Skip to main content
SpringerLink
Log in

Mathematical modelling on transport of petroleum hydrocarbons in saturated fractured rocks

  • Published:
Sadhana Aims and scope Submit manuscript

Abstract

The present paper addresses critical issues that describe the dissolution mass transfer of petroleum hydrocarbons in a saturated subsurface system. The field procedure associated with the estimation of Light Non-Aqueous Phase Liquid (LNAPL) thickness in site monitor wells is revisited. A brief theory has been included on the composition and transport of petroleum hydrocarbons following an onshore oil spill in order to demonstrate the level of complexity associated with the LNAPL dissolution mass transfer even in a classical porous medium. However, such studies in saturated fractured rocks are highly complex and limited, and hence, deserve a special attention as the fate and transport of the petroleum hydrocarbons are not uncommon in saturated fractured rocks. In this context, an improved mathematical model has been proposed that will better describe the dissolution kinetics of petroleum hydrocarbons in saturated fractured rocks at the scale of a single fracture using dual-porosity concept. The lumped mass transfer coefficient in a classical porous medium proposed depends on mean grain size, while the same parameter has been replaced by an equivalent average thickness of fracture aperture that better describes the LNAPL dissolution rate in a coupled fracture-matrix system. A set of nonlinear coupled partial differential equations is deduced for a coupled fracture-matrix system in analogy with the differential equations of a classical porous medium. The proposed mathematical model may work well for the fracture aperture thicknesses varying between 100 and 500 microns with a relatively low Reynolds Number and initial NAPL saturation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • API Interactive LNAPL Guide Version 2 2004 American Petroleum Institute, Washington D.C. (http://api-ep.api.org/environment/index.cfm)

  • Bear J 1972 Dynamics of fluids in porous media. New York: Elsevier

    MATH  Google Scholar 

  • Bradley H B 1987 Petroleum engineering handbook, 1st edition, Society of Petroleum Engineers, ISBN 1-55563-010-3

  • Brewster M L, Annan A P, Greenhouse J P, Kueper B H, Olhoeft G R, Redman J D and Sander K A 1995 Observed migration of a controlled DNAPL release by geophysical methods. J. Ground Water 33(6): 977–987

    Article  Google Scholar 

  • Brush D and Thomson N R 2003 Fluid flow in synthetic rough-walled fractures: Navier–Stokes, Stokes and local cubic law simulations. Water Resour. Res. 39(4): 1085 doi: 10.1029/2002WR001346

    Google Scholar 

  • BrusseauML 1992 Rate-limited mass transfer and transport of organic solutes in porous media that contain immobile immiscible organic fluid. Water Resour. Res. 28: 33–46

    Article  Google Scholar 

  • Charbeneau R J 2000 Groundwater hydraulics and pollutant transport. New Jersy: Prentice Hall, Englewood Cliffs

  • Charbeneau R J 2003 Models for design of free-product recovery systems for petroleum hydrocarbon liquids. API Publication Number 4729, American Petroleum Institute, Washington D.C

  • Charbeneau R J,Weaver J W and Lien B K 1995 The hydrocarbon spill screening model (HSSM), Volume 2: Theoretical background and source codes. EPA/600/R-94/039b, Robert S. Kerr Environmental Research Laboratory, U.S. Environmental Protection Agency, Ada, Oklahoma

  • Charbeneau R J, Johns R T, Lake L W and McAdams III M J 1999 Free-product recovery of petroleum hydrocarbon liquids. API Publication Number 4682, American Petroleum Institute, Washington D.C

  • Clement T P, Gautam T R, Lee K K, Truex M J and Davis G B Modeling Coupled NAPL-dissolution and rate-limited sorption reactions in biologically active porous media. Bioremediation J. 8(1–2): 47–64

    Article  Google Scholar 

  • De Pastrovich I L, Barthel Y, Chiarelli A and Fussell D R 1979 Protection of groundwater from oil pollution, CONCAWE Report No: 3/79, Den Haag, Netherlands

  • EPSRP 2012 New Jersey Department of Environmental Protection Site Remediation Program: Light Non-Aqueous Phase Liquid (LNAPL) Initial Recovery and Interim Remedial Measures Technical Guidance. Released 29th June 2012, Version 1.2, 33 pages

  • Freeze A R and McWhorter D B 1997 A framework for assessing risk reduction due to DNAPL mass removal from low-permeability soils. Ground Water 35(1): 111–123

    Article  Google Scholar 

  • Ghassemi A and Suresh Kumar G 2007 Changes in fracture aperture and fluid pressure due to thermal stress and silica dissolution/precipitation induced by heat extraction from subsurface rocks. Geothermics 36: 115–140

    Article  Google Scholar 

  • Giordano M 2009 Global groundwater? issues and solutions. Ann. Rev. Environ. Resour. 34: 153–178

