Francesco Parisio
Francesco Parisio has a total of 46 co-authors. Here are the top co-authors by number of shared publications:
- Victor Vilarrasa
Spanish National Research Council (CSIC)
12 shared publications - Keita Yoshioka
Department Geoenergy Montanuniversität Leoben Leoben Austria
5 shared publications - Olaf Kolditz
Helmholtz Centre for Environmental Research - UFZ, Leipzig, Germany
5 shared publications - Thomas Nagel
Technische Universität Bergakademie Freiberg, Geotechnical Institute, Gustav-Zeuner-Str. 1, 09599 Freiberg, Germany
5 shared publications - Roman Y. Makhnenko
University of Illinois at Urbana-Champaign, Urbana, USA
4 shared publications Dmitri Naumov
3 shared publications
Latest Publications
- Open Access
- 21 August 2026
- Published by American Geophysical Union (AGU) in Water Resources Research
- Vol. 62 (8)
On the Leaky Nature of Fractures in Low‐Permeability Rock
Hydraulic‐test interpretation in fractured rock commonly assumes impermeable confining matrices, an assumption we show is systematically incorrect, even when the matrices are 7–14 orders of magnitude less permeable than the fracture. Fluid injected into a fracture begins to leak into the surrounding rock matrices within milliseconds to seconds, causing the slope of the pressure evolution with respect to the logarithm of time to halve, equivalent to a factor‐of‐two overestimation of fracture transmissivity if leakage is neglected. Here, we investigate the flow regimes induced by constant flow rate water injection into a fracture surrounded by low‐permeability matrices and the implications for hydraulic‐test interpretation. We find that even for a low‐permeability confining rock matrix, leakage is non‐negligible on the pressure evolution due to the small fracture aperture, which leads to a large pressure gradient between the fracture and matrix. Negligible leakage exists only for an extremely short period, and then a transient flow regime arises with a slope of −1/4 in the log‐log derivative plot, that is, flow dimension equal to 2.5. Subsequently, the flow regime becomes radial, with the slope of pressure evolution in a semi‐log plot corresponding to that of a leaky aquifer, that is, twice the actual fracture transmissivity. We validate this finding against step‐rate injection data from the Bedretto Underground Laboratory, for which only the model accounting for matrix leakage reproduces the measured pressure evolution. As a result, one could mistakenly overestimate the fracture transmissivity in injection tests in fractured media if the leaky nature of fractures is not considered.
- 21 August 2026
- Published by American Geophysical Union (AGU) in Water Resources Research
- Vol. 62 (8)
Open AccessOn the Leaky Nature of Fractures in Low‐Permeability Rock
Hydraulic‐test interpretation in fractured rock commonly assumes impermeable confining matrices, an assumption we show is systematically incorrect, even when the matrices are 7–14 orders of magnitude less permeable than the fracture. Fluid injected into a fracture begins to leak into the surrounding rock matrices within milliseconds to seconds, causing the slope of the pressure evolution with respect to the logarithm of time to halve, equivalent to a factor‐of‐two overestimation of fracture transmissivity if leakage is neglected. Here, we investigate the flow regimes induced by constant flow rate water injection into a fracture surrounded by low‐permeability matrices and the implications for hydraulic‐test interpretation. We find that even for a low‐permeability confining rock matrix, leakage is non‐negligible on the pressure evolution due to the small fracture aperture, which leads to a large pressure gradient between the fracture and matrix. Negligible leakage exists only for an extremely short period, and then a transient flow regime arises with a slope of −1/4 in the log‐log derivative plot, that is, flow dimension equal to 2.5. Subsequently, the flow regime becomes radial, with the slope of pressure evolution in a semi‐log plot corresponding to that of a leaky aquifer, that is, twice the actual fracture transmissivity. We validate this finding against step‐rate injection data from the Bedretto Underground Laboratory, for which only the model accounting for matrix leakage reproduces the measured pressure evolution. As a result, one could mistakenly overestimate the fracture transmissivity in injection tests in fractured media if the leaky nature of fractures is not considered.
