THESIS

DIRECT MEASUREMENT OF LNAPL FLOW USING SINGLE WELL PERIODIC MIXING REACTOR TRACER

TESTS

Submitted by

Tim Smith

Department of Civil and Environmental Engineering

In partial fulfillment of the requirements

For the Degree of Master of Science

Colorado State University

Fort Collins, Colorado

Summer 2008

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COLORADO STATE UNIVERSITY May XX, 2008 WE HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER OUR SUPERVISION BY TIM SMITH ENTITLED “DIRECT MEASUREMENT OF LNAPL FLOW USING SINGLE WELL PERIODIC MIXING REACTOR TRACER TESTS” BE ACCEPTED AS FULFILLING, IN PART, REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE. Committee on Graduate Work

_______________________________________ Committee member: Dr. Charles D. Shackelford _______________________________________ Committee member: Dr. David McWhorter _______________________________________ Advisor: Dr. Thomas Sale _______________________________________ Department Head: Dr. Luis Garcia

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Abstract of Thesis

DIRECT MEASUREMENT OF LNAPL FLOW USING SINGLE WELL

PERIODIC MIXING REACTOR TRACER TESTS

Through standard industrial practices, Light Non-Aqueous Phase Liquids

(LNAPLs) have been inadvertently released into the environment. LNAPL management

strategies are often based on the stability of LNAPL bodies. Numerous methods have

been developed for estimating LNAPL stability. The purpose of this thesis is to present a

simple direct method for estimating LNAPL stability under natural gradients involving

periodic mixing of a tracer in LNAPL.

The approach builds on single well tracer dilution techniques with the variation

that mixing is periodic versus the conventional approach of continuous mixing. The

approach is referred to as Periodic Mixing Reactor (PMR) tests. Advantages of the PMR

test include simplified field procedures and an ability to conduct multiple concurrent

tests. The PMR solution presented is an implicit equation iteratively solved for a

vertically-averaged horizontal LNAPL flow rate through a monitoring well. The input

parameters are change in tracer concentration over the elapsed time, the elapsed time

between periodic mixing, and the diameter of the monitoring well. As elapsed time

between period mixing events approaches zero, the PMR solution converges to the

conventional “Well-Mixed” Reactor (WMR) solution.

Laboratory and field experiments were conducted. These experiments

demonstrate the ability of the PMR test to resolve LNAPL flow rates in porous media.

Two separate laboratory experiments were conducted, a beaker experiment and a large

sand tank experiment. The beaker experiment was a proof of concept experiment to see

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if further testing was warranted. LNAPL discharge through the beaker was 1.32

milliliters per minute. The PMR test underestimated the LNAPL discharge by

approximately 12%. This is likely due to the experimental procedures rather than

limitations in the PMR method. A large sand tank experiment was conducted. This

experiment tested the PMR method in a monitoring well in porous media. Eight PMR

tests were conducted in the sand tank involving four LNAPL thicknesses ranging from

4.0 to 28.3 centimeters and eight LNAPL discharge rates ranging from 0.2 to 7.2

milliliters per minute. The percent differences between known and measured LNAPL

discharges through the sand tank range from 1.3% to 6.9%.

Two separate field experiments took place at a former refinery in Casper, Wyoming.

The first experiment took place adjacent to LNAPL recovery wells. The formation

LNAPL discharge within the radius of influence of the LNAPL recovery well was known

based on LNAPL recovery rates. The formation LNAPL discharge was estimated using

PMR tests conducted in monitoring wells within the radius of influence of the LNAPL

recovery well. Four PMR tests were conducted. The average percent differences

between the known and estimated formation LNAPL discharge range from 24% to 45%.

The second field experiment was conducted in areas where the LNAPL bodies are

thought to be stable. LNAPL flow rates varied from 0.02 to 1.23 feet per year. The PMR

tests yielded repeatable low LNAPL flow rates.

Opportunities for further mathematical and equipment development are presented.

Mathematical developments could include accounting for diffusive losses of tracer from

the monitoring well to the formation and time varying LNAPL volumes in wells.

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Equipment developments could include acquiring a spectrometer that is insensitive to

weather conditions experienced during field testing.

Tim Smith Department of Civil and Environmental Engineering

Colorado State University Fort Collins, CO 80523

Summer 2008

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Table Of Contents

1 Introduction ......................................................................................................................................... 1

2 Review of Current Methods to Estimate LNAPL Flow ................................................................... 4

2.1 Estimation of LNAPL Flow ......................................................................................................... 4 2.1.1 Estimation of Conductivity to LNAPL ................................................................................... 5 2.1.2 Issues with Estimation Forces Driving LNAPL Flow ............................................................ 7 2.1.3 Summary of LNAPL Flow Discussion ................................................................................... 9

2.2 Direct Measurement of LNAPL Flow ........................................................................................ 10

2.3 Conclusions ............................................................................................................................... 14

3 Theory ................................................................................................................................................ 16

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

3.2 Derivation .................................................................................................................................. 19

3.3 Calculation of LNAPL Flow Through the Formation ............................................................... 25

3.4 Potential Sources of Error, Approximate Solutions, and Critical Assumptions ........................ 30 3.4.1 Issues Associated with the Nonlinearity of the Displaced Volume with Respect to ....... 30 3.4.2 Approximate Solution for LNAPL Discharge Through a Monitoring Well ......................... 34 3.4.3 Comparison between the PMR Solution and the WMR Solution ......................................... 38 3.4.4 Critical Assumptions for the PMR Test ................................................................................ 41

3.5 Conclusions ............................................................................................................................... 42

4 Laboratory Experiments .................................................................................................................. 43

4.1 Beaker Experiment .................................................................................................................... 43 4.1.1 Materials ............................................................................................................................... 43 4.1.2 Methods ................................................................................................................................ 44 4.1.3 Results .................................................................................................................................. 45

4.2 Large Tank Experiment ............................................................................................................. 48 4.2.1 Materials ............................................................................................................................... 48 4.2.2 Methods ................................................................................................................................ 50 4.2.3 Results .................................................................................................................................. 51

4.3 Laboratory Experiments Conclusions ....................................................................................... 54

5 Field Experiments ............................................................................................................................. 55

5.1 Site Introduction ........................................................................................................................ 55

5.1.1 Historic Site Operations ............................................................................................................ 55 5.1.2 Site Geology and Hydrogeology........................................................................................... 58 5.1.3 Current Remedial Measures ................................................................................................. 59

5.2 PMR Tests Adjacent to Active LNAPL Recovery Wells ............................................................. 59 5.2.1 Materials ............................................................................................................................... 62 5.2.2 Methods ................................................................................................................................ 62 5.2.3 Results .................................................................................................................................. 63 5.2.4 Discussion ............................................................................................................................. 67

5.3 PMR Tests in Areas with Low LNAPL Flow Rates .................................................................... 69 5.3.1 Materials ............................................................................................................................... 70 5.3.2 Methods ................................................................................................................................ 70

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5.3.3 Results .................................................................................................................................. 71 5.3.4 Discussion ............................................................................................................................. 71

5.4 Field Experiments Conclusion .................................................................................................. 72

6 Thesis Conclusions ............................................................................................................................ 74

7 Opportunities for Further Method Development........................................................................... 77

8 References .......................................................................................................................................... 80

Appendix A Theory ........................................................................................................................... A-1

Appendix A.1 Maximum Time Allowed Between Periodic Mixing ................................................... A-1

Appendix A.2 Derivation of Volume Displaced using a Trigonometric Approach ........................... A-5

Appendix A.3 Derivation of Volume Displaced using a Calculus-based Approach ......................... A-8

Appendix A.4 Data Output from Randomly Generated Vertical Flow Profiles .............................. A-13

Appendix B Laboratory Experiments ..............................................................................................B-1

Appendix B.1 Beaker PMR Test Reduced Data ................................................................................ B-1

Appendix B.2 Large Tank Experiment Reduced Data ...................................................................... B-2

Appendix C Field Experiments ........................................................................................................ C-1

Appendix C.1 PMR Test Field Procedure Flow Chart .....................................................................C-1

Appendix C.2 Field Experiment Well Data .......................................................................................C-3

Appendix C.3 First Field Experiment Data Reduction .....................................................................C-4

Appendix C.4 First Field Experiment Calculations ..........................................................................C-5

Appendix C.5 Second Field Experiment Data Reduction and Calculations .....................................C-7

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List of Figures Figure 3.1 Periodic mixing reactor conceptual model ...................................................... 18 Figure 3.2 Coordinate system ........................................................................................... 18 Figure 3.3 Volume displaced conceptual model ............................................................... 25 Figure 3.4 Flow convergence factor conceptual model .................................................... 26 Figure 3.5 Variable LNAPL flow conceptual model ........................................................ 31 Figure 3.6 Nonlinearity of volume displaced with respect to ....................................... 32 Figure 3.7 Linear volume displaced conceptual model .................................................... 35 Figure 3.8 Percent error assuming linear volume displaced with respect to ................ 36 Figure 3.9 Percent error assuming linear volume displaced in terms of ....................... 37 Figure 3.10 WMR signal loss compared to the PMR signal loss ..................................... 39 Figure 3.11 Error associated with analyzing a PMR test as a WMR ................................ 40 Figure 4.1 Beaker PMR test experiment configuration .................................................... 44 Figure 4.2 Beaker experiment: normalized fluorescence intensity versus time ............... 46 Figure 4.3 Beaker experiment: reduced data .................................................................... 47 Figure 4.4 Large sand tank configuration ......................................................................... 49 Figure 4.5 Large tank experiment: reduced data .............................................................. 52 Figure 4.6 Large tank experiment: flow convergence factor versus formation LNAPL thickness ............................................................................................................................ 53 Figure 4.7 Large tank experiment: flow convergence factor versus known LNAPL discharge ........................................................................................................................... 53 Figure 5.1 BP Casper former refinery South Properties Area map .................................. 57 Figure 5.2 LNAPL recovery well cluster conceptual model ............................................ 60 Figure 5.3 R93 area wells ................................................................................................. 61 Figure 5.4 R91 area wells ................................................................................................. 61 Figure 5.5 R91 area LNAPL discharges ........................................................................... 66 Figure 5.6 R93 area LNAPL discharges ........................................................................... 66 Figure A.1 Trigonometric derivation: conceptual model and coordinate system ........... A-6 Figure A.2 Calculus derivation: conceptual model and coordinate system .................... A-8 Figure A.3 Randomly generated vertical flow profile .................................................. A-14

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List of Tables Table 3.1 Potential error due to the nonlinearity of volume displaced with respect to . 33 Table 4.1 Large tank experiment: best fit flow convergence factors ................................ 52 Table 5.1 Observation well information .......................................................................... 63 Table 5.2 Measured LNAPL discharges ........................................................................... 65 Table 5.3 Estimated formation LNAPL discharges .......................................................... 65 Table 5.4 Percent difference between estimated and known formation LNAPL discharges........................................................................................................................................... 67 Table 5.5 Flow convergence factors ................................................................................. 67 Table 5.6 Measured LNAPL flow rates ............................................................................ 71

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1 Introduction

Petroleum liquids have been central to modern living for the last 100 years.

Unfortunately, historic management practices have resulted in release and accumulation

of petroleum liquids in subsurface environments beneath petroleum production,

transmission, refining, and storage facilities. Petroleum liquids in subsurface

environments are widely referred to as Light Non-Aqueous Phase Liquids (LNAPLs).

Concerns with LNAPLs center on impacts to groundwater quality, impacts to indoor air

quality, and migration of LNAPLs into clean soils and/or surface water bodies. While

active release of LNAPLs occurs subsurface LNAPL bodies expand. After the release of

LNAPLs cease and forces driving LNAPL migration diminish and bodies of LNAPL

become more stable.

Rates of LNAPL flow are commonly estimated using Darcy’s equation.

Unfortunately, this approach has a number of limitations. First, estimation of input

parameters is challenging (Sale, 2001 and Devlin and McElwee, 2007). Secondly,

inherent assumptions including an areally extensive continuum of a homogenous LNAPL

body are often not met.

In 2002 an ongoing collaboration between Colorado State University (CSU),

Chevron, and Aquiver Inc. led to the concept of using a LNAPL soluble tracer to measure

LNAPL flow rates using single well tracer dilution techniques. For these techniques,

LNAPL in a monitoring well is treated as a “well-mixed reactor” (WMR). A LNAPL

soluble tracer is mixed into the LNAPL in the monitoring well. The tracer and LNAPL

are continually mixed. The principle behind single well tracer dilution techniques for

LNAPL is that the rate of tracer loss is proportional to the LNAPL flow rate through the

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monitoring well. This concept has been developed and used to measure groundwater

flow rates (Freeze and Cherry, 1979).

The WMR approach for measuring LNAPL flow was validated in laboratory studies

(Taylor, 2004 and Sale et. al., 2007b). Also, extensive field testing was conducted

(Taylor, 2004; Sale and Taylor, 2005; and Iltis, 2007). Unfortunately, experience from

field studies led to the recognition of a number of limitations of the WMR approach.

To address the limitations of the WMR approach, a new approach (the topic of this

thesis) has been developed. The new approach involves the introduction of a LNAPL

soluble tracer into LNAPL in a monitoring well, periodic mixing of the LNAPL, and

measurement of tracer concentration at the time of mixing. The new approach is referred

as a Periodic Mixing Reactor (PMR) test. PMR tests overcome many of the limitations

of the WMR single well tracer test.

The objectives of this thesis are to:

1. Introduce the concept of a PMR

2. Derive a solution for a LNAPL flow rate using periodic mixing

3. Demonstrate PMR tests in LNAPL at a laboratory scale

4. Demonstrate PMR tests in LNAPL at a field scale

This thesis is organized into seven sections:

1. Introduction – This is presented above.

2. Review of Current Methods to Estimate or Measure LNAPL Flow Rates – This

section provides a review of the conventional Darcy equation approach and two

mass balance approaches. Limitations described in this section sets a foundation

for advancing the PMR approach.

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3. Theory – This section presents the PMR conceptual model, PMR derivation, and

additional mathematical considerations. The PMR solution is used to estimate

LNAPL flow rates from experimental data presented in Sections 4 and 5.

4. Laboratory Experiments – This section presents two laboratory experiments

which were conducted. The first experiment was a beaker experiment testing the

conceptual model of the PMR. The second experiment consisted of conducting

PMR tests in a large sand tank with a range of LNAPL formation thicknesses and

LNAPL discharges.

5. Field Experiments – This section describes two experiments conducted at a

former refinery. The first experiment was conducted in areas of known LNAPL

discharge. PMR tests were completed in monitoring wells adjacent to LNAPL

recovery wells. The LNAPL discharge measured at the monitoring well was then

compared to the known LNAPL discharge at the LNAPL recovery well. The

second experiment consisted of conducting PMR tests in areas far from LNAPL

recovery wells, where LNAPL bodies are thought to be stable.

6. Thesis Conclusions – The PMR theory, laboratory experiments, and field

experiments are summarized in this section.

7. Opportunities for Further Method Development – This section presents additional

ideas to improve the PMR method. Suggestions include broadening the

derivation to include diffusive flux and transient volume terms and improvements

to equipment.

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2 Review of Current Methods to Estimate or Measure LNAPL Flow Rates

This section provides a review of current methods for estimating LNAPL flow.

This review provides the foundation for advancement of the PMR test methods.

2.1 Estimation of LNAPL Flow

Darcy’s equation is widely used to estimate LNAPL flux. A LNAPL flux is a

vector quantity having both magnitude and direction. Given Equation 2.1 below, the

input for Darcy’s equation are conductivity to LNAPL and the derivative of LNAPL head

with respect to distance. The equation is applicable to a body of LNAPL that exists as a

continuum. In one dimension, assuming homogenous isotropic porous media, Darcy’s

equation for volumetric flux is defined as

dx

dhKq L

L

2.1 where: q = LNAPL volumetric flux (L/T)

LK = conductivity to LNAPL (L/T)

Lh = LNAPL hydraulic head (L) x = distance (L)

LK is a function of the aquifer’s ability to transmit fluid and the fluid being transmitted.

This is illustrated in Equation 2.2 as

L

LrLL

gkkK

2.2 Where: k = intrinsic permeability (L2)

rLk = LNAPL relative permeability (unitless)

L =LNAPL density (M/L3) g = gravitational acceleration coefficient (L/T2)

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L = LNAPL absolute viscosity (M/L-T)

dx

dhL is the driving force expressed as a force per unit weight divided by a distance.

Regardless of a formation’s ability to transmit fluid, in the absence of a driving force, no

LNAPL movement will occur. Conversely, if a driving force appears to exist between

two points but there is a discontinuity in the fluid of interest, the apparent driving force

measured can not be applied.

2.1.1 Estimation of Conductivity to LNAPL

LNAPL baildown tests, petrophysical techniques, and LNAPL pumping tests are

methods used to measure an aquifer’s conductivity to LNAPL. LNAPL baildown tests

are described in Huntley (2000). LNAPL pumping tests are advanced in McWhorter and

Sale (2000). Iltis (2007) provides a rigorous review of baildown tests and petrophysical

techniques through development and comparison of estimates of formation

transmissivities to LNAPL at laboratory and field scales. LNAPL pumping tests will not

be discussed.

