Development of a pore network simulation model to study nonaqueous phase liquid dissolution

A pore network simulation model was developed to investigate the fundamental physics of nonequilibrium nonaqueous phase liquid (NAPL) dissolution. The network model is a lattice of cubic chambers and rectangular tubes that represent pore bodies and pore throats, respectively. Experimental data obtained by Powers [1992] were used to develop and validate the model. To ensure the network model was representative of a real porous medium, the pore size distribution of the network was calibrated by matching simulated and experimental drainage and imbibition capillary pressure-saturation curves. The predicted network residual styrene blob-size distribution was nearly identical to the observed distribution. The network model reproduced the observed hydraulic conductivity and produced relative permeability curves that were representative of a poorly consolidated sand. Aqueous-phase transport was represented by applying the equation for solute flux to the network tubes and solving for solute concentrations in the network chambers. Complete mixing was found to be an appropriate approximation for calculation of chamber concentrations. Mass transfer from NAPL blobs was represented using a corner diffusion model. Predicted results of solute concentration versus Peclet number and of modified Sherwood number versus Peclet number for the network model compare favorably with experimental data for the case in which NAPL blob dissolution was negligible. Predicted results of normalized effluent concentration versus pore volume for the network were similar to the experimental data for the case in which NAPL blob dissolution occurred with time.

[1]  L. Scriven,et al.  Effect of Wettability on Two-Phase Relative Permeabilities and Capillary Pressures , 1983 .

[2]  Martin J. Blunt,et al.  A Physically Based Model of Dissolution of Nonaqueous Phase Liquids in the Saturated Zone , 2000 .

[3]  D. Sabatini,et al.  Effects of flow bypassing and nonuniform NAPL distribution on the mass transfer characteristics of NAPL dissolution , 1998 .

[4]  James W. Mercer,et al.  A review of immiscible fluids in the subsurface: properties, models, characterization and remediation , 1990 .

[5]  Scher,et al.  Simulation and theory of two-phase flow in porous media. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[6]  Evangelos A. Voudrias,et al.  Dissolution of a Toluene Pool Under Constant and Variable Hydraulic Gradients with Implications for Aquifer Remediation , 1994 .

[7]  George F. Pinder,et al.  An experimental study of complete dissolution of a nonaqueous phase liquid in saturated porous media , 1994 .

[8]  Susan E. Powers,et al.  Phenomenological models for transient NAPL-water mass-transfer processes , 1994 .

[9]  M. Celia,et al.  The effect of heterogeneity on the drainage capillary pressure‐saturation relation , 1992 .

[10]  Norman R. Morrow,et al.  Capillary behavior of a perfectly wetting liquid in irregular triangular tubes , 1991 .

[11]  Martin J. Blunt,et al.  Relative permeabilities from two- and three-dimensional pore-scale network modelling , 1991 .

[12]  Susan E. Powers,et al.  Theoretical Study of the Significance of Nonequilibrium Dissolution of Nonaqueous Phase Liquids in Subsurface Systems , 1991 .

[13]  Brian Berkowitz,et al.  Mass transfer at fracture intersections: An evaluation of mixing models , 1994 .

[14]  Cass T. Miller,et al.  Dissolution of Trapped Nonaqueous Phase Liquids: Mass Transfer Characteristics , 1990 .

[15]  Martin J. Blunt,et al.  Three-dimensional modeling of three phase imbibition and drainage , 1998 .

[16]  J. Philip,et al.  The fluid mechanics of fracture and other junctions , 1988 .

[17]  T. J. Lasseter,et al.  Two-phase flow in random network models of porous media , 1985 .

[18]  James F. Pankow,et al.  Dissolution of dense chlorinated solvents into groundwater. 2. Source functions for pools of solvent , 1992 .

[19]  C. Tsakiroglou,et al.  A new simulator of mercury porosimetry for the characterization of porous materials , 1990 .

[20]  John C. Slattery,et al.  Three‐dimensional, randomized, network model for two‐phase flow through porous media , 1982 .

[21]  Steven Robert McDougall,et al.  The impact of wettability on waterflooding: Pore-scale simulation , 1995 .

[22]  Kristian Mogensen,et al.  A Dynamic Two-Phase Pore-Scale Model of Imbibition , 1998 .

[23]  Madalena M. Dias,et al.  Network models for two-phase flow in porous media Part 1. Immiscible microdisplacement of non-wetting fluids , 1986, Journal of Fluid Mechanics.

