Master Thesis Three Phase (Water, Air and NAPL) Modeling ... · Master Thesis Three Phase (Water, Air and NAPL) ... Waqas Ahmed Matriculation number 2708711 Stuttgart, 7 March,2014

Universitat Stuttgart - Institut fur Wasser- undUmweltsystemmodellierung

Lehrstuhl fur Hydromechanik und HydrosystemmodellierungProf. Dr.-Ing. Rainer Helmig

Master Thesis

Three Phase (Water, Air and NAPL)

Modeling of Bail-Down Test

Submitted by

Waqas Ahmed

Matriculation number 2708711

Stuttgart, 7 March,2014

Examiner: apl. Prof. Dr.-Ing. Holger Class

Supervisors: Olivier Atteia and Cedric Palmier

Author’s Statement

I hereby certify that I have prepared this master’s thesis independently, and that only

those sources, aids and advisors that are duly noted herein have been used and / or

consulted.

Signature: Date:

Acknowledgements

Throughout the entire thesis I was lucky enough to receive full support both intellec-

tually and emotionally by my adviser Holger Class, for that I am greatly indebted and

thankful. I am also thankful for the time and technical support by my supervisors

Cedric Palmier and Olivier Atteia without their help it would be impossible to com-

plete the thesis. I would also like to thank my family, especially my mother and father

for always believing in me, for their continuous love and their support in my decisions,

without whom I could not have made it here.

Abstract

Bail-down tests are commonly used to determine the LNAPL transmissivity, volume

and initial recovery rate for LNAPL contamination in the soil. In this work a non-

compositional 3p (three phase) LNAPL/water/air bail-down test model was simulated

on multiphase simulator DUMUX (Sec. 2.4). Model includes a radial flow of Light

Non Aqueous Phase Liquid (LNAPL) to well through the filter pack. Initially the

contaminated soil with LNAPL was allowed to reach equilibrium under capillary forces

using Van Genuchten (1980) [9] capillary relation. The applied model accurately de-

scribes the physical process during the bail-down test and shows the consistency with

the field data. The response of LNAPL recovery in the well to different soil and fluid

parameters was investigated. The results showed that LNAPL recovery time and ini-

tial recovery rates are dependent on soil capillary characteristics, permeability, initial

LNAPL thickness and fluid properties. In this work two analytical approaches were

used for analysis of the bail-down test model results to determine the LNAPL trans-

missivity. The First approach is based on a modified Bouwer and Rice analysis for slug

test (Huntley, 2000) [11]. The second approach is based on measured well thickness for

multi-layered soil (Jeong, 2014) [14]. The modified Bouwer and Rice method (Huntley,

2000) [11] showed good estimates, if the bail-down test is conducted such that poten-

tiometric head (total head in terms of water column) remains constant throughout the

test. A comparison for both approaches for multi-layered soil showed consistency with

the estimated LNAPL transmissivity.

Contents

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Bail-Down Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Semi-Analytical Solution for Bail-Down Test Interpretation . . . 3

1.3 Scope of this Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Structure of Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Fundamentals of Multiphase (Three Phase) Porous Media Model 9

2.1 General terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.1 Phases and Components . . . . . . . . . . . . . . . . . . . . . . 9

2.1.2 Wettability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.3 Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.4 Capillary Pressure . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.5 Capillary Pressure Saturation Relationship . . . . . . . . . . . . 10

2.1.6 Relative Permeability and Extended Darcy’s Law . . . . . . . . 11

2.1.7 Saturation-Relative Permeability Relationship . . . . . . . . . . 12

2.2 Mathematical Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.1 Mass Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Three Phase Model Concept . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4 DUMUX Numerical Simulator . . . . . . . . . . . . . . . . . . . . . . . 15

3 Light Non Aqueous Phase Liquids (LNAPL) 16

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Fate and Transport of LNAPL in Subsurface . . . . . . . . . . . . . . . 17

3.2.1 Parameters Effecting LNAPL Transport During Bail-Down test 17

3.3 Bail-Down Test Applied Problem . . . . . . . . . . . . . . . . . . . . . 19

3.3.1 Boundary and Initial Condition . . . . . . . . . . . . . . . . . . 19

3.4 Different Simulation Cases . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4.1 CASE I: Model Validation . . . . . . . . . . . . . . . . . . . . . 20

3.4.2 CASE II: Effect of Different Parameter to LNAPL Recovery in

Well . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.4.3 CASE III: Effect of Multi-Layered Soil . . . . . . . . . . . . . . 22

I

CONTENTS II

4 Results and Discussion 24

4.1 CASE I: Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.2 CASE II: Effect of Different Parameter to LNAPL Recovery in Well . . 27

4.2.1 CASE II-A: Effect of Different Permeability . . . . . . . . . . . 28

4.2.2 CASE II-B: Effect of Different Van Genuchten α . . . . . . . . 29

4.2.3 CASE II-C: Effect of Different Initial Oil Thickness . . . . . . . 30

4.2.4 Case II-D: Effect of Different LNAPL Viscosity . . . . . . . . . 31

4.3 CASE III: Effect of Multi-Layered Soil . . . . . . . . . . . . . . . . . . 32

4.3.1 CASE III-A: 2m Fine Layer Between Silt and Coarse Layer

(LNAPL in Fine Layer) . . . . . . . . . . . . . . . . . . . . . . 32

4.3.2 CASE III-B: 1m Fine Layer Between Silt and Coarse Layer

(LNAPL in Fine and Coarse Layer) . . . . . . . . . . . . . . . . 33

5 Summary and Outlook 34

5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

List of Figures

1.1 Transport and migration process of LNAPL (Newell, 1995) [18] . . . . . 1

1.2 Concept of LNAPL thickness in well and distribution in domain . . . . 3

1.3 Graphical interpretation of bail-down test data using Bouwer and Rice

method(Bouwer and Rice, 1976) [4] . . . . . . . . . . . . . . . . . . . . 6

2.1 Fluid distribution in pores (Helmig, 1997) [10] . . . . . . . . . . . . . . 10

2.2 Three phase three component model (Flemisch, 2007) [8] . . . . . . . . 14

2.3 Model concept bail-down test . . . . . . . . . . . . . . . . . . . . . . . 14

3.1 Applied model for bail-down simulation . . . . . . . . . . . . . . . . . . 19

3.2 Initial condition case I . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3 Case III: Schematic of layered soil . . . . . . . . . . . . . . . . . . . . . 23

4.1 Case I: Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 Case I: Profiles along radial direction . . . . . . . . . . . . . . . . . . . 26

4.3 Case II-A: Effect of different permeability . . . . . . . . . . . . . . . . . 28

4.4 Case II-B: Effect of different Van Genuchten α . . . . . . . . . . . . . . 29

4.5 Case II-C: Effect of different initial oil thickness . . . . . . . . . . . . . 30

4.6 Case II-D: Effect of different LNAPL viscosity . . . . . . . . . . . . . . 31

4.7 Case III-A: 2m fine layer (LNAPL in fine layer) . . . . . . . . . . . . . 32

4.8 Case III-B: 1m fine layer (LNAPL in fine and coarse layer) . . . . . . . 33

III

List of Tables

3.1 Fluid and porous media properties case I . . . . . . . . . . . . . . . . . 21

3.2 Case II: Variable parameters . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3 Fluid and porous media properties for case III (Huntley 2002) [13] . . . 23

