Paul William John Glover
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Paul William John Glover has a total of 84 co-authors. Here are the top co-authors by number of shared publications:
Piroska Lorinczi
School of Earth and Environment, University of Leeds, Leeds, UK
15 shared publicationsRichard Collier
7 shared publications- Bo Li
School of Earth Sciences and Resources, China University of Geosciences, Beijing 100083, China
4 shared publications - Piroska Lorinczi
School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK
4 shared publications - Piroska Lorinczi
School of Earth and Environment University of Leeds Leeds UK
4 shared publications - Wei Wei
School of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China
4 shared publications
Latest Publications
- Open Access
- 16 June 2026
- Published by IOP Publishing in Environmental Research Letters
- Vol. 21 (12) , 124011
Measurements of gas permeability and gas fraction in thawing permafrost: permafrost climate feedback implications
Climate-driven permafrost thaw releases greenhouse gases (CO 2 and CH 4 ). Fully frozen permafrost has extremely low gas permeability, acting as a seal that limits gas migration while low temperatures also inhibit gas generation. Permeability changes during thaw–refreeze cycles, however, remain very poorly understood because of the sparsity of experimental data. We report laboratory measurements of gas fraction and gas permeability during thawing of 16 synthetic permafrost samples with a range of initial ice fractions from 5.2% to 62%, for samples considered either fully frozen or fully thawed, as well as a subset of 11 samples with a range of initial ice fractions from 19.3% to 51.2% for which it was possible to make measurements as a function of temperature during thawing. The data show clearly that gas permeability increases during thawing by up to 2.5 orders of magnitude, depending on the initial ice fraction, with the main thawing occurring between −5 ± 0.5 °C and −1 ± 0.8 °C. The gas permeability uncertainty is in the range ±20% to ±30% for the samples that remained intact. Gas fraction showed similar variation to permeability increasing from 2.62% to 6.16% for fully frozen samples to between 3.16% and 12.51% for fully thawed samples, which is consistent with the ice–water density difference and initial ice fractions. The uncertainty in gas fraction measurements is in the range ±8% to ±12%. These findings confirm that thawing compromises the gas-sealing function of permafrost and provides data to improve large-scale permafrost models. Importantly, they also show that the increase in gas permeability only appears to be the result of increasing gas fraction, with no implied rearrangement of the gas fraction into preferred flow pathways.
- 16 June 2026
- Published by IOP Publishing in Environmental Research Letters
- Vol. 21 (12) , 124011
Open AccessMeasurements of gas permeability and gas fraction in thawing permafrost: permafrost climate feedback implications
Climate-driven permafrost thaw releases greenhouse gases (CO 2 and CH 4 ). Fully frozen permafrost has extremely low gas permeability, acting as a seal that limits gas migration while low temperatures also inhibit gas generation. Permeability changes during thaw–refreeze cycles, however, remain very poorly understood because of the sparsity of experimental data. We report laboratory measurements of gas fraction and gas permeability during thawing of 16 synthetic permafrost samples with a range of initial ice fractions from 5.2% to 62%, for samples considered either fully frozen or fully thawed, as well as a subset of 11 samples with a range of initial ice fractions from 19.3% to 51.2% for which it was possible to make measurements as a function of temperature during thawing. The data show clearly that gas permeability increases during thawing by up to 2.5 orders of magnitude, depending on the initial ice fraction, with the main thawing occurring between −5 ± 0.5 °C and −1 ± 0.8 °C. The gas permeability uncertainty is in the range ±20% to ±30% for the samples that remained intact. Gas fraction showed similar variation to permeability increasing from 2.62% to 6.16% for fully frozen samples to between 3.16% and 12.51% for fully thawed samples, which is consistent with the ice–water density difference and initial ice fractions. The uncertainty in gas fraction measurements is in the range ±8% to ±12%. These findings confirm that thawing compromises the gas-sealing function of permafrost and provides data to improve large-scale permafrost models. Importantly, they also show that the increase in gas permeability only appears to be the result of increasing gas fraction, with no implied rearrangement of the gas fraction into preferred flow pathways.