[24]  Madalena M. Dias,et al.  Network models for two-phase flow in porous media Part 2. Motion of oil ganglia , 1986, Journal of Fluid Mechanics.

[25]  Cass T. Miller,et al.  Pore‐Scale Modeling of Nonwetting‐Phase Residual in Porous Media , 1995 .

[26]  N. Wardlaw,et al.  Sensitivity of drainage and imbibition to pore structures as revealed by computer simulation of displacement process , 1986 .

[27]  P. Oren,et al.  Pore-Scale Network Modelling of Waterflood Residual Oil Recovery by Immiscible Gas Flooding , 1994 .

[28]  Alkiviades C. Payatakes,et al.  A three dimensional network model for consolidated porous media. Basic studies , 1989 .

[29]  J. Geller,et al.  Mass Transfer From Nonaqueous Phase Organic Liquids in Water-Saturated Porous Media. , 1993, Water resources research.

[30]  Michael A. Celia,et al.  Prediction of relative permeabilities for unconsolidated soils using pore‐scale network models , 1997 .

[31]  K. Sorbie,et al.  A Pore-Level Investigation of Relative Permeability Hysteresis in Water-Wet Systems , 1998 .

[32]  Michael A. Celia,et al.  A Functional Relationship Between Capillary Pressure, Saturation, and Interfacial Area as Revealed by a Pore‐Scale Network Model , 1996 .

[33]  Jianting Zhu,et al.  Stochastic Analysis of Macrodispersion in a Semi‐Confined Aquifer , 1999 .

[34]  Robert P. Ewing,et al.  Modeling percolation properties of random media using a domain network , 1993 .

[35]  J. H. Henderson,et al.  Imbibition Relative Permeability in Unconsolidated Porous Media , 1962 .

[36]  Bryant,et al.  Prediction of relative permeability in simple porous media. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[37]  Ioannis Chatzis,et al.  Magnitude and Detailed Structure of Residual Oil Saturation , 1983 .

[38]  David Wilkinson,et al.  Invasion percolation: a new form of percolation theory , 1983 .

[39]  Cass T. Miller,et al.  The influence of porous medium characteristics and measurement scale on pore-scale distributions of residual nonaqueous-phase liquids , 1992 .

[40]  Alkiviades C. Payatakes,et al.  Stochastic simulation of the motion, breakup and stranding of oil ganglia in water‐wet granular porous media during immiscible displacement , 1980 .

[41]  M. C. Leverett,et al.  Capillary Behavior in Porous Solids , 1941 .

[42]  John L. Wilson,et al.  A lattice‐gas and lattice Boltzmann study of mixing at continuous fracture Junctions: Importance of boundary conditions , 1997 .

[43]  E. A. Sudicky,et al.  Dissolution of non-aqueous-phase liquids and aqueous-phase contaminant transport in discretely-fractured porous media , 1996 .

[44]  L. E. Scriven,et al.  Statistical network theory of three-phase relative permeabilities , 1984 .

[45]  D. Russo,et al.  Analytical models of steady state organic species transport in the vadose zone with kinetically controlled volatilization and dissolution , 1993 .

[46]  Susan E. Powers,et al.  An experimental investigation of nonaqueous phase liquid dissolution in saturated subsurface systems: Transient mass transfer rates , 1992 .

[47]  A. C. Payatakes,et al.  Effects of pore-size correlations on mercury porosimetry curves , 1991 .

[48]  S. Bakke,et al.  3-D Pore-Scale Modelling of Sandstones and Flow Simulations in the Pore Networks , 1997 .

[49]  Mark L. Brusseau,et al.  Rate‐limited mass transfer and transport of organic solutes in porous media that contain immobile immiscible organic liquid , 1992 .

[50]  Martin J. Blunt,et al.  Effects of Heterogeneity and Wetting on Relative Permeability Using Pore Level Modeling , 1997 .

[51]  R. Mann,et al.  Application of a stochastic network pore model to oil-bearing rock with observations relevant to oil recovery , 1981 .

[52]  W. Lennox,et al.  A pore-scale investigation of mass transport from dissolving DNAPL droplets , 1997 .

[53]  K. Mohanty.  Multiphase Flow in Porous Media: III. Oil Mobilization, Transverse Dispersion, and Wettability , 1983 .

[54]  Kerry T.B. MacQuarrie,et al.  Dissolution of creosote in groundwater: an experimental and modeling investigation , 1994 .

[55]  M. Blunt.  Pore Level Modeling of the Effects of Wettability , 1997 .