LNAPL baildown tests are performed by removing a volume of LNAPL from the

monitoring well using a bailer and measuring the depth to the air-LNAPL and LNAPL-

water interfaces until 90% of the initial LNAPL thickness has returned. Huntley (2000)

proposed that LNAPL baildown tests could be used to measure LNAPL transmissivity

using two different techniques. The two techniques are based on slug test solutions

presented by Jacob and Lohman (1952) and Bouwer and Rice (1976) modified for two

fluids (LNAPL and water). LNAPL transmissivity can be converted to conductivity to

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LNAPL by dividing LNAPL transmissivity by the continuous thickness of LNAPL in the

formation. The conductivity to LNAPL can be used in Darcy’s equation to estimate a

LNAPL flow rate.

There is some subjectivity when analyzing the data from LNAPL baildown tests.

Testa and Paczkowski (1989) list sources of error including:

Inaccuracy of probe used to measure the depth of fluid levels in a well

Inability to measure early time recovery data due rapid fluid level changes

Depression of the LNAPL-water interface due to bailing water in low flow

formations

Borehole/gravel pack effects

Subjectivity in curve matching

Estimation of conductivity to LNAPL can also be developed through

petrophysical analysis. This involves collection of representative soil samples,

laboratory-scale measurement of relevant parameters (Sale, 2001) and use of models

presented in Farr et. al. (1990) or Lenhard and Parker (1990). Both Farr et. al. (1990) and

Lenhard and Parker (1990) rely on the assumptions of vertical equilibrium and

homogenous porous media through the interval of concern. Additionally, petrophysical

analyses require knowledge of the LNAPL thickness in a monitoring well, LNAPL

density, LNAPL viscosity, air-LNAPL surface tension, and the LNAPL-water surface

tension. The LNAPL thickness is used to estimate the vertical distribution of capillary

pressure in the formation. The calculated capillary pressures are then used to estimate

LNAPL and water saturations in the formation using either a Brooks-Corey (1966) or

Van Genuchten (1980) capillary pressure-saturation model. The calculated saturations

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are corrected based on Parker et. al. (1987) to reflect that if at a given elevation the

saturation is based on an air-LNAPL or LNAPL-water capillary pressure/saturation

relationship. The corrected saturations are then used to estimate a relative permeability

of LNAPL as a function of elevation.

Following Iltis (2007), limitations of the petrophysical analyses include:

1. The analysis ignores soil heterogeneities and hysteresis. Ignoring soil

heterogeneities could eliminate discrete intervals highly saturated with LNAPL or

discrete intervals without LNAPL present.

2. Hysteretic effects cause the LNAPL saturations to be bounded by an upper

saturation, which is the initial drainage curve and a lower saturation, which is the

initial imbibition curve. As fluid levels rise and fall in the well, the formation

saturations correspond with scanning saturation curves that fall somewhere

between the upper and lower bounds of LNAPL saturations. Lenhard (1992)

suggests that ignoring hysteresis could result in error in LNAPL saturations as

great as 50% (Iltis, 2007).

3. Disturbances to field collected soil samples lead to difficulty in quantifying pore

fluid characteristics (Sale, 2001). These errors would be propagated through the

calculations.

2.1.2 Issues with Estimation Forces Driving LNAPL Flow

In a field situation the LNAPL gradient can be estimated by measuring the surface

of the LNAPL table at three points. The LNAPL table is the surface where the pressure

of LNAPL is equal to atmospheric pressure. From a practical standpoint, the force

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driving LNAPL flow, dx

dhL , is typically estimated by x

hL

where Lh is the difference in

the elevation of the air-LNAPL interface at two points located along the direction of

maximum head loss separated by a distance x .

Key assumptions for LNAPL gradient include:

1. The porous media between the two points is isotropic.

2. The change in head between the two points is linear.

3. The LNAPL between the two points is a continuous body with uniform density.

Commingled LNAPL bodies consisting of LNAPL from different sources can

have different densities. At a microscopic scale, LNAPLs from different sources

are miscible, but at a macroscopic scale, LNAPLs from different sources can

behave as immiscible fluids. Also, LNAPL cannot “pinch-out” and there cannot

be capillary barriers between the two points.

4. LNAPL in the well is in direct hydraulic communication with LNAPL in the

formation. The monitoring well must be screened across the interval of interest,

and the well screen must not occlude LNAPL due to capillary effects. Monitoring

well design can affect fluid interface measurement. An example of poor

monitoring well construction is a monitoring well where the LNAPL-water

interface in the well is above the top of the screened interval so the LNAPL is not

hydraulically connected to the formation.

5. LNAPL in the well is in hydrostatic equilibrium with the LNAPL in the

formation. This assumption is violated in tidal settings where LNAPL and water

in the formation are constantly migrating vertically. Marinelli and Durnford

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(1996) discuss situations where the fluids in monitoring wells can change

suddenly due to hysteresis.

6. The two points are far enough apart such that the magnitude of head loss between

the points is larger than the error associated with measuring the head (Devlin,

2007). Error can be a result of top-of-casing survey error. Error can also be a

result of measurement error. Measurement error can be due to highly viscous

LNAPL, LNAPL that forms a LNAPL-water emulsion, and/or monitoring wells

fouled from biologic activity.

2.1.3 Summary of LNAPL Flow Discussion

The preceding sections introduce two methods used to estimate LNAPL flow.

LNAPL baildown tests estimate conductivity to LNAPL from in situ field tests.

Petrophysical analyses estimate conductivity to LNAPL using laboratory testing of field

collected “undisturbed” soil samples. In both cases the LNAPL flux is found by taking

the product of the conductivity to LNAPL and the LNAPL gradient. As discussed by Iltis

(2007), both LNAPL baildown tests and petrophysical analyses have many sources of

error when estimating conductivity to LNAPL. Also, as discussed in Section 2.1.2, an

accurate estimate of a LNAPL gradient is difficult to determine. Iltis (2007) reaches the

following conclusions. First, if the objective is to obtain a formation’s conductivity to

LNAPL, then baildown tests should be used before tracer tests (discussed in Section 2.2)

and petrophysical analyses. Secondly, if the objective is to obtain the LNAPL flow rate,

then tracer tests should be used before baildown tests and petrophysical analyses. The

reason that baildown tests are preferable to tracer tests for estimating conductivity to

LNAPL is that the gradient is not needed to make an estimate. The reason that tracer

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tests are preferable to baildown tests for estimating LNAPL flow is that the gradient is

not needed to make the estimate.

An error analysis has not been conducted to quantify the cumulative effects of

individual sources of error, but such an analysis could be an important component when

presenting LNAPL flow rates obtained from estimation.

2.2 Direct Measurement of LNAPL Flow

This section describes direct measurement of LNAPL flow using tracer dilution

techniques. In addition, a related technique developed by Hatfield et. al. (2004) for

measuring fluxes of aqueous phase constituents is presented.

Taylor (2004), Sale et. al. (2007b), and Sale et. al. (2007c) developed a method to

directly measure LNAPL flow using single well tracer dilution tests assuming a WMR. A

primary advantage of this method is that the knowledge of local LNAPL gradient is not

required to estimate a LNAPL flow rate. LNAPL flow rate is determined using a mass

balance on the tracer introduced to a monitoring well.

Single well tracer dilution tests assuming a WMR require continuous mixing. The

mixing device must be designed to minimize non-flow related tracer displacement from

the well. A mixing device was developed to operate in LNAPL (Taylor, 2004; Sale et.

al., 2007b; and Sale et. al., 2007c), which in many cases is a low flow environment.

Special attention had to be given to a low energy but thorough mixing system since any

tracer displaced from the well due to mixing during a tracer test could result in higher

than actual apparent LNAPL flow rates. The core of the mixing device is a piece of

hollow stainless steel pipe. The stainless steel pipe would occlude a volume of LNAPL

inside the pipe’s solid section, which effectively reduces the mixed LNAPL volume.

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This made the WMR smaller so that the tests could occur over a shorter period of time.

Six “diffusive” mixing rods surround the hollow stainless steel pipe. Three of the

diffusive mixing rods pump LNAPL into the tool through a port from which fluorescence

measurements are made with a fiber optic cable. The other three mixing rods are used to

discharge LNAPL from the tool back into the monitoring well. A detailed explanation of

the tool and mixing system can be found in Taylor (2004), Sale et. al. (2007b), and Sale

et. al. (2007c).

The LNAPL flux tool worked well in laboratory settings (Taylor, 2004; Sale et. at.,

2007b; and Sale et. al., 2007c). Also, successful field applications at a former refinery in

Casper, Wyoming were described in Taylor (2004) and Sale and Taylor (2005).

Unfortunately, further field tests using the LNAPL flux tool led to the recognition of a

number of limitations that are described.

Subsequent to the testing in Casper, it was realized that a practical tool for real

world application at active petroleum sites would need a number of substantial

modifications. The Taylor (2004) field version of the LNAPL flux tool was modified to

have low energy requirements for remote field deployment. Energy requirements were

reduced until the operation of the flux tool, spectrometer, laptop computer, thermistor,

and pressure transducer could be powered by a 12 volt DC battery charged by a solar

panel array. The reduced power supply did not allow for a constant temperature storage

container for the spectrometer. Despite best efforts to insulate the spectrometer from

weather conditions, the temperature of the spectrometer would vary throughout the test.

Unfortunately, the spectrometer output was not directly dependent on temperature alone.

The spectrometer could also be affected by humidity, which would vary throughout the

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test. Also, voltage output from the 12 volt DC battery would vary with time affecting the

spectrometer. Lastly, there was the potential for instrument reading to drift over

extended periods of operation. Post-test correction for voltage, temperature, humidity,

and instrument drift often resulted in variations in tracer intensity on the same magnitude

of the observed tracer loss measured during the test.

The placement of the LNAPL flux tool in a monitoring well was also challenging.

The flux tool had to be placed at an accurate elevation with respect to the air-LNAPL

interface in the well. The diffuser mixing rods had a series of small holes to either draw

LNAPL into or discharge LNAPL from the tool. If the holes in the diffuser rods that

drew LNAPL into the tool were above the air-LNAPL interface, mostly or only air would

be circulated through the tool. Also, if the tool was too low in the LNAPL, a hole drilled

in the hollow stainless steel pipe (to relieve pressure) would be in the LNAPL, and the

volume of LNAPL that was supposed to be occluded by the stainless steel pipe would

become part of the WMR. Also, the tool was hung in the well with a static steel cable. If

the flux tool was initially set correctly, and the fluid levels changed during the test, then

the above mentioned problems could result. Furthermore, the monitoring well had to be

deep enough to accommodate the tool beneath the LNAPL-water interface, so the tool

could only work in wells with more than one meter of water saturated thickness. Lastly,

the flux tool could only be deployed in wells with greater than 0.3 feet and less than 3.0

feet of LNAPL.

The mechanical operation of the flux tool was also challenging in some field

settings. The small holes in the diffuser mixing rods were not effective in settings with

high viscosity LNAPL and/or in wells with suspended solids. The diffuser mixing rods

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were powered by a small self-priming pump with a series of check valves. If particulate

material entered the recirculation loop, it tended to plug the pump’s filter or disable the

pump’s check valves. Other operational issues were the complex and numerous electrical

components and wireless phone connection. On their own, the individual electrical

components were largely reliable, but collectively the failure rate was high enough that

the tool needed to be monitored closely during operation.

There were also practical issues related to operating the flux tool on a site-wide

scale. At most sites the flux tool would remain in a monitoring well for 4-7 days, so the

signal loss was large enough to distinguish from spectrometer drift. If testing were to

occur in multiple wells at a site with only one set of equipment, the field activities would

occur over a long period of time, introducing temporal variation into a site-wide dataset.

Multiple equipment sets to conduct numerous tests, would be prohibitively expensive.

Overall, the concept of the LNAPL flux tool was correct and validated in laboratory

conditions. As the flux tool evolved for field conditions, many unforeseen design issues

arose that ultimately resulted in a system that was challenging to deploy. Any further use

of the flux tool approach would require substantial redesign and testing.

Hatfield et. al. (2004) introduces a device called the passive flux meter which is a

permeable sock that fits tightly into a monitoring well. Contained within the permeable

sock is a mixture of hydrophobic and/or hydrophilic sorbents. The sorptive matrix is

spiked with a known quantity of soluble “resident tracers.” The test is conducted by

placing the passive flux meter into a monitoring well. After a period of time, the passive

flux meter is removed from the monitoring well. The sorbent from within the permeable

unit is analyzed for the mass of contaminant sorbed onto the sorbent and the mass of

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resident tracer eluded from the sorbent. Contaminant mass flux through the well can be

estimated by measuring the amount of contaminant that has sorbed onto the sorbent. A

groundwater flux through the monitoring well can be measured by analyzing the amount

of resident tracer eluded from the sorbent (Hatfield et. al., 2004). Although derived

differently, the general form of the solution for groundwater flux through the well is

mathematically equivalent to the solution presented in Section 3.2 and the alternative

solution presented in Appendix A.3. The solution assumes that advection dominates

through the monitoring well. A Peclet number is presented to quantify the low flux rate

limit.

Given a conservative value for the effective diffusion coefficient, the low flux limit

for the method is 0.7 centimeters per day. This low flux limit is still an order of

magnitude higher than expected LNAPL flow rates in some formations. Although the

general solution is equivalent to that of the PMR test, given the current configuration of

the passive flux meter and its lower limit of sensitivity, the passive flux meter seems

impractical to use to measure LNAPL flow.

2.3 Conclusions

This section introduced current methods to estimate LNAPL flow rates. Two

methods were presented using a Darcy approach, and the issues inherent to both were

discussed. Two methods were described for directly measuring LNAPL (and

groundwater) flow using a mass balance. The LNAPL flux tool (Taylor, 2004) overcame

some of the limitations of the Darcy-based approach by using a technique that directly

measures LNAPL flow rates using tracer dilution techniques. Unfortunately, the flux tool

as developed was challenging to deploy in field settings. The passive flux meter

15

presented by Hatfield et. al. (2004) is not sensitive enough in its current configuration to

measure expected low LNAPL flow rates. The PMR test method described in the

following section provides solutions to limitations of the current LNAPL flow rate

measurement techniques described in this section.

16

3 Theory

In this section a derivation is presented that advances a novel approach for using

tracers in LNAPL to measure a vertically-averaged horizontal LNAPL flow rate in a

monitoring well and the adjacent geologic formation. The scenario is:

1. A tracer is introduced at time t into LNAPL in a monitoring well.

2. At a later time ( t ) the tracer and LNAPL in the monitoring well are remixed.

3. The tracer concentration is re-measured.

This procedure is referred to as a Periodic Mixing Reactor (PMR) test. The principle

underlying the procedure and derivation is that the change tracer concentration in LNAPL

in the monitoring well over the period t is proportional to the rate of flow through the

well and the adjacent geologic formation. Also included in this section is an alternative

approximate solution, a comparison between the PMR and the WMR solutions, and a

review of critical assumptions.

3.1 Introduction

The PMR solution is based on a tracer mass balance under the condition of

periodic mixing. The procedure is illustrated in Figure 3.1. The coordinate system and

reference volume for the mass balance is the cylinder of LNAPL in the monitoring well,

as illustrated in Figure 3.2. The following derivation assumes LNAPL flow is in the

direction of 0 . Given the coordinate system, the PMR solution has a magnitude and

direction and results in LNAPL flux (L/T) (a vector quantity). From a practical

standpoint, the direction of LNAPL flux is not defined through a PMR test. Without

knowledge of LNAPL gradient, the PMR solution solves for the LNAPL flow rate (L/T)

17

(a scalar quantity). Throughout this thesis “LNAPL flow rate” will be used rather than

“LNAPL flux” since the local LNAPL flow direction is not known. LNAPL gradient can

be measured independent of the PMR method.

The test is initiated by adding a LNAPL soluble tracer into LNAPL in a

monitoring well at time ot . The tracer is initially “well-mixed” in the LNAPL at a

concentration of otTC . Over the period tttt oo , LNAPL from the formation flows

into the monitoring well, displacing LNAPL with tracer from the monitoring well. The

concentration of tracer in LNAPL flowing into the well inTC is assumed to be zero. This

is described in cylindrical coordinates in as

0,0,2

3

2,

ttttbzrC oowLwTin

3.1

The concentration of tracer in LNAPL flowing out of the well outTC is assumed be a

constant equal to otTC over the period t as shown below

oout tToowLwT CttttbzrC

,0,

22

3,

3.2

At time tto , LNAPL with tracer in the well is re-mixed and the concentration is

remeasured.

18

t<to to< t < t+tt=to t=t+t

Well-mixed tracer added at

time to

No tracer in well prior to to

LNAPL flow in the formations

displaces tracer from the well

Tracer in well is remixed at time

t +t

Figure 3.1 Periodic mixing reactor conceptual model

zContinuous LNAPL occurring about the watertable.

Direction ofLNAPL flow

rw

bwLbfL

/2

/2

0

Monitoring well intercepting LNAPL

Mass balance reference volume

Figure 3.2 Coordinate system

The PMR test has several important operational and practical advantages over the

WMR flux tool approach described in Section 2.2. First, no dedicated in-well equipment

is needed during a PMR test, so multiple wells can be tested concurrently. This allows

for acquisition of concurrent of LNAPL flow rates across a site without temporal

variation. Secondly, the PMR approach eliminates the need to introduce a downhole

pump into the monitoring well (potential ignition source). Lastly, every time a tracer

19

concentration is measured, the spectrometer can be calibrated. Spectrometer calibration

eliminates the effects of temperature, humidity, voltage, and long periods of operation on

the spectrometer readings.

