Staff profile

Summary

Simon teaches hydraulics, hydrology and environmental engineering.

Simon's research focuses on the development of mathematical models to describe the movement of fluids and contaminants in porous media. He works on a range of different applications including groundwater recharge, carbon capture and storage, nutrient transport and rainfall runoff modelling.

www.linkedin.com/in/samathias

Authored book

• Hydraulics, Hydrology and Environmental Engineering
  
  Mathias, S. A. (2023). Hydraulics, Hydrology and Environmental Engineering. Springer International Publishing. https://doi.org/10.1007/978-3-031-41973-7

Conference Paper

• Mathematical modelling of pressure induced freezing point depression within soils exhibiting strong capillary pressure effect
  
  Lgotina, E., Mathias, S., Lloret-Cabot, M., & Ireson, A. (2024). Mathematical modelling of pressure induced freezing point depression within soils exhibiting strong capillary pressure effect. In W. M. Coombs (Ed.), UKACM Proceedings 2024 (pp. 52-55). UK Association for Computational Mechanics. https://doi.org/10.62512/conf.ukacm2024.079

Conference Proceeding

• UKACM Proceedings 2024
  
  Coombs, W. M. (Ed.). (2024). UKACM Proceedings 2024. UK Association for Computational Mechanics and Durham University. https://doi.org/10.62512/conf.ukacm2024

Edited book

• Geological storage of carbon dioxide (CO2) - Geoscience, technologies, environmental aspects and legal frameworks
  
  Gluyas, J., & Mathias, S. (Eds.). (2013). Geological storage of carbon dioxide (CO2) - Geoscience, technologies, environmental aspects and legal frameworks. Woodhead Publishing.
• Groundwater Modelling in Arid and Semi-arid Areas
  
  Wheater, H., Mathias, S., & Li, X. (Eds.). (2010). Groundwater Modelling in Arid and Semi-arid Areas. Cambridge University Press.

Journal Article

• Rainfall–runoff modelling in a tropical climate (Citarum basin, West Java, Indonesia): model and climate data intercomparison
  
  Vesuviano, G., Mathias, S. A., Rahayu, R., & Reaney, S. M. (2025). Rainfall–runoff modelling in a tropical climate (Citarum basin, West Java, Indonesia): model and climate data intercomparison. Hydrology Research. Advance online publication. https://doi.org/10.2166/nh.2025.021
• Two Film Approach to Continuum Scale Mixing and Dispersion with Equilibrium Bimolecular Reaction
  
  Mathias, S. A., Bolster, D., & Veremieiev, S. (2024). Two Film Approach to Continuum Scale Mixing and Dispersion with Equilibrium Bimolecular Reaction. Transport in Porous Media, 151(8), 1709-1727. https://doi.org/10.1007/s11242-024-02091-y
• Banding in the Margins of Basaltic Dykes Indicates Pulsatory Propagation During Emplacement
  
  Allgood, C., Llewellin, E. W., Humphreys, M. C. S., Mathias, S. A., Brown, R. J., & Vye‐Brown, C. (2024). Banding in the Margins of Basaltic Dykes Indicates Pulsatory Propagation During Emplacement. Journal of Geophysical Research: Solid Earth, 129(4), Article e2023JB028007. https://doi.org/10.1029/2023jb028007
• Revisiting Salvucci’s Semi-analytical Solution for Bare Soil Evaporation with New Consideration of Vapour Diffusion and Film Flow
  
  Mathias, S. A., Sander, G. C., Leung, J., & Newall, S. R. (2023). Revisiting Salvucci’s Semi-analytical Solution for Bare Soil Evaporation with New Consideration of Vapour Diffusion and Film Flow. Transport in Porous Media, 147(2), 463-493. https://doi.org/10.1007/s11242-023-01917-5
• Impact of land cover, rainfall and topography on flood risk in West Java
  
