__Revisiting The Buckley-Leverett Question Again__

(An Overview of a Proposed GRC/2004 Poster Presentation)^{1}

By Walter Rose^{2}

ABSTRACT

Like the writings of many Authors^{1
to 21} during the 20^{th} Century^{3},
some less-remembered ones to be recalled here in the presentation of
the Poster Presentation mentioned in the first footnote below, are
in a series of papers published by Rose and collaborators (1951 *et
seq.)*^{22 to 47} where both parallel and perpendicular
attempts also were being made again and again. The aim, of course,
was (and indeed still is!) to simplify, upgrade and extend the
utility of vintage Buckley-Leverett algorithms (1942)^{25} so
that at least partial proof of the proposed revisions could be
confidentially employed as useful algorithms for productively
modeling certain multiphase porous media transport processes. In
particular, the cases to be considered are those where explicit
account of classical coupling phenomena needs to be properly applied.
This means that attention is being given to all low intensity
irreversible processes where linearity between thermodynamic
measurements involving conjugate macroscopically observed *fluxes
and forces* on the one side, and between thermostatic measurements
of *displacements and equilibrium forces* on the other. While
many perplexing (indeed critical) issues still remain unresolved, the
reader should not expect any of them to be fully illuminated by
anything that will be displayed in any of the disclosures made during
this Poster Presentation. After all, it has been generally conceded
that for more than a Century the full proof of the underlying
Darcian-based Buckley-Leverett dogma will not be available until
coherent experimental proof of at least one of the many postulated
theories that have appeared in the published literature so far has
been fully confirmed. What will be found, however, in what follows is
a new way to slightly (but perhaps significantly) rephrase a very old
question. In particular, upon accepting equations that appear in Rose
(1988)^{11} and
at many other locations, we simply give a verbal and equivalent
analytical algorithm as a sensible way for future workers
(particularly gifted modern experimentalists) to confirm an *ad-hoc
*theoretical to model two-phase, isothermal. and low-intensity
flow of immiscible Newtonian fluid pairs in homogeneous and isotropic
consolidated water-wet porous rock samples that are perturbed because
of superimposed viscous coupling and spontaneous capillary imbibition
effects.

KEY WORDS

porous media, transport process modeling, classical Buckley-Leverett. two-phase systems, viscous coupling, spontaneous capillary imbibition.

THEORETICAL BACKGROUND

As in Rose^{1} we start with the obvious but ingenious
conservation of mass and Darcy-based statements which is where
Buckley & Leverett^{2} left things some 60 years ago …
as indeed many modern authorities also do as a way to utilize the
simpler Darcian-based formulations. ^{3 } Thus, without
apology we write:

LITERATURE CITATIONS

__Some 20 ^{th}
Century Writings About Porous Media Transport Phenomena__

^{1 }E.
Buckingham (1907), "Studies in the Movement of Soil Moisture",
*U.S.Department of Agriculture, Bureau of Soils,* Bulletin 28,

^{2 }L. A.
Richards (1931), "Capillary Conduction of Liquids through Porous
Media", *Physics, *1: 318-333.

^{3 }M. Muskat
(1937), The Flow of Homogeneous Fluids Through Porous Media; cf. also
Muskat (1949), *Physical Principles of Oil Production,* both
being McGraw-Hill Books (New York).

^{4} M. K.
Hubbert (1940), "Theory of Ground Water Motion",* Journal
of Geology,* 48: 785-044: see also in (1956), "Darcy Law and
the Field Equations of the flow of underground fluids",
Transactions AIME, 207: 222-239; and see below reference to the
Deffeyes (2001) .

^{5} S. E.
Buckley and M. C. Leverett (1942), "Mechanism of Fluid
Displacement in Sands", *Transactions AIME*, __146:__
107-116.

^{6 }A. E.
Scheidegger (1957), *The Physics of Flow through Porous Media,*
University of Toronto Press; see (1960) and (1974) for the 2^{nd}
and 3^{rd} Editions of this one of his many relevant
monographs.

^{7 }M. Tribus (1961), *Thermostatics and Thermodynamics
(*D. Van Nostrand (especially see Chapter 15, p. 519 ff.).

