Plenary Abstracts 2023

Tu1 - Introduction to poroelasticity in MRST

Odd Andersen

SINTEF Digital

Keywords: poroelasticity, coupled systems, mechanics, mandel

Module dependencies: ad-mechanics, vemmech


This presentation gives a brief overview of the MRST ad-mechanics module, which allows defining and solving coupled mechanical/flow problems within the framework of linear poroelasticity. A brief outline of the theory and the module will be presented. Two well-konwn examples from poroelastic theory will be used as illustration: the uniaxial compression of a wet sample (Terzaghi problem), as well as Mandel's problem, which demonstrates an unique poroelastic phenomenon, the Mandel-Cryer effect.

A more in-depth treatment of the topic covered in this presentation is found in Chapter 14 in the open-access book "Advanced Modeling with the MATLAB Reservoir Simulation Toolbox" (2021).

Video recording:

Tu2 - Near-wellbore modeling for vertical wells and its application in water control operations 

Author: Junjian Li 1,2, Lin Zhao 3, Hanqiao Jiang 1

1 China University of Petroleum (Beijing), Changping District, 102200 Beijing, China
2 Mathematics and Cybernetics, SINTEF Digital, 0314 Oslo, Norway
3 CNOOC Research Institute, Chaoyang District, 100028 Beijing, China

Keywords: Near-wellbore modeling, vertical well, reservoir-wellbore coupling, water control 

Module dependencies:  nwm, ad-blackoil, ad-core, upr 


The high water-cut oil wells require water control operations to balance the heterogeneous waterflooding induced by high-permeability channels or thief zones. The physical process of such operations mostly occurs in well vicinity, which calls for a fine-scale near-wellbore simulation routine to predict the production performance. This paper introduces a near-wellbore modeling method for vertical wells under the framework of MRST module nwm that initially implements the near-wellbore modeling for horizontal wells. The hybrid gridding retains the original Corner-point grid (CPG) in far-HW region, and reconstructs the CPG to refinement grids in near-wellbore region. The refinement grids comprise a layered unstructured grid and a segmented radial grid. The new method highlights two new gridding workflow classes for vertical wells inheriting from those for horizontal wells without much modifications as a result of topological analogous between the hybrid grids of two types of wells. The new gridding workflow classes are intended for the unstructured grid and radial grid, respectively. The difference of Voronoi grid between two types of wells comes from the geometry of sub Cartesian grid. A pseudo horizontal well trajectory extending along x-axis with user-input segmental number is made to construct a Cartesian grid in which the vertical well is located. The half-radial sub grid for horizontal wells are removed. As for the radial grid, the geometry information of VOI grid in near-well region is generated at each x-y plane instead of y-z plane for horizontal wells. The griddings functiones in original workflow classes produce a layered unstructured grid and a segmented radial grid without any other operations. Moreover, the simulation workflow, involving routines such as grid assembing, transmissibility calculation, can be employed for the vertical wells without any changes. Moreover, the void region inside wellbore is also gridded with a segmental wellbore grid which shares same segment configuration with radial grid. The wellbore grid has tailored geometry according to downhole tools, such as tubing, packers, and ICDs. The performance of the new model is demonstrated in validation and application cases. The application cases further show the use of flow diagnostics in the target well selection and the use of new-wellbore method in production prediction. 

Video recording:

Tu3 - Characterization of capillary driven flow in layered petroleum reservoirs 

Author: Akshit Agarwal1*, Jyoti Phirani2

1Department of Chemical Engineering, Indian Institute of Technology Delhi, India, 2Department of Civil and Environmental Engineering, University of Strathclyde, Glasgow

Keywords: Spontaneous imbibition, capillary pressure, wettability, saturation profiles, darcy scale

Module dependencies: ad-core, ad-blackoil


For gas storage in the geological petroleum reservoirs, it is important to understand fluid flow behaviour when capillary forces are dominant i.e. after the gas injection stops. In this work, we use MRST for numerically simulating unidirectional flow assuming horizontal displacement in co-current mode to understand the phenomenon of spontaneous imbibition in layered petroleum reservoirs at Darcy scale. Using our model we want to predict if capillary breakthrough is possible and how the gas distribution takes place in layered reservoirs. The core dimensions of 5 m x 1 m x 1 m are used for two-layered reservoirs. We placed an additional grid cell of pore volume ten times to that of the core at one end of the setup which acts as a water tank. The boundary conditions in simulation are controlled using the wells. We positioned one injector well in the water tank and one production well at the other side of the core with pressures of both the wells being the same to allow for capillary driven flow. For a single layered, homogeneous system, we compared the obtained saturation profiles from the simulation with the analytical solution published in the literature. Comparisons are provided for three different wettability states for oil-water systems. For mixed wet and weakly water wet cases, the numerical solutions show an excellent match with the analytical solutions. We validated our simulation model using several cases of the homogeneous reservoirs of different petrophysical properties, relative permeability, capillary pressure - saturation curves, and varying mobility ratios. Using our model for homogeneous porous media, we observed that the fluids propagate with different velocity in the sediments and wetting fluid reaches farther through the larger permeability layer. However, in the case of layered reservoirs, the fluid propagation velocity seems to be similar in high and low permeability layers. We observed that the interaction of layers has a significant impact on fluid flow and there is a fluid transfer between layers. One of the applications of this model is to estimate gas migration in layered sediments for determining the long term CO2 storage capacity and security. 