- Open Access
- 24 March 2026
- Published by American Geophysical Union (AGU) in Earth's Future
- Vol. 14 (3)
Measurement of Gas Fraction and Gas Permeability of Thawing Permafrost Caused by Climate Change
Thawing of permafrost due to climate change is known to release gases such as the climate drivers carbon dioxide and methane, as well as the carcinogen radon. Gas permeability is extremely low in fully frozen permafrost and can be considered both to function as a seal preventing subsurface gases being released, and to prevent the creation of new CO 2 and CH 4 . However, the permeability of permafrost as it thaws and refreezes is unknown. In this paper we present initial measurements of changes in gas fraction and gas permeability during the thawing of synthetic permafrost using a newly developed pycno‐permeameter. Initial results show that gas permeability increases by multiple orders of magnitude (from 4.94 mD to 112.54 mD and from 0.26 mD to 21.43 mD for our two samples), depending on the initial water saturation of the sample, with most permeability change occurring in the −5°C to −1°C range. Upon refreezing, the permeability drops again to approximately its previous low values providing no water is allowed to drain from the sample, but with a hysteresis. Measurements of gas fraction show a similar variation to thawing and refreezing but with a hysteresis opposite to that for permeability. These initial results indicate that the protective gas seal previously provided by permafrost will be lost as permafrost thaws. These data are also able to inform large scale permafrost modeling, as well as suggesting that thawing and refreezing operate differently at a microstructural level.
- 24 March 2026
- Published by American Geophysical Union (AGU) in Earth's Future
- Vol. 14 (3)
Open AccessMeasurement of Gas Fraction and Gas Permeability of Thawing Permafrost Caused by Climate Change
Thawing of permafrost due to climate change is known to release gases such as the climate drivers carbon dioxide and methane, as well as the carcinogen radon. Gas permeability is extremely low in fully frozen permafrost and can be considered both to function as a seal preventing subsurface gases being released, and to prevent the creation of new CO 2 and CH 4 . However, the permeability of permafrost as it thaws and refreezes is unknown. In this paper we present initial measurements of changes in gas fraction and gas permeability during the thawing of synthetic permafrost using a newly developed pycno‐permeameter. Initial results show that gas permeability increases by multiple orders of magnitude (from 4.94 mD to 112.54 mD and from 0.26 mD to 21.43 mD for our two samples), depending on the initial water saturation of the sample, with most permeability change occurring in the −5°C to −1°C range. Upon refreezing, the permeability drops again to approximately its previous low values providing no water is allowed to drain from the sample, but with a hysteresis. Measurements of gas fraction show a similar variation to thawing and refreezing but with a hysteresis opposite to that for permeability. These initial results indicate that the protective gas seal previously provided by permafrost will be lost as permafrost thaws. These data are also able to inform large scale permafrost modeling, as well as suggesting that thawing and refreezing operate differently at a microstructural level.
- Open Access
- 14 March 2026
- Published by Copernicus GmbH
Stress-controlled fracture closure and anisotropic flow in carbonate reservoirs: implications for CO₂ storage
Natural fractures exert a first-order control on permeability, sealing capacity, and stress sensitivity of carbonate reservoirs, yet quantitative links between measured fracture-surface roughness and evolving transport properties remain poorly constrained across scales. We present a workflow that combines high-resolution optical surface profilometry with numerical closure and flow modelling to evaluate fracture hydraulic behaviour under effective stress, with implications for CO₂ storage efficiency and containment in fractured carbonates. A 4 × 4 cm fractured carbonate sample is split along the fracture plane to expose complementary surfaces, which are imaged using 3D optical microscopy in the metrology laboratory. Surface height grids are processed in Vision64 and exported for analysis. We computed roughness statistics and constructed aperture fields by digitally pairing the two surfaces, thereby enabling progressive mechanical closure to be simulated as either a prescribed displacement (closure) or field-stress-controlled loading.Using closure-dependent aperture maps, we quantified transport anisotropy by solving pressure-driven flow through the fracture for orthogonal directions. Conductivity/permeability proxies are calculated using both cubic-law scaling and a spatially variable conductivity formulation (k ∝ b³) solved on the aperture grid. In parallel, capillary entry pressure is estimated from aperture distributions to evaluate stress-dependent sealing. Results show a nonlinear reduction in connected aperture with increasing closure, producing rapid declines in fracture conductivity and increases in capillary entry pressures as contact patches expand and percolating pathways collapse. Directional differences in flow and sealing metrics reveal pronounced anisotropy inherited from the surface topography, with dominant flow aligned with the most persistent connected channels.Finally, stress-path sweeps (injection/depletion and shear ramp scenarios) demonstrate how effective normal stress and shear-related dilation can produce contrasting permeability–capillary responses, highlighting the potential for hysteresis and path dependence during CO₂ injection and pressure cycling. This integrated approach provides a quantitative bridge between laboratory-scale roughness measurements and stress-sensitive fracture transport, supporting improved parameterisation of fractured carbonate reservoirs in CO₂ storage models and risk assessment for leakage versus immobilisation.Keywords: capillary entry pressure, fracture roughness, CO₂ storage integrity, anisotropy.