3.2 Derivation

The derivation begins with a mass balance on the tracer in the LNAPL in the monitoring

well defined as

outin TTT QQ

dt

dm

3.3 where:

Tm = mass of tracer in the LNAPL in the well (M) t = time (T)

inTQ = tracer mass inflow into well (M/T)

outTQ = tracer mass outflow from well (M/T)

The mass inflow and outflow terms are expanded to

in

uw

TuTuwLininTT A

dr

dCDCqAJQ

in

*

3.4

out

dw

TdTdwLoutoutTT A

dr

dCDCqAJQ

out

*

3.5 where:

inTJ = tracer mass flow into well (M/L2-T)

inA = influent cross-sectional area normal to flow (L2)

uwLq = LNAPL flow into well from up-gradient side (L/T)

uTC = tracer concentration on the up-gradient side (M/L3)

20

*D = effective diffusion coefficient (L2/T)

wr = radius of well (L)

outTJ = mass flow into well (M/L2-T)

outA = effluent cross-sectional area normal to flow (L2)

dwLq = LNAPL flow out of well from down-gradient side (L/T)

dTC = tracer concentration on the down-gradient side (M/L3)

Next, four assumptions are employed:

1. Diffusive transport is small relative to advective transport on the up-gradient

side of the well.

uw

TuTuwL dr

dCDCq *

3.6

2. Diffusive transport is small relative to advective transport on the down-gradient

side of the well.

dw

TdTdwL dr

dCDCq *

3.7 3. LNAPL flow is at steady state.

wLdwLuwL qqq 3.8

4. The up-gradient and down-gradient cross-sectional areas of flow are equal and

constant.

AAA outin 3.9

Employing the four assumptions yields

ACqQ

uTwLTin

3.10

21

ACqQdTwLTout

3.11 Substitution of 3.10 and 3.11 into 3.3 yields

ACqACqdt

dmdTwLuTwL

T

3.12 This simplifies to

dTuTwL

T CCAqdt

dm

3.13 Separation of the variables and integration yields

tt

tdTuTwL

m

m

T

o

o

totT

otT

dtCCAqdm

3.14 where:

otTm = initial mass in well (M)

totTm

= mass remaining in well after an elapsed time (M)

tt

tdTuTwL

m

mT

o

o

totT

otTtCCAqm

3.15 Applying the limits of integration shown in 3.15 yields

tCCAqmmdTuTwLTT

ottot

3.16 The initial condition in cylindrical coordinates is

otTowLwT CtbzrrC ,0,20,

3.17 where:

wLb = thickness of LNAPL in the well (L)

otTC = initial tracer concentration in the well (M/L3)

22

Substituting of the initial condition into 3.16 yields tCAqmm

otottotTwLTT

3.18 At time tto the well is instantaneously remixed such that the concentration in the well

is uniform. This results in

tot

TowLwT CttbzrrC

,0,20,

3.19 Two conditions are worth noting. First, given LNAPL flow,

totTC

will always be less

than ot

TC . Secondly, the solution is only valid as long as the distance LNAPL flows

along the fastest flow path through the well, over the period t , is less than the well’s

diameter. This limits application of the solution to those conditions where

max

2

wL

w

q

rt

3.20 where:

maxwLq = the maximum LNAPL flow rate through the well (L/T)

The maximum period, t , can be determined after the first data set is collected using

Equation 3.21. The complete derivation of Equation 3.21 is presented in Appendix A.1.

max

2

r

r

wL

w

k

k

q

rt ave

3.21 where:

averk = the average relative permeability of the aquifer (unitless)

maxrk = the maximum relative permeability of the aquifer (unitless)

Simplifying the right hand side of Equation 3.18 yields

23

dTT mmmottot

3.22 where:

dm = mass displaced from well after an elapsed time (M)

Equation 3.22 is rearranged to get

dTT mmmottot

3.23 where:

toto TwLtt CVm

3.24

ottotTwLT CVm

3.25

otTdLd CVm

3.26 and

wLV = volume of LNAPL in the monitoring well (L3)

dLV = volume of LNAPL that has been displaced from the well (L3)

Equations 3.24, 3.25, and 3.26 are substituted into Equation 3.23 yielding

dLwLTwLT VVCVCottot

3.27 Equation 3.27 is rearranged yielding

wL

dL

T

T

V

V

C

C

ot

tt 10

3.28 For clarity, the subscripts “T” (denoting tracer) and the subscripts tt 0 and 0t

(denoting time) are dropped, resulting in

24

wL

dL

o

t

V

V

C

C1

3.29 where:

cos2sin)cos(22 aarbV wwLdL (L3) 3.30

wLwwL brV 2 (L3) 3.31

D

tqwL (unitless)

3.32 and

D = diameter of well (L)

The derivation of dLV from Equation 3.30, is based on a trigonometric approach and is

presented in Appendix A.2. An alternative derivation of dLV found using calculus is

presented in Appendix A.3. An illustration of the process and key variables are presented

in Figure 3.3. It can be envisioned from Figure 3.3 that as LNAPL gets displaced from

the well, the volume displaced per unit width of the monitoring well is not constant.

Potential error associated with the nonlinearity of dLV with respect to is addressed in

Section 3.4.1.

25

/2

/2

0

/2

/2

0

rw

/2

/2

Volume LNAPL displaced VdL

Formation with LNAPL

Perforated well casing

to< t < t+tt=tot=t+t

Post remix uniform tracer

in LNAPL

Uniform initial tracer distribution in LNAPL

tqwL

/2

/2

to< t < t+t

tqwL

0

Figure 3.3 Volume displaced conceptual model

Equations 3.30 and 3.31 are substituted into Equation 3.29 yielding

cos2sincos2 aa

C

C

o

t

3.33

Equation 3.33 is the solution for PMR tests. The LNAPL flow rate through the

well must be found using an iterative approach because Equation 3.33 is an implicit

solution. An alternative but mathematically equivalent solution using a calculus-based

approach for finding the volume of dLV is presented in Appendix A.3.

3.3 Calculation of LNAPL Flow Through the Formation

This section provides a set of equations that converts the LNAPL flow rate

through a monitoring well to a LNAPL flow rate through the formation about a

26

monitoring well. Since the monitoring well provides an area of higher conductivity, flow

lines tend to converge through the well, as illustrated in Figure 3.4.

...

...

.

.

cross-section plan view

Wf 2rwbfLbwL

LNAPL in formation

monitoring well

LNAPL flow and equipotential lines

LNAPL in well

Figure 3.4 Flow convergence factor conceptual model

The flow convergence factor is defined as

wr

w

2

3.34 where:

= flow convergence factor (unitless) w = maximum width of converging flow lines (L)

The flow convergence factor can be determined if properties of the formation, gravel

pack and well screen are known. Halevy et. al. (1967) modified Ogilvi’s (1958) equation

to develop

27

2

3

2

2

3

1

1

2

2

3

2

2

3

1

2

3

2

2

1

1

2

2

2

1

2

3 1111

8

r

r

r

r

k

k

r

r

r

r

k

k

r

r

k

k

r

r

k

k

3.35

where:

3k = hydraulic conductivity of the formation (L/T)

2k = hydraulic conductivity of the gravel pack (L/T)

1k = hydraulic conductivity of the well screen (L/T)

1r = inner radius of well screen (L)

2r = outer radius of well screen (L)

3r = outer radius of gravel pack (L)

A new flow convergence factor for multiphase flow is offered using vertically-averaged

relative permeabilities and intrinsic permeabilities, which is more applicable when

conducting tests in LNAPL. Vertically-averaged relative permeabilities assuming a non-

zero entry pressure are defined in Equation A.3. The flow convergence factor applied to

multiphase flow is presented in Equation 3.36 as

2

3

2

2

3

1

11

222

3

2

2

3

1

22

332

2

1

11

222

2

1

22

331111

8

r

r

r

r

kk

kk

r

r

r

r

kk

kk

r

r

kk

kk

r

r

kk

kk

aver

aver

aver

aver

aver

aver

aver

aver

3.36

where:

3k = intrinsic permeability of the formation (L2)

averk3 = vertically-averaged relative permeability of the formation (unitless)

2k = intrinsic permeability of the gravel pack (L2)

averk2 = vertically-averaged relative permeability of the gravel pack (unitless)

1k = intrinsic permeability of the well screen (L2)

averk1 = vertically-averaged relative permeability of the well screen (unitless)

1r = inner radius of well screen (L)

28

2r = outer radius of well screen (L)

3r = outer radius of gravel pack (L)

Freeze and Cherry (1979) state that the practical limits of the flow convergence

factor for groundwater is between 0.5-4.0, and Equation 3.36 has theoretical limits of

80 . Although not represented in Equation 3.35, it is possible for 0 . A flow

convergence factor of zero would mean that the LNAPL in the well is completely

disconnected from the LNAPL in the formation. An example of this would be LNAPL

flow entirely in the LNAPL capillary fringe. Iltis (2007) tested flow convergence factors

for LNAPL in a large sand tank (described in Section 4.2.1) with laboratory grade

LNAPL (Soltrol 220) and a WMR approach. Results show flow convergence factors

vary from 0.9 for a 0.01 inch slotted PVC well screen and 1.8 for a 0.03 inch stainless

steel wire wrap well screen (Iltis, 2007). Equation 3.37 applies the flow convergence

factor to convert LNAPL flow rates measured in the well to LNAPL flow rates through

the formation, yielding

wL

fLfLwL b

bqq

3.37 where:

fLb = thickness of continuous LNAPL in the formation (L)

The definitions of volumetric LNAPL discharge through the monitoring well and

volumetric LNAPL discharge through the formation are defined as

DbqQ wLwLwL 3.38

DbqQ fLfLfL 3.39

where:

fLq = LNAPL flow through the formation (L/T)

29

wLQ = LNAPL discharge through the monitoring well (L3/T)

fLQ = LNAPL discharge through the formation (L3/T)

Equations 3.38 and 3.39 can be substituted into Equation 3.37. Equation 3.40 relates the

measured LNAPL discharge through a monitoring well to the LNAPL discharge through

the formation, yielding

fLwL QQ 3.40

Following Brooks-Corey (1966), a threshold capillary pressure (displacement pressure) is

needed to achieve a continuous LNAPL saturation in the formation. This results in a

“heel” of LNAPL in a monitoring well that extends below the elevation of continuous

LNAPL in the formation. The displacement pressure can be related to the height of the

heel by

dLwd ghP 3.41

where:

dP = displacement pressure of LNAPL and height of heel in well (M/L-T2)

dh = displacement pressure head of LNAPL and height of heel in well (L)

w = density of water (M/L3)

L = density of LNAPL (M/L3)

As a first order approximation, the thickness of LNAPL in the formation, fLb , is defined

as

dwLfL hbb 3.42

Assuming the displacement pressure is zero, the ratio of LNAPL thickness in the

formation to LNAPL thickness in the well in reduces to one. For this condition

30

fLwL qq 3.43

Other parameters of potential interest such as transmissivity, seepage velocity, and

conductivity to LNAPL can also be found. These equations are developed in Taylor

(2004) and Sale et. al. (2007b).

3.4 Potential Sources of Error, Approximate Solutions, and Critical Assumptions

This section presents information on potential sources of error in conducting PMR

tests. Also, a simpler approximate solution is advanced. The approximate solution has

the advantage that it does not require the assumption of vertically-averaged horizontal

LNAPL flow. Also, a comparison is made between the PMR test solution and WMR

solution developed in Taylor (2004) and Sale et. al. (2007b). Lastly, critical assumptions

associated with applying the PMR test are reviewed.

3.4.1 Issues Associated with the Nonlinearity of the Displaced Volume with Respect to

The PMR method estimates a vertically-averaged horizontal LNAPL flow rate.

More rigorously, LNAPL flow rates will vary based on vertical variation in formation

conductivity to LNAPL. The volume of displaced LNAPL, dLV , is not linear with respect

to . A discrete interval at one elevation could displace either more or less LNAPL than

another discrete interval at a different elevation due to vertical variation in conductivity

to LNAPL. When the two discrete intervals are averaged together by periodic mixing,

the measured tracer concentration will not reflect that one interval may have displaced

more (or less) than another interval. LNAPL in a monitoring well can be thought of as

31

having many thin discrete intervals being displaced at different rates. With periodic

mixing the thin discrete vertical intervals are averaged together, and any discrete interval

that may have displaced more (or less) LNAPL is averaged with the other intervals. By

averaging the intervals (with periodic mixing), the measured concentration ignores the

nonlinearity of dLV with respect to . Figure 3.5 shows a conceptual model of the

variable LNAPL flow with depth.

tttt oo tt o ttt o

Monitoring well

LNAPL in formation

LNAPL in well

Figure 3.5 Variable LNAPL flow conceptual model

The nonlinearity of dLV with respect to is shown graphically in Figure 3.6.

Figure 3.6 shows the normalized volume displacement, which is defined as wL

dL

V

V, plotted

against . Recall from Equation 3.23 that the solution is in violation of the mass balance

at values where 1 .

32

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

No

rmal

ized

Vo

lum

e D

isp

lace

men

t

Figure 3.6 Nonlinearity of volume displaced with respect to

To further examine the potential error of averaging together discrete intervals of

variable LNAPL flow a spreadsheet was created that divides a fixed thickness of LNAPL

in a well into 1,000 discrete intervals each with a thickness of 000,1

1 of the LNAPL

thickness in the well. LNAPL flow rates from the 1,000 discrete intervals are allowed to

be variable and independent of one another while maintaining the same average LNAPL

flow rate. Random LNAPL flows were generated by applying a normally-distributed

randomly generated relative permeability value for each discrete interval. Each

simulation consisted of generating 10,000 random vertical flow profiles and adding up

the volume of each discrete interval (1,000 intervals) to get the volume displaced from

the randomly generated vertical flow profile. Also, five separate simulations were run,

varying the normalized volume displacement value to determine if the maximum amount

of error was based on the percentage of LNAPL displaced from the well. Raw data and

33

an example random vertical profile can be found in Appendix A.4. Allowing each

discrete interval to be totally independent from adjacent intervals does not match variable

flow based on a vertical relative permeability profile, but it does allow for maximum

error. The maximum (or minimum) volume of LNAPL displaced from the simulations,

iabledV var , was compared with the volume of LNAPL displaced assuming a vertically-

averaged value, averagedV . The maximum error associated with the various percentages of

the normalized volume displacement value is reported in Table 3.1. Simulations could

not be conducted at normalized volume displacement values of greater than 0.60 because

this would violate the mass balance from Equation 3.23. Percent error in Table 3.1 is

defined as:

100% var

average

iableaverage

d

dd

V

VVerror

3.44

where:

averagedV = volume of LNAPL displaced using an average LNAPL flow rate (L3)

iabledVvar

= volume of LNAPL displaced using variable LNAPL flow rate with depth

(L3)

Table 3.1 Potential error due to the nonlinearity of volume displaced with respect to

Percentage of LNAPL Displaced 5 10 20 40 60

Average Percent Error 1.762 1.765 1.769 2.379 5.371

One Standard Deviation of Percent Error 1.319 1.333 1.331 1.623 2.020

Maximum Percent Error 9.225 9.060 8.898 8.823 12.217

Minimum Percent Error 1.559E-04 7.549E-04 1.397E-04 9.000E-05 1.584E-03

The overall error is small when compared to other potential sources of error

inherent to the method. As shown in Figure 3.6, the volume of LNAPL displaced, dLV ,

is nonlinear with respect to . Also, as shown in Table 3.1, there is error associated with

34

averaging vertically variable LNAPL flow. dLV is close to being linear with respect to

for normalized volume displacement values as high as 0.20. Furthermore, the error due

to averaging vertically variable LNAPL flow does not change significantly for

20.0wL

dL

V

V.

3.4.2 Approximate Solution for LNAPL Discharge Through a Monitoring Well

The following derivation assumes that for small normalized volume displacement

values

20.0

wL

dL

V

V, that dLV can be treated as linear. By treating dLV as linear, the

derivation is no longer dependent on the assumption of vertically-averaged horizontal

LNAPL flow through a monitoring well.

The conceptual model in this case is a beaker with one point of recharge and one

point of discharge, as shown in Figure 3.7. The volume in the beaker is constant with

time, so the rate of recharge is equal to the rate of discharge. The graphic on the left,

tttt oo , shows LNAPL without tracer recharging into the beaker and LNAPL

with the initial tracer concentration discharging from the beaker. The graphic on the right

ttt o shows the instant that the monitoring well becomes “well-mixed.”