4.1 Case I: Analytical solution using modified Bouwer and Rice approach . 24

4.2 Case II-A: Analytical solution using modified Bouwer and Rice approach 28

4.3 Case II-B: Analytical solution using modified Bouwer and Rice approach 29

4.4 Case II-C: Analytical solution using modified Bouwer and Rice approach 30

4.5 Case II-D: Analytical solution using modified Bouwer and Rice approach 31

4.6 Case III-A: Analytical solution . . . . . . . . . . . . . . . . . . . . . . . 32

4.7 Case III-B: Analytical solution . . . . . . . . . . . . . . . . . . . . . . 33

IV

Nomenclature

Symbol Description Dimension/Units

α Van Genuchten parameter [Pa−1]

β Surface tension scaling parameter [-]

λα Phase mobility [Pa−1 s−1]

µ Viscosity [Pa s]

φ Porosity [-]

ρr Relative LNAPL density [-]

K Intrinsic soil permeability [m2]

krn LNAPL relative permeability [-]

Kws Hydraulic conductivity [m s−1]

m Van Genuchten parameter [-]

n Van Genuchten parameter [-]

pc Capillary pressure [Pa]

rc Radius of well casing [m]

Re Radius of infleunce [m]

rw Radius of bore hole [m]

so Initial LNAPL draw down [m]

st LNAPL draw down at time t [m]

Sn LNAPL saturation [-]

Sw Water saturation [-]

Tn Transmissivity of LNAPL [m2 s−1]

Chapter 1

Introduction

1.1 Motivation

Leakage from industrial sites is one of the major sources of ground water contamina-

tion. Once the contamination i.e. Non Aqueous Phase Liquids (NAPL) is released

from the site it migrates into the ground under the forces of gravity. NAPL moves

through the unsaturated zones where it is trapped by capillary forces, and if the

amount is sufficient it then moves until it reaches the water table. If it is a Light Non

Aqueous Phase Liquid (LNAPL) it lies above the water table and does not enter the

water saturated zone. When the capillary fringe is fully developed the LNAPL moves

laterally as a continuous, free phase layer along the upper boundary of the water

saturated zone due to gravity and capillary forces (Newell, 1995) [18]. After some time

when the infiltration of LNAPL is stopped, the hydro-static pressure is lowered and

water tends to rise, this water then comes in contact with LNAPL making an aqueous

phase contamination plume. Fig. 1.1 shows the transport and migration process of

LNAPL.

Figure 1.1: Transport and migration process of LNAPL (Newell, 1995) [18]

1

1.1 Motivation 2

These industrial sites are prone to contaminate the groundwater, and as such there is

strong emphasis by federal and local governments for remediation of LNAPL from these

sites (Testa, 1989) [24]. To efficiently design remedial options for LNAPL removal it is

necessary to determine the LNAPL distribution, composition, volume, transmissivity

and initial recovery rate. To obtain this information different methods are used such

as excavations and test pits, soil borings, and monitoring wells.

If monitoring wells are properly installed, they can be used to estimate the volume,

transmissivity and initial recovery rate of contaminate. Bail-down test and aquifer

pumping test are commonly used methods to determined this information by con-

structing monitoring well. Both methods have their advantages and disadvantages.

Aquifer pumping test are time consuming and expensive to conduct, as pumping and

observation wells are required. Moreover in some case the extracted water is contam-

inated and need to be treated or the low permeable material do not allow these tests

to determine the information. A better alternative to aquifer pumping is a bail-down

test, where one well is used to determine all the information.

In this work the focus is on evaluating the process and estimates of transmissivity and

initial recovery rate obtain by the bail-down test. Further sections in this report will

give an understanding of the bail-down test.

1.2 Bail-Down Test 3

1.2 Bail-Down Test

In the bail-down test a well is constructed. All of the LNAPL which enters the well is

bailed down (pumped) in a short period of time. Once the bailing of LNAPL is finished

(pumping is stopped), water level in the well rises and LNAPL/water interface reaches

a maximum height in the well. Then after some time LNAPL starts to flow again into

the well from the contaminated zone, at this point LNAPL/water interface changes

from rising to a falling level (known as the inflection point). At this point of LNAPL

recovery the depth to LNAPL surface, LNAPL depth and depth of water surface is

measured. The LNAPL/air, LNAPL/water interface and potentiometric head (total

head in terms of water column) is plotted over time. The interface data obtained

by bail-down test is then use to calculate LNAPL transmissivity by using analytical

solutions (Bouwer and Rice (1976) [4], Skibitzki (1958) [23], Cooper (1967) [6]).

Figure 1.2: Concept of LNAPL thickness in well and distribution in domain

1.2.1 Semi-Analytical Solution for Bail-Down Test Interpre-

tation

The LNAPL thickness measured in the well is referred as apparent thickness; it is not

the true thickness in the formation. The draw down data obtained from the bail-down

test is use to interpret the thickness of LNAPL in the formation. There are different

analytical solutions proposed (from basic assumptions to complex assumptions) which

relates the draw down data in the well and estimates the phase transmissivity.

The theory to estimate the hydraulic transmissivity from a bail-down test started to

develop during the second part of the last century. Skibitzke (1958) [23], Coopers


(1967) [6], Lohman (1972) [15], Bouwer and Rice (1976) [4] and others developed

theories based on completely different assumptions. As an example, Cooper’s (1967) [6]

approach considers a fully penetrated well in a homogeneous isotropic artesian confined

aquifer. His solution used the differential equation governing non-steady radial flow

of confined groundwater. On the other hand, Bouwer and Rice (1976) [4] considered

a partially or fully penetrated well in an unconfined aquifers. The solution is based

on Thiem’s equation developed for steady flow with equilibrium condition in an

unconfined aquifer. Even if the Bouwer and Rice (1976) [4] solution is developed for

an unconfined aquifer, one can use this solution for a confined aquifer.

For an LNAPL/water system, the bail-down test analytical solutions to assess the

LNAPL transmissivity were developed around 2000. The commonly used solutions

are the modified Bouwer and Rice approaches (Lundy and Zimmerman (1996) [16],

Huntley (2000) [11]) and the modified Cooper solution (Beckett and Lyverse, 2002) [3].

The Lundy and Zimmerman (1996) [16] method assumes that no water enters the well

after the free LNAPL is removed. This assumption implies that the LNAPL/water

interface is not moving during the test which is quite uncommon and not expected.

Huntley (2000) [11] makes the assumption that the water transmissivity is for a

majority of the time much higher than the LNAPL transmissivity and so the total

potentiometric surface remains almost constant during the test.

In this work two analytical approaches are used for analysis of bail-down test model re-

sults to determine the LNAPL transmissivity. The first approach is based on modified

Bouwer and Rice analysis for the slug test (Huntley, 2000) [11]. The second approach

is based on measured LNAPL thickness in well for multi-layered soil (Jeong, 2014) [14].

1.2.1.1 Modified Bouwer and Rice Analysis for the Slug Test

The modified solution given by Huntley (2000) [11] is based on the work of Bouwer and

Rice (1976) [4], where they gave a solution for the slug test for water. To obtain the

LNAPL phase transmissivity (Tn) using the modified solution, it is required that the

(Tn) values be corrected by the reciprocal of the difference between the density of the

water and the density of the LNAPL ( 11−ρn ). This correction is required because unlike

water, as the LNAPL draw down changes, the volume change in the well is greater by

this density factor because water is being depressed in the well bore as LNAPL recovers

(Beckett and Lyverse, 2002) [3].