Video recording:

Tu4 - Impact of pressure-dependent permeability and fracture conductivity on well productivity in a tight reservoir 

Author: Oscar Molina


Keywords: multi-fractured horizontal wells, reservoir performance, geomechanics, controlled drawdown

Module dependencies: ad-props, ad-core, ad-blackoil, linearsolvers, deckformat 


The goal of this study is to analyze the impact of to pressure drawdown on well productivity due to permeability loss in a multi-fractured horizontal well model in a tight black-oil reservoir which accounts for both non-uniform distribution of water saturation and non-uniform pressure-dependent permeability and fracture conductivity across different regions. We implemented a lower-bound exponential permeability loss model with distinct permeability moduli for the hydraulic fracture, stimulated reservoir volume (SRV), and matrix. In addition, we considered the hydraulic fracture to be initially filled with water. In addition, the SRV has a higher water saturation compared to the matrix due to invasion of fracturing fluid. We adopted a controlled pressure drawdown to mimic realistic depletion plans often utilized for unconventional reservoirs, for which production rates smoothly increase early on before dropping sharply. To account for uncertainties in the model, we allocated a Gaussian distribution to each permeability moduli and set up a Montecarlo simulation using the MATLAB Parallel Computing Toolbox to statistically assess the variability on well productivity, both in rate and cumulative production, due to pressure-dependent permeability effects. 


We1 - Model calibration in MRST using adjoints 

Author: Stein Krogstad

SINTEF Digital

Keywords: adjoints, parameter-sensitivities, quasi-Newton, Levenberg-Marquardt

Module dependencies: ad-*, optimization 


Adjoint capabilities based on automatic differentiation (AD) have been an integral part of MRST since the first AD-based solvers appeared more than ten years ago. While initial implementations only provided gradients for objectives with respect to well controls, later developments have focused more towards having a framework for providing gradients or sensitivities with respect to any collection of parameters a model may contain. In particular, this led to the development of the ModelParameter-class. 

While sensitivities can be valuable on their own (e.g., for visualization), most MRST-applications use them inside an optimization loop. Almost any smooth optimization problem can be solved much more efficiently using gradient-based rather than gradient free methods. Likewise, methods utilizing second order derivatives (Hessians) will typically outperform those utilizing only first order. Although implementation of second order adjoints (based on second order AD) is possible, it is usually not considered worth the effort (neither in man-hours nor in computational performance). For non-linear least square problems, however, the Hessian can often be approximated well by using the parameter-to-output sensitivity matrix (residual Jacobian). In MRST, Jacobians can be calculated using the same adjoint framework as used for sensitivity calculations. However, for Jacobian calculations, each linear adjoint system will have multiple right-hand-sides (corresponding to the size of the residual vector).

In this talk, we will describe how to set up and run model calibrations problems in MRST using both gradient-based (quasi-Newton) and Jacobian-based (Levenberg-Marquardt) optimization routines with focus on Coarse Grid Network (CGNet) models. Since these models are relatively small (up to a few thousand parameters) they are efficiently calibrated the Levenberg-Marquardt method. We show how calibration problems can be set up both by using stand-alone scripts and by using the OptimizationProblem-class. Finally, we discuss how the nullspace of the misfit Jacobian can be utilized to assess quality of model output outside the training data. 