  Rahayu, R., Mathias, S. A., Reaney, S., Vesuviano, G., Suwerman, R., & Ramdhan, A. M. (2023). Impact of land cover, rainfall and topography on flood risk in West Java. Natural Hazards, 116(2), 1735-1758. https://doi.org/10.1007/s11069-022-05737-6
• A simple, efficient, mass-conservative approach to solving Richards' equation (openRE, v1.0)
  
  Ireson, A. M., Spiteri, R. J., Clark, M. P., & Mathias, S. A. (2023). A simple, efficient, mass-conservative approach to solving Richards’ equation (openRE, v1.0). Geoscientific Model Development, 16(2), 659-677. https://doi.org/10.5194/gmd-16-659-2023
• Numerical investigation on origin and evolution of polygonal cracks on rock surfaces
  
  Chen, T., Foulger, G. R., Tang, C., Mathias, S. A., & Gong, B. (2022). Numerical investigation on origin and evolution of polygonal cracks on rock surfaces. Engineering Geology, 311, Article 106913. https://doi.org/10.1016/j.enggeo.2022.106913
• Effect of H2S content on relative permeability and capillary pressure characteristics of acid gas/brine/rock systems: A review
  
  Zhang, X., Li, Q., Mathias, S., Zheng, G., & Tan, Y. (2022). Effect of H2S content on relative permeability and capillary pressure characteristics of acid gas/brine/rock systems: A review. Journal of Rock Mechanics and Geotechnical Engineering, 14(6), 2003-2033. https://doi.org/10.1016/j.jrmge.2022.03.014
• Transmission loss estimation for ephemeral sand rivers in Southern Africa
  
  Mathias, S. A., Reaney, S. M., & Kenabatho, P. K. (2021). Transmission loss estimation for ephemeral sand rivers in Southern Africa. Journal of Hydrology, 600, Article 126487. https://doi.org/10.1016/j.jhydrol.2021.126487
• A Model for the Soil Freezing Characteristic Curve That Represents the Dominant Role of Salt Exclusion
  
  Amankwah, S., Ireson, A., Maulé, C., Brannen, R., & Mathias, S. (2021). A Model for the Soil Freezing Characteristic Curve That Represents the Dominant Role of Salt Exclusion. Water Resources Research, 57(8), Article e2021WR030070. https://doi.org/10.1029/2021wr030070
• Pseudospectral methods provide fast and accurate solutions for the horizontal infiltration equation
  
  Mathias, S. A., & Sander, G. C. (2021). Pseudospectral methods provide fast and accurate solutions for the horizontal infiltration equation. Journal of Hydrology, 598, Article 126407. https://doi.org/10.1016/j.jhydrol.2021.126407
• Strain characteristics and permeability evolution of faults under stress disturbance monitoring by fibre bragg grating sensing and pressure pulses
  
  Xu, L., Li, Q., Mathias, S. A., Tan, Y., Yang, D., & Fan, C. (2021). Strain characteristics and permeability evolution of faults under stress disturbance monitoring by fibre bragg grating sensing and pressure pulses. Geomechanics and Geophysics for Geo-Energy and Geo-Resources, 7(4), Article 93. https://doi.org/10.1007/s40948-021-00289-8
• An experimentally validated numerical model for bubble growth in magma
  
  Coumans, J., Llewellin, E., Wadsworth, F., Humphreys, M., Mathias, S., Yelverton, B., & Gardner, J. (2020). An experimentally validated numerical model for bubble growth in magma. Journal of Volcanology and Geothermal Research, 402, Article 107002. https://doi.org/10.1016/j.jvolgeores.2020.107002
• An experimentally-validated numerical model of diffusion and speciation of water in rhyolitic silicate melt
  
  Coumans, J. P., Llewellin, E. W., Humphreys, M. C., Nowak, M., Brooker, R. A., Mathias, S. A., & McIntosh, I. M. (2020). An experimentally-validated numerical model of diffusion and speciation of water in rhyolitic silicate melt. Geochimica Et Cosmochimica Acta, 276, 219-238. https://doi.org/10.1016/j.gca.2020.02.026
• Gas diffusion in coal powders is a multi-rate process
  
