigorous machine learning-assisted (ML) workflow for the uncertainty and global sensitivity analysis of CO2 storage prediction in deep saline aquifers. The proposed workflow comprises three main steps: The first step concerns dataset generation, in which we identify the uncertainty parameters impacting CO2 flow and transport and then determine their corresponding ranges and distributions. The training data samples are generated by combining the Latin Hypercube Sampling (LHS) technique with high-resolution simulations. The second step involves ML model development based on a data-driven ML model, which is generated to map the nonlinear relationship between the input parameters and corresponding output interests from the previous step. We show that using Bayesian optimization significantly accelerates the tuning process of hyper-parameters, which is vastly superior to a traditional trial–error analysis. In the third step, uncertainty and global sensitivity analysis are performed using Monte Carlo simulations applied to the optimized surrogate. This step is performed to explore the time-dependent uncertainty propagation of model outputs. The key uncertainty parameters are then identified by calculating the Sobol indices based on the global sensitivity analysis. The proposed workflow is accurate and efficient and could be readily implemented in field-scale CO2 sequestration in deep saline aquifers.
... We generated twenty thousand samples for five uncertain parameters within the reported range for the Bunter Closure 36 model and ran forward simulations for each input set. The vertical equilibrium model implemented in MRST-co2lab [27,28] was used to maintain a feasible computational cost. A forward simulation performed on the Bunter Closure 36 took around 8 and 14 h using the ECLIPSE Blackoil and ECLIPSE Compositional simulators, respectively; using MRST-co2lab reduced the simulation to less than 2 min. ...
The UK plans to bring all greenhouse gas emissions to net-zero by 2050. Carbon capture and storage (CCS), an important strategy to reduce global CO2 emissions, is one of the critical objectives of this UK net-zero plan. Among the possible storage site options, saline aquifers are one of the most promising candidates for long-term CO2 sequestrations. Despite its promising potential, few studies have been conducted on the CO2 storage process in the Bunter Closure 36 model located off the eastern shore of the UK. Located amid a number of oil fields, Bunter is one of the primary candidates for CO2 storage in the UK, with plans to store more than 280 Mt of CO2 from injections starting in 2027. As saline aquifers are usually sparsely drilled with minimal dynamic data, any model is subject to a level of uncertainty. This is the first study on the impact of the model and fluid uncertainties on the CO2 storage process in Bunter. This study attempted to fully accommodate the uncertainty space on Bunter by performing twenty thousand forward simulations using a vertical equilibrium-based simulator. The joint impact of five uncertain parameters using data-driven models was analysed. The results of this work will improve our understanding of the carbon storage process in the Bunter model before the injection phase is initiated. Due to the complexity of the model, it is not recommended to make a general statement about the influence of a single variable on CO2 plume migration in the Bunter model. The reservoir temperature was shown to have the most impact on the plume dynamics (overall importance of 41%), followed by pressure (21%), permeability (17%), elevation (13%), and porosity (8%), respectively. The results also showed that a lower temperature and higher pressure in the Bunter reservoir condition would result in a higher density and, consequently, a higher structural capacity.
... The Vertical-Equilibrium (VE) model was used for simulating CO 2 trapping in the subsurface. The primary assumption in a vertical equilibrium model is allowing the vertical distribution of fluid phases to be calculated using analytical expressions (Møll et al. 2016b). The flow equations can then be integrated vertically to obtain a simplified model. ...
... The flow equations can then be integrated vertically to obtain a simplified model. This is a common method used in many other branches of physics, such as explaining water waves, creep flow, and so on (Møll et al. 2016b). ...
... The effect of vertical direction decreases the number of field dimensions. This leads to reducing the coupling between pressure and fluid transport and improving the problem's characteristic time constants (Møll et al. 2016b). ...
Carbon dioxide (CO2) capture and storage (CCS) is presented as an alternative measure and promising approach to mitigate large-scale anthropogenic CO2 emissions into the atmosphere. In this context, CO2 sequestration into depleted oil reservoirs is a practical approach, as it boosts the oil recovery and facilitates the permanent storing of CO2 into the candidate sites. However, the estimation of CO2 storage capacity in the subsurface is a challenge to kick-start CCS worldwide. Thus, this paper proposes an integrated static and dynamic modeling framework to tackle the challenge of CO2 storage capacity in the Upper Qishn Formation of the S1A reservoir in the Masila Basin, Yemen. To achieve this work's ultimate goal, the geostatistical modeling was integrated with open-source code (MRST-CO2lab) for reducing the uncertainty assessment of CO2 storage capacity. Also, there is a significant difference between static and dynamic CO2 storage capacity. The static CO2 storage capacity varies from 4.54 to 81.98 million tons, while the dynamic CO2 simulation is estimated from 4.95 to 17.92 million tons. Based on the geological uncertainty assessment of three ranked realizations (P10, P50, P90), our work found that the Upper Qishn sequence of the S1A reservoir could store 15.64 million tons without leakage. This finding demonstrates that the S1A reservoir has the potential for geological CO2 storage. Ultimately, this study proposes a useful modeling framework that is easy to adapt for other reservoirs in the Masila Basin in Yemen.