35

to< t < t+t

t = t+t

Peristaltic pump

Siphon

Figure 3.7 Linear volume displaced conceptual model

Equation 3.29 is presented again as a starting point for this derivation.

wL

dL

o

t

V

V

C

C1

3.29 The dLV without assuming vertically-averaged horizontal flow is defined as

tQV wLdL

3.45 Equation 3.45 is substituted into Equation 3.29 to form Equation 3.46.

o

twLwL C

C

t

VQ 1

3.46

Equation 3.46 is a solution for LNAPL discharge through a well assuming a linear

volume displaced with time. Although this solution does not assume vertically-averaged

horizontal LNAPL flow through the well, it does assume that the mass balance in

36

Equation 3.23 is not violated. The error associated with this approximate solution when

compared to the vertically-averaged horizontal flow solution, assuming constant flow

with depth (Equation 3.33), can be seen graphically in Figure 3.8, where percent error is

defined as

100%DL

DLDL

NonlinearV

LinearVNonlinearVerror

3.47

0

10

20

30

40

50

60

70

80

90

100

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Normalized Volume Displacement

Per

ce

nt

Err

or

Figure 3.8 Percent error assuming linear volume displaced with respect to

For every normalized volume displacement value there a corresponding value of that

can be found. Figure 3.9 is Figure 3.8 plotted in terms of instead of normalized

volume displacement. The shape of the curves differ between the two figures because

is linear and dLV is not.

37

0

10

20

30

40

50

60

70

80

90

100

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Per

ce

nt

Err

or

Figure 3.9 Percent error assuming linear volume displaced in terms of

Applying the assumption that dLV is linear for small normalized volume

displacement values

20.0

wL

dL

V

Vresults in approximately 0.41% error when compared

to the solution found in Equation 3.33. This error is smaller than one standard deviation

(1.319%) of percent error expected due to the nonlinearity of dLV with respect to when

05.0wL

dL

V

V(shown in Table 3.1). This shows that the error for assuming a linear dLV is

smaller than the expected error due to the effects of vertically variable LNAPL flow on

dLV . The approximate solution shown in Equation 3.46 is simpler and results in very

little additional error when applied for small values of . The following section

discusses an alternative data analysis approach for small values of .

38

3.4.3 Comparison between the PMR Solution and the WMR Solution

As the elapsed time or the LNAPL flow rate gets small, the value approaches

zero. In a physical sense this represents frequently mixing the well, only allowing for

very small volumes of LNAPL to be displaced from the well between PMR tests. At

some point, as approaches zero, the monitoring well becomes “continually” mixed,

and the WMR solution can be applied. In Taylor (2004) the WMR solution is presented

as

wL

wL

V

tQ

o

t eC

C

3.48 Equation 3.48 can be written in terms of LNAPL flow through the well as

4

eC

C

o

t

3.49 Figure 3.8 shows graphically normalized tracer concentration versus normalized time,

*T , varying the magnitude of . Normalized time in Figure 3.8 is expressed as

timetestTotal

tT

__*

3.50

39

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

T*

No

rma

ilze

d C

on

cen

tra

tion

WMR solution

Figure 3.10 WMR signal loss compared to the PMR signal loss

As seen in Figure 3.10, as the product of LNAPL flow rate wLq and elapsed time t

gets smaller, the expected signal loss as modeled with the PMR test solution begins to

match the expected signal loss from a WMR data analysis. Figure 3.10 is slightly

misleading because it shows the full tracer decay curves with each method. In reality, as

a PMR test is conducted the measured tracer concentration during a given time step

becomes the initial concentration for the next time step. So, at each time step all of the

curves would be measured from a common point, and the lines of varying values

would not diverge as greatly. Figure 3.11 shows the error associated with modeling a

PMR test as a “well-mixed” reactor for an individual time step. This more accurately

reflects the true error, as would happen when conducting an actual test with successive

time steps. Percent error as seen in Figure 3.11 is defined as

40

100%WMR

WMRPMR

SignalLoss

SignalLossSignalLosserror

3.51

0

10

20

30

40

50

60

70

80

90

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Per

ce

nt

Err

or

Figure 3.11 Error associated with analyzing a PMR test as a WMR

Figure 3.11 quantitatively shows the error associated with modeling a periodically

mixed well as a “well-mixed” reactor. For small magnitudes of (<0.10) the error

between the two methods is small with respect to other potential sources of error. For

small magnitudes of , either a PMR analysis or a WMR analysis would be appropriate

when reducing the collected raw data. It is also important to note that as approaches

zero for the three solutions presented, (the PMR solution, the linear PMR solution, and

the WMR solution) the ratio of o

t

C

Capproaches one.

41

3.4.4 Critical Assumptions for the PMR Test

Halevy et. al. (1967) state that the change in concentration of tracer in a

monitoring well during a WMR is a function of flow and other non-flow related tracer

loss mechanisms. This section discusses mechanisms other than LNAPL flow that result

in tracer losses.

The tracer is used in concentrations of 1.0 to 5.0 parts per thousand (ppt). The low

concentration of tracer used reduces the effects of tracer flow from the well due to

temperature and density. Also, tracer loss due to vertical flow does not apply to

conducting tests in LNAPL (in unconfined settings), as the air-LNAPL interface and the

LNAPL-water interface eliminate the potential for vertical flow of LNAPL. Tracer loss

due to mechanical mixing needs to be recognized as a tracer loss mechanism when

conducting the PMR test. The goal of the PMR test is to remix the well after an elapsed

time so the tracer has a uniform concentration in the LNAPL, but too much mixing could

potentially force tracer out of the well, leading to losses in tracer that are greater than

tracer losses due solely to flow. When conducting a PMR test, the well should be

remixed as little as possible while ensuring a uniform tracer concentration in the LNAPL

in the monitoring well. Mixing methods are discussed in Section 5.2.2. Losses from

periodic mixing are expected to be small relative to losses due to continual mixing

associated with a WMR test.

There is a solution for diffusive losses of tracer to the formation (Taylor, 2004).

The conclusion is that tracer losses from diffusion are generally small relative to tracer

losses from LNAPL flow. At very low LNAPL flow rates, further analysis of diffusion

42

should be considered, but the most conservative approach is to ignore diffusion from the

monitoring well into the formation.

Other non-flow tracer loss mechanisms not mentioned by Halevy et. al. (1967)

include tracer sorption to the monitoring well and porous media, dissolution, and

volatilization. Long term tracer stability studies have been completed by Colorado State

University (Sale et. al, 2007a). Laboratory studies have shown that tracer used for this

research (BSL-715) is stable in laboratory grade LNAPL (Soltrol 220) and field LNAPL

from two sites. Another assumption implicitly made is that tracer concentration is

linearly related to intensity.

3.5 Conclusions

Section 3 presents an introduction to using a PMR test to estimate LNAPL flow

rates. This includes the mathematical derivation of the PMR test, an alternative solution

making a simplifying assumption, a comparison between the PMR solution and the

WMR solution, and a discussion of other critical assumptions for the PMR test.

The alternative solution, the PMR solution and the WMR solution yield similar

results for small displaced volumes of LNAPL. Also, the variation in results between the

three solutions is less than the variation in determining other parameters such as the flow

convergence factor and LNAPL formation thickness and resolving signal-to-noise in the

field equipment. A primary limitation inherent to the WMR method is the need for

dedicated downhole equipment. This limitation is removed by conducting a PMR test as

shown in the derivation and subsequent analyses.

43

4 Laboratory Experiments

This section presents laboratory experiments conducted using the PMR test

procedure. Two laboratory experiments were conducted. One experiment was conducted

in beakers using LNAPL and tracer. The second experiment was conducted in a large

tank containing uniform sand, LNAPL, and water. The following outlines materials,

methods, and results for each experiment.

4.1 Beaker Experiment

The objective of the beaker experiment was to test if a LNAPL discharge could be

accurately measured using the PMR test in a reactor of fixed volume.

4.1.1 Materials

Three 200 milliliter beakers were used in the experiment. Two peristaltic pumps

were employed, one to pump LNAPL through the reactor and the other to periodically

mix the LNAPL. The LNAPL was Soltrol 220, a laboratory grade paraffin. The Soltrol

was dyed red with Sudan IV. The fluorescent tracer used was Stay-Brite BSL-715. This

tracer has been used previously for single well tracer dilution tests conducted in LNAPL

(Taylor, 2004 and Sale et. al., 2007b). The experimental setup is shown Figure 4.1.

44

Fiber optic cable attached to reflectance probe

Peristaltic pump

Siphon

Airline

BAC

Figure 4.1 Beaker PMR test experiment configuration

The change in tracer concentration in beaker B was measured over time with a

dedicated fiber optic cable equipped with a reflectance probe and an Ocean Optics Inc.

temperature regulated S2000 spectrometer with a R-LS-450 470 nanometer emission

light source. The spectrometer was operated using a laptop computer equipped with an

Ocean Optics Inc. software package (OOIbase32). The fiber optic cable used was an

Ocean Optics Inc. six around one bifurcated 20 meter cable housed in a stainless steel

jacket. The light source was transmitted through six of the seven fibers. The seventh

fiber transmitted the fluorescence signal back to the spectrometer. More information on

the spectroscopy equipment and tracer stability can be found in Sale et. al. (2007a).

4.1.2 Methods

Beaker A contained 200 milliliters of Soltrol dyed with Sudan IV. Initially,

beaker B contained 100 milliliters of Soltrol dyed with Sudan IV and 0.1 milliliters of

45

BSL-715. Beaker C was initially empty. A steady discharge rate of 1.32 milliliters per

minute was sustained from beaker A to beaker B using the peristaltic pump. An equal

discharge rate from beaker B to beaker C was maintained using a siphon. The influent

and effluent lines in beaker B were placed in order to minimize short-circuiting of fluid

without tracer through the reactor (beaker B). Short-circuiting of fluid without tracer

from the influent line to the effluent line would lead to false steady tracer concentrations

with time. The end of the reflectance probe was placed close to the effluent line to detect

fluid short-circulating between periodic mixing intervals.

The test began with the condition that the BSL-715 in beaker B was “well-

mixed.” Beaker B was mixed for 30 seconds every 5 minutes. Continuous tracer

intensity data at 545 nm and 580 nm were collected throughout the experiment. The test

was concluded after 27 minutes when 25 percent of the tracer had been depleted.

4.1.3 Results

Work reported in Taylor (2004) and Iltis (2007) indicate that BSL-715

concentration is linearly related to fluorescence intensity at 545 and 580 nm. With this,

the observed fluorescence intensity (measured by the spectrometer) at 545 nm is taken as

a surrogate for tracer concentration. Tracer intensity normalized to the initial intensity

versus time is shown in Figure 4.2.

46

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25 30

Time (min)

No

rmal

ized

In

ten

sity

Figure 4.2 Beaker experiment: normalized fluorescence intensity versus time

The discharge through the reactor was estimated using data in Figure 4.2 and

Equation 3.46. Equation 3.46 was used to determine LNAPL discharge because loss in

tracer concentration between periodic mixing intervals was small (less than 7%), and the

volume displaced with respect to time was assumed to be linear.

Figure 4.3 shows the reduced data. Complete data reduction can be found in

Appendix B.1. One further normalization step took place to generate the values seen in

Figure 4.3. Each time the well is periodically mixed, the test in-effect restarts. For

example, in a hypothetical well, the second tracer concentration measured (one mixing

interval) was at 90% of the initial concentration. After the next periodic mixing interval

the tracer concentration is at 80% of the initial tracer concentration. During this time step

there was a 10% signal loss with respect to the initial concentration, but there was

actually an 11% signal loss with respect to the beginning concentration for the test

interval (90% initial signal remaining). As stated above, each time the beaker is remixed,

47

the initial concentration in which signal loss is recorded from is the previous measured

concentration. This is reflected in Figure 4.3. The first data point was omitted since it

was the initial tracer concentration from which subsequent data points were measured.

0.90

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1.00

0 5 10 15 20 25 30

Time (min)

Ob

se

rve

d R

ed

uc

tio

ns

in N

orm

aliz

ed

Tra

ce

r C

on

ce

ntr

ati

on

th

rou

gh

Ea

ch

Tim

e S

tep

Figure 4.3 Beaker experiment: reduced data

The measured discharge was 1.16 milliliters per minute, and the actual discharge

was 1.32 milliliters per minute. Measured discharge through the beaker was

underestimated with respect to the actual discharge through the beaker. There was a 12%

difference between the measured and the actual LNAPL discharge. Explanations for this

could have been a liquid “short-circuit” between influent and effluent tubing, or the

beaker was not completely remixed by the airline. While limitations were observed, it

appears that they are due more to the experimental methods than the limitation of the

PMR test. A more rigorous experiment reflecting the presence of a well in porous media

is presented next.

48

4.2 Large Tank Experiment

This section describes a laboratory experiment in which Soltrol dyed with Sudan

IV is pumped through a large sand tank at a known discharge. The sand tank contains a

monitoring well, which is used to conduct the PMR tests. The objective of this

experiment is to show that measured LNAPL discharge using the PMR test agreed with

known LNAPL discharge through the tank over a range of LNAPL discharges and

LNAPL thicknesses.

4.2.1 Materials

All experiments were conducted in the sand tank shown conceptually in Figure

4.4. The tank is approximately 8 feet wide, 4 feet tall, and 0.5 feet thick. The sand

(Unium 4095) in the tank is a well-sorted, medium-grained, angular quartz sand. All

PMR tests were conducted in the center well shown in Figure 4.4. The center well is a

vertical half section of a stainless steel wire-wrap well with a 2 inch inner diameter and

0.03 inch screen size. The open section of the well faced the glass in the tank. A filter

pack was constructed using a 3 inch diameter section of blank PVC pipe. The 3 inch

PVC pipe was placed around the outside of the 2 inch stainless steel well and was then

filled with a well-sorted, coarse-grained, angular quartz sand (Unium 2095). The PVC

pipe was then pulled from the tank vertically, leaving a filter pack approximately 0.25

inches thick (Taylor, 2004). The tank was filled with City of Fort Collins, Colorado, tap

water. The water was drained creating an unsaturated zone in the upper half of the tank.

Soltrol 220 dyed red with Sudan IV was released into the unsaturated zone until a

continuous body of LNAPL existed across the tank.

49

LNAPL thickness and LNAPL discharge were controlled by an influent peristaltic

pump and an effluent siphon. One limitation of the tank is that the thickness is only six

times greater than the well cross-sectional area. This could potentially cause bias in

convergent and divergent flow through the well, lessening the magnitude of flow

convergence factors measured (Taylor, 2004). The potential bias from the thickness of

the tank was avoided by only analyzing the relative magnitude of measured flow

convergence factors. The measured flow convergence factors would not be extrapolated

out to any other data collected.

The same spectrometer, fiber optic cable, and tracer as described in Section 4.1.1

were used. While a dedicated in-well fiber optic cable was not needed, the fiber optic

cable used for this experiment was not removed from the well during the experiment in

order to eliminate any variability associated with moving the spectrometer and/or fiber

optic cable.

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0.5m 0.5m0.5m0.5m0.05m 0.05m0.05m

Influent

head tank

Effluent

head tank

0.15m

Plan view

Water

saturated

sand

LNA PL ( Soltrol )

dyed red

Diffusive

mixing tool

0.125m

0.025m

Wire wrap

stainless steel

screen

Slotted PVC

screen

Slotted PVC

screen

Cross-section view

LNA PL

discharge

siphon

LNA PL

delivery

pump

Spectrometer

and computer

Peristaltic pump and airline

Unsaturated

sand

0.1m 0.1m

2.4m

1.2

m

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0.5m 0.5m0.5m0.5m0.05m 0.05m0.05m

Influent

head tank

Effluent

head tank

0.15m

Plan view

Water

saturated

sand

LNA PL ( Soltrol )

dyed red

0.125m

Wire wrap

stainless steel

screen

Slotted PVC

Screen (0.030)

Slotted PVC

Screen (0.010)

Fiber optic cable

Figure 4.4 Large sand tank configuration

50

The monitoring well was periodically mixed using a 0.125 inch airline that was

lowered into the well just below the LNAPL-water interface. The airline was powered by

a peristaltic pump. Although a dedicated airline was not needed for the PMR test, the

airline in this experiment was left in place.

4.2.2 Methods

Eight PMR tests were conducted. Prior to each test, the LNAPL delivery pump

was set to a known LNAPL discharge. During the PMR tests, the head tanks were

monitored to ensure LNAPL flow was at steady state. Steady state LNAPL flow was

assumed if the fluid levels in the head tanks were constant throughout the test. BSL-715

was injected into the monitoring well at a concentration of approximately 0.1 milliliters

per liter. Air was slowly pumped into the LNAPL column in the well until the tracer

intensity signal stabilized. The end of the fiber optic cable was lowered through the

LNAPL in the monitoring well to ensure tracer intensity signal was constant with depth.

This procedure is referred to as a vertical scan. After the airline was turned off, the tracer

was uniformly mixed in the LNAPL. This constitutes the beginning of a test.

The above procedure was repeated approximately 8 times until at least 20% of

the initial tracer concentration was displaced from the well. A triplicate test was

completed using a LNAPL formation thickness of 28.3 centimeters and a LNAPL

discharge of 7.2 milliliters per minute through the tank per 2.54 centimeters cross

sectional area.

51

4.2.3 Results

Raw data and the data reduction are presented in Appendix B.2. Figure 4.5 shows

the measured LNAPL discharge versus the known LNAPL discharge. The error bars in

Figure 4.5 represent the product of the known LNAPL discharge and (+) one standard

deviation of the average flow convergence factor calculated from all eight tests (shown in

Table 4.1). The solid line shown in Figure 4.5 represents the product of the known

LNAPL discharge and the average flow convergence factor. The average measured

LNAPL discharge calculated from each test was set equal to the actual LNAPL discharge

by varying the flow convergence factor using Equation 3.40. Since all of the PMR tests

occurred in the same well, the flow convergence factors should be the same for all tests

(independent of LNAPL discharge or formation LNAPL thickness). It is expected that

any variation in flow convergence factors due to varying relative permeabilites would be

less than the sensitivity of the PMR method. The variation in flow convergence factor

versus formation LNAPL thickness and flow convergence factor versus known LNAPL

discharge and is shown in Figure 4.6 and Figure 4.7, respectively. The solid line in both

figures represents the average flow convergence factor. The scale of the y-axis in both

figures represents the commonly accepted range of flow convergence factors from 0.5 to

4 as described in Freeze and Cherry (1979).