    Article  Google Scholar 

  • Grant G P and Gerhard J I 2007 Simulating the dissolution of a complex DNAPL source zone: 1.Model to predict interfacial area. Water Resour. Res. 43: W12410 doi: 10.1029/2007WR006038

  • Hamed M M, Nelson P D and Bedient P B 2000 A distributed site model for non equilibrium dissoltion of multi component residually trapped napl. Environ. Model. Softw. 15: 443–450

    Article  Google Scholar 

  • Imhoff P T, Jaffe P R and Pinder G F 1993 An experimental study of complete dissolution of a non-aqueous phase liquid in saturated porous media. Water Resour. Res. 30(2): 307–320

    Article  Google Scholar 

  • Kokkinaki A 2013 Modelling of dissolution and bioremediation of chlorinated ethane DNAPL source zones. Doctoral Thesis, Department of Civil Engineering, University of Toronto, 273 pages

  • Kueper B H, Redman D, Starr R C, Reitsma S and May M 1993 A field experiment to study the behavior of Tetrachloroethylene below the water table: Spatial distribution of residual and pooled DNAPL. Ground Water 31(5): 756–766

    Article  Google Scholar 

  • Lenhard R J and Parker J C 1990 Estimation of free hydrocarbon volume from fluid levels in monitoring wells. Groundwater 28(1): 57–67

    Article  Google Scholar 

  • Matar S and Hatch F H 2000 Chemistry of petrochemical processes 2nd ed. Houston: Gulf Pub. Co

    Google Scholar 

  • Mercer J W and Cohen R M 1990 A Review of Immiscible Fluids in the Subsurface: Properties, Models, Characterization and Remediation. J. Contam. Hydrol. 6: 107–163

    Article  Google Scholar 

  • Miller C T, Poirier-McNeill M M and Mayer A S 1990 Dissolution of trapped nonaqueous phase liquids: Mass transfer characteristics. Water Resour. Res. 26(11): 2783–2796

    Article  Google Scholar 

  • MoenchM2004 Groundwater: The challenge of monitoring and management. In: The World’s Water 2004–2005, P Gleick, (ed.), 79–100. Washington, DC: Island Press

  • Moutsopoulos K N 2009 Exact and approximate analytical solutions for unsteady fully developed turbulent flow in porous media and fractures for time dependent boundary conditions. J. Hydrol. 369(1–2): 78–89. doi: 10.1016/j.jhydrol.2009.02.025

    Article  Google Scholar 

  • Nambi I M and Powers S E 2003 Mass transfer correlations for non-aqueous phase liquid dissolution from regions with high initial saturations. Water Resources Research 39(2): 1030 doi: 10.1029/2001WR000667

  • Natarajan N and Suresh Kumar G 2010 Radionuclide and colloid co-transport in a coupled fracture-skin-matrix system. Colloids Surf. A Physicochem. Eng. Asp. 370(1): 49–57

    Article  Google Scholar 

  • Natarajan N and Suresh Kumar G 2011 Numerical modeling and spatial moment analysis of thermal fronts in a coupled fracture-skin-matrix system. Geotech. Geol. Eng. 29(4): 477–491

    Article  Google Scholar 

  • Newell C J, Acree S D, Ross R R and Huling S G 1995 EPA Groundwater Issue: Light non-aqueous phase liquids. Technology Support Project: EPA/540/S-95/500, pp. 1–28

  • Potter T L and Simmons K E 1998 Composition of petroleum mixtures. In: Sciences Taoeha, editor: The Total Petroleum Hydrocarbon Criteria Working Group

  • Poulsen M and Kueper B H 1992 A field experiment to study the behavior of tetrachloroethylene in unsaturated porous media. Environ. Sci. Technol. 26(5): 889–895

    Article  Google Scholar 

  • Powers S E, Loureiro C O, Abriola L M and Weber Jr W J 1991 Theoretical study of the significance of nonequilibrium dissolution of nonaqueous phase liquids in subsurface systems. Water Resour. Res. 27(4): 463–477

    Article  Google Scholar 

  • Powers S E, Abriola L M and Jr Weber W J 1992 An experimental inverstigation of nonaqueous phase liquid dissolution in saturated subsurface systems: Steady state mass transfer rates. Water Resour. Res. 28(10): 2691–2705

    Article  Google Scholar 

  • Powers S E, Abriola L M and Jr Weber W J 1994 An experimental inverstigation of NAPL dissolution in saturated subsurface systems: Transient mass transfer rates. Water Resour. Res. 30: 321–332

    Article  Google Scholar 

  • Renu V and Suresh Kumar G 2012 Numerical modeling and spatial moment analysis of solute mobility and spreading in a coupled fracture-skin-matrix system. Geotech. Geol. Eng. 30(6): 1289–1302