Link for free access: https://rdcu.be/cA7it
... One type of vertically-integrated models, referred to as vertical equilibrium model (VE) and initially developed for oil and gas flow in reservoirs (Coats et al., 1971;Yortsos, 1995), were introduced and developed to study the CO 2 -brine system by assuming a rapid segregation of the injected CO 2 and the resident brine due to strong buoyancy (Nordbotten et al., 2005a;Celia, 2006, 2011;Zheng et al., 2015;Guo et al., 2016c). The VE models have been extended to analyze a wide range of processes relevant to geological CO 2 storage Guo et al., 2016b;Bandilla et al., 2019), including convective mixing (Riaz et al., 2006;Gasda et al., 2011), capillary trapping (e.g., Hesse et al., 2008;MacMinn et al., 2011), hysteresis (Doster et al., 2012;Nilsen et al., 2016), slow drainage (Becker et al., 2017), leakage through old abandoned wells (e.g., Nordbotten et al., 2005bNordbotten et al., , 2009Gasda et al., 2009;Celia et al., 2011), background groundwater flow (e.g., Juanes et al., 2010;MacMinn et al., 2010), solubility trapping (Gasda et al., 2011;MacMinn et al., 2011), fluid compressibility (Andersen et al., 2015), geomechanics (Bjørnarå et al., 2016), caprock topography (Gasda et al., 2012;Nilsen et al., 2012), thermal effects (Andersen and Nilsen, 2018), and the presence of fractures (Tao et al., 2019). While VE models have been widely used to answer many important science and engineering questions related to geological CO 2 storage, they are limited by the vertical equilibrium assumption that may not be valid under certain conditions when the time scale of the buoyant segregation is large relative to the time scale of interest (Court et al., 2012;Bandilla et al., 2019). ...
Numerical modeling of CO2 injection in the deep saline aquifer is computationally expensive due to the large spatial and temporal scales. To address the computational challenge, reduced-dimensional models (e.g., vertical equilibrium (VE) and dynamic reconstruction (DR) models) based on vertical integration of the full-dimensional governing equations have been developed. VE models assume rapid segregation of the injected and the resident fluids due to strong buoyancy. Conversely, DR models employ a multiscale framework that relaxes the VE assumption and captures the vertical dynamics of CO2 and brine by solving the vertical two-phase flow dynamics as one-dimensional fine-scale problems. Although DR models relax the VE assumption while maintaining much of the computational efficiency of VE models, they are thus far limited to homogeneous and layered heterogeneous formations. We present a novel hybrid framework that couples a multilayer dynamic reconstruction model and a full-dimensional model. The new hybrid framework allows simulation of CO 2 injection in geological formations with local heterogeneities. It employs a full-dimensional model in local heterogeneous regions (where the full-dimensional model should be used for accuracy), while applying the dynamic reconstruction model in the rest of the domain. Numerical simulations of CO 2 injection in three heterogeneous reservoirs show that the hybrid model maintains the accuracy of the conventional full-dimensional models with significantly reduced computational cost.
... The Vertical-Equilibrium (VE) model was used for simulating CO 2 trapping in the subsurface. The primary assumption in a vertical equilibrium model is allowing the vertical distribution of uid phases to be calculated using analytical expressions (Møll et al. 2016b). The ow equations can then be integrated vertically to obtain a simpli ed model. ...
... The ow equations can then be integrated vertically to obtain a simpli ed model. This is a common method used in many other branches of physics, such as explaining water waves, creep ow, and so on (Møll et al. 2016b) The effect of vertical direction decreases the number of eld dimensions. Thus, this leads to reducing the coupling between pressure and uid transport and improving the problem's characteristic time constants (Møll et al. 2016b). ...
... This is a common method used in many other branches of physics, such as explaining water waves, creep ow, and so on (Møll et al. 2016b) The effect of vertical direction decreases the number of eld dimensions. Thus, this leads to reducing the coupling between pressure and uid transport and improving the problem's characteristic time constants (Møll et al. 2016b). ...
Carbon dioxide (CO2) capture and storage (CCS) is presented as an alternative measure and promising approach to mitigate the large-scale anthropogenic CO2 emission into the atmosphere. In this context, CO2 sequestration into depleted oil reservoirs is a practical approach as it boosts the oil recovery and facilitates the permanent storing of CO2 into the candidate sites. However, the estimation of CO2 storage capacity in subsurfaces is a challenge to kick-start CCS worldwide. Thus, this paper proposes an integrated static and dynamic modeling framework to tackle the challenge of CO2 storage capacity in a clastic reservoir, S1A filed, Masila basin, Yemen.
To achieve this work's ultimate goal, the geostatistical modeling was integrated with open-source code (MRST-CO2lab) for reducing the uncertainty assessment of CO2 storage capacity. Also, there is a significant difference between static and dynamic CO2 storage capacity. The static CO2 storage capacity varies from 4.54 to 81.98 million tons, while the dynamic CO2 simulation is estimated from 4.95 to 17.92 million tons. Based on the geological uncertainty assessment of three ranked realizations (P10, P50, P90), our work was found that the upper Qinshn sequence could store 15.64 Million tons without leakage. This result demonstrates that the potential of CO2 utilization is not only in this specific reservoir, but the further CO2 storage for the other clastics reservoirs is promising in the Masila Basin, Yemen.
