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Pore-Scale Analysis of NAPL Blob Dissolution and Mobilization in Porous Media

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Abstract

A pore-scale analysis of nonaqueous phase liquid (NAPL) blob dissolution and mobilization in porous media was presented. Dissolution kinetics of residual NAPLs in an otherwise water-saturated porous medium was investigated by conducting micromodel experiments. Changes in residual NAPL volume were measured from recorded video images to calculate the mass transfer coefficient, K and the lumped mass transfer rate coefficient, k. The morphological characteristics of the blobs such as specific and intrinsic area were found to be independent of water flow rate except at NAPL saturations below 2%. Dissolution process was also investigated by separating the mass transfer into zones of mobile and immobile water. The fractions of total residual NAPL perimeters in contact with mobile water and immobile water were measured and their relationship to the mass transfer coefficient was discussed. In general, residual NAPLs are removed by dissolution and mobilization. Although these two mechanisms were studied individually by others, their simultaneous occurrence was not considered. Therefore, in this study, mobilization of dissolving NAPL blobs was investigated by an analysis of the forces acting on a trapped NAPL blob. A dimensional analysis was performed to quantify the residual blob mobilization in terms of dimensionless Capillary number (Ca I). If Ca I is equal to or greater than the trapping number defined as \({{2\pi R_{\rm n} k_{\rm 0} k_{\rm rw}}/{\left[{(S_{\rm ni}-Da_{\rm I} P_{\rm v}^\# \Delta C^{\ast})V_{\rm p}}\right]}}\), then blob mobilization is expected.

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Abbreviations

a i :

Intrinsic interfacial area (L2 L−3)

a 0 :

Specific NAPL interfacial area (L2 L−3)

A f :

Adjacent upstream area immediately preceding A t (L2)

A 0 :

Total area occupied by the NAPL blobs within A f (L2)

A t :

Target area of porous medium selected for analysis (L2)

A :

Area occupied by NAPL blobs within A t (L2)

Bo :

Bond number (\({{Bo={\Delta \rho gk_{\rm 0} k_{\rm rw}}/\sigma}}\))

Ca I :

Capillary number for water phase (\({{Ca_{\rm I}={\mu_{\rm w} u}/\sigma}}\))

Ca II :

Capillary number for NAPL phase (\({{Ca_{\rm II}={\mu_{\rm 0} u_{\rm 0}}/\sigma}}\))

\({Ca_{\rm I}^{\prime}}\) :

Capillary number for momentum transfer from water to NAPL phase \({\left({Ca_{\rm I}^{\prime}={\mu_{\rm w}({u-({{S_{\rm w}}/{1-S_{\rm w}}})u_{\rm 0}})}/\sigma} \right)}\)

\({Ca_{\rm II}^{\prime}}\) :

Capillary number for momentum transfer from NAPL to water phase\({\left({Ca_{\rm II}^{\prime}={\mu_{\rm 0} ({u_{\rm 0}-({{1-S_{\rm w}}/{S_{\rm w}}})u})}/\sigma} \right)}\)

C :

Contaminant concentration in the water phase (ML−3)

C eq :

Equilibrium concentration or solubility limit of NAPL in the water phase (ML−3)

d m :

Volumetric intrinsic phase average of a characteristic length (L)

D diff :

Molecular diffusion coefficient of NAPL in the water phase (L2 T−1)

Da I :

First Damkohler number (Da I = KL c/u)

h :

Average thickness of the micromodel (L)

k 0 :

Absolute permeability (L2)

k rw :

Relative permeability for water phase (−)

k ro :

Relative permeability for NAPL (−)

k wo :

Cross permeability (L2)

k :

Mass transfer coefficient (L3 L−2 T−1)

K :

Lumped mass transfer rate coefficient (L3 L−3 T−1)

[L]:

Length dimension

L * :

Dimension of A f perpendicular to the flow direction (L)

L c :

Characteristic length (L)

L m :

Total width of the micromodel perpendicular to the flow direction (L)

[M]:

Mass dimension

n :

Porosity (L3L−3)

\({N_{\rm t}^{\ast}}\) :

Trapping number (\({{N_{\rm t}^{\ast}={2\pi R_{\rm n} k_{\rm 0} k_{\rm rw}}/{[{(S_{\rm ni} -Da_{\rm I} pv \Delta C^{\ast})V_{\rm p}}]}}}\))

\({P_{\rm v}^\#}\) :

Number of pore volume (\({{P_{\rm v}^\# ={ut}/{L_{\rm c} n}}}\))

P :

Total interfacial NAPL perimeter within the target volumehA t (L)

Pe :

Peclet number (Pe = ud m/D diff)

Q :

Total flow rate (L3 T−1)

R e :

Reynolds number (Re = ud m/ν)

R 0 :

Radius of NAPL blob (L)

R n :

Radius of a pore throat (L)

S n :

Volumetric NAPL saturation (L3 L−3)

S ni :

Initial volumetric NAPL saturation (L3 L−3)

S w :

Volumetric water saturation (L3 L−3)

Sh :

Sherwood number (Sh = kd m/D diff)

Sh′:

Modified Sherwood number (\({{Sh^{\prime}={Kd_{\rm m}^2}/{D_{\rm diff}}}}\))

St :

Stanton number (St = k/u)

t :

Temporal time (T)

[T]:

Time dimension

u :

Specific discharge for water phase (L3 L−2 T−1)

u 0 :

Specific discharge for NAPL blob (L3 L−2 T−1)

V :

Temporal volume of residual NAPL (L3)

V i :

Initial volume of residual NAPL (L3)

V p :

Pore volume (L3)

V t :

Total volume of the porous matrix (L3)

x :

Direction of the one-dimensional flow field

ρ :

Density of NAPL (M L−3)

ρ w :

Density of water phase (M L−3)

Δρ :

Difference between NAPL and water densities (Δρ = ρ w − ρ)

ν :

Kinematic viscosity of water phase (L2 T−1)

\({\sigma}\) :

Interfacial tension between NAPL and water phase (M T−2)

μ w :

Dynamic viscosity of water phase (M/LT)

μ 0 :

Dynamic viscosity of NAPL (M/LT)

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Maryland, College Park, MD, 20742, USA

    M. Yavuz Corapcioglu

  2. Department of Civil Engineering, Texas A&M University, College Station, TX, 77843, USA

    Sunhee Yoon & Sabina Chowdhury

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  1. M. Yavuz Corapcioglu
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  2. Sunhee Yoon
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  3. Sabina Chowdhury
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Correspondence to M. Yavuz Corapcioglu.

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Corapcioglu, M.Y., Yoon, S. & Chowdhury, S. Pore-Scale Analysis of NAPL Blob Dissolution and Mobilization in Porous Media. Transp Porous Med 79, 419–442 (2009). https://doi.org/10.1007/s11242-008-9331-8

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