  Mathias, S., Dentz, M., & Liu, Q. (2020). Gas diffusion in coal powders is a multi-rate process. Transport in Porous Media, 131, 1037-1051. https://doi.org/10.1007/s11242-019-01376-x
• Storage Coefficients and Permeability Functions for Coal-Bed Methane Production Under Uniaxial Strain Conditions
  
  Mathias, S. A., Nielsen, S., & Ward, R. L. (2019). Storage Coefficients and Permeability Functions for Coal-Bed Methane Production Under Uniaxial Strain Conditions. Transport in Porous Media, 130(2), 627-636. https://doi.org/10.1007/s11242-019-01331-w
• Closed-form equation for subsidence due to fluid production from a cylindrical confined aquifer
  
  Jayeoba, A., Mathias, S. A., Nielsen, S., Vilarrasa, V., & Bjørnarå, T. I. (2019). Closed-form equation for subsidence due to fluid production from a cylindrical confined aquifer. Journal of Hydrology, 573, 964-969. https://doi.org/10.1016/j.jhydrol.2019.03.041
• Capillary processes increase salt precipitation during CO2 injection in saline formations
  
  Kelly, H. L., & Mathias, S. A. (2018). Capillary processes increase salt precipitation during CO2 injection in saline formations. Journal of Fluid Mechanics, 852, 398-421. https://doi.org/10.1017/jfm.2018.540
• Masuda's sandstone core hydrate dissociation experiment revisited
  
  Hardwick, J., & Mathias, S. (2018). Masuda’s sandstone core hydrate dissociation experiment revisited. Chemical Engineering Science, 175, 98-109. https://doi.org/10.1016/j.ces.2017.09.003
• Analytical solution for clay plug swelling experiments
  
  Mathias, S., Greenwell, H., Withers, C., Erdogan, A., McElwaine, J., & MacMinn, C. (2017). Analytical solution for clay plug swelling experiments. Applied Clay Science, 149, 75-78. https://doi.org/10.1016/j.clay.2017.07.021
• Gas venting that bypasses the feather edge of marine hydrate, offshore Mauritania
  
  Li, A., Davies, R. J., Mathias, S., Yang, J., Hobbs, R., & Wilson, M. (2017). Gas venting that bypasses the feather edge of marine hydrate, offshore Mauritania. Marine and Petroleum Geology, 88, 402-409. https://doi.org/10.1016/j.marpetgeo.2017.08.026
• Soil moisture data as a constraint for groundwater recharge estimation
  
  Mathias, S. A., Sorensen, J. P., & Butler, A. P. (2017). Soil moisture data as a constraint for groundwater recharge estimation. Journal of Hydrology, 552, 258-266. https://doi.org/10.1016/j.jhydrol.2017.06.040
• Methane hydrate recycling offshore of Mauritania probably after the last glacial maximum
  
  Li, A., Davies, R. J., & Mathias, S. (2017). Methane hydrate recycling offshore of Mauritania probably after the last glacial maximum. Marine and Petroleum Geology, 84, 323-331. https://doi.org/10.1016/j.marpetgeo.2017.04.007
• A study of non-linearity in rainfall-runoff response using 120 UK catchments
  
  Mathias, S., McIntyre, N., & Oughton, R. (2016). A study of non-linearity in rainfall-runoff response using 120 UK catchments. Journal of Hydrology, 540, 423-436. https://doi.org/10.1016/j.jhydrol.2016.06.039
• Approximate solutions for Forchheimer flow during water injection and water production in an unconfined aquifer
  
  Mathias, S., & Moutsopoulos, K. (2016). Approximate solutions for Forchheimer flow during water injection and water production in an unconfined aquifer. Journal of Hydrology, 538, 13-21. https://doi.org/10.1016/j.jhydrol.2016.03.048
• Simulation of three-component two-phase flow in porous media using method of lines
  