52

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8

Known LNAPL Discharge (mL/min)

Mea

sure

d L

NA

PL

Dis

char

ge

(mL

/min

)

Figure 4.5 Large tank experiment: reduced data

Table 4.1 Large tank experiment: best fit flow convergence factors

LNAPL Formation Thickness

Known LNAPL Discharge

Measured LNAPL Discharge

Flow Convergence Factor

Percent Difference

(cm) (mL/min) (mL/min) (unitless)

4.0 0.2 0.3 1.13 4.4

4.0 0.6 0.7 1.24 4.3

4.5 1.2 1.4 1.16 2.0

14.1 0.9 1.1 1.21 2.0

14.1 3.0 3.7 1.22 2.9

28.3 7.2 8.7 1.21 1.8

28.3 7.2 8.0 1.11 6.9

28.3 7.2 8.6 1.20 1.3

1.18

One Standard Deviation= 0.05

Average Flow Convergence=

53

0.5

1

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30

Formation LNAPL Thickness (cm)

Flo

w C

on

ve

rge

nc

e F

ac

tor

~4 cm formation LNAPL thickness

~14 cm formation LNAPL thickness

~28 cm formation LNAPL thickness

Figure 4.6 Large tank experiment: flow convergence factor versus formation LNAPL thickness

0.5

1

1.5

2

2.5

3

3.5

4

0 1 2 3 4 5 6 7 8

Known LNAPL Discharge (mL/min)

Flo

w C

on

ve

rge

nc

e F

ac

tor

LNAPL discharge < 1 mL/min

1 mL/min < LNAPL discharge < 3 mL/min

3 mL/min < LNAPL discharge

Figure 4.7 Large tank experiment: flow convergence factor versus known LNAPL discharge

The variation in flow convergence values appears to be independent of formation

thickness and LNAPL discharge. This is expected, given the derivation presented in

Section 3.3, where the flow convergence factor is based on well radii, vertically-averaged

54

relative permeabilities, and intrinsic permeabilities. The variation in values measured

in the triplicate test most likely represents the limitations of the experimental method.

These include incomplete mixing of the well, adverse flow caused by mixing, and/or

pump drift throughout the tests. This percent difference is small relative to the actual

range of flow convergence values that would have to be estimated in field applications.

4.3 Laboratory Experiments Conclusions

The objective of the beaker experiment was to show that LNAPL discharge could

be measured using the PMR test. The percent difference between the measured and

known LNAPL discharge was 12% in this experiment. The percent difference was

attributed to experimental procedure rather than the PMR solution. The objective of the

large tank experiment was to show that measured LNAPL discharges using the PMR test

agreed with known LNAPL discharges through the tank over a range of LNAPL

discharges and LNAPL thicknesses. The measured LNAPL discharges agreed closely to

the known LNAPL discharges. The percent differences between the measured and

known LNAPL discharge range from 1.3% to 4.4%.

The primary limitation of the laboratory experiments is that the flow rates were

higher than would be expected in most field settings. With successful application of the

PMR test in laboratory settings, field scale testing of the method was conducted with

known LNAPL discharges near LNAPL recovery wells and in areas where LNAPL

bodies are thought to be stable.

55

5 Field Experiments

This section describes two sets of field experiments that were conducted at a

former refinery in Casper, Wyoming. The first set of experiments involved measuring

LNAPL discharges through monitoring wells adjacent to two active LNAPL recovery

wells. The objective of this experiment was to evaluate if field scale PMR tests could

accurately estimate a known LNAPL formation discharge. The second set of experiments

involved measuring LNAPL flow rates in monitoring wells in areas where LNAPL

bodies are thought to be stable. The objective of this experiment was to evaluate if field

scale PMR tests could accurately resolve LNAPL flow rates representative of site

conditions in areas of LNAPL stability. Figure 5.1 shows a site-wide map and the

monitoring well locations where PMR tests were conducted. The aerial photograph in

Figure 5.1 shows the site before a public golf course was constructed.

5.1 Site Introduction

The following sections describe the site operational history, the hydrogeologic

setting, and current remedial measures.

5.1.1 Historic Site Operations

The site is located in Natrona County, Wyoming, on the western edge of

downtown Casper. Refining operations occurred on both the north and south sides of the

North Platte River. In 1913, Amoco began refining operations using the then new

process of Burton-Humphrey thermal cracking. This produced larger quantities of

marketable gasoline compared to other refining methods of the era (WDEQ, 2002). The

56

Amoco Refinery continued to grow, and had a peak production in 1987, processing an

average of 48,000 barrels per day (WDEQ, 2002).

57

South Properties Area

Opportunity Area

GIPPS Area Wells

R93 Area

R91 Area

North Platte River

N

Figure 5.1 BP Casper former refinery South Properties Area map

58

The facility was closed in 1991 due to limited crude oil feedstock (WDEQ, 2001).

Process units, storage tanks and ancillary equipment were drained, cleaned and removed

by 1995 (WDEQ, 2001). Also, abandoned pipelines were removed and contaminated

soils were excavated and removed to eight feet below grade. The area where the field

experiments occurred is known as the South Properties Area (SPA), and is currently

undergoing redevelopment that includes a public golf course and a commercial business

park.

5.1.2 Site Geology and Hydrogeology

The SPA is located within the North Platte River valley floor. The topography is

generally flat with an average elevation of approximately 5,120 above mean sea level

(WDEQ, 2001).

Depth to bedrock, the Cody Shale, in the SPA varies from 30 to 40 feet below

ground surface (WDEQ, 2001). Above the bedrock there is Quaternary alluvium

composed of two stratigraphic units, both consisting of sand and gravel with minimal

interbedded silts and clays. The lower alluvial stratigraphic unit consists of fluvial

channel sands and gravels, and the upper stratigraphic unit consists of fluvial overbank

sediments. A shallow unconfined aquifer exists in the alluvial stratigraphic units, with

the Cody Shale acting as an aquitard limiting vertical migration of groundwater. Depth

to groundwater varies from 5 to 21 feet below ground surface (WDEQ, 2001).

Historically, groundwater flow direction was towards the North Platte River. A

groundwater recovery system and a barrier wall have been installed between the SPA and

the North Plate River to intercept impacted groundwater and to prevent migration of

LNAPLs to the North Platte River (WDEQ, 2001).

59

5.1.3 Current Remedial Measures

Several interim remediation measures are employed in the SPA. A physical

barrier wall extends 8,600 feet along the south bank of the North Platte River (WDEQ,

2001). A hydraulic control barrier and a LNAPL recovery system exist on the refinery

side of the barrier wall. There are also LNAPL recovery systems in the interior of the

site. An air sparge/soil vapor extraction system for groundwater treatment is located on

the eastern side of the site.

5.2 PMR Tests Adjacent to Active LNAPL Recovery Wells

The objective of the first set of experiments was to demonstrate field scale PMR

tests could accurately estimate known formation LNAPL discharges. This was

accomplished using monitoring wells with LNAPL located in close proximity to active

LNAPL recovery wells with known production rates. This experiment assumed that the

monitoring wells selected were within the radius of influence of the LNAPL recovery

well, and LNAPL in the formation has uniform radial flow towards the LNAPL recovery

well. A conceptual illustration is shown in Figure 5.2. The LNAPL discharge from the

LNAPL recovery wells is recorded on a monthly basis. LNAPL recovery rates were

provided by ENSR and are included in Appendix C.2.

60

LNAPL Recovery Well

Observation Wells

fLb

Figure 5.2 LNAPL recovery well cluster conceptual model

The interior active LNAPL recovery well clusters in the SPA consist of a central

LNAPL recovery well and monitoring wells that extend radially off of the central

LNAPL recovery well at various distances. Two LNAPL recovery wells, R91 and R93,

and their monitoring wells were chosen for the study. The LNAPL recovery wells and

their monitoring wells are shown in Figure 5.3 and Figure 5.4.

61

N

30.0 feet

R93 TW-416TW-418

18.33 feet

Figure 5.3 R93 area wells

19.9 feet

R91TW-420

TW-419 10.0 feet

N

Figure 5.4 R91 area wells

62

5.2.1 Materials

An Ocean Optics Inc. S2000 spectrometer, OOIbase 32 software, a laptop

computer, and a 50 meter bifurcated fiber optic cable (as described in Section 4.1.1) were

used to measure tracer concentration. The fluorescent tracer used was BSL-715.

Fluorescence intensity of the tracer was assumed to be linear to tracer concentration.

One half inch PVC piping was used to occlude volumes of LNAPL with and without

tracer in a separate monitoring well. The laptop computer and spectrometer were

powered using a 12 volt DC battery equipped with a 120 volt AC power inverter. A 20

mL vial attached to nylon string was lowered downhole into the monitoring well to

retrieve LNAPL to be spiked with tracer. Subsequently the vial was lowered downhole

again to introduce the tracer to the LNAPL in the well. A downhole mixing airline

consisting of 0.125 inch irrigation drip line attached to an aluminum rod (for weight) was

used as the downhole mixing system. An empty 60 mL syringe was attached to the

irrigation drip line. The air in the syringe was injected through the irrigation drip line and

into the well during mixing events.

5.2.2 Methods

A detailed description of field methodology can be found in Appendix C.1.

Two LNAPL recovery well clusters, R91 and R93, were selected for testing. Around

each LNAPL recovery well, two monitoring wells were selected to conduct PMR tests.

PMR tests were conducted at the R93 cluster in wells TW-416 and TW-418. PMR tests

were conducted at the R91 cluster in wells TW-419 and TW-420. Monitoring well

information is found in Table 5.1. Appendix C.2 provides LNAPL recovery information

from R91 and R93.

63

Table 5.1 Observation well information Radius from Recovery Well LNAPL Well Thickness

(rw) (bwL)

Area Well ID (ft) (ft)R91 TW-419 10.00 0.28R91 TW-420 19.9 0.57R93 TW-416 18.33 0.61R93 TW-418 30.66 0.65

For these tests a third monitoring well at the R91 and R93 clusters was used as a

“calibration well.” The one half inch PVC pipes were inserted to occlude a volume of

LNAPL without tracer and a volume of LNAPL with the initial tracer concentration. A

PVC pipe was inserted into the calibration well, through the LNAPL thickness before

tracer was added. Then the tracer was added and initially “well-mixed.” Then a second

PVC pipe was inserted into the calibration well through the LNAPL thickness. The two

PVC pipes, one without tracer and one with the initial tracer concentration allow for in-

well spectrometer calibrations to be made with each tracer concentration measurement.

5.2.3 Results

The estimated formation LNAPL discharges can be compared to the known

formation LNAPL discharges. The estimated formation LNAPL discharge can be found

by dividing the measured LNAPL discharge using the PMR test by the flow convergence

factor (see Equation 3.40). The known formation LNAPL discharges were provided by

ENSR. Iltis (2007) provides flow convergence factors for various sizes of PVC well

screen. Iltis (2007) did not test the well screen size used in the completion of the

monitoring wells at Casper (0.05 inch slotted screen). Also, as shown in Equation 3.36,

the flow convergence factor is a function of the vertically-averaged relative permeability

and the intrinsic permeability of the well screen, the gravel pack, and the porous media.

64

The relative permeabilities and intrinsic permeabilities of the porous media, gravel pack

and well screen at Casper will be different than those tested by Iltis (2007). Despite

these differences, the reported flow convergence factors (Iltis, 2007) will provide a good

point for comparison between the estimated and known formation LNAPL discharges.

The tests were conducted on October 27-28, 2007. All of the PMR tests occurred

concurrently and lasted less than 24 hours. Monitoring well information is found in

Table 5.1. Calculations are shown in Appendix C.3. Also, Round 2 data had the longest

elapsed time between periodic mixing and data collection. The Round 2 data (collected

overnight) most likely represent a condition violating the mass balance (Equation 3.23).

The data from Round 2 are not considered valid and therefore are not given further

consideration.

The measured LNAPL discharge through the monitoring well is found using the

measured LNAPL flow rate through the monitoring well, the LNAPL thickness in the

monitoring well, and the radial distance between the monitoring well and the LNAPL

recovery well. Results are presented in Table 5.2. The estimated formation LNAPL

discharge is found by dividing the measured LNAPL discharge through the monitoring

well by the flow convergence factor. Table 5.3 presents estimated formation LNAPL

discharges assuming a flow convergence factor of 0.91. This is the flow convergence

factor measured for a 0.03 inch slotted PVC well screen (Iltis, 2007).

65

Table 5.2 Measured LNAPL discharges Round 1 (10/27) Round 3 (10/28)

QwL QwL

Area Well ID gal/day gal/dayR91 R91 37.4 37.4R91 TW-419 20.3 22.2R91 TW-420 43.1 26.7R93 R93 85.2 85.2R93 TW-416 144.9 80.7R93 TW-418 123.9 67.2

Table 5.3 Estimated formation LNAPL discharges Round 1 (10/27) Round 3 (10/28)

QwL QwL

Area Well ID gal/day gal/dayR91 R91 37.4 37.4R91 TW-419 22.4 24.4R91 TW-420 47.3 29.4R93 R93 85.2 85.2R93 TW-416 159.2 88.7R93 TW-418 136.1 73.8

The estimated formation LNAPL discharges (with a flow convergence factor of

0.91 applied) are presented in Figure 5.5 for R91 and in Figure 5.6 for R93. Calculations

are presented in Appendix C.4.

66

0

5

10

15

20

25

30

35

40

45

50

R91 TW-419 TW-420

LN

AP

L d

isch

arg

e (g

allo

ns/

day

)

Round 1

Round 3

Average from Round 1 and 3

Figure 5.5 R91 area LNAPL discharges

0

20

40

60

80

100

120

140

160

180

R93 TW-416 TW-418

LN

AP

L d

isch

arg

e (g

allo

ns/

day

)

Round 1

Round 3

Average from Round 1 and 3

Figure 5.6 R93 area LNAPL discharges

The percent difference between estimated and known formation LNAPL

discharges is shown in Table 5.4. The average percent difference varied from 23.2% to

45.4%. Potential causes for the percent differences are discussed in Section 5.2.4.

67

Table 5.4 Percent difference between estimated and known formation LNAPL discharges Round 1 Round 3 Average

Percent Difference

Percent Difference

Percent Difference

Area Well IDR91 TW-419 40.3 34.9 37.6R91 TW-420 26.5 21.6 24.0R93 TW-416 86.8 4.1 45.4R93 TW-418 59.7 13.4 23.2

The second way to evaluate the results from the PMR tests is to compare flow

convergence factors calculated for each well. The completions of the monitoring wells

are the same and the monitoring wells are in the same geologic formation, so the flow

convergence factors from each well should be similar. Variations in flow convergence

factors between wells could result from violating the assumptions of the analysis,

differences in relative and intrinsic permeabilities, and/or measurement error. The flow

convergence factors from each well are calculated by dividing the estimated formation

LNAPL discharge by the known formation LNAPL discharge (see Equation 3.40). The

flow convergence factors from each well are reported in Table 5.5. The average flow

convergence factor measured was 0.99 + 0.42. Calculations are shown in Appendix C.4.

Table 5.5 Flow convergence factors Round 1 (10/27) Round 3 (10/28)

Well ID unitless unitlessTW-419 0.54 0.59TW-420 1.15 0.71TW-416 1.45 0.79TW-418 1.70 0.95

Average= 0.99One Standard Devation= 0.42

5.2.4 Discussion

The objective of the first set of experiments was to demonstrate that estimated

formation LNAPL discharges using PMR tests agreed with known formation LNAPL

68

discharges. This was accomplished by conducting PMR tests in monitoring wells within

the radius of influence of LNAPL recovery wells. The PMR tests were conducted at

different locations and different radial distances around two different LNAPL recovery

wells, R91 and R93. Table 5.4 shows the percent difference between the estimated and

known formation LNAPL discharges using a flow convergence factor of 0.91 (Iltis,

2007). Given the assumptions of the experiment and the flow convergence factor used,

the estimated and known formation LNAPL discharges are in good agreement. Also, if

the results from TW-420 were ignored and a larger flow convergence factor was chosen,

the percent difference in the three remaining tests would be smaller.

The second data analysis approach was to compare flow convergence factors

calculated at each well. Table 5.5 shows the actual flow convergence factors calculated

from each monitoring well. The monitoring wells in this experiment were completed

with 0.05 inch PVC slotted well screen. The largest PVC well screen tested by Iltis

(2007) was 0.03 inch PVC slotted well screen. Iltis (2007) reports a flow convergence

factor of 0.91 for the 0.03 inch PVC slotted well screen. As expected, the average flow

convergence factor measured in this experiment was larger than the value reported by

Iltis (2007). The variation in measured flow convergence factors most likely results from

violating the assumptions of the analysis and measurement error.