Huntley (2000) [11] states that if the total potentiometric surface remains relatively

constant during the test, the LNAPL transmissivity is given by:

Tn =2.3rc

2(1/1− ρr)2t

ln(Re

rw) log(

sost

) (1.1)

where Tn is the LNAPL transmissivity, rc is the radius of the casing, t is the elapsed

time, Re is the radius of influence, rw is radius of the well, so is the drawdown at t = 0,


st is the drawdown at time t and (1/1 − ρr) is the density factor. The transmissivity

is obtained plotting the log(s) versus t (Fig. 1.3b ).

The values of ln(Rerw

) were determined by Bouwer and Rice (1976) [4] with an electrical

resistance network analog for different values of Le (effective length of the well screen

across which fluid flows), Lw(depth of the well penetration below the water table), rwand H (Fig. 1.3c ). In a water system, when the screen straddles the water table,

Lw = Le. In our study case, LNAPL always straddles the screen, so Lw = Le which

are equal to the LNAPL thickness.

For an LNAPL/water system, as the entire free LNAPL thickness crosses the screened

section, we always consider that H=Lw.

If Lw = H (fully penetrating well):

ln(Re

rw) =

[1.1

ln(Lw/rw)+

C

(Le/rw)

]−1

(1.2)

If H > Lw, then:

ln(Re

rw) =

[1.1

ln(Lw/rw)+A+B ln[(H − Lw)/rw]

(Le/rw)

]−1

(1.3)

where A, B and C are dimensionless parameters that are functions of Le/rw as shown

in Fig. 1.3d. The graphical interpretation to determine so and st considers the second

straight line which corresponds to the formation response, after the filter pack drainage.

When the LNAPL/air interface crosses the screening section and if the filtering pack

porosity is higher than the porous media porosity, the casing radius rc should be re-

calculated to include the gravel envelop porosity in the cross-sectional area of the well.

This recalculated radius can be used to calculate the LNAPL transmissivity using Eq.

1.1.

rcr = [r2c + φ(r2

w − r2c )]

1/2 (1.4)


(a) Interface of phases in the well after

bailing

(b) Log of draw-down versus time

(c) Geometry and symbols of a partially

penetrating well in unconfined aquifer

with gravel pack

(d) Curves relating coefficients A, B and

C to Le/rw

Figure 1.3: Graphical interpretation of bail-down test data using Bouwer and Rice

method(Bouwer and Rice, 1976) [4]

1.3 Scope of this Work 7

1.2.1.2 Analytical Approach for Multi-Layered Soil Based on LNAPL

Thickness in Well

In this approach the LNAPL/water and LNAPL/air interface in the well are measured.

The measured interfaces are used to estimate the saturation profile and relative per-

meability of the fluids. The LNAPL layer transmissivity is then calculated. It is given

by,

Tn(dn) =ρrµr

∫ zmax

znw

Kws(z)krn(Sw, Sn)dz (1.5)

where dn is the LNAPL thickness in well, ρr relative LNAPL density, µr relative LNAPL

viscosity, znw is the LNAPL/water interface in well, zmax is the maximum capillary

height, Kws is water saturated hydraulic conductivity (which implicitly includes the

vertical heterogeneity of soil),krn is the relative permeability of LNAPL.

Water saturation distribution in the stratified soil is defined by Eq. 1.6 and total

saturation by Eq. 1.7 which is based on Van Genuchten’s (1980) [9] capillary rela-

tion. Based on the capillary pressure relation, the permeability (krn) is given by a

combination of Van Genuchten’s (1980) [9] and Burdine’s (1953) [5] models (Eq. 1.9).

Sw(z) = Swr,i + (1− Swr,i − Snr,i)(

1

1 + (1 + (αnw,i(z − znw))n)

)m(1.6)

St(z) = Swr,i + Snr,i + (1− Swr,i − Snr,i)(

1

1 + (1 + (αan,i(z − zan))n)

)m(1.7)

i = 1, 2...nthlayer

Sn(z) = St(z)− Sw(z) (1.8)

krn(Sw, Sn) = S2n

[(1−(

Sw − Swr1− Swr − Snr

)1/m)m−(

1−(Sw + Sn − Swr − Snr

1− Swr − Snr

)1/m)m](1.9)

where α, m, n are empirical parameter for Van Genuchten’s capillary pressure relation-

ship, Swr is water residual saturation and Snr is LNAPL residual saturation.

1.3 Scope of this Work

In this work a 3p (three phase) LNAPL/water/air bail-down test model is simulated

on the multiphase simulator DUMUX (Sec. 2.4). The model includes a radial flow

of LNAPL to well through the filter pack which is included in the model. Initially

the contaminated soil with LNAPL is allowed to reach equilibrium under capillary

forces using Van Genuchten’s (1980) [9] capillary pressure relation. Then different

simulation’s are conducted to observe the response of model. The aim of the thesis is,

1.4 Structure of Report 8

1. To setup a 3p (LNAPL/water/air) model for bail-down test.

2. To check the reliability of an analytical solution.

3. To see the development of LNAPL in the well by changing the soil and fluid

parameters.

4. To check the performance of the model to multi-layered soil.

1.4 Structure of Report

The fundamentals of the applied multiphase (LNAPL, water and air ) model and the

implementation of the different relationships such as capillary pressure and relative

permeability in the three phase system are described in chapter 2. The description of

the contaminate NAPL (i.e LNAPL/DNAPL), LNAPL transport process in the sub-

surface, and its response to the soil parameters are summarized in chapter 3. Further,

in this chapter the applied problem setup and different simulation cases are defined.

Chapter 4 provides the results describing the draw-down response in the well to dif-

ferent cases and comparison of LNAPL transmissity calculated by analytical solution.

In the last chapter a summary of this work and recommendations for future work are

provided.

Chapter 2

Fundamentals of Multiphase (Three

Phase) Porous Media Model

2.1 General terms

To conduct a numerical simulation it is necessary to transfer the physical process in

the mathematical formulation based on assumptions which reduces the complexity but

adequately describes the physical process. In in this chapter a short description of

important terms in multiphase flow in porous media are given and conceptualization

of the LNAPL/water/air fluid distribution in porous media and monitoring well is

explained. It will give a brief understanding of how physical process are mathematically

modeled.

2.1.1 Phases and Components

Phase is described as a matter with homogeneous chemical properties which is sepa-

rated by a sharp interface and it is characterized by continuous fluid properties. Thus

it is possible for several fluid phases to exists in a porous media, while there is only one

gaseous phase present because there is no interface between the gasses . In the problem

of NAPL contamination, three possible phases can exist: water, air and LNAPL.

The term components can be define as constituents of a phase, which are associated

with unique chemical species (Flemisch, 2007) [8]. Example can be a dissolved NAPL

component in a water phase see Fig. 2.2.

2.1.2 Wettability

Wettability is defined as the overall tendency of one fluid to spread onto or adhere on

a solid in the presence of another fluid with which it is immiscible. This is used to

define the fluid distribution at the pore scale.

The wetting fluid will coat the solid surface and tend to occupy small pores, while the

9

2.1 General terms 10

non-wetting fluid will occupy the largest interconnected pores. In LNAPL/water/air

system, usually the water preferentially wet the solid surface. However, under condi-

tions where only LNAPL and air are present,LNAPL will preferentially coat the solid

and displace air from the pores. Fig. 2.1 shows the idealized distribution of fluid ac-

cording to their wettability, where phase I is water, phase II is LNAPL and Phase III

is air if all three phases are present in pore space.