^{8 }S. R.
DeGroot and P. Mazur (1962), *Non-Equilibrium Thermodynamics, *for
an overview of Onsager's Nobel Prize awardwed work (North-Holland
Publishing Company. Amsterdam).

^{9 }J. Bear
(1972), *Dynamics of Fluids in Porous Media, *American Elsevier
(New York); also see later ^{the} J. Bear & Y. Bachmat
(1990), *Introduction to Modeling of Transport Phenomena in Porous
Media*,* *cf. §5.3.5 in particular, (Kluwer Academic
Publishers).

^{ 10
}C. Marle (1981) in *Multiphase Flow in Porous Media, *(Gulf
Publishing Company).

^{11 }F. A. L. Dullien (1992a) in *Porous
Media: Fluid Transfer and Pore Structure, *2^{nd}
Edition, (Academic Press. New York)

^{12 } F. Siddiqui and Larry Lake (1992b), "A Dynamic
Theory of Hydrocarbon Migration", *Mathematical Geology*
24: 305-328.

^{13} Zarcone &
Lenormand (1994), "Determination experimentale de couplage
visqueux dans les ecoulements diphasiques en Milieu poreux", *C.
R. Acad. Sci. Paris Serie II* , 1429-1438.

^{14} Dullien &
Dong (1995) "Experimental Determination of the Flow Transport
Coefficients in the Coupled Equations of Two-phase Flow in Porous
Media", *Transport in Porous Media*, __25__: 97-120.

^{15 }M. Kaviany
(1995) in * Principles of Heat Transfer in Porous Media*.* *2^{nd}
Edition, (Springer Verlag. Berlin).

^{16 }A. Hadad,
J. Benbat, H. Rubin (1996), "Simulation of Immiscible Multiphase
Flow in Porous Media. A Focus on the Capillary Fringe" in
*Transport in Porous Media,* __12__: 229-240.

^{17 }A. Babchin and J-. Y. Yuan (1997), "On the
capillary coupling between two phases n a Droplet rain Model",
*Transport in Porous Media,* 26: 226-228.

^{18 }Ayub, Muhammad and Bentsen, Ramon, (1999), “Interfacial
viscous coupling: a myth or reality?”, *Journal of Petroleum
Science & Engineering, *23: 13-26.

^{19 }Bentsen, R. G. (2001), “The Physical Origin of
Interfacial Coupling in 2-Phase Flow in Porous Media”,
*Transport in Porous Media, *44: 109-122./

^{20 } K. S. Deffeyes (2001), *Hubbert's
Peak, The Impending World Oil Shortags*, cf. especially page 201
for his discussion where a deivation is given for Hubberrt's use if
the 'logiatic equation' firasgt employed in 1838 by Verlust in his
analysis of Malthus's famous unlimited population growth theory in
*Corr. Math. et Phys.*,10: 113.

^{21
}R. Byron Bird, Warren Stewart, Edwin Lightfootl (2002)
*Tr/ansport Phenomena,* cf. 2^{nd} Edition in
(2002), Wiley, New York.

__Some
Post-1950 to Date Papers by W. Rose & Collaborators__

^{22 }W. Rose
(1951). "Some problems of Relative Permeability Measurement",
*Proceedings of the 3 ^{rd} World Petoleum Congress*, II:
446-459, this being a companion paper to the one presented by Yuster
at the same conference.

^{23} W. Rose and P. H. Scott (1953), "An Explanation
of the Yusteerr Effect", *Journal of Petroleum Technology,*
4:* *19-20; see also W. Rose (1960), "Effect of Fluid/Fluid
Interfacial Boundary Condition in Affecting Multiphase Fluid Flow",
*Illinois State Geologic Survey,* Circular 291 (19 pages).

^{24} W. Rose and R. Heins (1962), "Moving Iterfaces
and Contact Angle Rate-Dependentcy", *Jounal of Colloid
Science, *17: 39-48; cf. Rose (1961),"Fluid/Fluid Interfaees
in Steady Motion", *Nature*, 191, 242=243.

^{25 }W. Rose (1963). "Aspects des Processus de
Mouillage dans les Solides Poreaux" in *l'Institut Française
du Petrole.* XVIII: 1571-1590.