    Article  Google Scholar 

  • Saba T and Illangasekare T H 2000 Effect of groundwater flow dimensionality on mass transfer from entrapped nonaqueous phase liquid contaminants. Water Resour. Res. 36(4): 971–979

  • Sekhar M and Suresh Kumar G 2006 Modeling transport of linearly sorbing solutes in a single fracture:asymptotic behavior of solute velocity and dispersivity. Geotech. Geol. Eng. 24(1): 183–201

    Article  Google Scholar 

  • Sekhar M, Suresh Kumar G and Mishra D 2006 Numerical modeling and analysis of solute velocity and macrodispersion for linearly and nonlinearly sorbing solutes in a single fracture with matrix diffusion. J. Hydrol. Eng. 11(4): 319–328

    Article  Google Scholar 

  • Shah T 2009 Taming the anarchy: Groundwater governance in South Asia. Washington, DC: Resources for the Future Press

  • Suresh Kumar G 2008 Effect of sorption intensities on dispersivity and macro-dispersion coefficient in asingle fracture with matrix diffusion. Hydrogeol. J. 16(2): 235–249

    Article  Google Scholar 

  • Suresh Kumar G 2009 Influence of sorption intensity on solute mobility in a fractured formation. J. Environ. Eng. 135(1): 1–7

    Article  MathSciNet  Google Scholar 

  • Suresh Kumar G 2014 Mathematical modeling of groundwater flow and solute transport in a saturated fractured rock using dual-porosity approach. J. Hydrologic Eng. doi: 10.1061/(ASCE)HE.1943%965584.0000986 (Feb. 18, 2014)

  • Suresh Kumar G and Ghassemi A 2005 Numerical modeling of non-isothermal quartz dissolution/precipitation in a coupled fracture-matrix system. Geothermics 34(4): 411–439

    Article  Google Scholar 

  • Suresh Kumar G and Sekhar M 2005 Spatial moment analysis for transport of nonreactive solutes in fracture-matrix system. J. Hydrol. Eng. 10(3): 192–199

    Article  Google Scholar 

  • Suresh Kumar G, Sekhar M and Misra D 2006 Time dependent dispersivity behavior of non-reactive solutes in a system of parallel fractures. Hydrology and Earth System Sci. Discussions 3(3): 895–923

    Google Scholar 

  • Suresh Kumar G, Sekhar M and Misra D 2008 Time-dependent dispersivity of linearly sorbing solutes in a single fracture with matrix diffusion. J. Hydrologic Eng. 13(4): 250–257

    Article  Google Scholar 

  • TPHCWG 1997 Total petroleum hydrocarbon criteria working group series (Vorhees, Donna and Weisman, Wade) 1997. Volume 5 Human Health Risk-Based Evaluation of Petroleum Contaminated Sites: Implementation of the working Group Approach (http://www.aehs.com/)

  • United Nations 2003 United Nation world water assessement program (un/wwap) 2003. 1st UN world water development report: Water for people, water for life. Tech. rept. Paris/New York/Oxford: UNESCO Berghahn

  • Warren J E and Root P J 1963 The behaviour of naturally fractured reservoirs. SPE J. 245–255

  • Witherspoon P A,Wang J S Y, Iwai K and Gale J E 1980 Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour. Res. 16(6): 1016–1024 doi: 10.1029/WR016i006p01016

    Article  Google Scholar 

  • Zekster I S and Everett L G 2004 Groundwater resources of the world and their use. IHP-VI, Series on Groundwater No. 6. Paris, France: United Nations Educational, Scientific and Cultural Organization

  • Zhang Z and Brusseau M L 1999 Nonideal transport of reactive solutes in heterogeneous porous media: Simulating regional-scale behavior of a trichloroethane plume during pump-and-treat remediation. Water Resour. Res. 35(10): 2921–2935

    Article  Google Scholar 

  • Zimmerman R W, Al-Yaarubi A H, Pain C C and Grattoni C A 2004 Non-linear regimes of fluid flow in rock fractures. Int. J. Rock Mech. Min. Sci. 41(3): 163–169 doi: 10.1016/j.ijrmms.2003.12.045

    Article  Google Scholar 

Download references

Acknowledgement

The author would like to thank the anonymous reviewer and Prof. P P Mujumdar, Senior Associate Editor of this journal for valuable comments and suggestions to improve the quality of the manuscript.

Author information

Authors and Affiliations

  1. Petroleum Engineering Programme, Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai, 600 036, India

    G SURESH KUMAR

Authors
  1. G SURESH KUMAR
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G SURESH KUMAR.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

KUMAR, G.S. Mathematical modelling on transport of petroleum hydrocarbons in saturated fractured rocks. Sadhana 39, 1119–1139 (2014). https://doi.org/10.1007/s12046-014-0284-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12046-014-0284-z

Keywords

Search

Navigation