Video Recording:

We2 - PENTREACT: A non-isothermal reactive transport module in MRST to model coupled flow, heat transfer, and reactive transport processes in subsurface reservoirs 

Author: Sajjad Moslehi 1∗, Hossein Fazeli 2Shahin Kord 1

1Petroleum University of Technology, Ahvaz, Iran 
2Iran University of Science and Technology, Tehran, Iran

Keywords: PENTREACT, numerical Simulation, MRST, reactive transport, fracture network

Module dependencies: ad-core, ad-props, ad-blackoil, geochemistry, dfm, hfm 


Coupled modeling of subsurface fluid flow, heat transfer, solute transport, and chemical reactions can be applied to many geologic systems and environmental problems, including underground hydrogen storage, CO2 and hazardous waste disposal in subsurface reservoirs, geothermal heat extraction, hydrocarbon recovery, matrix acidizing of wells, diagenetic and weathering processes, acid mine drainage remediation, and contaminant transport. PENTREACT (Pressure-ENergy-TRansport-REACTion) is a numerical simulation module in MRST for reactive transport modeling and has been developed by using a fully-implicit sequential approach. The developed module can be applied to both non-fractured and fractured porous media and it considers equilibrium and kinetic reactions distinctively. To demonstrate the applicability of the program, here we investigate the sealing capacity of the caprock of the Mt. Simon aquifer in the Illinois Basin considered as a CO2 disposal site. In this example, the caprock is assumed to be fractured and the Discrete Fracture Matrix (DFM) model is used to model the fracture network. 

Video recording:

We3 - Modeling phase behavior and black-oil simulations for underground hydrogen storage 

Author: Elyes AhmedXavier RaynaudHalvor M. NilsenOlav Møyner

SINTEF Digital

Keywords: hydrogen storage, black-oil simulation, EoS, Pc-saft, PVT-data

Module dependencies: ad-blackoil 


Accurately understanding the mechanisms involved in hydrogen storage within underground H2 storage project necessitates detailed modeling of fluid flow and transport. However, employing equation-of-state (EOS) based compositional phase equilibrium methods for such modeling can result in significant computational complexity. In this study, we propose the utilization of a more efficient black-oil simulation approach, specifically tailored to the Brine-Hydrogen case, in order to alleviate the computational demands of flow simulations. 

To achieve this, we use a computationally intensive ePC-Saft EOS alongside simpler explicit reduced models based on the Redlich and Kwong EOS and Henry's law. The ePC-Saft Eos and the reduced models are compared and employed to transform hydrogen-brine phase equilibrium compositional data into black-oil pressure-volume-temperature (PVT) data. Through comprehensive numerical simulations, we establish that the reduced models perform comparably to the ePC-Saft EOS in predicting the essential hydrogen-brine transport properties essential for conducting black-oil flow simulations in the context of subsurface hydrogen storage. 

Our simulations encompass a range of scenarios, including standard benchmarks and conceptual challenges, such as a cyclic hydrogen injection-production process. This research contributes to advancing our understanding of hydrogen storage dynamics and underscores the feasibility of utilizing simplified models for accurate predictions in complex subsurface storage projects. 

Video recording:

We5 - Fast workflow for fault leakage modelling during CO2 storage 

Author: Hariharan Ramachandran1∗Florian Doster 1Rafael March 2Christine Maier 3Sebastian Geiger 4Iain de-Jonge Anderson 1Uisdean Nicholson 1 

1 Institute of GeoEnergy Engineering, Heriot-Watt University, Edinburgh, UK 
2 Halliburton Technology Center, Rio de Janeiro, Brazil 
3 State University of Campinas, Campinas, Brazil 
4 Department of Geoscience and Engineering, Delft University of Technology, Delft, Netherlands 

Keywords:  CO2 storage, fault leakage, uncertainty estimation, CCS screening

Module dependencies: co2lab, hfm


Storing carbon dioxide (CO2) in geological formations is a crucial method for mitigating climate change. However, CO2 leakage during injection and storage poses a significant risk, and faults represent a particular concern as they can act as major structural traps or connect pathways to shallower geological layers. Therefore, it is vital to understand the behavior of faults and related structures such as micro-cracks, joints, fracture networks, deformation bands, and fault cores to assess the risk of CO2 leakage and ensure safe and effective storage. 

Accurately simulating fault-related properties at different scales is crucial to predict the consequences of CO2 injection and storage. However, this task can be challenging, particularly in the early stages of a storage project when knowledge of the storage reservoir is limited, and the cost of obtaining high-quality well logs, cores, and seismic data is high. To address this issue, this study proposes a workflow for ultra-fast screening of fault leakage risk during injection and storage at the concept selection stage. The workflow employs a vertically integrated reservoir model coupled with an upscaled fault leakage flow function. 