- Open Access
- 22 December 2025
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Machine Learning and Computation
- Vol. 2 (4)
Bridging the Gap for Sparse Observations: Data‐Driven Versus Physics‐Informed Neural Networks for a Transient Flow Problem in a Heterogeneous Porous Medium
Assimilating field data is essential to calibrate rock properties in hydrogeological applications. While such workflows are challenging for physics‐based reservoir simulators, data‐driven Artificial Neural Networks (ANN) offer a potential solution by effectively managing noisy data to infer fluid pressure diffusion p ( x , t ). Nevertheless, the sparse observation wells in hydrogeology projects make training ANN models difficult. Therefore, we employ Physics‐Informed Neural Networks (PINN) to bridge this gap between sparse spatial data. We train both ANN and PINN on a synthetic p ( x , t ) data set within a low‐permeability porous medium containing a highly permeable material. Having an identical architecture, both models integrate direct observations of the target variable, while the PINN further optimizes the diffusion equation residual. By comparing the model output as a function of the number of observation wells, we find that the PINN outperforms the ANN when spatial observations are limited to a small number of wells. Adding noise to the training data further underscores the robustness of PINN against random measurement errors or ambient noise. Furthermore, we evaluate the effectiveness of PINN in representing a high‐permeability zone without observations inside the domain. The findings suggest that accuracy is maintained even with reduced thickness of the equivalent material, although this leads to an increase in computation time. Given the sparsity of observation wells in hydrogeological applications, PINNs potentially provide a more suitable machine learning workflow than purely data‐driven ANN for reservoir modeling.
- 22 December 2025
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Machine Learning and Computation
- Vol. 2 (4)
Open AccessBridging the Gap for Sparse Observations: Data‐Driven Versus Physics‐Informed Neural Networks for a Transient Flow Problem in a Heterogeneous Porous Medium
Assimilating field data is essential to calibrate rock properties in hydrogeological applications. While such workflows are challenging for physics‐based reservoir simulators, data‐driven Artificial Neural Networks (ANN) offer a potential solution by effectively managing noisy data to infer fluid pressure diffusion p ( x , t ). Nevertheless, the sparse observation wells in hydrogeology projects make training ANN models difficult. Therefore, we employ Physics‐Informed Neural Networks (PINN) to bridge this gap between sparse spatial data. We train both ANN and PINN on a synthetic p ( x , t ) data set within a low‐permeability porous medium containing a highly permeable material. Having an identical architecture, both models integrate direct observations of the target variable, while the PINN further optimizes the diffusion equation residual. By comparing the model output as a function of the number of observation wells, we find that the PINN outperforms the ANN when spatial observations are limited to a small number of wells. Adding noise to the training data further underscores the robustness of PINN against random measurement errors or ambient noise. Furthermore, we evaluate the effectiveness of PINN in representing a high‐permeability zone without observations inside the domain. The findings suggest that accuracy is maintained even with reduced thickness of the equivalent material, although this leads to an increase in computation time. Given the sparsity of observation wells in hydrogeological applications, PINNs potentially provide a more suitable machine learning workflow than purely data‐driven ANN for reservoir modeling.
- Open Access
- 10 December 2021
- Published by Wiley in ESS Open Archive
Coupled Thermo-Hydro-Mechanical Effects on Injection-Induced Seismicity in Fractured Reservoirs
With the urgent necessity of geo-energy resources to achieve carbon neutrality, fluid injection and production in the fractured media will significantly increase. Applications such as enhanced geothermal systems, geologic carbon storage, and subsurface energy storage involve pressure, temperature, and stress changes that affect fracture stability and may induce microseismicity. To eventually have the ability to control induced seismicity, it is first necessary to understand its triggering mechanisms. To this end, we perform coupled thermo-hydro-mechanical (THM) simulations of cold water injection and production into a rock containing two fracture sets perpendicular between them. The permeability of fractures being four orders of magnitude higher than the one of the rock matrix leads to preferential pressure and cooling advancement, which induce stress changes that affect fracture stability. We find that the fracture set that is oriented favorably to undergo shear slip in the considered stress regime becomes critically stressed, inducing microseismicity. In contrast, the fracture set that is not favorably oriented for shear remains stable. These results contrast with those obtained for an equivalent porous media that does not explicitly include fractures in the model, which fails to reproduce the direction-dependent stability of fractures present in the subsurface. We contend that fractures should be directly embedded in the numerical models when inhomogeneities are of the spatial scale of the reservoir to enable reproducing the THM coupled processes that may lead to induced microseismicity.