  Goudarzi, S., Mathias, S., & Gluyas, J. (2016). Simulation of three-component two-phase flow in porous media using method of lines. Transport in Porous Media, 112(1), 1-19. https://doi.org/10.1007/s11242-016-0639-5
• Comparison of relative permeability–saturation–capillary pressure models for simulation of reservoir CO2 injection
  
  Oostrom, M., White, M., Porse, S., Krevor, S., & Mathias, S. (2016). Comparison of relative permeability–saturation–capillary pressure models for simulation of reservoir CO2 injection. International Journal of Greenhouse Gas Control, 45, 70-85. https://doi.org/10.1016/j.ijggc.2015.12.013
• Impact of maximum allowable cost on CO2 storage capacity in saline formations
  
  Mathias, S., Gluyas, J., Goldthorpe, W., & Mackay, E. (2015). Impact of maximum allowable cost on CO2 storage capacity in saline formations. Environmental Science and Technology, 49(22), 13510-13518. https://doi.org/10.1021/acs.est.5b02836
• An irregular feather-edge and potential outcrop of marine gas hydrate along the Mauritanian margin
  
  Davies, R. J., Yang, J., Mathias, S., Hobbs, R., & Li, A. (2015). An irregular feather-edge and potential outcrop of marine gas hydrate along the Mauritanian margin. Earth and Planetary Science Letters, 423, 202-209. https://doi.org/10.1016/j.epsl.2015.04.013
• Numerical simulation of Forchheimer flow to a partially penetrating well with a mixed-type boundary condition
  
  Mathias, S., & Wen, Z. (2015). Numerical simulation of Forchheimer flow to a partially penetrating well with a mixed-type boundary condition. Journal of Hydrology, 524, 53-61. https://doi.org/10.1016/j.jhydrol.2015.02.015
• The late field life of the East Midlands Petroleum Province; a new geothermal prospect?
  
  Hirst, C., Gluyas, J., & Mathias, S. (2015). The late field life of the East Midlands Petroleum Province; a new geothermal prospect?. Quarterly Journal of Engineering Geology and Hydrogeology, 48(2), 104-114. https://doi.org/10.1144/qjegh2014-072
• A soil moisture accounting-procedure with a Richards' equation-based soil texture-dependent parameterization
  
  Mathias, S., Skaggs, T., Quinn, S., Egan, N., Finch, L., & Oldham, C. (2015). A soil moisture accounting-procedure with a Richards’ equation-based soil texture-dependent parameterization. Water Resources Research, 51(1), 506-523. https://doi.org/10.1002/2014wr016144
• Heat transport and pressure buildup during carbon dioxide injection into depleted gas reservoirs
  
  Mathias, S., McElwaine, J., & Gluyas, J. (2014). Heat transport and pressure buildup during carbon dioxide injection into depleted gas reservoirs. Journal of Fluid Mechanics, 756, 89-109. https://doi.org/10.1017/jfm.2014.348
• Dynamic modelling of a UK North Sea saline formation for CO2 sequestration
  
  Watson, F., Mathias, S., Daniels, S., Jones, R., Davies, R., Hedley, B., & van Hunen, J. (2014). Dynamic modelling of a UK North Sea saline formation for CO2 sequestration. Petroleum Geoscience, 20(2), 169-185. https://doi.org/10.1144/petgeo2012-072
• A pseudospectral approach to the McWhorter and Sunada equation for two-phase flow in porous media with capillary pressure
  
  Bjørnarå, T., & Mathias, S. (2013). A pseudospectral approach to the McWhorter and Sunada equation for two-phase flow in porous media with capillary pressure. Computational Geosciences, 17(6), 889-897. https://doi.org/10.1007/s10596-013-9360-4
• A statistical analysis of well production rates from UK oil and gas fields – Implications for carbon capture and storage
  