- 14 March 2026
- Published by Copernicus GmbH
Open AccessStress-controlled fracture closure and anisotropic flow in carbonate reservoirs: implications for CO₂ storage
Natural fractures exert a first-order control on permeability, sealing capacity, and stress sensitivity of carbonate reservoirs, yet quantitative links between measured fracture-surface roughness and evolving transport properties remain poorly constrained across scales. We present a workflow that combines high-resolution optical surface profilometry with numerical closure and flow modelling to evaluate fracture hydraulic behaviour under effective stress, with implications for CO₂ storage efficiency and containment in fractured carbonates. A 4 × 4 cm fractured carbonate sample is split along the fracture plane to expose complementary surfaces, which are imaged using 3D optical microscopy in the metrology laboratory. Surface height grids are processed in Vision64 and exported for analysis. We computed roughness statistics and constructed aperture fields by digitally pairing the two surfaces, thereby enabling progressive mechanical closure to be simulated as either a prescribed displacement (closure) or field-stress-controlled loading.Using closure-dependent aperture maps, we quantified transport anisotropy by solving pressure-driven flow through the fracture for orthogonal directions. Conductivity/permeability proxies are calculated using both cubic-law scaling and a spatially variable conductivity formulation (k ∝ b³) solved on the aperture grid. In parallel, capillary entry pressure is estimated from aperture distributions to evaluate stress-dependent sealing. Results show a nonlinear reduction in connected aperture with increasing closure, producing rapid declines in fracture conductivity and increases in capillary entry pressures as contact patches expand and percolating pathways collapse. Directional differences in flow and sealing metrics reveal pronounced anisotropy inherited from the surface topography, with dominant flow aligned with the most persistent connected channels.Finally, stress-path sweeps (injection/depletion and shear ramp scenarios) demonstrate how effective normal stress and shear-related dilation can produce contrasting permeability–capillary responses, highlighting the potential for hysteresis and path dependence during CO₂ injection and pressure cycling. This integrated approach provides a quantitative bridge between laboratory-scale roughness measurements and stress-sensitive fracture transport, supporting improved parameterisation of fractured carbonate reservoirs in CO₂ storage models and risk assessment for leakage versus immobilisation.Keywords: capillary entry pressure, fracture roughness, CO₂ storage integrity, anisotropy.
