Ph.D. position in multi-scale and multiphysics modelling of flow and transport processes in fractured porous media: applications to geothermal energy production
GeoRessources Laboratory, University of Lorraine
GeoRessources is among the most reputable geological research laboratories in France and covers the field of geological resources, from exploration to exploitation, including the processing and recovery stages, and its impact on society and the environment.
Homepage: https://georessources.univ-lorraine.fr/
Hydrological Sciences (HS)
Context: Interest in geothermal energy production as a sustainable energy source is growing and understanding geothermal processes is vital due to their complex nature. Simulating fluid flow and transport processes in fractured porous media is a crucial part of research on geothermal energy which has gained more attention in the previous decades. Some of these key issues and challenges include: (1) quantitative representation of fractures geometry, identification of individual fractures, network of fractures and their aperture, (2) definition of fractures and fracture network hydrodynamic properties, (3) simulation of flow and transport processes due to the multi-scale, multiphysics and non-linear nature of the complex couplings at stake and (4) complementary effects of the three previous issues. In order to address the fore-mentioned issues, various numerical methods have been developed. Implicit methods, such as single and multi-continuum methods, offer computational efficiency but lack accuracy
and description of details around individual fractures. Explicit methods, such as discrete fracture model, provide more realistic representations but are computationally intensive and require detailed prior descriptions fracture network geometry. Consequently, the applicability of the approach and the sensitivity of the results is highly dependent on the temporal and spatial scale of the problem. This topic needs to be further investigated when it comes to the geothermal energy production. In addition, geothermal reservoir assessment often employs a combination of geophysical methods to characterize the geological formation including the identification and mapping of fault and fractured zones. Time lapse electrical resistivity tomography and self-potential are only examples of such geophysical methods. In order to apply the electrical geophysical methods to geothermal systems, there is a need for high performance coupled simulators (i.e. both forward and inverse models) that can accurately and efficiently discretize the differential equations governing flow, heat transport and electrical current in fractured porous media.
This doctoral project aims to study and develop some advanced multiphysics simulators in fractured porous media and apply this knowledge to the geothermal energy production. More specifically, the motivation for undertaking this doctoral dissertation is an attempt for: (1) better understanding the exchange processes (i.e. fluid flow, heat transport and electrical charge) between fracture and matrix, (2) a sensitivity analysis for better adaptation of the type of the approach for fractures based on the lithology of the reservoir, (3) the application of electrical geophysics in thermal fractured reservoirs and (4) developing a numerical tool suitable for the simulation of flow and transport processes coupled with electrical charge migration at Darcy scale which is accurate and efficient (i.e. computationally) in highly fractured porous media.
Objectives and work summary: In the first step, a model discretizing the fluid and transport processes is going to be developed by applying assumptions that will reduce the nonlinearity of the system of equations mainly induced by the exchange between fracture and matrix. By establishing the base model from an existing DFN approach for the simulation of advection processes in fracture network and adding the heat exchange between fracture and matrix through a semi-analytical formulation we will be able to perform simulations on reservoirs which are densely fractured and simulate the process more efficiently than the classic conventional DFM model without losing considerable accuracy and information. After the development of this model, a series of simulation over a large range of hydrodynamical conditions will be performed and compared with counter-part model used as reference based on the DFM model.
Sensitivity analyses will be performed based on the difference of the results between the two models to contemplate the limitation and the criteria for the suitability of our proposed model (called DFM-CM at this point). The result will help us decide the suitability of DFM-CM in comparison to the DFM model and the applicability as a function of fracture network and matrix permeability. Different simplifications of the DFM-CM model will be explored for instance by including the secondary fracture network within the description of the porous matrix (i.e., a Dual Fracture Equivalent Matrix model). Comparison with multi-continuum models will be also investigated.
In the second step of the project, we focus on the coupled hydro-thermo-geophysical simulations. We propose developing first a forward model based on explicit approach which will act as the synthetic data generator. For this forward model, electrical charge distribution evolution (i.e. spatial and temporal) module will be added to the previously developed DFM-CM model through the discretization of Ohm’s law using the mixed hybrid finite element method. The existence of this model is essential to the following stages of the project, including a parameter estimation approach (i.e. inverse model) and also simulation of the electric resistivity evolution and distribution in the thermal fractured reservoir (similar model for fractured vadose zone is developed in Koohbor et al. (2024)). In the third and final step of the project, an inverse model is proposed to be developed (the inversion scheme is still put to discussion however either physics informed or convolutional neural network is proposed at this level). The modelling approach for flow and transport in the inverse model should be based on implicit multicontinuum approach (e.g. the dual porosity model). The advantage of having such inverse modelling tool applied on an implicit model is that the characteristics of individual fractures need not to be estimated and the bulk characteristic associated with the exchange of flow, heat and electrical charge can be estimated through much faster approach. The final goal of this part of the project would be to develop an inverse model that may estimate certain hydrodynamic properties of the fracture network in geothermal reservoirs. In order for the training and the development of this inverse model we need data
either from the field. Considering that field scale data might not be available at this stage, synthetic data generated by the forward model developed in the previous step can be used for the development and calibration of the inverse model.
This project will mainly be advantageous in terms of applied geoscience and completion of this project, the added values brought to the potential candidate as well as the laboratory and the collaborating partners will be numerous including: (1) Improvement on the general knowledge on geothermal energy production in densely fractured thermal reservoirs (2) Improvement of the knowledge on efficient modelling of flow and transfer processes in the fractured porous media on Darcy scale, (3) Development of fluid flow-electrical charge discretization in the fractured porous media applied on geothermal energy production, (4) The development of an efficient in-house numerical model which can be improved
constantly and gradually over the course of upcoming years. The results of this project is previewed to be published in reputable peer-reviewed relevant journals. National level and international level collaborations are previewed through different phases of the project.
Applicants should send via email a Curriculum Vitae, copy of the master thesis (if applicable) and the names and email addresses of two references to:
Fabrice Golfier (PR, fabrice.golfier@univ-lorraine.fr)
Behshad Koohbor (MCF, behshad.koohbor@univ-lorraine.fr )