  Mathias, S., Gluyas, J., Mackay, E., & Goldthorpe, W. (2013). A statistical analysis of well production rates from UK oil and gas fields – Implications for carbon capture and storage. International Journal of Greenhouse Gas Control, 19, 510-518. https://doi.org/10.1016/j.ijggc.2013.10.012
• A Lambert W function solution for estimating sustainable injection rates for storage of CO2 in brine aquifers
  
  Mathias, S., & Roberts, A. (2013). A Lambert W function solution for estimating sustainable injection rates for storage of CO2 in brine aquifers. International Journal of Greenhouse Gas Control, 17, 546-548. https://doi.org/10.1016/j.ijggc.2013.04.007
• Multiple well systems with non-Darcy flow
  
  Mijic, A., Mathias, S., & LaForce, T. (2013). Multiple well systems with non-Darcy flow. Groundwater, 51(4), 588-596. https://doi.org/10.1111/j.1745-6584.2012.00992.x
• On the importance of relative permeability data for estimating CO2 injectivity in brine aquifers
  
  Mathias, S., Gluyas, J., González Martínez de Miguel, G., Bryant, S., & Wilson, D. (2013). On the importance of relative permeability data for estimating CO2 injectivity in brine aquifers. International Journal of Greenhouse Gas Control, 12, 200-212. https://doi.org/10.1016/j.ijggc.2012.09.017
• Uncertainty in static CO2 storage capacity estimates: Case study from the North Sea, UK
  
  Hedley, B., Davies, R., Mathias, S., Hanstock, D., & Gluyas, J. (2013). Uncertainty in static CO2 storage capacity estimates: Case study from the North Sea, UK. Greenhouse Gases: Science and Technology, 3(3), 212-230. https://doi.org/10.1002/ghg.1343
• Farming for Water Quality: Balancing Food Security and Nitrate Pollution in UK River Basins
  
  Howden, N., Burt, T., Worrall, F., Mathias, S., & Whelan, M. (2013). Farming for Water Quality: Balancing Food Security and Nitrate Pollution in UK River Basins. Annals of the Association of American Geographers, 103, 397-407. https://doi.org/10.1080/00045608.2013.754672
• Hydraulic fractures: How far can they go?
  
  Davies, R., Mathias, S., Moss, J., Hustoft, S., & Newport, L. (2012). Hydraulic fractures: How far can they go?. Marine and Petroleum Geology, 37(1), 1-6. https://doi.org/10.1016/j.marpetgeo.2012.04.001
• Deepwater canyons: An escape route for methane sealed by methane hydrate
  
  Davies, R., Thatcher, K., Mathias, S., & Yang, J. (2012). Deepwater canyons: An escape route for methane sealed by methane hydrate. Earth and Planetary Science Letters, 323-324, 72-78. https://doi.org/10.1016/j.epsl.2011.11.007
• Analysis of momentum transfer in a lid-driven cavity containing a Brinkman–Forchheimer medium
  
  Yang, D., Xue, Z., & Mathias, S. (2012). Analysis of momentum transfer in a lid-driven cavity containing a Brinkman–Forchheimer medium. Transport in Porous Media, 92, 101-118. https://doi.org/10.1007/s11242-011-9893-8
• Analytical Model for CO2 Injection into Brine Aquifers-Containing Residual CH4
  
  Hosseini, S., Mathias, S., & Javadpour, F. (2012). Analytical Model for CO2 Injection into Brine Aquifers-Containing Residual CH4. Transport in Porous Media, 94, 795-815. https://doi.org/10.1007/s11242-012-0025-x
• Dissolution of CO2 from leaking fractures in saline formations
  
  Watson, F., Mathias, S., van Hunen, J., Daniels, S., & Jones, R. (2012). Dissolution of CO2 from leaking fractures in saline formations. Transport in Porous Media, 94, 729-745. https://doi.org/10.1007/s11242-012-0021-1
• Role of partial miscibility on pressure buildup due to constant rate injection of CO2 into closed and open brine aquifers
  
  Mathias, S., Gluyas, J., González Martínez de Miguel, G., & Hosseini, S. (2011). Role of partial miscibility on pressure buildup due to constant rate injection of CO2 into closed and open brine aquifers. Water Resources Research, 47(12), Article W12525. https://doi.org/10.1029/2011wr011051
• Nitrate pollution in intensively farmed regions: What are the prospects for sustaining high-quality groundwater?
  