^{26} W. Rose
(1966), "Reservoir Engineering, Reformulated" in the
*Bulletin of the Penn State Engineering Experiment Station,
*Circular 71: 23-68.

^{ }

^{27} W. Rose
(1969), "Transport through Interstitial Paths of Porous Solids",
*METU (Turkey) Journal of Pure & Applied Science, *2:
117-132.

^{28 }W. Rose
(1972), "Reservoir Engineering at the Crossroads. Ways of
Thinking and Ways of Doing", *Bulletin of the Iranian
Petroleum Institute, *46: 23-27; see also ^{17}
W. Rose (1974), "Second Thoughts on Darcy's Law", *ibid*,
48: 25-30.

^{29} W. Rose (1976), "Darcy's Law Revisited (cf.
especially Appendix therein)", *Journal of Mining Geology
(Nigeria), * 13: 38-44.

^{30} W. Rose & R. Gallegos (19-23 Matzo 1979 ),
"Measuring Relative Permeabilities for Estimating Reserves",
*Procedimiento Panamericano de Ingenieria del Petroleo, *Mexico,
Abstract in Programa Technico.

^{31} W. Rose (1987), "Relative Permeability", *SPE
Handbook Of Petroleum Engineering, *Chapter 28 (25 pages).

^{32} W. Rose,
(1988), "Attaching new meanings to the Equations of Buckley and
Leverett", * Journal of Petroleum Science & Engineering,*
__1__: 223-228.

^{33 } W. Rose
(1990a), Lagrangian Simulation of Coupled Two-phase Flows",
*Mathematical Geology,*__ 22__: 641-654.

^{34} W. Rose (1990b), "Optimising Experimental Design
for Coupled Porous Media Flow Studies", *Experimental Thermal
& Fluid Science, *3:613-532.* *

^{35} W. Rose
(1991a), "Richards Assumptions and Hassler's Presumptions",
*Transport in Porous Media*, 6: 91-99.

^{36 } W. Rose
(1991b), "Critical questions about the coupling hypothesis",
*Journal of Petroleum Science & Engineering,* 5: 299-307.

^{37 } W. Rose
(1995a), "Ideas about Viscous Coupling in Anisotropic Media",
*Transport in Porous Media,* 18: 87-93; cf.

^{38 }W. Rose
(1995b), "Generalized Description of Multiphase Flow in
Anisotropic Porous Media", *Proceedings 32 ^{nd} Annual
Tevhnical Meeting of the Society of Engineering Sciences *Abstract,
pp. 483- 489

^{39} W. Rose (1996), "Letter to the Editor of TiPM",
*Transport in Porous Media,* 22: 359-360.

^{
}

^{40} W. Rose, A. Babchin & J. Y. Yuan (1999a). "Coupled
Transport in and through Fractured Rocks", Proceedings Lawrence
Berkeley National Laboratory, #42717, Extended Abstract pp, 210-223.

^{41} W. Rose
(1999b), "Relative Permeability Ideas … Then and Now",
buried in the *Proceedings of the SPE Eastern Division Regional
Meeting,* SPE Paper 42718, pages 115-141.

^{42} W. Rose
(2000a), ” A Commentary on the Bartley/Ruth paper",
*Transport in Porous Media,* __40__: 355-358.

^{43 }W. Rose
(2000b), "Myths About Later-day Extensions of Darcy's Law",
in* J. of Petroleum Science & Engineering,* __26__:
187-198.

^{44}
M. Asadi, Ali Ghalambor, M. K. Shirazi & W. Rose
(2000c), "Anisotropic Permeability Measurement fo Coupled
Systems, *Proceedings SPE Asian- Pacific Conference on Integrated
Modeling for*

*Asset
Management, *Yokohoma, Japan, SPE Paper 59396.* *

^{45 }W. Rose
(2001a), "Modeling *Forced* versus *Spontaneous
*Capillary Imbibition Processes Commonly Occurring in Porous
Sediments*"*, *Journal Of Petroleum Science &
Engineering*, __30__: 155-166.