Figure 2.1: Fluid distribution in pores (Helmig, 1997) [10]

2.1.3 Saturation

Working on a macro or REV (Representative Elementary Volume) scale, the term

saturation defines the volume of a phase with respect to the total volume of the REV.

Saturation is defined as;

Sα =V olumeofphaseαinREV

TotalV olumeofREV(2.1)

2.1.4 Capillary Pressure

When multiple immiscible fluid phases exist in the pore they posses an interfacial

tension depending on the fluid combination, which creates a pressure difference known

as capillary pressure(pc).

In Fig. 2.1 there are three phases in the pore; if we consider phase I as water (w),

phase II as LNAPL (n) and phase III as air (a), then the capillary pressure (pc) is

given as;

pcn,a = pa − pn (2.2)

pcw,n = pn − pw (2.3)

2.1.5 Capillary Pressure Saturation Relationship

In mathematical modeling of the porous media we work on the macro scale and it is

not straight forward to define the capillary pressure because it is affected by other

2.1 General terms 11

parameters. The saturation of the phase (i.e wetting phase) has the strongest influence

on the capillary pressure, as describe in Sec. 2.1.2 that wetting phase occupies the

narrow pores and the non-wetting phase prefers the larger pores. If the wetting phase

saturation is low, the average radius of the meniscus is comparatively small and the

capillary pressure is accordingly high. There are different relationships which relates

the capillary pressure with saturation. The Van Genuchten (1980) [9] model is one of

the well known capillary pressure relationship where two phase exists.

pc =1

α(Sw

−1/m − 1)1/n (2.4)

Sw =Sw − Swr1− Swr

(2.5)

m = 1− 1

n(2.6)

Eq. 2.4 gives the general form Van Genuchten model for two phases, where Sw is the

effective saturation given by Eq. 2.5, Swr is the residual saturation (which describes

that the fluid is immobile below this saturation), α is the Van Genuchten pressure

scaling factor, m and n describes the soil uniformity.

For three phase system Parker (1987) [19] extended the Van Genuchten two phase

model by introducing new parameters (i.e βnw, βaw ). He considered the distribution

of phases in the pore based on their wettability as described in Sec. 2.1.2. Capillary

pressure at two interface pcn,a, pcw,n as describe by Eq. 2.3 are calculated. Parker

(1987) [19] gave the following capillary pressure-saturation relation for a three phase

system,

pcnw(Sw) =1

αβnw[(Sw)

n1−n − 1]1/n (2.7)

pcan(Sa) =1

αβan[(1− Sa)

n1−n − 1]1/n (2.8)

Where α, n,m and Sα(α = a, w) are the same parameters as that of Van Genuchten,

while β is the surface tension scaling parameter given as;

βan =σawσan

(2.9)

βnw =σawσnw

(2.10)

2.1.6 Relative Permeability and Extended Darcy’s Law

In a multiphase system, the pore space is occupied by more then one fluid, so the

fluids also experience the resistance in movement from each other. To account for this

resistance in a multiphase system, the permeability in Darcy’s law is multiplied by a

2.2 Mathematical Formulation 12

scalar nondimensional factor kr called relative permeability.

In multiphase flow in porous media, an extended version of Darcy’s law is used, given

by,

vα = −krαµα

K(5pα − ραg) (2.11)

where krα is the relative permeability of the phase α, µα is vicosity, K is intrinsic

permeability, pα pressure and g is the gravitational constant. The ratio krαµα

is called

the mobility λα of the phase.

2.1.7 Saturation-Relative Permeability Relationship

Relative permeability is dependent on the phase saturation. For fully saturated condi-

tions the krα = 1 and flow is considered as a single phase, while krα = 0 for saturation

below residual saturation and fluid is considered as immobile.

In a three phase system, fluid distribution is considered according to their wettability

as decribed in Sec. 2.1.2, so water is always considered as the wetting fluid occupying

small pores and gas as the non-wetting, thus the relative permeability for water and

gas(air) is only dependent on water and air saturation respectively. Their relationship

in a three phase system can be defined by two phase relationship,

krw =

√Sw[1− (1− S1/m

w )m]2 (2.12)

kra =3

√Sa[1− (1− Sa)1/m]2m (2.13)

The problem is with the NAPL, is that it is a intermediate wetting phase and its

distribution in the pores depends on the ratio of gas and water saturation. Parker’s

(1987) [20] approach based on Van Genuchten’s relationship is used here to give LNAPL

relative permeability,

krn =

√Sw

1− Swr

[(1− S

1mw )m − (1− S

1mt )m

]2

(2.14)

St =Sw + Sn − Swr

1− Swr(2.15)

2.2 Mathematical Formulation

The Reynold theorem is used to derive differential formulation of conserve quantity(as

mass). It states that,”the total rate of change of an extensive system property E equals

the rate of change of its corresponding intensive quantity e within a fixed control volume

(CV), plus the net rate change across its boundaries.” Mathematically it can be written

as,dE

dt=

∫Ω

∂(ρe)

∂tdΩ +

∫Γ

(ρe)(v.n)dΓ (2.16)

2.3 Three Phase Model Concept 13

2.2.1 Mass Balance

Considering that the change in mass in a closed system is zero, Reynold’s theorem

(Eq. 2.16) can be used to formulate a continuity equation by considering E in Eq. 2.16

equal to ”m”. In formulation we have to consider that the flow only occurs through

the pores, so porosity φ has to be taken in account. Secondly, this mass balance is

valid for all phases α. The formulation for continuity for each phase α can be given as,

∂(φSαρα)

∂t+5(ραvα) = 0 (2.17)

vα can be replaced by extended Darcy’s law Eq. 2.11, which gives the following form

of mass balance equation,

∂(φSαρα)

∂t︸︷︷︸accumulation term

−5(ραkrαµα

K(5pα − ραg)

)︸︷︷︸

advection term

− qc︸︷︷︸sink/source term

= 0 (2.18)

where φ is porosity, ρα is phase density, Sα is phase saturation, kr,α is relative per-

meability of phase α, µα dynamic viscosity, K intrinsic permeability and pα is phase

pressure.

2.3 Three Phase Model Concept

The general model concept for NAPL contamination can be described by the

Fig. 2.2, but in this work we assumed no dissolution of the NAPL. Model imple-

mented here only consists of three phases: LNAPL, air and water, without components.

A more elaborate description of our model concept can be seen in the Fig. 2.3, where

three distinct zones can be seen; first one is in the unsaturated zone where the three

phases exists but LNAPL is considered as immobile, second is where also three phases

exists but air is considered as immobile and third zone is considered as fully saturated

with water.

We also conceptualized the well; in Fig. 2.3 at the extreme left is the well. There are

also three distinct zones visible. The first is where only air exists, then only LNAPL

and below that only water. The well is in cooperated in porous media domain as a

single phase with porosity and relative permeability of one (for futher details see Sec.

3.3).

2.3 Three Phase Model Concept 14

Figure 2.2: Three phase three component model (Flemisch, 2007) [8]

Figure 2.3: Model concept bail-down test

2.4 DUMUX Numerical Simulator 15

2.4 DUMUX Numerical Simulator

In this work DUMUX 1 (DUNE for Multi Flow and Transport in Porous Media) is

used as a numerical simulator. It is based on Distributed and Unified Numerics Envi-

ronment (DUNE) 2 framework. DUMUX is provided as a DUNE module and inherits

functionality from the DUNE core modules. Its main purpose is to provide a framework

for for an easy and efficient implementation of models for porous media flow problems.