  Howden, N., Burt, T., Worrall, F., Mathias, S., & Whelan, M. (2011). Nitrate pollution in intensively farmed regions: What are the prospects for sustaining high-quality groundwater?. Water Resources Research, 47(6), Article W00L02. https://doi.org/10.1029/2011wr010843
• A trigonometric interpolation approach to mixed-type boundary problems associated with permeameter shape factors
  
  Klammler, H., Hatfield, K., Nemer, B., & Mathias, S. (2011). A trigonometric interpolation approach to mixed-type boundary problems associated with permeameter shape factors. Water Resources Research, 47(3), Article W03510. https://doi.org/10.1029/2010wr009337
• Probabilistic longevity estimate for the LUSI mud volcano, East Java.
  
  Davies, R., Mathias, S., Swarbrick, R., & Tingay, M. (2011). Probabilistic longevity estimate for the LUSI mud volcano, East Java. Journal of the Geological Society, 168, 517-523. https://doi.org/10.1144/0016-76492010-129
• Modelling long-term diffuse nitrate pollution at the catchment-scale: Data, parameter and epistemic uncertainty.
  
  Howden, N., Burt, T., Mathias, S., Worrall, F., & Whelan, M. (2011). Modelling long-term diffuse nitrate pollution at the catchment-scale: Data, parameter and epistemic uncertainty. Journal of Hydrology, 403(3-4), 337-351. https://doi.org/10.1016/j.jhydrol.2011.04.012
• An approximate solution for toughness-dominated near-surface hydraulic fractures
  
  Mathias, S., Fallah, A., & Louca, L. (2011). An approximate solution for toughness-dominated near-surface hydraulic fractures. International Journal of Fracture, 168, 93-100. https://doi.org/10.1007/s10704-010-9559-5
• Pressure buildup during CO2 injection into a closed brine aquifer
  
  Mathias, S., Gonzalez, G., Thatcher, K., & Zimmerman, R. (2011). Pressure buildup during CO2 injection into a closed brineaquifer. Transport in Porous Media, 89(3), 383-397. https://doi.org/10.1007/s11242-011-9776-z
• Analytical solution for Joule-Thomson cooling during CO2 geosequestration in depleted oil and gas reservoirs
  
  Mathias, S., Gluyas, J., Oldenburg, C., & Tsang, C.-F. (2010). Analytical solution for Joule-Thomson cooling during CO2 geosequestration in depleted oil and gas reservoirs. International Journal of Greenhouse Gas Control, 4(5), 806-810. https://doi.org/10.1016/j.ijggc.2010.05.008
• Transient divergent flow and transport in an infinite anisotropic porous formation
  
  Mathias, S. (2010). Transient divergent flow and transport in an infinite anisotropic porous formation. Groundwater, 48(3), 438-441. https://doi.org/10.1111/j.1745-6584.2009.00652.x
• Step-drawdown tests and the Forchheimer equation
  
  Mathias, S., & Todman, L. (2010). Step-drawdown tests and the Forchheimer equation. Water Resources Research, 46, Article W07514. https://doi.org/10.1029/2009wr008635
• Investigation of hydromechanical processes during cyclic extraction recovery testing of a deformable rock fracture
  
  Mathias, S., Tsang, C., & van Reeuwijk, M. (2010). Investigation of hydromechanical processes during cyclic extraction recovery testing of a deformable rock fracture. International Journal of Rock Mechanics and Mining Sciences, 47(3), 517-522. https://doi.org/10.1016/j.ijrmms.2009.12.008
• Screening and selection of sites for CO2 sequestration based on pressure buildup
  