Assumptions of the analysis include steady state LNAPL flow rates towards the

LNAPL recovery well and uniform LNAPL flow rates towards the LNAPL recovery

well. TW-419, TW-416, and TW-418 have higher flow convergence factors in Round 1

than in Round 3. The LNAPL recovery wells’ pumps cycle on and off depending on the

thickness of LNAPL in the recovery well, which violates the steady state LNAPL flow

69

assumption. It is possible that the flow convergence factors from Round 1 represent a

time period where the LNAPL recovery well was actively pumping, and the flow

convergence factors from Round 3 represent a time period where the LNAPL recovery

well was not pumping. TW-420 had consistent flow convergence factors for both Round

1 and Round 3. TW-420 was the closest monitoring well to its LNAPL recovery wells.

TW-420 may have been close enough to R91 that the response time in TW-420 was

different than the other wells tested. Also, TW-420 had the smallest volume of LNAPL,

and the other three wells had similar volumes of LNAPL. TW-420 could have been

located in an area of lower LNAPL flow which violates the uniform LNAPL flow

assumption. Another source for variation in the experiment was measurement error. The

methodology was still improving when the tests were conducted.

Following completion of the PMR tests in areas with known formation LNAPL

discharges, another series of PMR tests were conducted in areas with low LNAPL flow

rates.

5.3 PMR Tests in Areas with Low LNAPL Flow Rates

For the second set of experiments, four PMR tests were conducted in the SPA in

areas with low LNAPL flow rates. The objective of this experiment was to evaluate

LNAPL flow rates in areas where LNAPL bodies are thought to be stable. The extended

time period of these tests involved multiple spectrometer calibrations. Three of the wells

tested, PZ-334s, PZ-335s, and Well 45, were located on the eastern portion of the site in

the GIPPS area. The other well tested, Well 113 was located on the western portion of

the site in the Opportunity Area (see Figure 5.1).

70

5.3.1 Materials

The spectrometer, fiber optic cable, laptop computer, tracer, PVC pipes, and

airline used were the same as described in Section 5.2.1.

5.3.2 Methods

The three wells tested in the GIPPS area were close enough together that only one

well, Well 45, was needed for calibration standards. Well 45 was chosen to contain the

calibration standards because it was the largest diameter well (three inch PVC) tested of

the three GIPPS area monitoring wells. The other wells were two inch diameter PVC

wells. Since there was only one set of calibration standards for the three wells, the

background fluorescence in each well was measured before the tests began. The

variation in background fluorescence, albeit small, was accounted for throughout the

experiments by scaling the background LNAPL fluorescence measured at Well 45 to

match the background fluorescence at the other wells. The fourth well in the low flow

study (Well 113) was located in a different area of the site. Well 113 is a 4 inch diameter

well that accommodated its own in-well calibration standards.

The two wells with in-well calibration standards, Well 45 and Well 113, had a

volume of LNAPL occluded from the well by the two calibration PVC pipes. The actual

volume of LNAPL in the well was smaller than would be calculated using a standard

equation for the volume of a cylinder. For the data analysis, an effective diameter was

used to calculate the LNAPL flow rate. The effective diameter was calculated by

reducing the size of the well’s diameter until the volume of LNAPL in the well using a

cylindrical formula was equal to the actual volume of LNAPL in the well.

71

5.3.3 Results

The range of calculated LNAPL flow rates through the wells is shown in Table

5.6. Calculations are presented in Appendix C.5 No attempt was made to correct for

LNAPL volume changes in the wells during the PMR tests. The tests were initiated

October 28, 2007 and ended on January 4, 2008. The fourth test in well 113 ended on

April 18, 2008. All of the PMR tests occurred concurrently.

Table 5.6 Measured LNAPL flow rates Date 11/15/07 12/05/07 12/19/07 01/04/08 04/18/07

Area Well ID qwL (ft/yr) qwL (ft/yr) qwL (ft/yr) qwL (ft/yr) qwL (ft/yr)

GIPPS Well-45 - 0.45 - 0.05 -GIPPS PZ-334s 0.38 0.35 0.68 0.41 -GIPPS PZ-335s 1.03 0.52 1.23 0.53 -

Opp. Area Well-113 0.18 0.66 0.04 0.02 0.12

5.3.4 Discussion

The objective of this set of experiments was to use the PMR test to measure

LNAPL flow rates in areas where LNAPL is thought to be stable. The PMR test in Well

45 only yielded two quantifiable sets of data points. The results from this well are

questionable. There was no well completion information for Well 45. Also, Well 45 had

a break in its casing at approximately 10 ft below ground surface. When conducting

readings, the reflectance probe tip would become covered with sediment, varying the

amount of light the fiber optic cable could deliver to the LNAPL. It is not expected that

the in-well calibration standards in Well 45 caused the poor results.

PZ-334s and PZ-335s were close together and similar well completions. The

LNAPL flow rates from these two wells were expected to be in agreement. Although

LNAPL flow rates calculated from PZ-334s and PZ-335s are in agreement, the LNAPL

72

flow rates from PZ-335s were higher than those from PZ-334s. The cause for the higher

flow rates in PZ-335s is not known.

Well 113 had the lowest LNAPL flow rates of the four PMR tests conducted.

Also, the December 5 LNAPL flow rate was higher than the other LNAPL flow rates

calculated for Well 113. This data point had a higher ratio of initial concentration to

background concentration (seen in Appendix C.5), so measurement error may be the

cause of the higher reading, rather than an increased LNAPL flow rate during the time

period represented by this data point. Despite the problems with Well 45 and the elevated

reading of from Well 113, the PMR tests yielded repeatable results throughout the length

of the experiment.

5.4 Field Experiments Conclusion

This section described two sets of field experiments that occurred at a former

refinery in Casper, Wyoming. The objective of the first experiment was to show that

estimated formation LNAPL discharges were in agreement with known formation

LNAPL discharges after applying a flow convergence factor suggested by Iltis (2007).

The percent differences between estimated and known formation LNAPL discharges

range from 4 % to 87%. One well, TW-420, had the smallest measured formation

LNAPL discharge with respect to the known formation LNAPL discharge. TW-420 also

had the smallest volume of LNAPL in the monitoring well and was the closest to an

LNAPL recovery well. Either the proximity or the LNAPL volume in the well could

have caused the lower than expected flow convergence factors.

The objective of the second experiment was to evaluate LNAPL flow rates in areas

where LNAPL is thought to be stable. Three of the four wells tested yielded quantifiable,

73

repeatable results. The fourth well, Well 45, lost very little tracer concentration through

the length of the test. This result does not match the other two wells tested in the area,

PZ-334s and PZ335s. It is suspected that the well completion of Well 45 may be the

cause of the error.

The PMR test yielded results in good agreement with known formation LNAPL

discharges (first experiment) and yielded repeatable low LNAPL flow rates (second

experiment).

74

6 Thesis Conclusions

This thesis presents a new approach for conducting single well tracer dilution tests in

LNAPL. The method is referred to as a Periodic Mixing Reactor (PMR) test. The PMR

test removes the requirement of a maintaining a “well-mixed” reactor. Advantages

include simplified field procedures and an ability to conduct multiple concurrent tests.

The PMR solution presented is an implicit equation iteratively solved for a vertically-

averaged horizontal LNAPL flow rate through a monitoring well using input parameters

of change in tracer concentration, elapsed time between periodic mixing, and the

diameter of the monitoring well.

Laboratory and field experiments are presented. Two separate laboratory

experiments were conducted, a beaker experiment and a large sand tank experiment. The

beaker experiment was a simple proof of concept test to see if further experiments were

warranted. Actual LNAPL discharge through the beaker was 1.32 milliliters per minute.

The beaker experiment underestimated the LNAPL discharge rate by approximately 12%.

This is likely due to the experimental procedures rather than limitations of the PMR

method. Potential procedural causes for this difference were pump drift and fluid short

circuiting between the influent and effluent tubing.

A large sand tank experiment was conducted. PMR tests occurred in a monitoring

well in porous media. Eight PMR tests were conducted in the sand tank over four

LNAPL thicknesses ranging from 4.0 to 28.3 centimeters and eight LNAPL discharges

ranging from 0.2 to 7.2 milliliters per minute. The percent differences between known

and measured LNAPL discharges through the sand tank range from 1.3% to 6.9%. A

dimensionless analysis comparing flow convergence factors from each test was

75

conducted to evaluate the success of the large sand tank experiment. The flow

convergence factors ranged from 1.11 to 1.24 with an average flow convergence factor of

1.18 and a standard deviation of 0.05. The variation in calculated flow convergence

factors was small compared to the expected range of flow convergence factors which is

0.5 to 4 (Freeze and Cherry, 1979). The large sand tank experiment demonstrated that

measured LNAPL discharges using the PMR test agreed with known LNAPL discharges.

Two separate field experiments were conducted at a former refinery in Casper,

Wyoming. The first experiment took place adjacent to LNAPL recovery wells. PMR

tests were conducted in two monitoring wells in the vicinity of two different LNAPL

recovery wells, R91 and R93, for a total of four PMR tests. The four wells tested, TW-

420, TW-419, TW-416, and TW-420 had similar well completions, contained a similar

LNAPL type, and were located in the same alluvium. The formation LNAPL discharge

within the radius of influence of the LNAPL recovery well was known based on LNAPL

recovery rates. The formation LNAPL discharge was estimated using PMR tests

conducted in monitoring wells within the radius of influence of the LNAPL recovery

well. The percent differences between the known and estimated formation LNAPL

discharge range from 24% to 45%. The range of percent differences is small when

considering the assumptions of the analysis and potential measurement error. The

assumptions for this experiment included steady state LNAPL flow towards the LNAPL

recovery well from all points within the radius of influence of the LNPAL recovery well.

Due to the similarities in setting, a dimensionless comparison of the PMR tests

could be made between the four wells. This was accomplished using the known

formation LNAPL discharge and the measured LNAPL discharge through the monitoring

76

well using the PMR test by calculating a flow convergence factor for each well. The

flow convergence factors for the four tests ranged from 0.54 to 1.70 with an average flow

convergence factor of 0.99 and one standard deviation of 0.42. The calculated flow

convergence factors are within the range suggested by Iltis (2007) for the screen size of

the wells tested. Explanations for the variations in flow convergence factors include non-

steady state LNAPL flow during the test, variations in average relative permeabilities,

and measurement error.

The second field experiment conducted occurred in areas where LNAPL bodies were

thought to be stable. The LNAPL flow rate was measured in four wells, PZ-334s, PZ-

335s, Well 45, and Well 113, using the PMR test. Results from Well 45 did not yield

quantifiable results, potentially due to the well completion and/or well damage. LNAPL

flow rates varied from 0.02 to 1.23 feet per year. The PMR test yielded repeatable low

LNAPL flow rates. PZ-334s and PZ-335s were located in the same area, and had the

same well completions. The calculated LNAPL flow rates from these two wells were in

good agreement.

77

7 Opportunities for Further Method Development

Throughout the testing of the PMR solution areas of improvement were

recognized. The areas for improvement can be divided into two categories, theory and

equipment.

The PMR tests can occur over extended periods of time in areas with low LNAPL

flow rates. Over the testing periods, LNAPL volume in the well can change, and

diffusion from the well into formation can cause of loss in tracer. Changes in volume

commonly found with falling and rising watertables can cause tracer displacement due to

vertical flow rather than lateral migration. Also, loss of tracer due to diffusion can result

in calculated LNAPL flow rates that are higher than the actual LNAPL flow rates. Field

data collection could occur over a shorter period of time to avoid the changes in volume,

but the derivation could be updated to include a transient volume and a diffusive flow

term.

Further analysis of in-well diffusion should be conducted. Given low LNAPL

flow rates at some field sites, in-well diffusion could act as an in-well mixing method.

Also, with in-well diffusion, tracer concentrations less than the initial tracer concentration

could be displaced from the well. In this case the mass balance presented in Section 3

would be violated, but if there is enough in-well diffusion mixing the tracer within the

well, a WMR solution could be employed to calculate a LNAPL flow rate.

The PMR test does not account for LNAPL migration in the LNAPL capillary

fringe. In fine-grained soils it is possible that LNAPL migration in the LNAPL capillary

fringe is an important migration process.

78

Another area for improvement in theory would be gaining greater understanding

about LNAPL gradient. LNAPL gradient is measured independently of the PMR test, but

there are uncertainties with applying a three-point approach to resolve the LNAPL

gradient. Looking into the effects of heterogeneous yet continuous fluids on LNAPL

head at a point would add value in trying to understand the LNAPL gradient.

Also, explanation of plume wide forces that retard the rate of LNAPL flow could

help to explain the low LNAPL flow rates measured in this thesis and in Sale et. al.

(2007b). Although the LNAPL flow rates from the second field experiment are small,

LNAPL seepage velocities calculated are much higher. It may be possible to account for

the stability of LNAPL bodies despite high LNAPL seepage velocities by accounting for

natural mass removal mechanisms. Natural mass removal mechanisms include

volatilization and dissolution.

The other area for improvement is developing equipment specific to the

application of the PMR test. The current spectrometer is sensitive to weather conditions

encountered in most field situations. The ideal spectrometer would be able to self-

regulate temperature and be insensitive to humidity. Also, an ideal spectrometer would

be insensitive to attaching and detaching fiber optic cables.

Current configuration of the fiber optic cable has proved problematic during field

deployment. The current cable has a stainless steel jacket which is very strong, but

allows fluids to breach the stainless steel jacket and contact the fiber optic cables. The

individual fibers have failed, presumably due to contact with hydrocarbons. The ideal

cable would be as strong as the stainless steel jacketed cable, but also nonporous and

chemically inert to hydrocarbons. The end of the fiber optic cable is also housed in a

79

reflectance probe to protect the fibers and to optimize the transmission of light into the

LNAPL. This probe is currently attached to the fiber optic cable with two small screws.

Fluids can breach the probe through the screw holes or in the annulus between the cable

and the probe. The probe should be redesigned to either screw onto the cable and seal

with a O-ring, or be fastened in a way to create a waterproof seal.

80

8 References Bouwer, R. and Rice, R. C. (1976) A slug test for determining hydraulic conductivity of unconfined aquifers with complete or partially penetrating wells. Water Resources Research 12, 3, 423-428. Brooks, R. and Corey, A. T. (1966) Properties of porous media affecting fluid flow. Journal of the Irrigation and Drainage Division ASCE 92, IR2, 61-88. Devlin, J. F. and McElwee, C. D. (2007) Effects of measurement error on horizontal hydraulic gradient estimates. Ground Water 45, 1, 62-73. Farr, A. M., Houghtalen, R. J., and McWhorter, D. B. (1990) Volume estimation of light nonaqueous phase liquids in porous media. Ground Water 28, 1, 48-56. Freeze, R. A. and Cherry, J. A. (1979) Groundwater. Prentice-Hall Publishing Co., Engle Cliffs, NJ. Hatfield, K., Annable, M., Cho, J., Rao, P. C. S., and Klammler, H. (2004) A direct method for measuring water and contaminant fluxes in porous media. Journal of Contaminant Hydrology 75, 155-181. Halevy, E., Moser, H., Zellohefer, O., and Zuber, A. (1967) Borehole dilution techniques: a critical review. Proceedings of the 1996 Symposium of the International Atomic Energy Agency, 531-564. Huntley, D. (2000) Analytic determination of hydrocarbon transmissivity from baildown tests. Ground Water 38, 1, 46-52. Iltis, G. (2007) Evaluation of three methods for estimating formation transmissivity to LNAPL. M.S. thesis Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, Colorado. Jacob C. E. and Lohman, S. W. (1952) Nonsteady flow to a well of constant drawdown in an extensive aquifer. Transactions, American Geophysical Union 33, 4, 559-569. Lenhard, R. J. (1992) Measurement and modeling of three-phase saturation-pressure hysteresis. Journal of Contaminant Hydrology 9, 243-269. Lenhard, R. J. and Parker, J. C. (1990) Estimation of free hydrocarbon volume from fluid levels in monitoring wells. Ground Water 28, 1, 57-67. Marinelli, F. and Durnford, D. S. (1996) LNAPL thickness in monitoring wells considering hysteresis and entrapment. Ground Water 34, 3, 405-414.

81

McWhorter, D. B. and Sale, T., (2000) The mobility of liquid hydrocarbon below the water table. Unpublished document. Ogilvi, N.A. (1958) Electrolytic method for the determination of the ground water filtration velocity (in Russian). Bulletin of Science and Technology News, 4, Moscow, Russia: Gosgeoltehizdat. Parker, J. C., Lenhard, R. J., and Kuppusamy, T. (1987) A parametric model for constitutive properties governing multiphase flow in porous media. Water Resources Research 23, 4, 618-624. Sale, T. (2001) Methods for determining inputs to environmental petroleum hydrocarbon mobility and recovery models. American Petroleum Institute Publication 4711, Washington D. C. Sale, T. and Taylor, R. (2005) Addendum to 2004 in situ LNAPL flow meters studies. Unpublished Document. Sale, T., Smith, T. J., and LeMonde, K. (2007a) Laboratory studies supporting use LNAPL soluble tracers to resolve LNAPL stability at Honolulu Harbor. Unpublished document. Sale, T., Taylor, R., Iltis, G., and Lyverse, M. (2007b) Measurement of LNAPL flow using single well tracer dilution techniques. Groundwater 45, 5, 569-578. Sale, T., Taylor, R., and Lyverse, M. (2007c) Measurement of non-aqueous phase liquid flow in porous media by tracer dilution. United States Patent # 2007/0113676A1. Taylor, R. (2004) Direct measurement of LNAPL flow using tracer dilution techniques. M.S. thesis, Department of Civil Engineering, Colorado State University, Fort Collins, Colorado. Testa, S. M. and Paczkowski, M. T. (1989) Volume determination and recoverability of free hydrocarbon. Ground Water Monitoring Review 9, 1, 120-127. Van Genuchten, M. Th. (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44, 892-898. Wyoming Department of Environmental Quality. (2001) A remedy decision for the former BP Casper Refinery –South Properties Area. Wyoming Department of Environmental Quality. (2002) A remedy decision for the former BP Casper Refinery North Properties Area and North Platte River.