It has capability to provide spatial and temporal discretization and also has the capa-

bility of model coupling and selection of non linear solvers (Flemisch, 2007) [8]. It has

a modular design in its nature, which eases the customization of problem set-up code

according to the problem on hand.

1DUNE for Multi Flow and Transport in Porous Media http://www.dumux.org2Distributed and Unified Numerics Environment http://www.dune-project.org

Chapter 3

Light Non Aqueous Phase Liquids

(LNAPL)

3.1 Introduction

Hydrocarbons that make an interface with water and exist as a separate, immisci-

ble phase when in contact with water or air are known as Nonaqueous Phase Liquids

(NAPLs) (Newell, 1995) [18]. Hydrocarbon having density more then water are clas-

sified as Dense Non Aqueous Phase Liquids (DNAPLs), whereas hydrocarbon having

density less then water are classified as Light Non Aqueous Phase Liquids (LNAPLs).

In our study the contaminant is LNAPL, thus the focus further in this section will be

on the transport process of LNAPL.

As discussed in Sec. 1.1, LNAPL are a source of contamination and to design their

remediation it is necessary to predict their volume and transmissivity. Research on

LNAPL in subsurface has been going on for years and so different conceptual mod-

els have been proposed. Early models (as Testa, 1989) [24] considered LNAPL as a

layer floating on the water table creating an oil saturated zone above the water table

known as ”oilpancakes”. Lenhard and Parker (1990) [22] showed that in the major-

ity of aquifers where uniform pore size distribution is not considered oil pancakes do

not exist. They showed that above the water table there is a effect of capillary and

LNAPL/water occurs in variable saturation above water saturated zones, thus consid-

ering the early conceptual models can lead to over estimation of in situ LNAPL and

can set unrealistic precedents for site closure goals (Beckett, 1994) [2].

Lenhard and Parker (1990) [22], Farr (1990) [7] and others considered multiphase theory

with three phases (LNAPL/water/air) to give a new concept of LNAPL estimation in

subsurface and their results were verified by Huntley (1994) [12] with field observations.

Multiphase theory shows that the LNAPL recovery is dependent upon the distribution

of contaminant, volume, its mobility and contaminant chemistry, which are controlled

by specific soil and fluid properties such as capillary pressure (Peargin, 1999) [21]. It is

necessary to understand the multiphase process involved in LNAPL migration in the

16

3.2 Fate and Transport of LNAPL in Subsurface 17

subsurface. In the following sections, a brief discussion is given about the processes

and parameter effecting LNAPL in the subsurface while considering multiphase theory.

3.2 Fate and Transport of LNAPL in Subsurface

A brief introduction regarding transport of LNAPL after release from the source was

given in the motivation (Sec. 1.1). This section will extend that discussion and focus

will be on parameters effecting that transport. If you are interested in reading more

about LNAPL transport in porous media, see Mercer (1990) [17] and Newell (1995) [18].

When there is a spill on the ground or leakage from a industrial site, LNAPL start

to migrate into the ground under the forces of gravity and spread laterally due to

the capillary forces. As LNAPL continues to moves through the unsaturated zones it

is trapped into the pores due to the effects of surface tension (it is known as residual

liquid, parameter representing it is residual saturation Snr), making a permanent source

for contamination (if there is recharge or fluctuation of water table). While moving

through the unsaturated zone some of the immiscible fluid may volatilize and form

vapors (In this work volatilization and biodegradation are neglected, so there will not

much discussion regarding these effects). If the amount is sufficient then it moves until

it reaches the water table; if it is LNAPL it will lie above the water table and will

not enter the water saturated zone. When the capillary fringe is fully developed the

LNAPL moves laterally as a continuous, free phase layer along the upper boundary

of the water saturated zone due to gravity and capillary forces (Newell, 1995) [18].

After some time when the infiltration of LNAPL is stopped, the hydro-static pressure

of LNAPL is reduced and water tends to rise. This water then comes in contact with

residual LNAPL making an aqueous phase contamination plume. Fig. 1.1 shows the

transport and migration process of LNAPL.

According to multiphase theory the fluid exists as different phases in the subsurface

as described in Sec. 2.1.1. When LNAPL enters the unsaturated zone it can exist in

four physical states as a gas, sorbed to solid, dissolved in water or as immiscible liquid.

Further when it migrates to the water saturated zone, LNAPL constituents may be

dissolved in the water where it can exist as a component. In this work the model

concept is only three phase, so no dissolved components are considered.

3.2.1 Parameters Effecting LNAPL Transport During Bail-

Down test

As described previously, in the bail-down test the LNAPL is bailed, after which the

LNAPL starts entering the well. It can be seen from the extended Darcy’s law (Eq.

2.11) that the movement of LNAPL depends on its mobility λ (which in turn depends

on relative permeability, saturation, viscosity, density and capillary pressure).

If the soil in the formation is fine, the Van Genuchten α (which is a capillary pressure

3.2 Fate and Transport of LNAPL in Subsurface 18

scaling factor) will be low, according to Van Genuchten’s model (Eq. 2.4) the capillary

fringe will be high making the maximum saturation low. According to the saturation-

relative permeability relationship (Sec. 2.1.7), low saturation will lead to a low value

of relative permeability and LNAPL will be less mobile, thus causing LNAPL recovery

in the well to slow down.

Capillary pressure developed in the formation depends on the pore size, moisture con-

tent and interfacial tension. If LNAPL and water exists in the system, due to the

density difference/interfacial tension, there will be a capillary pressure (Sec. 2.1.4)

which will lead water to enter the pores above the saturated zone making a capil-

lary fringe. Capillary condition also affects the distribution and magnitude of trapped

LNAPL in the formation.

As the mobility of LNAPL depends on viscosity, and the viscosity depends on tem-

perature, the movement of LNAPL can also be governed by the temperature. High

temperature leads to low viscosity and high movement of LNAPL, so in the case of

high temperature the LNAPL development in the well will be fast because low vis-

cosity leads to high mobility. In this work the temperature is constant, so there is no

variation in viscosity and density with respect to temperature.

The development of LNAPL during the bail-down test is also dependent on well pa-

rameters such as well radius rw and on hydraulic conductivity of well filter pack (Aral

(2000) [1] , Zhu (1993) [25] ). Aral (2000) [1] gave a well parameter β0 (Eq. 3.1), which

is a linear function of the conductivity of well filter pack. He showed that the if β0

is large the increase of LNAPL thickness in the well will be fast. β0 does not effect

the rise of water in the well after the extraction of LNAPL before the inflection point

(the point from which the water level during the bail-down test changes from rising

to falling level) but it will effect the drainage of water from well to formation after

inflection point because the force which drives the water from the well to formation

comes from the high pressure created in the well by the LNAPL thickness. The other

possible effect which can be observed during the falling level of water is the possibility

of residual LNAPL to be re mobilized causing an increase of LNAPL thickness in the

well (R.J.Lenhard, 1990) [22].

βo =KfoKro

r2w ln(1 +4L/rw)

(3.1)

The effect of initial LNAPL thickness also influences the recovery of LNAPL (Aral,

2000) [1] . As the flow rate at which LNAPL comes into the well is dependent on the

area, the LNAPL thickness in the formation thus affects the LNAPL recovery process.

Aral (2000) [1] showed that the recovery of LNAPL is faster if the thickness of LNAPL

is high in the formation.