  Mathias, S., Hardisty, P., Trudell, M., & Zimmerman, R. (2009). Screening and selection of sites for CO2 sequestration based on pressure buildup. International Journal of Greenhouse Gas Control, 3(5), 577-585. https://doi.org/10.1016/j.ijggc.2009.05.002
• Approximate Solutions for Pressure Buildup During CO2 Injection in Brine Aquifers
  
  Mathias, S., Hardisty, P., Trudell, M., & Zimmerman, R. (2009). Approximate Solutions for Pressure Buildup During CO2 Injection in Brine Aquifers. Transport in Porous Media, 79(2), 265-284. https://doi.org/10.1007/s11242-008-9316-7
• A parameter sensitivity analysis of two Chalk tracer tests
  
  Mathias, S., Butler, A., Atkinson, T., Kachi, S., & Ward, R. (2009). A parameter sensitivity analysis of two Chalk tracer tests. Quarterly Journal of Engineering Geology and Hydrogeology, 42, 237-244. https://doi.org/10.1144/1470-9236/08-016
• Insights from a pseudospectral approach to the Elder problem
  
  van Reeuwijk, M., Mathias, S., Simmons, C., & Ward, J. (2009). Insights from a pseudospectral approach to the Elder problem. Water Resources Research, 45. https://doi.org/10.1029/2008wr007421
• A model for flow in the chalk unsaturated zone incorporating progressive weathering
  
  Ireson, A., Mathias, S., Wheater, H., Butler, A., & Finch, J. (2009). A model for flow in the chalk unsaturated zone incorporating progressive weathering. Journal of Hydrology, 365(3-4), 244-260. https://doi.org/10.1016/j.jhydrol.2008.11.043
• Analysis of flow processes in fractured chalk under pumped and ambient conditions
  
  Butler, A., Mathias, S., Gallagher, A., Peach, D., & Williams, A. (2009). Analysis of flow processes in fractured chalk under pumped and ambient conditions. Hydrogeology Journal, 17(8), 1849-1858. https://doi.org/10.1007/s10040-009-0477-4
• Hydraulic fracture propagation with 3-D leak-off
  
  Mathias, S., & van Reeuwijk, M. (2009). Hydraulic fracture propagation with 3-D leak-off. Transport in Porous Media, 80(3), 1573-1634. https://doi.org/10.1007/s11242-009-9375-4
• Approximate solutions for Forchheimer flow to a well
  
  Mathias, S., Butler, A., & Zhan, H. (2008). Approximate solutions for Forchheimer flow to a well. Journal of Hydraulic Engineering, 134(9), 1318-1325. https://doi.org/10.1061/%28asce%290733-9429%282008%29134%3A9%281318%29
• Modelling radioiodine transport across a capillary fringe
  
  Mathias, S., Butler, A., & Wheater, H. (2008). Modelling radioiodine transport across a capillary fringe. Journal of Environmental Radioactivity, 99(4), 716-729. https://doi.org/10.1016/j.jenvrad.2007.09.010
• Catchment-scale modelling of flow and nutrient transport in the Chalk unsaturated zone
  
  Jackson, B., Wheater, H., Wade, A., Butterfield, D., Mathias, S., Ireson, A., Butler, A., McIntyre, N., & Whitehead, R. (2007). Catchment-scale modelling of flow and nutrient transport in the Chalk unsaturated zone. Ecological Modelling, 209(1), 41-52. https://doi.org/10.1016/j.ecolmodel.2007.07.005
• Recent advances in modelling nitrate transport in the Chalk unsaturated zone
  