- 10 December 2021
- Published by Wiley in ESS Open Archive
Open AccessCoupled Thermo-Hydro-Mechanical Effects on Injection-Induced Seismicity in Fractured Reservoirs
With the urgent necessity of geo-energy resources to achieve carbon neutrality, fluid injection and production in the fractured media will significantly increase. Applications such as enhanced geothermal systems, geologic carbon storage, and subsurface energy storage involve pressure, temperature, and stress changes that affect fracture stability and may induce microseismicity. To eventually have the ability to control induced seismicity, it is first necessary to understand its triggering mechanisms. To this end, we perform coupled thermo-hydro-mechanical (THM) simulations of cold water injection and production into a rock containing two fracture sets perpendicular between them. The permeability of fractures being four orders of magnitude higher than the one of the rock matrix leads to preferential pressure and cooling advancement, which induce stress changes that affect fracture stability. We find that the fracture set that is oriented favorably to undergo shear slip in the considered stress regime becomes critically stressed, inducing microseismicity. In contrast, the fracture set that is not favorably oriented for shear remains stable. These results contrast with those obtained for an equivalent porous media that does not explicitly include fractures in the model, which fails to reproduce the direction-dependent stability of fractures present in the subsurface. We contend that fractures should be directly embedded in the numerical models when inhomogeneities are of the spatial scale of the reservoir to enable reproducing the THM coupled processes that may lead to induced microseismicity.
- Open Access
- 16 November 2021
- Published by Springer Nature in Scientific Reports
- Vol. 11 (1) , 1-16
A laboratory study of hydraulic fracturing at the brittle-ductile transition
Developing high-enthalpy geothermal systems requires a sufficiently permeable formation to extract energy through fluid circulation. Injection experiments above water’s critical point have shown that fluid flow can generate a network of highly conductive tensile cracks. However, what remains unclear is the role played by fluid and solid rheology on the formation of a dense crack network. The decrease of fluid viscosity with temperature and the thermally activated visco-plasticity in rock are expected to change the deformation mechanisms and could prevent the formation of fractures. To isolate the solid rheological effects from the fluid ones and the associated poromechanics, we devise a hydro-fracture experimental program in a non-porous material, polymethyl methacrylate (PMMA). In the brittle regime, we observe rotating cracks and complex fracture patterns if a non-uniform stress distribution is introduced in the samples. We observe an increase of ductility with temperature, hampering the propagation of hydraulic fractures close to the glass transition temperature of PMMA, which acts as a limit for brittle fracture propagation. Above the glass transition temperature, acoustic emission energy drops of several orders of magnitude. Our findings provide a helpful guidance for future studies of hydro-fracturing of supercritical geothermal systems.
- 16 November 2021
- Published by Springer Nature in Scientific Reports
- Vol. 11 (1) , 1-16
Open AccessA laboratory study of hydraulic fracturing at the brittle-ductile transition
Developing high-enthalpy geothermal systems requires a sufficiently permeable formation to extract energy through fluid circulation. Injection experiments above water’s critical point have shown that fluid flow can generate a network of highly conductive tensile cracks. However, what remains unclear is the role played by fluid and solid rheology on the formation of a dense crack network. The decrease of fluid viscosity with temperature and the thermally activated visco-plasticity in rock are expected to change the deformation mechanisms and could prevent the formation of fractures. To isolate the solid rheological effects from the fluid ones and the associated poromechanics, we devise a hydro-fracture experimental program in a non-porous material, polymethyl methacrylate (PMMA). In the brittle regime, we observe rotating cracks and complex fracture patterns if a non-uniform stress distribution is introduced in the samples. We observe an increase of ductility with temperature, hampering the propagation of hydraulic fractures close to the glass transition temperature of PMMA, which acts as a limit for brittle fracture propagation. Above the glass transition temperature, acoustic emission energy drops of several orders of magnitude. Our findings provide a helpful guidance for future studies of hydro-fracturing of supercritical geothermal systems.