[56]  W. E. Soll,et al.  A modified percolation approach to simulating three-fluid capillary pressure-saturation relationships , 1993 .

[57]  Clayton J. Radke,et al.  Laminar flow of a wetting liquid along the corners of a predominantly gas-occupied noncircular pore , 1988 .

[58]  Stig Bakke,et al.  Extending Predictive Capabilities to Network Models , 1998 .

[59]  N. Morrow,et al.  Effect of Capillary Number on the Microstructure of Residual Oil in Strongly Water-Wet Sandstones , 1988 .

[60]  François Kalaydjian,et al.  Origin and quantification of coupling between relative permeabilities for two-phase flows in porous media , 1990 .

[61]  H. Holman,et al.  Evaluation of Transient Dissolution of Slightly Water-Soluble Compounds From a Light Nonaqueous Phase Liquid Pool , 1996 .

[62]  Norman C. Wardlaw,et al.  Pore-throat size correlation from capillary pressure curves , 1987 .

[63]  Laurence C. Hull,et al.  Streamline routing through fracture junctions , 1986 .

[64]  J. Pankow,et al.  Dissolution of Dense Chlorinated Solvents into Ground Water: 1. Dissolution from a Well‐Defined Residual Source , 1992 .

[65]  Robert C. Borden,et al.  Evaluation of groundwater extraction for remediation of petroleum‐contaminated aquifers , 1992 .

[66]  Steven L. Bryant,et al.  Network model evaluation of permeability and spatial correlation in a real random sphere packing , 1993 .

[67]  Kent S. Udell,et al.  Nonaqueous phase liquid transport and cleanup: 1. Analysis of mechanisms , 1988 .

[68]  R. Lenormand,et al.  Mechanisms of the displacement of one fluid by another in a network of capillary ducts , 1983, Journal of Fluid Mechanics.

[69]  A. W. Talash.  Experimental and Calculated Relative Permeability Data for Systems Containing Tension Additives , 1976 .

[70]  Yoram Cohen,et al.  Multiphase Chemical Transport in Porous Media , 1989 .

[71]  Evangelos A. Voudrias,et al.  Theoretical evaluation of dissolution and biochemical reduction of TNT for phytoremediation of contaminated sediments , 1996 .

[72]  Martin J. Blunt,et al.  Network Modeling of Three-Phase Flow in Porous Media , 1998 .

[73]  R. Flumerfelt,et al.  Oil ganglion dynamics during immiscible displacement: Model formulation , 1980 .

[74]  Evangelos A. Voudrias,et al.  DNAPL pool dissolution in saturated porous media: procedure development and preliminary results , 1994 .

[75]  James F. Pankow,et al.  Dissolution of dense chlorinated solvents into groundwater. 3. Modeling contaminant plumes from fingers and pools of solvent , 1992 .

[76]  G. R. Jerauld,et al.  The effect of pore-structure on hysteresis in relative permeability and capillary pressure: Pore-level modeling , 1990 .

[77]  C. Chrysikopoulos,et al.  Numerical modeling of three-dimensional contaminant migration from dissolution of multicomponent NAPL pools in saturated porous media , 1995 .

[78]  Scher,et al.  Pore-level modeling of wetting. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[79]  Tom Clemo,et al.  Laboratory and simulation studies of solute transport in fracture networks , 1987 .

[80]  N. Sitar,et al.  Nonaqueous phase liquid transport and cleanup: 2. Experimental studies , 1988 .

[81]  J. Parker,et al.  Comparing Simulated and Experimental Hysteretic Two‐Phase Transient Fluid Flow Phenomena , 1991 .

[82]  W. Shiu,et al.  Dissolution of non-aqueous phase liquids in groundwater , 1991 .

[83]  Lincoln Paterson,et al.  Pore-scale network model for drainage-dominated three-phase flow in porous media , 1996 .

[84]  Ioannis Chatzis,et al.  Modelling Pore Structure By 2-D And 3-D Networks With ApplicationTo Sandstones , 1977 .

[85]  Cass T. Miller,et al.  An experimental investigation of pore-scale distributions of nonaqueous phase liquids at residual saturation , 1993 .

[86]  R. Ewing,et al.  Percolation and permeability in partially structured networks , 1993 .

[87]  F. Dullien,et al.  Simulation of capillary pressure curves using bond correlated site percolation on a simple cubic network , 1987 .

[88]  Cass T. Miller,et al.  The influence of mass transfer characteristics and porous media heterogeneity on nonaqueous phase dissolution , 1996 .