- Open Access
- 3 December 2025
- Published by Copernicus GmbH in Advances in Geosciences
- Vol. 67, 79-89
Quantifying carbonate microstructure using classical segmentation pipelines for CCS and radioactive waste applications
Digital-rock analysis can now simulate pore-scale flow and geomechanics with high fidelity, yet routine application is still limited by the cost of converting images into pixel-accurate pore masks. Some porosity measurements measure total porosity, but flow requires connected porosity. The need to distinguish between isolated and connected pores is clearly important. The question is why it is difficult to identify connected and unconnected pores. To tackle this, we present a fully labelled 2-D scanning-electron-microscope (SEM) image dataset of outcrop carbonates designed to separate isolated intragranular pores from the connected fracture–pore network. This distinction controls seal performance in carbon-capture and storage (CCS) and radioactive-waste repositories. Each of the 29 056 × 22 952 px images were partitioned into 100 tiles (2048 × 2048 px), annotated by polygon tracing. We then employ and benchmark eight unsupervised computer-vision algorithms: Morphological Gradient, Distance Transform, Local Contrast, Watershed, Global Threshold, Gabor Texture, Refined Morphology, and Edge-based methods. We contribute (i) an open carbonate SEM dataset with labels separating connected and isolated pores, (ii) an efficient polygon-based labelling workflow, and (iii) a quantitative comparison of eight classical pipelines plus a Hybrid voting ensemble. These resources shorten the path from raw images to pore-network predictions, and provide a foundation for future learning-based methods.
- 3 December 2025
- Published by Copernicus GmbH in Advances in Geosciences
- Vol. 67, 79-89
Open AccessQuantifying carbonate microstructure using classical segmentation pipelines for CCS and radioactive waste applications
Digital-rock analysis can now simulate pore-scale flow and geomechanics with high fidelity, yet routine application is still limited by the cost of converting images into pixel-accurate pore masks. Some porosity measurements measure total porosity, but flow requires connected porosity. The need to distinguish between isolated and connected pores is clearly important. The question is why it is difficult to identify connected and unconnected pores. To tackle this, we present a fully labelled 2-D scanning-electron-microscope (SEM) image dataset of outcrop carbonates designed to separate isolated intragranular pores from the connected fracture–pore network. This distinction controls seal performance in carbon-capture and storage (CCS) and radioactive-waste repositories. Each of the 29 056 × 22 952 px images were partitioned into 100 tiles (2048 × 2048 px), annotated by polygon tracing. We then employ and benchmark eight unsupervised computer-vision algorithms: Morphological Gradient, Distance Transform, Local Contrast, Watershed, Global Threshold, Gabor Texture, Refined Morphology, and Edge-based methods. We contribute (i) an open carbonate SEM dataset with labels separating connected and isolated pores, (ii) an efficient polygon-based labelling workflow, and (iii) a quantitative comparison of eight classical pipelines plus a Hybrid voting ensemble. These resources shorten the path from raw images to pore-network predictions, and provide a foundation for future learning-based methods.
- Open Access
- 19 November 2025
- Published by American Geophysical Union (AGU) in Earth and Space Science
- Vol. 12 (11)
Measuring the Fractal Properties of Reservoirs for Use in Modeling CCUS Potential
The injection of CO 2 underground into reservoirs for carbon capture and underground storage (CCUS) is highly sensitive to heterogeneity and anisotropy. Although conventional geological modeling cannot take explicit account of heterogeneity or anisotropy or operate at a resolution that encompasses the small scales at which fluid flow is controlled, advanced fractal reservoir models (AFRMs) can be used. These AFRMs require fractal dimensions and anisotropy ratios for the target reservoir, and these values are unavailable. This paper describes the development, validation, and application of a software tool for measuring reservoir fractal dimensions. The code has been validated extensively using SynFrac data, recognizing four potential sources of systematic error, all of which can be corrected for. The resulting code has been used to measure the fractal dimension of a seismic data cube taken from the Chandon reservoir. The analysis reveals that the reservoir is multifractal with high heterogeneity (fractal dimension) at small scales and lower but still significant heterogeneity at larger scales. The fractal dimension can be calculated as a function of depth, providing a new type of log data that is not specific to a given well but rather specific to an area of seismic data.