^{46} W. Rose
(2001b), "Theory of Spontaneous versus Induced Capillary
Imbibition", *Transport in Porous Media, Technical Note*
44: 591-598.

^{47} W. Rose
and Derek Robinson (2003, in press), "Transport Processes in
Fluid-saturated Porous Media" in a __Letter-to-the-Editor__
format, *Transport in Porous Media*.

Unsaturated Flow:

Hassanizadeh,
S.M., M.A. Celia, and H.K. Dahle, "Dynamic effects in the
capillary pressure-saturation relationship and their impacts on
unsaturated flow," *Vadose Zone Journal*, 1,
pp. 38-57, 2002.

********************

Density-dependent Flow and Transport:

Watson, S.J., D.A.
Barry, R.J. Schotting, and S.M.
Hassanizadeh, "Validation of classical density-dependent
solute transport theory for stable, high-concentration brine
displacements in coarse and medium sands," *Advances in Water
Resources*, 25, pp.
611-635, 2002.

Watson, S.J., D.A.
Barry, R.J. Schotting, and S.M.
Hassanizadeh, "On the validity of Darcy's Law for stable
high-concentration displacements in granular porous media,"
*Transport in Porous Media*, 47,
149-167, 2002.

********************************

Virus Transport

Schijven, J.F. and
Hassanizadeh, S.M., "Virus
removal by soil passage at filed scale and groundwater protection of
sandy aquifers", *Water Sci. Tech.*, 46
pp 123-129, 2002

Schijven J.F., de Bruin
H.A.M., Hassanizadeh, S.M.,
Roda Husman A.M. de, "Bacteriophages and clostridium spores as
indicator organisms for removal of pathogens by passage through
saturated dune sand." *Water Res.*, pp. 2186-2194, 2003.

Schijven, J.F., S.M.
Hassanizadeh, R.A.H.M. de Bruin, "Two-site kinetic
modeling of bacteriophage transport through columns of saturated dune
sand," *Journal of Contaminant Hydrology*, 57,
pp 259-279, 2002.

Schijven, J.F. ,
R.A.H.M. de Bruin, S.M.
Hassanizadeh, "Column experiments for evaluating field
data on removal rates of bacteriophages by passage through saturated
dune sand," *Journal of Contaminant Hydrology*, 58,
pp. 243-259, 2002.

Schijven, J.F., G.
Medema, A.J. Vogelaar, and S.M.
Hassanizadeh, "Removal of microorganisms by deep well
injection," *J. Contam. Hydrol.*, 44,
pp. 301-327, 2000.

Schijven, J.F., S.M.
Hassanizadeh, S.E. Dowd, and S.D. Pillai, "Modeling
virus adsorption in batch and column experiments," *Quantitative
Microbiology*, 2, pp.
5-20, 2000.

Schijven, J.F.and S.M.
Hassanizadeh, "Removal of viruses by soil passage:
overview of modeling, processes and parameters," *Critical
Rev. Env. Sci. Tech.*, 30,
49-127, 2000.

Schijven, J.F., G.
Medema, and S.M. Hassanizadeh
"Virusverwijdering door kunstmatige infiltratie: Veilig ontwerp"
(in Dutch; Removal of viruses by artificial recharge: A safe design),
*H _{2}O*, 34,
no. 6, pp. 28-30, 2001.

Schijven, J.F., S.M. Hassanizadeh, "Calculation of zone of protection of drinking water wells against microbial pollution," In: J.N. Bandyopandhyay and D.Nagesh Kumar (eds.), Proceedings of the Int'l Conf. on Advances in Civil Engineering, 3-5 January 2002, Kharagpur, India, Allied Publ. Limited, New Delhi, pp. 11-20, 2002.

Schijven, J.F., S.M. Hassanizadeh, "Calculation of zone of protection of drinking water wells against microbial pollution," In: J.N. Bandyopandhyay and D.Nagesh Kumar (eds.), Proceedings of the Int'l Conf. on Advances in Civil Engineering, 3-5 January 2002, Kharagpur, India, Allied Publ. Limited, New Delhi, pp. 11-20, 2002.