3.3 Bail-Down Test Applied Problem 19

3.3 Bail-Down Test Applied Problem

DUMUX (Sec. 2.4 ) was used to simulate the vertical and radial distribution of LNAPL

in a radially symmetric domain (Fig. 3.1 ) for all simulations. The radial domain cross-

dimensions are 10 m by 10 m and 30 in circular direction, which represents the model

as a piece of cake (see Fig. 3.1 ). The saturated zone is assumed to be at 4.785 m

from the top of the domain. The well is incorporated in the domain as porous media

with porosity φ = 1, relative permeability kr = 1, high permeability (i.e 100 K),

casing radius rc of 0.0575 m and bore hole radius rw of 0.1425 m. The model grid is

finely discretised near the well and in the zone of LNAPL saturation. The grid in the

radial direction starts with a fine grid and expands outward. Similarly, in the vertical

direction the grid is fine in the LNAPL saturated zone and it expands as it reaches top

or bottom of domain.

Figure 3.1: Applied model for bail-down simulation

3.3.1 Boundary and Initial Condition

The boundary at the top is considered to be a no flow neumann boundary; right and

bottom are considered to be constant pressure-saturation dirchlet boundaries. The

boundary at the left varies before equilibrium and after equilibrium. Before equilibrium

the boundary is taken as a dirchlet boundary because the values in the well remains

constant when the system is achieving its equilibrium under the capillary forces. Then

3.4 Different Simulation Cases 20

when equilibrium is achieved, a neumann flow boundary is applied to represent the

extraction of LNAPL.

The initial condition for the formation and the well varies according to the simulation

cases such as LNAPL thickness, viscosity, hydraulic conductivity and Van Genuchten

α (which are described for each simulation in Sec. 3.4 ) to quantify their effect on well

draw down, the general initial conditions which remain the same for all simulations

are,

• Saturated zone is assumed to be constant for all simulations, which is at 4.785 m

below from top of domain, where the saturation of water Sw = 0.99 in formation

and well.

• The initial reservoir pressure is given by hydro-static pressure distribution, using

p = patm + dwρwg + dnρng. With patm assumed to be 1.013 bar, dw (depth of

water) and dn (depth of LNAPL) varies according to the point where the pressure

is calculated.

• Temperature is assumed to be constant at T = 293 K.

• Density ( ρn = 882 kg/m3, ρw = 1000 kg/m3 ) is assumed to be constant.

3.4 Different Simulation Cases

3.4.1 CASE I: Model Validation

Case I was simulated to validate the model. The input parameters used for this sim-

ulation are described in Tab. 3.1. The soil was considered to be homogeneous with

mostly coarse sand and gravel. Initial LNAPL contamination was considered to be 2 m

above saturated zone. Fig. 3.2 shows the initial condition used for this case. The draw

down by numerical solution in the well was fitted with the observed data. The draw

down which was calculated by numerical solution was used to estimate the LNAPL

transmissivity and soil permeability using the analytical solution.


Figure 3.2: Initial condition case I

Fluid Properties Well characteristics

Parameter Value Parameter Value

Relative density ρnρw

0.882 Casing radius rc 0.0575 m

Viscosity µ 0.100 Pa s Borehole radius rw 0.1425 m

Molar mass M 0.100 kg mol−1 Permeability screen Kscreen 3× 10−10 m2

Porous media Properties

Parameter value

Porosity φ 0.3

Permeability K 3× 10−11 m2

Van Genutchen α 0.0025 Pa−1

Van Genutchen n 1.62

Residual Saturation water Swr 0.27

Residual Saturation LNAPL Sor 0.15

Residual Saturation gas Sgr 0.01

Table 3.1: Fluid and porous media properties case I


3.4.2 CASE II: Effect of Different Parameter to LNAPL Re-

covery in Well

Case II was simulated to see the effect of different parameters on the LNAPL recovery

in the well. All the conditions were assigned the same as case I, except the specific

parameter which was varied. Tab. 3.2 shows the sub cases with variable parameters.

The draw down which was calculated by numerical solution was used to estimate

the LNAPL transmissivity and soil permeability using the analytical solution. The

following sub cases based on the variable parameter were simulated,

− CASE II-A: Effect of different permeability.

− CASE II-B: Effect of different capillary pressure scaling factor Van Genuchten α.

− CASE II-C: Effect of different initial oil thickness.

− CASE II-D: Effect of different LNAPL viscosity.

CASE II-A CASE II-B


KI 3× 10−10 m2 αI 0.0005 Pa−1

KII 3× 10−11 m2 αII 0.0015 Pa−1

KIII 3× 10−12 m2 αIII 0.0025 Pa−1

KIV 3× 10−13 m2 αIV 0.0035 Pa−1

CASE II-C CASE II-D


dnI 2 m µI 0.100 Pa s

dnII 1.0 m µII 0.050 Pa s

dnIII 0.75 m µIII 0.020 Pa s

Table 3.2: Case II: Variable parameters

3.4.3 CASE III: Effect of Multi-Layered Soil

For case III, three horizontal soil layers were considered (see Fig. 3.3 ). Tab. 3.3 shows

the soil properties of each layer: Soil properties were considered same as (Huntley,

2002) [13]. The gravel pack around the well casing was considered to be of the coarse

sand. Initial LNAPL contamination was considered to be 2 m above the water table.

The arrangement and thickness of layers were considered according to the following

cases;

− CASE III-A: Two meter thick fine layer sandwiched between silt and coarse layer.

The initial LNAPL thickness was considered such that contamination lies only

in the fine layer.


− CASE III-B: One meter thick fine layer sandwiched between silt and coarse layer.

The initial LNAPL thickness was considered such that contamination lies in the

fine and coarse layer.

Porous media Properties

Layer I Layer II Layer III

Silty sand Fine sand Coarse sand

Porosity φ 0.3 0.34 0.384

Permeability K 2.95× 10−13 m2 1.18× 10−12 m2 2.95× 10−11 m2

Van Genutchen α 0.000 36 Pa−1 0.000 75 Pa−1 0.0025 Pa−1

Van Genutchen n 1.6 1.9 2.8

Residual Saturation water Swr 0.19 0.15 0.04

Residual Saturation LNAPL Snr 0.16 0.14 0.10

Residual Saturation gas Sgr 0.01 0.01 0.01

Fluid Properties

Relative Density ρrn 0.73

Viscosity µ 0.100 Pa s

Scaling factor βnw 1.45

Scaling factor βan 3.2

Table 3.3: Fluid and porous media properties for case III (Huntley 2002) [13]

(a) Case III-A: 2 m fine layer (LNAPL in

fine fayer)

(b) Case III-B: 1 m fine layer (LNAPL in

fine and coarse Layer)

Figure 3.3: Case III: Schematic of layered soil

Chapter 4

Results and Discussion

4.1 CASE I: Model Validation

Fig. 4.1a shows the saturation profile which was achieved at the equilibrium. Equilib-

rium condition was considered to have been reached when the capillary pressure in the

domain was minimized and the pressure profile in the system became linear (see Fig.

4.1b). At the equilibrium the maximum LNAPL saturation of 0.68 was achieved.

Fig. 4.1c shows the fluid interface and the potentiometric head (total head in term

of water height) achieved after the bailing of LNAPL in the well. It can be seen that

after the extraction of LNAPL from the well, water level rises in the well and after

certain time the LNAPL starts to enter the well from the formation until it achieves

an asymptotic height. The 80 % recovery time of LNPAL thickness in the well was

achieved at 1200 min which refer to 0.0225 gal/min estimated recovery rate (see Tab.

4.1).