- 19 November 2025
- Published by American Geophysical Union (AGU) in Earth and Space Science
- Vol. 12 (11)
Open AccessMeasuring the Fractal Properties of Reservoirs for Use in Modeling CCUS Potential
The injection of CO 2 underground into reservoirs for carbon capture and underground storage (CCUS) is highly sensitive to heterogeneity and anisotropy. Although conventional geological modeling cannot take explicit account of heterogeneity or anisotropy or operate at a resolution that encompasses the small scales at which fluid flow is controlled, advanced fractal reservoir models (AFRMs) can be used. These AFRMs require fractal dimensions and anisotropy ratios for the target reservoir, and these values are unavailable. This paper describes the development, validation, and application of a software tool for measuring reservoir fractal dimensions. The code has been validated extensively using SynFrac data, recognizing four potential sources of systematic error, all of which can be corrected for. The resulting code has been used to measure the fractal dimension of a seismic data cube taken from the Chandon reservoir. The analysis reveals that the reservoir is multifractal with high heterogeneity (fractal dimension) at small scales and lower but still significant heterogeneity at larger scales. The fractal dimension can be calculated as a function of depth, providing a new type of log data that is not specific to a given well but rather specific to an area of seismic data.
- Open Access
- 17 November 2025
- Published by California Digital Library (CDL) in EarthArXiv
Comparative Evaluation of Threshold Pressure Measurement Techniques in Faulted and Shale Formations
Reliable estimation of capillary threshold pressure is essential for evaluating the sealing capacity of subsurface flow barriers, which has important applications in fluid storage. This study compares the results of capillary threshold pressure measurements obtained from four experimental techniques: (i) gas breakthrough, (ii) mercury injection capillary pressure (MICP), (iii) Porosimetry under Confining Stress (PUCS), and (iv) Field’s metal injection with SEM imaging, applied to faulted sandstone from the Vale of Eden and mudstone from the Sidmouth Formation of the Mercia Mudstone Group (MMG). Gas breakthrough tests demonstrated strong internal consistency and repeatability; however, the technique is inherently slow and has very low throughput, often requiring several months to complete a single test on a typical mudstone sample. The MICP method exhibited considerable variability among the analysed samples and was unable to access the matrix porosity of mudstone due to compressibility and pore structure collapse. Mercury instead, preferentially occupied fractures and micro-cracks, as confirmed by SEM imaging of Field’s metal injection, an artefact that is often misinterpreted as mercury filling pore volume. Field’s metal injection yielded higher threshold pressures and provided valuable pore-scale insights from SEM imaging, but the method lacks standardized conversion parameters, making comparison with other methods difficult. These findings underscore the limitations of conventional methods in characterizing tight formations and highlight the need for caution when interpreting MICP results, particularly for shale and other low-permeability rocks. Furthermore, they emphasize the importance of developing a robust experimental framework that addresses these shortcomings, especially for tight gas and shale formations where accurate measurement of flow properties is critical for subsurface storage applications, including CO₂ sequestration and the disposal of nuclear waste in deep geological repositories.
- 17 November 2025
- Published by California Digital Library (CDL) in EarthArXiv
Open AccessComparative Evaluation of Threshold Pressure Measurement Techniques in Faulted and Shale Formations
Reliable estimation of capillary threshold pressure is essential for evaluating the sealing capacity of subsurface flow barriers, which has important applications in fluid storage. This study compares the results of capillary threshold pressure measurements obtained from four experimental techniques: (i) gas breakthrough, (ii) mercury injection capillary pressure (MICP), (iii) Porosimetry under Confining Stress (PUCS), and (iv) Field’s metal injection with SEM imaging, applied to faulted sandstone from the Vale of Eden and mudstone from the Sidmouth Formation of the Mercia Mudstone Group (MMG). Gas breakthrough tests demonstrated strong internal consistency and repeatability; however, the technique is inherently slow and has very low throughput, often requiring several months to complete a single test on a typical mudstone sample. The MICP method exhibited considerable variability among the analysed samples and was unable to access the matrix porosity of mudstone due to compressibility and pore structure collapse. Mercury instead, preferentially occupied fractures and micro-cracks, as confirmed by SEM imaging of Field’s metal injection, an artefact that is often misinterpreted as mercury filling pore volume. Field’s metal injection yielded higher threshold pressures and provided valuable pore-scale insights from SEM imaging, but the method lacks standardized conversion parameters, making comparison with other methods difficult. These findings underscore the limitations of conventional methods in characterizing tight formations and highlight the need for caution when interpreting MICP results, particularly for shale and other low-permeability rocks. Furthermore, they emphasize the importance of developing a robust experimental framework that addresses these shortcomings, especially for tight gas and shale formations where accurate measurement of flow properties is critical for subsurface storage applications, including CO₂ sequestration and the disposal of nuclear waste in deep geological repositories.