- Open Access
- 10 May 2021
- Published by American Geophysical Union (AGU) in Geophysical Research Letters
- Vol. 48 (9)
How Equivalent Are Equivalent Porous Media?
Geoenergy and geoengineering applications usually involve fluid injection into and production from fractured media. Accounting for fractures is important because of the strong poromechanical coupling that ties pore pressure changes and deformation. A possible approach to the problem uses equivalent porous media to reduce the computational cost and model complexity instead of explicitly including fractures in the models. We investigate the validity of this simplification by comparing these two approaches. Simulation results show that pore pressure distribution significantly differs between the two approaches even when both are calibrated to predict identical values at the injection and production wells. Additionally, changes in fracture stability are not well captured with the equivalent porous medium. We conclude that explicitly accounting for fractures in numerical models may be necessary under some circumstances to perform reliable coupled thermohydromechanical simulations, which could be used in conjunction with other tools for induced seismicity forecasting.
- 10 May 2021
- Published by American Geophysical Union (AGU) in Geophysical Research Letters
- Vol. 48 (9)
Open AccessHow Equivalent Are Equivalent Porous Media?
Geoenergy and geoengineering applications usually involve fluid injection into and production from fractured media. Accounting for fractures is important because of the strong poromechanical coupling that ties pore pressure changes and deformation. A possible approach to the problem uses equivalent porous media to reduce the computational cost and model complexity instead of explicitly including fractures in the models. We investigate the validity of this simplification by comparing these two approaches. Simulation results show that pore pressure distribution significantly differs between the two approaches even when both are calibrated to predict identical values at the injection and production wells. Additionally, changes in fracture stability are not well captured with the equivalent porous medium. We conclude that explicitly accounting for fractures in numerical models may be necessary under some circumstances to perform reliable coupled thermohydromechanical simulations, which could be used in conjunction with other tools for induced seismicity forecasting.
- 24 March 2021
- Published by Springer Nature in Rock Mechanics and Rock Engineering
- Vol. 54 (6) , 2959-2974
Creating Cloud-Fracture Network by Flow-induced Microfracturing in Superhot Geothermal Environments
- 24 March 2021
- Published by Springer Nature in Rock Mechanics and Rock Engineering
- Vol. 54 (6) , 2959-2974
Creating Cloud-Fracture Network by Flow-induced Microfracturing in Superhot Geothermal Environments
- Open Access
- 19 January 2021
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Solid Earth
- Vol. 126 (1)
Analytical Solution to Assess the Induced Seismicity Potential of Faults in Pressurized and Depleted Reservoirs
Displaced faults crossing the reservoir could significantly increase the induced earthquake frequency in geo‐energy projects. Understanding and predicting the stress variation in such cases is essential to minimize the risk of induced seismicity. Here, we adopt the inclusion theory to develop an analytical solution for the stress response to pore pressure variations within the reservoir for both permeable and impermeable faults with offset ranging from zero to the reservoir thickness. By analyzing fault stability changes due to reservoir pressurization/depletion under different scenarios, we find that (1) the induced seismicity potential of impermeable faults is always larger than that of permeable faults under any initial and injection conditions—the maximum size of the fault undergoing failure is 3–5 times larger for impermeable than for permeable faults; (2) stress concentration at the corners results in the occurrence of reversed slip in normal faults with a normal faulting stress regime; (3) while fault offset has no impact on the slip potential for impermeable faults, the slip potential increases with the offset for permeable faults, which indicates that non‐displaced permeable faults constitute a safer choice for site selection; (4) an impermeable fault would rupture at a lower deviatoric stress, and at a smaller pressure buildup than a permeable one; and (5) the induced seismicity potential is overestimated and the injectivity underestimated if the stress arching (i.e., the poromechanical coupling) is neglected. This analytical solution is a useful tool for site selection and for supporting decision making during the lifetime of geo‐energy projects.