  Mathias, S., Butler, A., Ireson, A., Jackson, B., McIntyre, N., & Wheater, H. (2007). Recent advances in modelling nitrate transport in the Chalk unsaturated zone. Quarterly Journal of Engineering Geology and Hydrogeology, 40, 353-359. https://doi.org/10.1144/1470-9236/07-022
• The significance of colloids in the transport of pesticides through Chalk
  
  Gooddy, D., Mathias, S., Harrison, I., Lapworth, D., & Kim, A. (2007). The significance of colloids in the transport of pesticides through Chalk. Science of the Total Environment, 385(1-3), 262-271. https://doi.org/10.1016/j.scitotenv.2007.06.043
• Recovering tracer test input functions from fluid electrical conductivity logging in fractured porous rocks
  
  Mathias, S., Butler, A., Peach, D., & Williams, A. (2007). Recovering tracer test input functions from fluid electrical conductivity logging in fractured porous rocks. Water Resources Research, 43(7). https://doi.org/10.1029/2006wr005455
• Flow to a finite diameter well in a horizontally anisotropic aquifer with wellbore storage
  
  Mathias, S., & Butler, A. (2007). Flow to a finite diameter well in a horizontally anisotropic aquifer with wellbore storage. Water Resources Research, 43(7). https://doi.org/10.1029/2006wr005839
• Shape factors for constant-head double-packer permeameters
  
  Mathias, S., & Butler, A. (2007). Shape factors for constant-head double-packer permeameters. Water Resources Research, 43(6). https://doi.org/10.1029/2006wr005279
• An improvement on Hvorslev's shape factors
  
  Mathias, S., & Butler, A. (2006). An improvement on Hvorslev’s shape factors. Géotechnique, 56(10), 705-706. https://doi.org/10.1680/geot.2006.56.10.705
• A simple model of variable residence time flow and nutrient transport in the chalk
  
  Jackson, B., Wheater, H., Mathias, S., McIntyre, N., & Butler, A. (2006). A simple model of variable residence time flow and nutrient transport in the chalk. Journal of Hydrology, 330(1-2), 221-234. https://doi.org/10.1016/j.jhydrol.2006.04.045
• Transient simulations of flow and transport in the Chalk unsaturated zone
  
  Mathias, S., Butler, A., Jackson, B., & Wheater, H. (2006). Transient simulations of flow and transport in the Chalk unsaturated zone. Journal of Hydrology, 330(1-2), 10-28. https://doi.org/10.1016/j.jhydrol.2006.04.010
• Hydrological processes in the Chalk unsaturated zone - Insights from an intensive field monitoring programme
  
  Ireson, A., Wheater, H., Butler, A., Mathias, S., Finch, J., & Cooper, J. (2006). Hydrological processes in the Chalk unsaturated zone - Insights from an intensive field monitoring programme. Journal of Hydrology, 330(1-2), 29-43. https://doi.org/10.1016/j.jhydrol.2006.04.021
• Linearized Richards' equation approach to pumping test analysis in compressible aquifers
  
  Mathias, S., & Butler, A. (2006). Linearized Richards’ equation approach to pumping test analysis in compressible aquifers. Water Resources Research, 42(6). https://doi.org/10.1029/2005wr004680
• The significance of flow in the matrix of the Chalk unsaturated zone
  
  Mathias, S., Butler, A., McIntyre, N., & Wheater, H. (2005). The significance of flow in the matrix of the Chalk unsaturated zone. Journal of Hydrology, 310(1-4), 62-77. https://doi.org/10.1016/j.jhydrol.2004.12.009
• Laplace transform inversion for late-time behavior of groundwater flow problems
  
  Mathias, S., & Zimmerman, R. (2003). Laplace transform inversion for late-time behavior of groundwater flow problems. Water Resources Research, 39(10). https://doi.org/10.1029/2003wr002246

Other (Digital/Visual Media)

• A Short Course in Mathematics for Engineering and Science Students. Durham University.
  
  Mathias, S. (2023). A Short Course in Mathematics for Engineering and Science Students. Durham University [Online self-published textbook].