- Open Access
Comparative Analysis of CO2 Sequestration Potential in Shale Reservoirs: Insights from the Longmaxi and Qiongzhusi Formations
Shale reservoirs offer significant potential for CO2 geological sequestration due to their extensive nanopore networks and heterogeneous pore systems. This study comparatively assessed the CO2 storage potential of the Lower Silurian Longmaxi and Lower Cambrian Qiongzhusi shales through an integrated approach involving organic geochemical analysis, mineralogical characterization through X-ray diffraction (XRD), mercury intrusion capillary pressure (MICP), low-pressure nitrogen and carbon dioxide physisorption, field-emission scanning electron microscopy (FE-SEM), stochastic 3D microstructure reconstruction, multifractal analysis, and three-dimensional succolarity computation. The results demonstrate that mineral assemblages and diagenetic history govern pore preservation: Longmaxi shales, with moderate maturity and shallower burial, retain abundant organic-hosted mesopores, whereas overmature and deeply buried Qiongzhusi shales are strongly compacted and mineralized, reducing pore availability. Multifractal spectra and 3D reconstructions reveal that Longmaxi develops broader singularity spectra and higher succolarity values, reflecting more isotropic meso-/macropore connectivity at the SEM scale, while Qiongzhusi exhibits narrower spectra and lower succolarity, indicating micropore-dominated and anisotropic networks. Longmaxi has nanometer-scale throats (D50 ≈ 10–25 nm) with high CO2 breakthrough pressures (P10 ≈ 0.57 MPa) and ultra-low RGPZ permeability (mean ≈ 1.5 × 10−2 nD); Qiongzhusi has micrometer-scale throats (D50 ≈ 1–3 μm), very low breakthrough pressures (P10 ≈ 0.018 MPa), and much higher permeability (mean ≈ 4.63 × 103 nD). Storage partitioning further differs: Longmaxi’s median total capacity is ≈15.6 kg m−3 with adsorption ≈ 93%, whereas Qiongzhusi’s median is ≈12.8 kg m−3 with adsorption ≈ 70%. We infer Longmaxi favors secure adsorption-dominated retention but suffers from injectivity limits; Qiongzhusi favors injectivity but requires reliable seals.
Open AccessComparative Analysis of CO2 Sequestration Potential in Shale Reservoirs: Insights from the Longmaxi and Qiongzhusi Formations
Shale reservoirs offer significant potential for CO2 geological sequestration due to their extensive nanopore networks and heterogeneous pore systems. This study comparatively assessed the CO2 storage potential of the Lower Silurian Longmaxi and Lower Cambrian Qiongzhusi shales through an integrated approach involving organic geochemical analysis, mineralogical characterization through X-ray diffraction (XRD), mercury intrusion capillary pressure (MICP), low-pressure nitrogen and carbon dioxide physisorption, field-emission scanning electron microscopy (FE-SEM), stochastic 3D microstructure reconstruction, multifractal analysis, and three-dimensional succolarity computation. The results demonstrate that mineral assemblages and diagenetic history govern pore preservation: Longmaxi shales, with moderate maturity and shallower burial, retain abundant organic-hosted mesopores, whereas overmature and deeply buried Qiongzhusi shales are strongly compacted and mineralized, reducing pore availability. Multifractal spectra and 3D reconstructions reveal that Longmaxi develops broader singularity spectra and higher succolarity values, reflecting more isotropic meso-/macropore connectivity at the SEM scale, while Qiongzhusi exhibits narrower spectra and lower succolarity, indicating micropore-dominated and anisotropic networks. Longmaxi has nanometer-scale throats (D50 ≈ 10–25 nm) with high CO2 breakthrough pressures (P10 ≈ 0.57 MPa) and ultra-low RGPZ permeability (mean ≈ 1.5 × 10−2 nD); Qiongzhusi has micrometer-scale throats (D50 ≈ 1–3 μm), very low breakthrough pressures (P10 ≈ 0.018 MPa), and much higher permeability (mean ≈ 4.63 × 103 nD). Storage partitioning further differs: Longmaxi’s median total capacity is ≈15.6 kg m−3 with adsorption ≈ 93%, whereas Qiongzhusi’s median is ≈12.8 kg m−3 with adsorption ≈ 70%. We infer Longmaxi favors secure adsorption-dominated retention but suffers from injectivity limits; Qiongzhusi favors injectivity but requires reliable seals.