Schijven, J.F., S.M. Hassanizadeh, "Virus removal by soil passage at field scale," In: Tenth Biennial Symposium on Artifical Recharge of Groundwater, Tucson, Arizona, June 7-9 2001, pp. 191-200, 2001.

Schijven, J.F., S.M. Hassanizadeh, "Modeling of virus transport and removal in the subsurface," The Encyclopedia of Environmental Microbiology (Chief-Editor Gabriel Bitton, John Wiley & Sons, Inc, USA.), 2094-2107, 2002.

J.F. Schijven and S.M.
Hassanizadeh, "An overview of modelling removal of
viruses by soil passage," Proceedings of Future Groundwater
Resources at Risk, Changchun, P.R. China, 14-16 July 1998, UNESCO
Technical Documents in Hydrology No. 27, UNSECO, Paris, pp 56-69,
2000. Hassanizadeh, S.M.,
J.F Schijven, "Use of bacteriophages as tracers for the study of
removal of viruses," in: Tracers and Modeling in Hydrogeology,
ed. A. Dassargues (Proceedings of TRAM'2000 held in Liege, Belgium,
23-26 May 2000), pp. 167-174, 2000.

__
__

*****************************************

Basic Theories of Flow and Transport:

Hassanizadeh, S.M., M.A. Celia, and H.K. Dahle, "Dynamic effect in the capillary pressure-saturation relationship and its impacts on unsaturated flow,"

*Agricultural Sciences*, 7, pp. 69-71, 2002.Hassanizadeh, S.M., M.A. Celia, and H.K. Dahle, "Dynamic effects in the capillary pressure-saturation relationship and their impacts on unsaturated flow,"

*Vadose Zone Journal*, 1, pp. 38-57, 2002.Murdoch, A.I. and S.M. Hassanizadeh, "Macroscale balance relations for bulk, interfacial, and common line systems in multiphase flows through porous media on the basis of molecular considerations,"

*International Journal of Multiphase Flow*, 28, pp. 1091-1123, 2002.Beliaev, A.Y. and S.M. Hassanizadeh, "A Theoretical Model of Hysteresis and Dynamic Effects in the Capillary Relation for Two-phase Flow in Porous Media,"

*Transport in Porous Media, 43, pp. 487-510,*2001.

*********************************

Upscaling Multiphase flow in Porous Media:

Ataie-Ashtiani, B., S.M. Hassanizadeh, O. Oung, F.A. Weststrate, and A. Bezuijen, "Numerical modelling of two-phase flow in a geocentrifuge,"

*Environmental*Ataie-Ashtiani, B., S.M. Hassanizadeh, and M.A. Celia, "Effects of heterogeneities on capillary pressure-saturation-relative permeability relationships,"

*Journal of Contaminant Hydrology*, 56, pp. 175-192, 2002. oAtaie-Ashtiani, B., S.M. Hassanizadeh, M. Oostrom, M.A. Celia, and M. White, "Effective parameters for two-phase flow in a porous medium with periodic heterogeneities,"*J. Contam. Hydrol.*, 49, 87-109, 2001.Ataie-Ashtiani, B., S.M. Hassanizadeh, "Upscaling two-phase flow in porous media with randomly distributed microheterogeneities" in Computational Methods in Water Resources, Eds. S.M. Hassanizadeh, R.J. Schotting, W.G. Gray, and G.F. Pinder Eds. S.M. Hassanizadeh, R.J. Schotting, W.G. Gray, and G.F. Pinder (Proceedings of CMWR2002, Delft, The Netherlands, June 23-28), pp. 1187-1194, 2002.

Ataie-Ashtiani, B., S.M. Hassanizadeh, O. Oung, F.A. Weststrate, A. Bezuijen, 'Numerical simulation of two-phase flow in a geocentrifuge' Computational Methods in Water Resources, Eds. S.M. Hassanizadeh, R.J. Schotting, W.G. Gray, and G.F. Pinder (Proceedings of CMWR2002, Delft, The Netherlands, June 23-28), pp. 225-232, 2002.

Ataie-Ashtiani, B., S.M. Hassanizadeh, M.A. Celia, M. Oostrom and M.D. White "Effective two-phase flow parameters for heterogeneous porous media," in: Computational Methods in Water Resources, ed. L.R. Bentley et al. (Proceedings of CMWR XIII, Calgary, Canada, June 25-29, 2000), 755-762, 2000.