- 19 January 2021
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Solid Earth
- Vol. 126 (1)
Open AccessAnalytical Solution to Assess the Induced Seismicity Potential of Faults in Pressurized and Depleted Reservoirs
Displaced faults crossing the reservoir could significantly increase the induced earthquake frequency in geo‐energy projects. Understanding and predicting the stress variation in such cases is essential to minimize the risk of induced seismicity. Here, we adopt the inclusion theory to develop an analytical solution for the stress response to pore pressure variations within the reservoir for both permeable and impermeable faults with offset ranging from zero to the reservoir thickness. By analyzing fault stability changes due to reservoir pressurization/depletion under different scenarios, we find that (1) the induced seismicity potential of impermeable faults is always larger than that of permeable faults under any initial and injection conditions—the maximum size of the fault undergoing failure is 3–5 times larger for impermeable than for permeable faults; (2) stress concentration at the corners results in the occurrence of reversed slip in normal faults with a normal faulting stress regime; (3) while fault offset has no impact on the slip potential for impermeable faults, the slip potential increases with the offset for permeable faults, which indicates that non‐displaced permeable faults constitute a safer choice for site selection; (4) an impermeable fault would rupture at a lower deviatoric stress, and at a smaller pressure buildup than a permeable one; and (5) the induced seismicity potential is overestimated and the injectivity underestimated if the stress arching (i.e., the poromechanical coupling) is neglected. This analytical solution is a useful tool for site selection and for supporting decision making during the lifetime of geo‐energy projects.
- Open Access
- 29 November 2020
- Published by American Geophysical Union (AGU) in Geophysical Research Letters
- Vol. 47 (23)
Sinking CO2 in Supercritical Reservoirs
Geologic carbon storage is required for achieving negative CO2 emissions to deal with the climate crisis. The classical concept of CO2 storage consists in injecting CO2 in geological formations at depths greater than 800 m, where CO2 becomes a dense fluid, minimizing storage volume. Yet CO2 has a density lower than the resident brine and tends to float, challenging the widespread deployment of geologic carbon storage. Here, we propose for the first time to store CO2 in supercritical reservoirs to reduce the buoyancy‐driven leakage risk. Supercritical reservoirs are found at drilling‐reachable depth in volcanic areas, where high pressure (p > 21.8 MPa) and temperature (T > 374°C) imply CO2 is denser than water. We estimate that a CO2 storage capacity in the range of 50–500 Mt yr−1 could be achieved for every 100 injection wells. Carbon storage in supercritical reservoirs is an appealing alternative to the traditional approach.
- 29 November 2020
- Published by American Geophysical Union (AGU) in Geophysical Research Letters
- Vol. 47 (23)
Open AccessSinking CO2 in Supercritical Reservoirs
Geologic carbon storage is required for achieving negative CO2 emissions to deal with the climate crisis. The classical concept of CO2 storage consists in injecting CO2 in geological formations at depths greater than 800 m, where CO2 becomes a dense fluid, minimizing storage volume. Yet CO2 has a density lower than the resident brine and tends to float, challenging the widespread deployment of geologic carbon storage. Here, we propose for the first time to store CO2 in supercritical reservoirs to reduce the buoyancy‐driven leakage risk. Supercritical reservoirs are found at drilling‐reachable depth in volcanic areas, where high pressure (p > 21.8 MPa) and temperature (T > 374°C) imply CO2 is denser than water. We estimate that a CO2 storage capacity in the range of 50–500 Mt yr−1 could be achieved for every 100 injection wells. Carbon storage in supercritical reservoirs is an appealing alternative to the traditional approach.