- Open Access
- 16 September 2025
- Published by Springer Nature in Transport in Porous Media
- Vol. 152 (11) , 1-31
Connectedness Theory of Relative Permeability
The Connectedness Theory is a mathematical approach to understanding the interactions between any number of phases in a complex medium that have different physical properties. It arose from the development of an Archie’s Law for n -phases when it is applied to fluid permeability. We have shown that Connectedness Theory allows for relative permeabilities to be expressed as ratios of connectednesses. This approach demonstrates why the sum of the non-wetting phase and wetting phase relative permeabilities is always less than unity. In its most general form the Connectedness Theory for two-phase relative permeabilities has eight independent parameters and allows both the fractions of immobile and mobile wetting phase and non-wetting phase, and the phase exponents to vary as a function of wetting phase and non-wetting phase saturation. However, if we make the common assumption that the irreducible wetting phase saturation and residual non-wetting phase saturation are constant and that the phase exponents are also constant, we can use the Connectedness Theory to prove the Brooks and Corey approach to relative permeability modelling and to relate its lambda parameters to phase exponents. In doing so, we also show that the wetting phase relative permeability endpoint is not an independent parameter but arises from variability of phase exponents and hence connectednesses as a function of fluid saturations, and that the two Brooks and Corey coefficients are interdependent. Finally, the Connectedness Theory also predicts that in principle one relative permeability curve can be calculated from the other. Since the theory upon which it is based is valid for any number of different phases, the two-phase scenario followed by most of this work is easily extended to three-phase relative permeabilities.
- 16 September 2025
- Published by Springer Nature in Transport in Porous Media
- Vol. 152 (11) , 1-31
Open AccessConnectedness Theory of Relative Permeability
The Connectedness Theory is a mathematical approach to understanding the interactions between any number of phases in a complex medium that have different physical properties. It arose from the development of an Archie’s Law for n -phases when it is applied to fluid permeability. We have shown that Connectedness Theory allows for relative permeabilities to be expressed as ratios of connectednesses. This approach demonstrates why the sum of the non-wetting phase and wetting phase relative permeabilities is always less than unity. In its most general form the Connectedness Theory for two-phase relative permeabilities has eight independent parameters and allows both the fractions of immobile and mobile wetting phase and non-wetting phase, and the phase exponents to vary as a function of wetting phase and non-wetting phase saturation. However, if we make the common assumption that the irreducible wetting phase saturation and residual non-wetting phase saturation are constant and that the phase exponents are also constant, we can use the Connectedness Theory to prove the Brooks and Corey approach to relative permeability modelling and to relate its lambda parameters to phase exponents. In doing so, we also show that the wetting phase relative permeability endpoint is not an independent parameter but arises from variability of phase exponents and hence connectednesses as a function of fluid saturations, and that the two Brooks and Corey coefficients are interdependent. Finally, the Connectedness Theory also predicts that in principle one relative permeability curve can be calculated from the other. Since the theory upon which it is based is valid for any number of different phases, the two-phase scenario followed by most of this work is easily extended to three-phase relative permeabilities.