Simulation results of various CO2 injection scenarios in a storage reservoir with potential for fault leakage demonstrate that the workflow can produce reliable saturation profiles with substantially reduced computation time compared to fine-scale models. Matching CO2 saturation profiles obtained from fine-scale and vertically integrated models adds confidence to the proposed workflow. The fast workflow presented in this study provides a useful tool for identifying the uncertainties associated with key fault parameters, reservoir architecture, and other constitutive relations that affect the behavior of the storage reservoir and potential fault leakage outcomes. By incorporating this workflow at the concept selection stage, stakeholders can quickly assess the risk of CO2 leakage and evaluate the feasibility of the storage site. Overall, the proposed workflow provides a cost-effective and efficient method for screening fault leakage risk during CO2 injection and storage, helping to ensure safe and effective carbon storage. 

Video recording:

We6 - MRST vertical equilibrium model analysis for CO2 storage 

Author: Mohammadsajjad Zeynolabedini1∗Ashkan Jahanbani Ghahfarokhi1Per Eirik Bergmo 2 

1 Norwegian University of Science and Technology 
2 SINTEF Industry 

Keywords: MRST, CO2 plume comparison, grid model, PVT model

Module dependencies: ad-blackoil, ad-core, co2lab, deckformat, coarsegrid 


The main goal of this study is to import the Aurora model, which was created at the University of Oslo in collaboration with Gassnova and Ross Offshore, into the MATLAB Reservoir Simulation Toolbox (MRST) in order to use the Vertical Equilibrium (VE) function of this simulator. Since the VE feature converts the 3D reservoir model into a 2D model, which simulates the reservoir model much more quickly, the primary goal of the VE application in MRST is to reduce the long simulation time. To guarantee that the entire reservoir model, including the PVT and Grid models, are correctly imported from ECLIPSE into MRST, the grid and PVT models of MRST and ECLIPSE have been compared. The relative permeability comparison between gas and water demonstrates that the relative permeability model, which is based on the ECLIPSE relative permeability model, is accurately described. A problem with pressure initialization existed between MRST and ECLIPSE, but it was fixed by adjusting the water density. The ECLIPSE PVT model is used to define the water and gas density models in MRST by considering the water and gas compressibility equations. A comparison of the Gas and Water viscosity between MRST and ECLIPSE reveals that both models exhibit the same trend. There are differences between the CO2 plume shape in MRST and ECLIPSE, despite the fact that MRST PVT and Grid Model are confirmed based on the ECLIPSE model. The primary cause of this variation is "Reservoir Heterogeneity." The one-layer averaged MRST model has more permeability than the upper layers in the ECLIPSE reservoir model, which has a high contribution to CO2 flow because the permeability in the upper layers of the Aurora reservoir model is significantly lower than the lower layers. Therefore, in comparison to the ECLIPSE plume, the MRST plume shape is significantly wider. Five reservoir model parameters, including permeability, porosity, residual gas saturation, rock compressibility, and relative permeability curve, have undergone sensitivity analysis. Although the porosity, residual gas saturation, and relative permeability curves do not exhibit any sensitivity for the injection well bottom-hole pressure, this parameter is sensitive to permeability and rock compressibility change. 

Video recording:

We7 - Numerical simulation of CO2 migration in the FluidFlower using MRST

Author: Lluís Saló-Salgado1∗Malin Haugen2Kristoffer Eikehaug 2Martin Fernø2Ruben Juanes1 

1 Massachusetts Institute of Technology 
2 University of Bergen 

Keywords: CO2 storage, two-phase flow, history matching, FluidFlower

Module dependencies: ad-core, ad-blackoil, ad-props, deckformat, linearsolvers, upr


The FluidFlower is a meter-scale, quasi-2D laboratory rig with a transparent front panel and flexible injection ports. It was developed at the University of Bergen (UiB) with multiple research and outreach goals related to geologic carbon sequestration ( One of these goals is the generation of high-quality experimental datasets from direct visualization of subsurface CO2 migration, which can be used to benchmark simulation models. 

Here, we use the ad-blackoil module to simulate miscible CO2-water migration in two versions of the FluidFlower (porous media dimensions 0.897 x 0.47 x 0.0105 m and 2.86 x 1.33 x 0.019 m). In particular, we evaluate (1) the value of prior knowledge of the system, expressed in terms of local measurements of the quartz sands in the tank, to history-match the simulation model; and (2) the predictability of the matched numerical model, when applied to different injection scenarios and stratigraphic sections. We use timelapse images of the corresponding experiments to assess simulation model concordance. 

Results show that our model can qualitatively match CO2 plume migration and convective mixing of the experimental truth. Quantitatively, our simulations are accurate during the injection phase, but their concordance decreases with time in specific domain areas. Using local data reduces the time required to history match. Where heterogeneous structures are present, accurate deterministic estimates of CO2 migration are difficult to obtain. 

 Video recording:

Published September 9, 2021