A-1

Appendix A Theory

Appendix A.1 Maximum Time Allowed Between Periodic Mixing

This section provides a derivation and solution for maxt , the maximum time

allowed before the mass balance in Equation 3.23 is violated. maxt can be estimated

after the first change in tracer concentration is measured using the relative permeabilities

of the formation about the well. The PMR solution assumes a vertically-averaged

horizontal LNAPL flow rate for the calculations. LNAPL will not have a uniform flow

rate through the monitoring well due to vertical variation in conductivity to LNAPL. The

potential exists for LNAPL in discrete thicknesses to have higher flow rates through the

monitoring well. The solution for maxt assumes a non-zero entry pressure. The solution

uses formulas derived in Farr et. al. (1990). The solution assumes unconfined conditions

and homogenous porous media in the zone of LNAPL saturation.

After the first change in tracer concentration is measured, the ratio of o

t

C

C is

known, and the vertically-averaged horizontal LNAPL flow rates through the well can be

calculated using Equation 3.33. This is restated below as

cos2sincos2 aa

C

C

o

t

3.33 The vertically-averaged horizontal LNAPL flow rate through the well, wLq , is inserted

into Darcy’s equation yielding

A-2

dx

dhkq L

rwL ave

A.1 where:

averk = the average relative permeability of the aquifer (unitless)

and

Lw

LwwK

(L/T)

A.2

where:

wK = hydraulic conductivity (L/T)

w = dynamic viscosity of water (M/L-T)

L = density of LNAPL (M/L3)

w = density of water (M/L3)

L = dynamic viscosity of LNAPL (M/L-T)

Ldh = change in LNAPL head (L) dx = change in distance (L)

averk is further defined as

aow

owa

D

D

rr

DD

dzzkk

aow

owa

ave

A.3 where:

aoaD = Depth to the air-LNAPL interface in the monitoring well (L) owaD = Depth in the aquifer where the oil-water capillary pressure is the minimum

required for LNAPL and water to exist continuously as described in Farr et. al. 1990 (L)

The upper limit of integration is the air-LNAPL interface in the well. This is

because LNAPL above this interface will not flow into the well because it exists at

negative gauge pressure. LNAPL above the air-LNAPL interface can have formation

A-3

LNAPL flow, but the single well test as described is unable to measure flow through this

thickness.

zkr is further defined as

2

2 11 eer SSzk

A.4 where:

rw

rwoe S

SzSS

1

1

A.5 where:

eS = effective saturation (unitless)

= Brooks-Corey pore size distribution index (unitless)

oS = LNAPL saturation (unitless)

rwS = residual water saturation (unitless)

Equations A.4 and A.5 are valid only for roo SzS .

The LNAPL saturation as a function of depth seen in Equation A.4 can be

determined from analyzing soil cores within the immediate area of a monitoring well or

by using a petrophysical analysis, as outlined in Farr et al. (1990).

Assuming a non-zero entry pressure, there will be a portion of LNAPL in the

monitoring well that is below the elevation of the continuous LNAPL in the formation.

This immobile LNAPL thickness in the monitoring well is equal to the displacement

pressure head of LNAPL in the formation (Equation 3.41). When conducting an analysis

on LNAPL flow rates through a monitoring well, a correction must be made to account

for LNAPL in the well that is not being displaced. This is the same correction factor as

presented in Equation 3.37. It is repeated as

A-4

wL

fLfLwL b

bqq

ave

A.6 The average LNAPL flow rate through the formation is defined as

dx

dhkq L

ravefL ave

A.7 where:

avefLq = average LNAPL flow rate through the formation (L/T)

Equation A.6 is manipulated and substituted into Equation A.7 and solved for the

LNAPL gradient, resulting in

averfL

wLwLL

kb

bq

dx

dh

A.8 The maximum flow rate through the formation occurs at the depth of maximum relative

permeability. This is expressed as

dx

dhkq L

rfL maxmax

A.9 where:

maxfLq = maximum LNAPL flow rate through the formation (L/T)

maxrk = the maximum relative permeability of the aquifer (unitless)

Equation 3.37 is again modified in Equation A.10, yielding

wL

fLfLwL b

bqq

maxmax

A.10 where:

maxwLq = maximum LNAPL flow rate through the formation (L/T)

A-5

Equation A.10 is manipulated and substituted into Equation A.9 and solved for the

LNAPL gradient resulting in

max

max

rfL

wwLL

kb

bq

dx

dhL

A.11 Equation A.8 is set equal to Equation A.11, yielding

max

max

rfL

wLwL

rfL

wLwL

kb

bq

kb

bq

ave

A.12 Equation A.12 is simplified as

max

max

r

wL

r

wL

k

q

k

q

ave

A.13 Equation 3.20 is substituted in Equation A.13 and solved for t , resulting in

max

2

r

r

wL

w

k

k

q

rt ave

A.14 Equation A.14 is the solution for maximum time allowed between periodic mixing.

Appendix A.2 Derivation of Volume Displaced using a Trigonometric Approach

Figure A.1 shows a simplified plan view of LNAPL being displaced from a

monitoring well.

A-6

/2

/2

0

/2

/2

rw

Volume LNAPL displaced VdL

Formation with LNAPL

Perforated well casing

to< t < t+tt=to

Uniform initial tracer distribution in LNAPL

tqwL

Coordinate system-plan view

0

t=t+t

A

B

C

D E F

/2

/2

0

/2

/2

0

rw

Volume LNAPL displaced VdL

Formation with LNAPL

Perforated well casing

to< t < t+tt=tot=t+t

Uniform initial tracer distribution in LNAPL

tqwL

/2

/2

to< t < t+t

tqwL

0 G

Figure A.1 Trigonometric derivation: conceptual model and coordinate system

Point B is the center of circle on the right, which represents the LNAPL being

displaced from the monitoring well.

DE is the line that connects the circle representing

the monitoring well and the circle representing the displaced LNAPL along the diameter

of both circles from to 0. The circles are offset by the DELength . DELength is the

product of the LNAPL flow rate through the well and the elapsed time.

FBLength is one half of DELength and is defined as

tqLength wLFB 2

1

A.15

The ABCAngle is defined as

cos2cos22

cos2 aD

tqa

r

tqaAngle wL

w

wLABC

A.16

A-7

The volume displaced, dLV , is the volume of the shape connected by the points AECD.

Equations A.17 through A.21 are used to find dLV .

First, the volume of sector ABCEV is defined as

cos22

1 2 abrV wLwABCE

A.17 The volume of the prism ABCFV is defined as

cos2sin2

1 2 abrV wLwABCF

A.18 The volume of lens AGCEV is twice the difference between sector ABCEV and the prism

ABCFV , yielding

cos2sincos22 aabrV wLwAGCE A.19

The volume displaced, dLV , is difference between the volume of the monitoring well,

wLV , and the volume of lens AGCEV , yielding

cos2sincos222 aabrbrV wLwwLwdL

A.20 Equation A.20 simplifies to Equation 3.30, which is stated as

cos2sin)cos(22 aarbV wwLdL

A.21

This is the definition of dLV used in Section 3.2.

A-8

Appendix A.3 Derivation of Volume Displaced using a Calculus-based Approach

This derivation is presented as an alternative derivation of the displaced volume

of LNAPL, dLV . This derivation of dLV and subsequent solution of the PMR test is not

used throughout the thesis. It is presented here for completeness.

/2

/2

0

rw

Volume LNAPL displaced VdL

Formation with LNAPL

Perforated well casing

t=tot=t+t

Uniform initial tracer distribution in LNAPL

Coordinate system-Top view

/2

0

/2/2

/2

to< t < t+t

tqwL

0

Figure A.2 Calculus derivation: conceptual model and coordinate system

Figure A.2 shows LNAPL being displaced from a well. The graphic on the right

shows the vertical line of intersection, the Y-axis, and the horizontal line through the

diameter, the X-axis. The LNAPL being displaced is moving at a distance equal to the

product of the LNAPL flow rate, wLq , and the elapsed time, t . For the Y-axis to

remain at the line of intersection of the circles the monitoring well will move in the

negative x-direction, and the circle representing the LNAPL being displaced from the

well will move in the positive x-direction. Both circles will move at one half the length

of the product of the LNAPL flow rate, wLq , and the elapsed time, t .

A-9

The distance displaced for this derivation of dLV is defined as

tqwLc

A.22 The monitoring well is defined in polar coordinates in Equation A.23 as

22

4cos w

cc rrr

A.23 The LNAPL being displaced is defined in polar coordinates in Equation A.24 as

22

4cos w

cc rrr

A.24 where:

= angle in radians on the unit circle r = distance (L)

Solving Equations A.23 and A.24 for r using the quadratic formula yields Equations A.25

and A.26, respectively, defined as

222

1cos4

cos2 w

ccu rxr

A.25

222

1cos4

cos2 w

ccL rxr

A.26 The subscripts u and L signify that Equations A.25 and A.26 will become the upper and

lower limits of integration. Solving for dLV yields

wL u

L

b r

r

dL dzrdrdV0

2

2

A.27 where: z = vertical distance (L)

A-10

The first integral is evaluated in Equation A.27, resulting in

wLb

wccwcc

dL dzd

rr

V0

2

2

2222

222

2

4

81cos22

2

cos

4

81cos22

2

cos

A.28 Equation A.28 is simplified to

wLb

wc

cdL dzdrV0

2

2

222

1cos4

cos

A.29 The half angle identity is substituted into Equation A.29, yielding

wLb

wc

cdL dzdrV0

2

2

222

sin4

cos

A.30 Equation A.30 is integrated with respect to d , yielding

wLb

c

w

c

w

c

w

wc

cdL dzrr

rr

V0

2

2

2

2

2

2

22

2

222

42

4sin1

4

1cos

ln2

4

1cos

)sin(

A.31 The limits are evaluated, resulting in

wLb

c

w

c

w

c

w

cw

cdL dzrr

rr

V0

2

2

2

2

2

2

22

42

441

ln2

42

A.32 Equation A.32 is further simplified to

A-11

wLb

w

c

w

c

c

wc

cw

cdL dzr

ir

rrV

0

222

22

221ln2

242

A.33 Equation A.33 is further simplified as

dzrr

iirrVwLb

w

c

w

ccw

cwcdL

0

2

22

2

21

2ln2

4

A.34 Part of Equation A.34 takes the form of the definition of arcsine. The definition of the

arcsine is shown in Equation A.35. Equation A.34 is defined in Equation A.36 as

21ln)sin( ziziza A.35

dzr

arrVwLb

w

ccw

cwcdL

0

22

2

2sin2

4

A.36 The last integral is evaluated, yielding

w

ccw

cwcwLdL r

arrbV2

sin24

22

2

A.37 Equations A.37 and 3.31 are substituted into Equation 3.29, yielding

Da

DDC

C ccc

o

t

sin2

142

A.38 Equation A.38 can be simplified further, noting that

D

tq

DwLc

A.39

A-12

Equation A.38 is simplified using Equation A.39, yielding

sin

21 42 a

C

C

o

t

A.40 Equation A.40 is equivalent to Equation 3.33.

A-13

Appendix A.4 Data Output from Randomly Generated Vertical Flow Profiles

Data from assessing error from nonlinearity of VDL with respect to

Column: A B C D ERow:

1 Units2 Percent error NA %3 LNAPL thickness in well 1 ft4 Well radius 0.166666667 ft5 Well diameter 0.333333333 ft6 Time 60.5 day7 Input well flow rate 0.005479452 ft/day8 Output average flow rate 0.0025872619 LNAPL volume well 0.087266463 ft3

10 Average volume displaced 0.050190 ft3

11 Total variable volume displaced 0.001718 ft3

12 Normalized displacement volume 0.58 unitless

Intervals Thickness (L) Random Output Flux Rate (ft/day) Vd (ft^3)

Distance traveled as a normalized to well diameter

1 0.1 0.001 0.9379 5.14E-03 8.54579E-05 0.9332 0.2 0.001 0.0140 7.68E-05 1.5482E-06 0.0143 0.3 0.001 0.9751 5.34E-03 8.67182E-05 0.9704 0.4 0.001 0.8859 4.85E-03 8.30447E-05 0.8815 0.5 0.001 0.2325 1.27E-03 2.54584E-05 0.2316 0.6 0.001 0.1533 8.40E-04 1.6874E-05 0.1527 0.7 0.001 0.8297 4.55E-03 7.98136E-05 0.8258 0.8 0.001 0.8945 4.90E-03 8.34872E-05 0.8909 0.9 0.001 0.3019 1.65E-03 3.28514E-05 0.300

10 1 0.001 0.3636 1.99E-03 3.92841E-05 0.36211 1.1 0.001 0.3284 1.80E-03 3.56315E-05 0.32712 1.2 0.001 0.3502 1.92E-03 3.78983E-05 0.34813 1.3 0.001 0.2534 1.39E-03 2.76967E-05 0.25214 1.4 0.001 0.9257 5.07E-03 8.49505E-05 0.92115 1.5 0.001 0.1584 8.68E-04 2.61508E-05 0.15816 1.6 0.001 0.5336 2.92E-03 7.89104E-05 0.53117 1.7 0.001 0.1435 7.86E-04 3.70964E-05 0.14318 1.8 0.001 0.7789 4.27E-03 4.50979E-05 0.77519 1.9 0.001 0.5910 3.24E-03 2.54821E-05 0.58820 2 0.001 0.2970 1.63E-03 3.12236E-05 0.29521 2.1 0.001 0.7838 4.29E-03 7.25717E-05 0.78022 2.2 0.001 0.7193 3.94E-03 2.41336E-05 0.71523 2.3 0.001 0.5580 3.06E-03 6.75955E-05 0.55524 2.4 0.001 0.6351 3.48E-03 4.09701E-05 0.63225 2.5 0.001 0.7102 3.89E-03 3.81073E-05 0.70626 2.6 0.001 0.3822 2.09E-03 6.94379E-05 0.38027 2.7 0.001 0.0121 6.65E-05 3.888E-05 0.01228 2.8 0.001 0.2350 1.29E-03 7.95522E-05 0.23429 2.9 0.001 0.6367 3.49E-03 5.51546E-05 0.63330 3 0.001 0.0400 2.19E-04 2.89177E-05 0.04031 3.1 0.001 0.2469 1.35E-03 3.53926E-05 0.24632 3.2 0.001 0.1899 1.04E-03 1.77201E-05 0.18933 3.3 0.001 0.4829 2.65E-03 4.26577E-05 0.48034 3.4 0.001 0.4518 2.48E-03 6.12487E-05 0.44935 3.5 0.001 0.4937 2.71E-03 8.09808E-05 0.491

Notes:1. Colunm C is the normally-distributed random generated numbers ranging from 0-12. Colunm D is the product of the random number and the input well flow rate from cell B73. Colunm E is the volume of the dispalced interval based on the output flow rate from Colunm D4. The Average output flow rate is found in Cell B8 from averaging colunm D5. Colunm E is summed in Cell B116. Cell B10 is caluclated from using the output average flow rate (cell B8)7. Percent error in Cell B2 is found by ((B10-B11)/B10)8. This analysis was repeated 10,000 times to generate values in Table 3.19. Data set is truncated to fit data on one page, the whole data set conctains 1,000 intervals

A-14

Vertical Profile of in-Well Flow Rates

0.000 0.200 0.400 0.600 0.800 1.000

0.1

0.6

1.1

1.6

2.1

2.6

3.1

Depth (0.1 % intervals of total LNAPL thickness in

well)

Normalized distance traveled across well (L/L)

Vertical graph of in-w ell f lowrates

Figure A.3 Randomly generated vertical flow profile

B-1

Appendix B Laboratory Experiments

Appendix B.1 Beaker PMR Test Reduced Data

Date 14-Jan Test DataTime of tracer inject 1620 Time Time elapsed (min) Ct Ct/Co Measured Q Test (bfL, qfL) 28, 25 0 0 1164.178 1.00 0Int, Ave, BC 100, 5, 2 1 5.5 1094.137 0.94 1.093877853QfL (act) (mL/min)= 1.32 2 11 1025.668 0.94 1.137792224Elapsed Time (minutes) 5.5 3 16.5 965.5911 0.94 1.064966198Volume (mL) 100 4 22 895.1743 0.93 1.325928887bwL (cm)= 5.3 5 27.5 842.8144 0.94 1.063477745

bfL (cm)= 5.3 6 33 782.9338 0.93 1.291789495

qwL (act) (cm/min)= 0.080Co= 1164.178QwL (measured) (mL/min)= 1.162972 Pump facts mL/minPercent Difference 11.89606 time Pre

influ.1545 1.321600 1.321700 1.32

notes: This test will have the probes left in place, but turning on the sparge line when collecting data