- Open Access
- 23 August 2025
- Published by Wiley
Measuring the Fractal Properties of Reservoirs for use in Modelling CCUS Potential
The injection of CO2 underground into reservoirs for carbon capture and underground storage (CCUS) is highly sensitive to heterogeneity and anisotropy. Although conventional geological modelling cannot take explicit account of heterogeneity or anisotropy or operate at a resolution that encompasses the small scales at which fluid flow is controlled, advanced fractal reservoir models (AFRMs) can be used. These AFRMs require fractal dimensions and anisotropy ratios for the target reservoir, and these values are unavailable. This paper describes the development, validation, and application of a software tool for measuring reservoir fractal dimensions. The code has been validated extensively using SynFrac data, recognising four potential sources of systematic error, all of which can be corrected for. The resulting code has been used to measure the fractal dimension of a seismic data cube taken from the Chandon reservoir. The analysis reveals that the reservoir is multifractal with high heterogeneity (fractal dimension) at small scales and lower but still significant heterogeneity at larger scales. The fractal dimension can be calculated as a function of depth, providing a new type of log data that is not specific to a given well but rather specific to an area of seismic data.
- 23 August 2025
- Published by Wiley
Open AccessMeasuring the Fractal Properties of Reservoirs for use in Modelling CCUS Potential
The injection of CO2 underground into reservoirs for carbon capture and underground storage (CCUS) is highly sensitive to heterogeneity and anisotropy. Although conventional geological modelling cannot take explicit account of heterogeneity or anisotropy or operate at a resolution that encompasses the small scales at which fluid flow is controlled, advanced fractal reservoir models (AFRMs) can be used. These AFRMs require fractal dimensions and anisotropy ratios for the target reservoir, and these values are unavailable. This paper describes the development, validation, and application of a software tool for measuring reservoir fractal dimensions. The code has been validated extensively using SynFrac data, recognising four potential sources of systematic error, all of which can be corrected for. The resulting code has been used to measure the fractal dimension of a seismic data cube taken from the Chandon reservoir. The analysis reveals that the reservoir is multifractal with high heterogeneity (fractal dimension) at small scales and lower but still significant heterogeneity at larger scales. The fractal dimension can be calculated as a function of depth, providing a new type of log data that is not specific to a given well but rather specific to an area of seismic data.
- 27 May 2025
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Solid Earth
- Vol. 130 (6)
A Fractal Interpretation of Archie‐Like Equation for Partially Saturated Porous Media
The complex mechanism by which the conducting phase in pore space influences the electrical conductivity of rocks has been a critical focus in geophysical exploration. In this study, the Pore‐Solid Fractal model is used to accurately describe the fluid distribution within pore space, and the resistivity index follows a form analogous to Archie equation, being expressed in terms of the tortuosity fractal dimension, the pore fractal dimension, and saturation. The physically based fractal parameters then determine the saturation exponent. We find a reasonable prediction for experimental data with a feasible parameter linking the cementation exponent and the saturation exponent. Furthermore, the interrelationship between cementation exponent and saturation exponent is also analyzed under various conditions. An alternative expression for the exponents is introduced, exhibiting good agreement with experimental measurements. Additionally, a bounds model is presented in order to address the uncertainty of tortuosity due to uncertainties of the tortuosity fractal dimension during the saturating process. The boundary is a useful constraint on the range of the resistivity index, particularly in cases where structural parameters are insufficiently constrained.
- 27 May 2025
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research: Solid Earth
- Vol. 130 (6)
A Fractal Interpretation of Archie‐Like Equation for Partially Saturated Porous Media
The complex mechanism by which the conducting phase in pore space influences the electrical conductivity of rocks has been a critical focus in geophysical exploration. In this study, the Pore‐Solid Fractal model is used to accurately describe the fluid distribution within pore space, and the resistivity index follows a form analogous to Archie equation, being expressed in terms of the tortuosity fractal dimension, the pore fractal dimension, and saturation. The physically based fractal parameters then determine the saturation exponent. We find a reasonable prediction for experimental data with a feasible parameter linking the cementation exponent and the saturation exponent. Furthermore, the interrelationship between cementation exponent and saturation exponent is also analyzed under various conditions. An alternative expression for the exponents is introduced, exhibiting good agreement with experimental measurements. Additionally, a bounds model is presented in order to address the uncertainty of tortuosity due to uncertainties of the tortuosity fractal dimension during the saturating process. The boundary is a useful constraint on the range of the resistivity index, particularly in cases where structural parameters are insufficiently constrained.