- Open Access
- 13 November 2020
- Published by Wiley in ESS Open Archive
Sinking CO2 in supercritical reservoirs
Geologic carbon storage is required for achieving negative CO2 emissions to deal with the climate crisis. The classical concept of CO2 storage consists in injecting CO2 in geological formations at depths greater than 800 m, where CO2 becomes a dense fluid, minimizing storage volume. Yet, CO2 has a density lower than the resident brine and tends to float, challenging the widespread deployment of geologic carbon storage. Here, we propose for the first time to store CO2 in supercritical reservoirs to reduce the buoyancy-driven leakage risk. Supercritical reservoirs are found at drilling-reachable depth in volcanic areas, where high pressure (p>21.8 MPa) and temperature (T>374 ºC) imply CO2 is denser than water. We estimate that a CO2 storage capacity in the range of 50-500 Mt yr-1 could be achieved for every 100 injection wells. Carbon storage in supercritical reservoirs is an appealing alternative to the traditional approach.
- 13 November 2020
- Published by Wiley in ESS Open Archive
Open AccessSinking CO2 in supercritical reservoirs
Geologic carbon storage is required for achieving negative CO2 emissions to deal with the climate crisis. The classical concept of CO2 storage consists in injecting CO2 in geological formations at depths greater than 800 m, where CO2 becomes a dense fluid, minimizing storage volume. Yet, CO2 has a density lower than the resident brine and tends to float, challenging the widespread deployment of geologic carbon storage. Here, we propose for the first time to store CO2 in supercritical reservoirs to reduce the buoyancy-driven leakage risk. Supercritical reservoirs are found at drilling-reachable depth in volcanic areas, where high pressure (p>21.8 MPa) and temperature (T>374 ºC) imply CO2 is denser than water. We estimate that a CO2 storage capacity in the range of 50-500 Mt yr-1 could be achieved for every 100 injection wells. Carbon storage in supercritical reservoirs is an appealing alternative to the traditional approach.
- Open Access
- 31 October 2020
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Solid Earth
- Vol. 125 (11)
A Model of Failure and Localization of Basalt at Temperature and Pressure Conditions Spanning the Brittle‐Ductile Transition
Natural phenomena such as seismicity, volcanism, and fluid circulation in volcanic areas are influenced by the mechanical response of intact basalt. When subjected to a wide range of environmental loading conditions, basalt exhibits inelastic deformation characteristics ranging from brittle to ductile behavior. In this manuscript, we present a new constitutive model of basalt that spans the brittle‐ductile transition by covering a wide range of mean effective stress, temperature, and strain rate. The model has been implemented into the automatic constitutive model code generator MFront, which we have coupled with the finite element solver OpenGeoSys. The software employed for the computations is open source, accessible and offers a versatile solution to model thermomechanical failure of rocks. Within this framework, we have performed numerical simulations that highlight the localization of strains and stresses under triaxial compression. Predictions of the constitutive response, of the depth of the brittle‐ductile transition, and of the localization patterns are in agreement with laboratory and in situ observations. The results have important geophysical implications as they provide a constitutive basis that explains the mechanisms through which basalt can deform in a brittle fashion at temperatures above 600°C.
- 31 October 2020
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Solid Earth
- Vol. 125 (11)
Open AccessA Model of Failure and Localization of Basalt at Temperature and Pressure Conditions Spanning the Brittle‐Ductile Transition
Natural phenomena such as seismicity, volcanism, and fluid circulation in volcanic areas are influenced by the mechanical response of intact basalt. When subjected to a wide range of environmental loading conditions, basalt exhibits inelastic deformation characteristics ranging from brittle to ductile behavior. In this manuscript, we present a new constitutive model of basalt that spans the brittle‐ductile transition by covering a wide range of mean effective stress, temperature, and strain rate. The model has been implemented into the automatic constitutive model code generator MFront, which we have coupled with the finite element solver OpenGeoSys. The software employed for the computations is open source, accessible and offers a versatile solution to model thermomechanical failure of rocks. Within this framework, we have performed numerical simulations that highlight the localization of strains and stresses under triaxial compression. Predictions of the constitutive response, of the depth of the brittle‐ductile transition, and of the localization patterns are in agreement with laboratory and in situ observations. The results have important geophysical implications as they provide a constitutive basis that explains the mechanisms through which basalt can deform in a brittle fashion at temperatures above 600°C.