This LNAPL draw down shows good correlation with observed data (Fig. 4.1d). A

good fit between calculated LNAPL thickness and observed values was achieved withR2

of 0.9831 (see Fig. 4.1e). Further validation was done by estimating the transmissivity

with a modified Bouwer and Rice analytical solution. LNAPL transmissivity estimated

by analytical solution was 2.52× 10−6 m2/s which corresponds to 1.45× 10−11 m2 per-

meability for the soil which is in the same order of magnitude as the input to the

numerical solution.

KInput Tn Kanalytical 80 % Recovery time Estimated

m2 m2/s m2 min Recovery rate gal/min

3.00× 10−11 2.52× 10−6 1.45× 10−11 1200 0.0225

Table 4.1: Case I: Analytical solution using modified Bouwer and Rice approach

24

4.1 CASE I: Model Validation 25

(a) Fluid saturation at equilibrium

(plot over line A-B)

(b) Pressure distribution at equilibrium

(plot over line A-B)

(c) Fluid interface in well after bailing (d) LNAPL thickness in well after bailing

(e) Correlation between observed to cal-

culated LNAPL thickness in well.

Figure 4.1: Case I: Model validation

4.1 CASE I: Model Validation 26

(a) LNAPL saturation before bailing (b) Water saturation before bailing

(c) LNAPL saturation after bailing (d) Water saturation after bailing

(e) LNAPL mobility and velocity vector after 120 seconds

of bailing

Figure 4.2: Case I: Profiles along radial direction

4.2 CASE II: Effect of Different Parameter to LNAPL Recovery in Well 27

The simulation showed that the modified Bouwer and Rice method (Huntley, 2000) [11]

yields good results for the bail-down test simulations. The reason that it worked well

is due to the assumption that the draw down induced by the water removal is to be

much more lower than the saturated aquifer thickness and the LNAPL mobility only

depends on a thin part of the entire LNAPL layer where the Sn is maximal. From

Fig. 4.2e it can be seen that the maximum velocity vectors are at the top of LNAPL

contaminated layer where the LNAPL saturation is at a maximum.

4.2 CASE II: Effect of Different Parameter to

LNAPL Recovery in Well

The resulting LNAPL transmissivity for different sub cases demonstrates its depen-

dency on different input parameters. Tab. 4.2 shows result for different soil perme-

ability K; it can be seen that the values calculated from the analytical solution are in

the same order of magnitude as the input value to the model. The estimated values

comes closer when the input values of the soil permeability K is in the range of coarse

sand and gravel because other input parameters are for the coarse sand and gravel (as

Case-I). Similarly Tab. 4.3 shows the results for different Van Genuchten α. It can be

seen that when the value of α is smaller as 5 × 10−4 (as for sandy loam or silt), the

analytically calculated LNAPL transmissivity is lower and the value of permeability of

soil K does not corresponds to the input value.

Case II-C (Sec. 4.2.3 ) shows that the initial LNAPL thickness in the formation also

has significant influence on the estimation of LNAPL transmissivity. Larger thickness

yields higher maximum saturation, thus higher LNAPL recovery rate. Tab. 4.4 shows

that the larger thickness gives higher transmissivity of LNAPL.

Case II-D (Sec. 4.2.4 ) shows that the high viscosity of LNAPL leads to low trans-

missivity of LNAPL. Tab. 4.4 shows that the soil permeability recalculated from the

analytical solution does not corresponds to the input value for high viscous LNAPL

because the recovery of LNAPL is slow in this case. Additionally, the initial LNAPL

thickness in the formation is considered to be 1 m, which makes the LNAPL recovery

in the well slower then the 2 m LNAPL thickness as in Case I (Sec. 4.1 ).


4.2.1 CASE II-A: Effect of Different Permeability

The saturation profile (Fig. 4.3a ) achieved at equilibrium for different permeability

cases is same because the capillary pressure scaling factors (as Van Genuchten α, n

and m) for all sub cases are the same. Maximum saturation achieved is 0.68, the same

as case I.

The response of LNAPL recovery for high permeable soil is faster then low permeable

soil (Fig. 4.3b), from Tab. 4.2 it can be seen that the 80% recovery of LNAPL height

in the well is quicker for high permeable soil and the estimated initial recovery rates

are also high.

(a) Fluid saturation at equilibrium (b) LNAPL thickness in well after bailing

Figure 4.3: Case II-A: Effect of different permeability

KInput Tn Kanalytical 80 % recovery time Estimated recovery rate

m2 m2/s m2 min gal/min

3.00× 10−10 2.14× 10−5 1.24× 10−10 240 0.1124

3.00× 10−11 2.52× 10−6 1.45× 10−11 1200 0.0225

3.00× 10−12 5.03× 10−7 2.91× 10−12 10897 0.0025

3.00× 10−13 3.77× 10−8 2.18× 10−13 40000 0.0007

Table 4.2: Case II-A: Analytical solution using modified Bouwer and Rice approach


4.2.2 CASE II-B: Effect of Different Van Genuchten α

Van Genuchten α is the capillary pressure scaling factor and it effects the saturation

distribution in the soil (see Sec. 2.1.5). Fig. 4.4a shows the saturation profile achieved

at equilibrium for different Van Genuchten α: it can be seen that when the α is small

such as 5× 10−4 1/Pa the maximum saturation achieved is low, which slows down the

LNAPL recovery process (Fig. 4.4b). The 80% recovery time of LNAPL height in the

well is high, which estimates a small initial LNAPL recovery rate (see Tab. 4.3). This

is because the relative permeability of LNAPL (which is saturation dependent) is low

for low saturation.


Figure 4.4: Case II-B: Effect of different Van Genuchten α

αInput Tn Kanalytical 80 % recovery time Estimated recovery rate

1/Pa m2/s m2 min gal/min

5× 10−4 2.52× 10−7 1.45× 10−12 2518 0.0107

15× 10−4 2.52× 10−6 1.45× 10−11 1440 0.0187

25× 10−4 2.52× 10−6 1.45× 10−11 1200 0.0225

35× 10−4 3.65× 10−6 2.11× 10−11 1015 0.0266

Table 4.3: Case II-B: Analytical solution using modified Bouwer and Rice approach


4.2.3 CASE II-C: Effect of Different Initial Oil Thickness

Result shows that the higher thickness in the formation gives high saturation (Fig.

4.5a) at the equilibrium which makes the LNAPL recover faster in the well (Fig.4.6b).

Another reason is that the high thickness in the formation gives high LNAPL recovery

rate (for the 2 m thickness the recovery rate is faster then for the 1 m and 0.75 m see

Tab. 4.4). The 80% LNAPL recovery height in the well for 2 m is 1200 min, which is

significantly earlier then the 1 m and 0.75 m scenarios.


Figure 4.5: Case II-C: Effect of different initial oil thickness

dn Tn Kanalytical 80 % recovery time Estimated recovery rate

m m2/s m2 min gal/min

2.00 2.52× 10−6 1.45× 10−11 1200 0.0225

1.00 2.59× 10−7 2.99× 10−12 2880 0.0047

0.75 4.29× 10−7 6× 10−12 4212 0.0024

Table 4.4: Case II-C: Analytical solution using modified Bouwer and Rice approach


4.2.4 Case II-D: Effect of Different LNAPL Viscosity

The parameter which is influenced by changing the viscosity of LNAPL is the LNAPL

mobility (see Eq. 2.11). Less viscous liquids results in higher LNAPL mobility (see

Fig. 4.6a) which makes LNAPL recovery faster in the well (Fig. 4.6b).