Ataie-Ashtiani, B., S.M. Hassanizadeh, M. Oostrom and M.D. White, "Numerical simulation and homogenization of two-phase flow in heterogeneous porous media," in:

*Groundwater Updates*, proceedings of the IAHR International Symposium on Groundwater, Sonic City, Japan, 8-10 May 2000, K. Sato and Y. Iwasa (eds.), Springer-Verlag, Tokyo, pp. 333-338, 2000.

******************************************************

Watershed Modeling:

Reggiani, P., M. Sivapalan, S.M. Hassanizadeh, and W.G. Gray, "Coupled equations for mass and momentum balance in a bifurcating stream channel network: Theoretical derivation and numerical implementation,"

*Proceedings of the Royal Society (London) Series A: Mathematical, Physical & Engineering Sciences,*Vol. 457, No. 2005, 157-189, 2001.Reggiani, P., M. Sivapalan, and S.M. Hassanizadeh, "Conservation equations governing hillslope responses: Physical basis of water balance,"

*Water Resour. Res.*, 36, 1845-1864, 2000.

*********************************************************

Solute Transport Modeling:

Leijnse, A., H. van de Weerd, and S.M. Hassanizadeh, "Modelling of uranium transport in Koongarra, Australia; The effect of a moving weathering zone,"

*Mathematical Geology*, 33, no. 1, pp. 1, 2001

**************************************************

Transport of radionuclides in porous media:

O Leijnse, A., H. van
de Weerd, and S.M. Hassanizadeh,
"Modelling of uranium transport in Koongarra, Australia; The
effect of a moving weathering zone," *Mathematical Geology*,
33, no. 1, pp. 1, 2001.

************************************************

Multiphase Flow Modeling:

Hassanizadeh, S.M and W.G. Gray, "Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries,"

*Adv. Water Resour.*, 13, 169-186, 1990.Gallo C., S.M. Hassanizadeh, A.E. Rosenbom, and K.E.S. Klint, "NAPL migration in a fractured-till soil: the Ringe Site case (Denmark)"Computational Methods in Water Resources, Eds. S.M. Hassanizadeh, R.J. Schotting, W.G. Gray, and G.F. Pinder (Proceedings of CMWR2002, Delft, The Netherlands, June 23-28), pp. 655-662, 2002.

Dahle, H.K., M. A. Celia, S. M. Hassanizadeh, and K.H. Karlsen, 'A total pressure-saturation formulation of two-phase flow incorporating dynamic effects in the capillary-pressure-saturation relationship' Computational Methods in Water Resources, Eds. S.M. Hassanizadeh, R.J. Schotting, W.G. Gray, and G.F. Pinder (Proceedings of CMWR2002, Delft, The Netherlands, June 23-28), pp. 1067-1074, 2002.

Ataie-Ashtiani, B., S.M. Hassanizadeh, O. Oung, F.A. Weststrate, A. Bezuijen, 'Numerical simulation of two-phase flow in a geocentrifuge' Computational Methods in Water Resources, Eds. S.M. Hassanizadeh, R.J. Schotting, W.G. Gray, and G.F. Pinder (Proceedings of CMWR2002, Delft, The Netherlands, June 23-28), pp. 225-232, 2002.

Hassanizadeh, S.M. and Zhao Yongsheng, "Simulation of underground migration of NAPL," Proceedings of Future Groundwater Resources at Risk, Changchun, P.R. China, 14-16 July 1998, UNESCO Technical Documents in Hydrology No. 27, UNSECO, Paris, pp 225-228, 2000.

Koopmans, M.P., Hassanizadeh, M., Hofstee, C., Leijnse, A., Meurs, G. van, Taat, J., Timmerman, T., "Development of a Numerical Simulator for LNAPL weathering, Phase 1: P{reliminary Studies,"TNO-NITG-report, Netherlands Institute of Applied Geoscience TNO-NITG, 15 July 2002

********************************

Groundwater Flow Modeling:

Hassanizadeh, S.M., "Steady State Radial Flow into Wells in Stratified Aquifers", Agricultural Engineering Journal (in Persian), 2, June 1983.

I. Wemaere, Marivoet, J., Pitsch, H., Beaucaire, C., Marline, C., Michelot, J.-L., Phillipot, A.-C., Hassanizadeh, S.M., and van Weert, F., "The PHYMOL Project," in:

*Use of hydrogeological information in testing groundwater flow*(Proceedings of Workshop on Site evaluation and design of experiments for radioactive waste disposal; Borgholm, Sweden, 1-3 September, 1997), Nuclear Energy Agency, ISBN 92-64-16153-8, pp. 347-353, 1999.van Weert, F. and Hassanizadeh, S.M., "Supra-Regional Groundwater Modelling of the Northwest Euorpe over the Last 125000 Years," PHYMOL Project Technical Report, Report No. DOC RID/53/2000-EN, European Commission, Brussels, 86 pages, 2000.

Marivoet, J., van Keer, I., Wemaere, I., Ha*rdy, L., Pitsch, H., Beaucaire, C., Michelot, J.-L., Marlin, C., Phillipot, A.C., Hassanizadeh, S.M., and van Weert, F., "A Paleohydrogeological study of the Mol Site," PHYMOL Project Final Report, Report No. 19146EN, European Commission, Brussels, 101 pages, 2000.

*****************************************/

General Hydrology:

*********************************

Pore-scale network Modeling:

T. Gielen, S.M. Hassanizadeh, M.A. Celia, and H.K. Dahle, "Study of Pc-Sw relationships using a dynamic pore-scale network model,"Computational Methods in Water Resources, Eds. S.M. Hassanizadeh, R.J. Schotting, W.G. Gray, and G.F. Pinder (Proceedings of CMWR2002, Delft, The Netherlands, June 23-28), pp. 1099-1107, 2002.

Celia M.A., H.K. Dahle, and S.M. Hassanizadeh, "Dynamic pore-scale network models for two-phase flow in porous media," in: Computational Methods in Water Resources, ed. L.R. Bentley et al. (Proceedings of CMWR XIII, Calgary, Canada, June 25-29, 2000), 217-223, 2000

**********************************

Modeling Biodegradation of

Organic Contaminants:

Gallo C. and S.M. Hassanizadeh, Modeling NAPL dissolution and biodegradation interactions: effect of toxicity and biomass growth limitations' Computational Methods in Water Resources, Eds. S.M. Hassanizadeh, R.J. Schotting, W.G. Gray, and G.F. Pinder (Proceedings of CMWR2002, Delft, The Netherlands, June 23-28), pp. 859-866, 2002.

Bouw, L., S.M. Hassanizadeh, and A. Leijnse, "Multiphase flow and enhanced biodegradation of dense non-aqueous phase liquids: Experimental design" to appear in IAHS Red Book series, 2002.

Gallo, C. and S. M. Hassanizadeh, "Influence of biodegradation on NAPL flow and dissolution in groundwater," in: Computational Methods in Water Resources, ed. L.R. Bentley et al. (Proceedings of CMWR XIII, Calgary, Canada, June 25-29, 2000), 129-138, 2000

1
This manuscript is an abbreviated version of a much larger paper
which since 11/15/2003 is being editorially peer reviewed for
possible exclusive publication in Elsevier's *Journal of Petroleum
Science & Engineering,* It is displayed here, however, to
describe the subject of an off-the-record Poster Presentation
which, if wanted, can be a poster part of the 2004 Gordon Research
Conference of :"Flow & Transport in Permeable Media"
that is scheduled to be chaired by Professor S. M. Hassanizadeh
next July at Queen's College, Oxford, UK.

2
Contact Addresses for the Author ^{Illini
Technologists International, P. O. Box 2424},
Champaign, Illinois 61825, USA, Facsimile: 1.217.358.9289; e-mail:
__wdrose@uiuc.edu__.

3 Where for brevity only a few of the names of some of them like Buckingham (1907), to Richards (1931), to Muskat (1937) and (1949). to Hubbert (1940) and (1956), to Scheidegger (1951), Bear (1972) and Bear & Bachmat (1990)