(a) Maximum LNAPL mobility during

bail-down test

(b) LNAPL thickness in well after bailing

Figure 4.6: Case II-D: Effect of different LNAPL viscosity

µInput Tn Kanalytical 80 % recovery time Estimated recovery rate

10−3 Pa s m2/s m2 min gal/min

100 2.59× 10−7 2.99× 10−12 2880 0.0047

50 2.59× 10−6 1.50× 10−11 1680 0.0080

20 2.19× 10−5 2.53× 10−11 1015 0.0133

Table 4.5: Case II-D: Analytical solution using modified Bouwer and Rice approach

4.3 CASE III: Effect of Multi-Layered Soil 32

4.3 CASE III: Effect of Multi-Layered Soil

4.3.1 CASE III-A: 2m Fine Layer Between Silt and Coarse

Layer (LNAPL in Fine Layer)

In this case LNAPL contamination lies only in the fine soil layer, so a unique satu-

ration profile is achieved at the equilibrium with a maximum saturation of 0.47 (Fig.

4.7a). The LNAPL transmissivity estimated by the modified Bouwer and Rice ap-

proach (Huntley, 2000) [11] is nearly the same as that estimated by analytical solution

for the measured thickness of LNAPL in the well (Joeng, 2014) [14]. The recalculated

soil permeability by both solutions corresponds to the same order of magnitude as of

the input value of the fine layer (Tab. 4.6). As most of the LNAPL is flowing to the

well from the fine layer, the process of LNAPL recovery in the well is correspondingly

slow (Fig. 4.7b).


Figure 4.7: Case III-A: 2m fine layer (LNAPL in fine layer)

Huntley 2000 Jeong 2013

Tn Kanalytical Tn Kanalytical

m2/s m2 m2/s m2

2.27× 10−7 1.58× 10−12 2.93× 10−7 2.05× 10−12

Table 4.6: Case III-A: Analytical solution

4.3 CASE III: Effect of Multi-Layered Soil 33

4.3.2 CASE III-B: 1m Fine Layer Between Silt and Coarse

Layer (LNAPL in Fine and Coarse Layer)

In this case LNAPL contamination lies in the fine and coarse soil layers. It can be seen

from Fig. 4.8a that there is a discontinuity in the saturation profile at the interface

of the two soil layers. The maximum LNAPL saturation jumps from 0.69 in the fine

layer to 0.9 in the coarse layer.

The LNAPL transmissivity estimated by the modified Bouwer and Rice approach

(Huntley, 2000) [11] is in the same order of magnitude as estimated by the analyt-

ical solution for the measured thickness of LNAPL in the well (Joeng, 2014) [14]. The

recalculated soil permeability by both solutions corresponds to the same order of the

magnitude as the average value of the fine and coarse layers (Tab. 4.7). In this case

LNAPL also flows from the coarse layer to the well, thus the process of LNAPL recovery

in the well is faster (Fig. 4.8b).


Figure 4.8: Case III-B: 1m fine layer (LNAPL in fine and coarse layer)

Huntley 2000 Jeong 2013

Tn Kanalytical Tn Kanalytical

m2/s m2 m2/s m2

2.59× 10−6 3.62× 10−11 9.51× 10−6 6.64× 10−11

Table 4.7: Case III-B: Analytical solution

Chapter 5

Summary and Outlook

5.1 Summary

When there is a leakage from an industrial site it is necessary to remove the contami-

nate from the site. To design an efficient and effective recovery system information

regarding the type of contaminate, its chemical composition, transmissivity, volume

and recovery rate from an aquifer are required. There are different methods to get

this information, among which one of the commonly used methods is the bail-down

test. Data from the bail-down test can not be used directly to get all the information,

thus an analytical solution is required to get the information such as transmissivity,

volume and initial recovery rate. In this work two analytical approaches were used for

analysis of bail-down test model results to determine the LNAPL transmissivity. The

first approach is based on modified Bouwer and Rice analysis for slug test (Huntley,

2000) [11]. The second approach is based on measured well thickness for multi-layered

soil (Jeong, 2014) [14]. A comparison was done for multi-layered soil between the

results obtained by both analytical methods.

In this study the contaminate considered was a Light Non Aqueous Phase Liquid

(LNAPL) with fluid properties defined in Tab. 3.1 for the homogeneous cases and

Tab. 3.3 for the multi-layered soil. To observe the process during LNAPL recovery by

bail-down test a multiphase (i.e 3p LNAPL/water/air) non-compositional model was

simulated on Dumux numerical simulator. The effects of capillary pressure, saturation

and relative permeability were incorporated in the model via Van Genuchten’s

(1980) [9] and Parker’s (1987) [19] models.

A radial symmetric domain with radius of 10 m and depth of 10 m was setup. The

model was simulated for different cases to see the effect of LNAPL recovery in the

well by varying different parameters such as soil permeability K, Van Genuchten α,

initial oil thickness dn and viscosity. The model was also simulated for a multi-layered

soil configuration in the formation.

34

5.2 Conclusion 35

5.2 Conclusion

The applied multiphase (i.e 3p LNAPL/water/air) model replicates the physical pro-

cess observed during the bail-down test, thus the instantaneous extraction of LNAPL

from the well and its recovery in the well during baildown test can be described by

modeling three phase LNAPL/water/air flow in a radial domain. Results show that

the model is physically realistic and is capable of describing field data.

Numerical solution results show that if the bail-down test is done properly and water in

the well rises quickly enough, so that the potentiometric head remains constant during

the test, then the modified Bouwer and Rice method (Huntley, 2000) [11] can predict

good estimates of LNAPL transmissivity and initial recovery rates.

LNAPL recovery in the well and LNAPL transmissivty are highly dependent on the

input soil parameters and fluid properties. It was seen that when all the input param-

eters were in the proper range for a specific soil, the analytical solution estimated good

results. Reliable results from this model are only possible when the input parameters

are fitted with field data and sensitivity of parameters are done. In this work we only

showed the response of LNAPL recovery in a well by changing parameters, but no

sensitivity analysis was done.

LNAPL transmissivity for a mulit-layered soil predicted by the modified Bouwer and

Rice method (Huntley, 2000) [11] and the measured LNAPL thickness in the well (Jo-

eng, 2014) [14] was in the same order of magnitude. In the cases tested the arrangement

of the layers were idealized, the bottom layer in the two cases simulated were coarse

and the water rise in the well was quick that was the reason that modified Bouwer and

Rice method (Huntley, 2000) [11] performed well. The estimated LNAPL transmissiv-

ity can be erroneous if the bottom soil is considered to be silt then the water rise will

be slow, so further model validation for different soil arrangement has to done.

5.3 Outlook

The applied model in this work was tested for idealized conditions for a bail-down test.

Additional work is required to see the model’s response to other reservoir conditions,

well parameters and for random heterogeneity in the formation. In this work the

effects of different parameters were shown but the sensitivity analysis of parameters

was not done, so unknown parameters can be estimated by optimization algorithms

that minimize the difference between observed and field fluid elevations in the well.

The applied model for the bail-down test in this work is a three phase non compositional

model which neglects the dissolution, volatization and biodegradation of LNAPL. In

Dumux this bail-down problem can easily be extend to a compositional model where

these effects can be observed. The compostional model then can be tested to see the

efficiency of different LNAPL recovery options.

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Master Thesis Three Phase (Water, Air and NAPL) Modeling ... · Master Thesis Three Phase (Water, Air and NAPL) ... Waqas Ahmed Matriculation number 2708711 Stuttgart, 7 March,2014