%differenceActual Measured

Actual

B-2

Appendix B.2 Large Tank Experiment Reduced Data

Tank DataTest bfL (cm): 4 Pump Data

Test qfL (cm/day) 5.439722 Time Pump rate

Intensity, Average, Box Car 150,5, 2 (mL/min)Date 7/9/2007 825 0.2125Time of tracer inject 840 833 0.246DTO center well (cm) 42.6 937 0.244444444DTW center well (cm) 55.6 1253 0.218181818Actual QfL (mL/min)= 0.2302816Diameter Well (cm) 5.08bwL (cm)= 13

bfL (cm)= 4

Actual qfL (cm/min)= 0.003778

Actual qwL (cm/min) 0.00132Average measured qfL (cm/min)= 0.003778

alpha (unitless) 1.1343318Volume LNAPL in-well (cm3)= 131.744Co= 2373.80

% flow though well= 19.28364

Test Data

TimeTime

elapsed Intensity

measurementStandard deviation

Ct/Co(pi)Right hand side of Equation 3.33

qwL, LNAPL flow in-well

qfL, LNAPL formation flow

w/o alpha

Predicted intensity

measurement

Actual intensity

normalized

Predicted intensity

normalizedActual minutes Intensity units unitless unitless unitless cm/min cm/min Intensity units unitless unitless

848 0 2373.799 2.242 3.142 3.142 2373.799 1.000 1.000929 41 2353.220 3.899 3.114 3.114 0.00084 0.00274 2341.637 0.991 0.986

1040 112 2308.022 3.844 3.081 3.081 0.00108 0.00351 2286.699 0.972 0.9631102 134 2292.686 3.006 3.121 3.121 0.00120 0.00392 2270.075 0.966 0.9561242 236 2212.660 2.586 3.032 3.032 0.00136 0.00443 2193.567 0.932 0.9241352 306 2172.492 4.884 3.085 3.085 0.00103 0.00336 2142.828 0.915 0.9031448 362 2138.380 3.863 3.092 3.092 0.00112 0.00364 2103.175 0.901 0.8861603 437 2086.811 4.048 3.066 3.066 0.00128 0.00417 2051.052 0.879 0.8641701 495 2028.415 6.393 3.054 3.054 0.00192 0.00625 2011.742 0.855 0.8471745 539 1983.236 2.423 3.072 3.072 0.00202 0.00656 1982.491 0.835 0.835

Predicted Versus Actual Signal Loss

0.820

0.840

0.860

0.880

0.9000.920

0.940

0.960

0.980

1.000

1.020

0 100 200 300 400 500 600

Time (min)

No

rma

lize

d In

ten

sit

yPredicted NormalizedSignal Loss

Measured NormalizedSignal Loss

B-3

Tank DataTest bfL (cm): 4 Pump Data

Test qfL (cm/day) 13.700787 Time Pump rate

Intensity, Average, Box Car 150,10,2 (mL/min)Date 7/8/2007 840 0.577777778Time of tracer inject 845 1105 0.58DTO center well (cm) 42.5 1737 0.6DTW center well (cm) 55.5Actual QfL (mL/min)= 0.58

Diameter Well (cm) 5.08bwL (cm)= 13

bfL (cm)= 4

Actual qfL (cm/min)= 0.009514

Actual qwL (cm/min) 0.00363Average measured qfL (cm/min)= 0.009514

alpha (unitless) 1.2383156

Volume LNAPL in-well (cm3)= 131.744Co= 1926.92

% flow though well= 21.051366

Test Data

TimeTime

elapsed Intensity

measurementStandard deviation

Ct/Co(pi)Right hand side of Equation 3.33

qwL, LNAPL flow in-well

qfL, LNAPL formation flow

w/o alpha

Predicted intensity

measurement

Actual intensity

normalized

Predicted intensity

normalized

Actual minutes Intensity units unitless unitless unitless cm/min cm/min Intensity units unitless unitless855 0 1926.924 1.864 3.1416 3.1416 1926.924 1.000 1.000925 30 1892.812 2.413 3.0860 3.0861 0.00235 0.00764 1874.403 0.982 0.973

1005 70 1825.598 3.385 3.0300 3.0300 0.00354 0.01151 1806.288 0.947 0.9371100 125 1737.063 4.183 2.9892 2.9895 0.00351 0.01142 1716.045 0.901 0.8911145 170 1663.679 3.229 3.0089 3.0090 0.00374 0.01217 1645.892 0.863 0.8541230 215 1570.115 6.261 2.9649 2.9653 0.00498 0.01617 1578.607 0.815 0.819

Predicted Versus Actual Signal Loss

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 50 100 150 200 250

Time (min)N

orm

aliz

ed

Inte

ns

ity

Predicted NormalizedSignal Loss

Measured NormalizedSignal Loss

B-4

Tank DataTest bfL (cm): 4.5 Pump Data

Test qfL (cm/day) 25.19685 Time Pump rate

Intensity, Average, Box Car 150,10,2 (mL/min)Date 7/5/2007 1145 1.35Time of tracer inject 1145 1300 1.16DTO center well (cm) 42.5 1310 1.17DTW center well (cm) 56 1600 1.2Actual QfL (mL/min)= 1.2Diameter Well (cm) 5.08bwL (cm)= 13.5

bfL (cm)= 4.5

Actual qfL (cm/min)= 0.017498

Actual qwL (cm/min) 0.00677Average measured qfL (cm/min)= 0.017498alpha (unitless) 1.1607Volume LNAPL in-well (cm3)= 136.811Co= 2704.19

% flow though well= 19.7319

Test Data

TimeTime

elapsed Intensity

measurementStandard deviation

Ct/Co(pi)Right hand side of Equation 3.33

qwL, LNAPL flow in-well

qfL, LNAPL formation flow

w/o alpha

Predicted intensity

measurement

Actual intensity

normalized

Predicted intensity

normalizedActual minutes Intensity units unitless unitless unitless cm/min cm/min Intensity units unitless unitless

1150 0 2704.191913 2.3326794 3.1416 3.1416 2704.192 1.000 1.0001205 15 2646.364429 6.4547807 3.0744 3.0744 0.00569 0.01706 2635.370 0.979 0.9751220 30 2589.311286 4.1260526 3.0739 3.0739 0.00573 0.01719 2568.299 0.958 0.9501240 50 2513.501033 5.6027116 3.0496 3.0496 0.00584 0.01753 2481.152 0.929 0.9181300 70 2419.256559 9.0000595 3.0238 3.0238 0.00748 0.02243 2396.962 0.895 0.8861320 90 2342.067059 10.971694 3.0414 3.0414 0.00636 0.01908 2315.628 0.866 0.8561340 110 2247.938 3.8925889 3.0153 3.0153 0.00802 0.02406 2237.055 0.831 0.8271400 130 2179.051291 8.3277255 3.0453 3.0454 0.00611 0.01834 2161.148 0.806 0.7991440 170 2040.646351 10.601609 2.942 2.942 0.00633 0.01898 2014.536 0.755 0.7451510 200 1926.528289 3.2510912 2.966 2.966 0.00743 0.02229 1912.016 0.712 0.7071530 220 1856.692886 2.8186985 3.027711954 3.028 0.00723 0.02169 1847.138 0.687 0.6831600 250 1745.42113 12.276451 2.953316751 2.953 0.00797 0.02391 1753.137 0.645 0.6481615 265 1699.173241 2.3225828 3.058350835 3.058 0.00705 0.02115 1708.519 0.628 0.632

Predicted Versus Actual Signal Loss

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 50 100 150 200 250 300

Time (min)N

orm

aliz

ed

Inte

ns

ity

Predicted NormalizedSignal Loss

Measured NormalizedSignal Loss

B-5

Tank DataTest bfL (cm): 14.1 Pump Data

Test qfL (cm/day) 5.9939316 Time Pump rate

Intensity, Average, Box Car 150,10,2 (mL/min)Date 7/12/2007 600 0.9Time of tracer inject 615 610 0.933333333DTO center well (cm) 42.1 741 0.9DTW center well (cm) 65.2 1050 0.844444444Actual QfL (mL/min)= 0.8944444Diameter Well (cm) 5.08bwL (cm)= 23.1

bfL (cm)= 14.1

Actual qfL (cm/min)= 0.004162

Actual qwL (cm/min) 0.00307Average measured qfL (cm/min)= 0.004162

alpha (unitless) 1.2084Volume LNAPL in-well (cm3)= 234.099Co= 2135.47

% flow though well= 20.5436

Test Data

TimeTime

elapsed Intensity

measurementStandard deviation

Ct/Co(pi)Right hand side of Equation 3.33

qwL, LNAPL flow in-well

qfL, LNAPL formation flow

w/o alpha

Predicted intensity

measurement

Actual intensity

normalized

Predicted intensity

normalizedActual minutes Intensity units unitless unitless unitless cm/min cm/min Intensity units unitless unitless

635 0 2135.471 2.340 3.1416 3.1416 2135.471 1.000 1.000709 34 2092.719 2.979 3.0787 3.0788 0.00234 0.00384 2079.602 0.980 0.974734 59 2061.009 1.861 3.0940 3.0940 0.00242 0.00396 2039.595 0.965 0.955747 72 2039.860 2.929 3.1094 3.1094 0.00314 0.00515 2019.191 0.955 0.946759 84 2022.895 2.083 3.1155 3.1155 0.00276 0.00452 2000.545 0.947 0.937814 99 2000.461 2.319 3.1068 3.1068 0.00295 0.00483 1977.453 0.937 0.926829 114 1978.061 3.057 3.1064 3.1064 0.00298 0.00488 1954.628 0.926 0.915844 129 1957.823 3.138 3.1095 3.1095 0.00272 0.00445 1932.066 0.917 0.905859 144 1925.346 2.167 3.0895 3.0890 0.00445 0.00730 1909.764 0.902 0.894914 159 1901.663 2.595 3.1029 3.1030 0.00327 0.00535 1887.720 0.891 0.884929 174 1878.856471 3.509519 3.1039 3.1039 0.00319 0.00523 1865.930 0.880 0.874944 189 1853.791742 2.439582 3.0997 3.0997 0.003547427 0.00581 1844.392 0.868 0.864

Predicted Versus Actual Signal Loss

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 50 100 150 200

Time (min)N

orm

aliz

ed

Inte

ns

ity

Predicted NormalizedSignal Loss

Measured NormalizedSignal Loss

B-6

Tank DataTest bfL (cm): 14.1 Pump Data

Test qfL (cm/day) 20.10387 Time Pump rate

Intensity, Average, Box Car 150,10,2 (mL/min)Date 7/11/2007 800 3.1Time of tracer inject 1340 1350 3DTO center well (cm) 42.1 1435 3DTW center well (cm) 65.2Actual QfL (mL/min)= 3Diameter Well (cm) 5.08bwL (cm)= 23.1

bfL (cm)= 14.1

Actual qfL (cm/min)= 0.013961

Actual qwL (cm/min) 0.01039Average measured qfL (cm/min)= 0.013961alpha (unitless) 1.2197Volume LNAPL in-well (cm3)= 234.099Co= 1087.04

% flow though well= 20.734164

Test Data

TimeTime

elapsed Intensity

measurementStandard deviation

Ct/Co(pi)Right hand side of Equation 3.33

qwL, LNAPL flow in-well

qfL, LNAPL formation flow

w/o alpha

Predicted intensity

measurement

Actual intensity

normalized

Predicted intensity

normalizedActual minutes Intensity units unitless unitless unitless cm/min cm/min Intensity units unitless unitless

1347 0 1087.035 2.165 3.1416 3.1416 1087.035 1.000 1.0001355 8 1063.625 2.411 3.0739 3.0739 0.01075 0.01761 1064.382 0.978 0.9791410 23 1027.574 2.607 3.0351 3.0351 0.00902 0.01477 1022.798 0.945 0.9411425 38 994.057 2.503 3.0391 3.0391 0.00868 0.01422 982.839 0.914 0.9041432 45 973.749 2.692 3.0774 3.0774 0.01165 0.01908 964.917 0.896 0.8881440 53 951.668 2.341 3.0704 3.0704 0.01130 0.01852 944.809 0.875 0.8691447 60 931.726 2.187 3.0758 3.0758 0.01194 0.01956 927.581 0.857 0.8531455 68 910.886 1.290 3.0713 3.0713 0.01116 0.01828 908.251 0.838 0.8361503 76 893.517 1.752 3.0817 3.0817 0.00951 0.01558 889.324 0.822 0.8181510 83 877.596 2.804 3.0856 3.0865 0.01000 0.01638 873.108 0.807 0.8031518 91 860.3847059 1.6715976 3.0800 3.0800 0.00978 0.01602 854.913 0.791 0.7861530 103 833.0688462 2.4471533 3.0419 3.0419 0.01055 0.01729 828.191 0.766 0.762

Predicted Versus Actual Signal Loss

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 20 40 60 80 100 120

Time (min)N

orm

aliz

ed

Inte

ns

ity

Predicted NormalizedSignal Loss

Measured NormalizedSignal Loss

B-7

Tank DataTest bfL (cm): 28.3 Pump Data

Test qfL (cm/day) 24.039398 Time Pump rate

Intensity, Average, Box Car 150, 10, 2 (mL/min)Date 7/17/2007 935 7.25Time of tracer inject 940 1050 7.2DTO center well (cm) 0 1223 7.1DTW center well (cm) 37.3Actual QfL (mL/min)= 7.2Diameter Well (cm) 5.08bwL (cm)= 37.3

bfL (cm)= 28.3

Actual qfL (cm/min)= 0.016694

Actual qwL (cm/min) 0.01403Average measured qfL (cm/min)= 0.016694alpha (unitless) 1.1076

Volume LNAPL in-well (cm3)= 378.004Co= 1016.34

% flow though well= 18.8292

Test Data

TimeTime

elapsed Intensity

measurementStandard deviation

Ct/Co(pi)Right hand side of Equation 3.33

qwL, LNAPL flow in-well

qfL, LNAPL formation flow

w/o alpha

Predicted intensity

measurement

Actual intensity

normalized

Predicted intensity

normalizedActual minutes Intensity units unitless unitless unitless cm/min cm/min Intensity units unitless unitless

945 0 1016.338 7.249 3.1416 3.1416 1016.338 1.000 1.000954 9 988.795 6.078 3.0565 3.0565 0.01201 0.01583 984.179 0.973 0.968

1004 19 964.262 1.938 3.0636 3.0636 0.00991 0.01306 949.578 0.949 0.9341013 28 938.097 3.261 3.0563 3.0563 0.01204 0.01586 919.532 0.923 0.9051025 40 884.687 10.407 2.9627 2.9627 0.01894 0.02496 880.740 0.870 0.8671033 48 852.011 2.690 3.0256 3.0256 0.01842 0.02427 855.968 0.838 0.8421043 58 824.527 2.354 3.0403 3.0403 0.01287 0.01696 825.874 0.811 0.813

Predicted Versus Actual Signal Loss

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 20 40 60 80

Time (min)N

orm

aliz

ed

Inte

ns

ity

Predicted NormalizedSignal Loss

Measured NormalizedSignal Loss

B-8

Tank DataTest bfL (cm): 28.3 Pump Data

Test qfL (cm/day) 24.039398 Time Pump rate

Intensity, Average, Box Car 150, 10, 2 (mL/min)Date 7/17/2007 935 7.25Time of tracer inject 1100 1050 7.2DTO center well (cm) 0 1223 7.1DTW center well (cm) 37.3Actual QfL (mL/min)= 7.2Diameter Well (cm) 5.08bwL (cm)= 37.3

bfL (cm)= 28.3

Actual qfL (cm/min)= 0.016694

Actual qwL (cm/min) 0.01520Average measured qfL (cm/min)= 0.016694alpha (unitless) 1.1997

Volume LNAPL in-well (cm3)= 378.004Co= 882.71

37.80% flow though well= 20.3949

Test Data

TimeTime

elapsed Intensity

measurementStandard deviation

Ct/Co(pi)Right hand side of Equation 3.33

qwL, LNAPL flow in-well

qfL, LNAPL formation flow

w/o alpha

Predicted intensity

measurement

Actual intensity

normalized

Predicted intensity

normalizedActual minutes Intensity units unitless unitless unitless cm/min cm/min Intensity units unitless unitless

1118 0 882.714 6.778 3.1416 3.1416 882.714 1.000 1.0001126 8 850.728 3.791 3.0278 3.0280 0.01803 0.02377 855.822 0.964 0.9701134 16 824.150 1.719 3.0434 3.0434 0.01559 0.02055 829.749 0.934 0.9401144 26 803.349 3.138 3.0623 3.0623 0.01007 0.01327 798.152 0.910 0.9041152 34 776.415 2.256 3.0363 3.0363 0.01672 0.02203 773.836 0.880 0.8771200 42 754.789 2.150 3.0541 3.0541 0.01389 0.01831 750.261 0.855 0.8501209 51 727.420 3.283 3.0277 3.0277 0.01607 0.02119 724.548 0.824 0.8211218 60 701.177 2.374 3.0283 3.0283 0.01599 0.02107 699.715 0.794 0.793

Predicted Versus Actual Signal Loss

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 20 40 60 80

Time (min)N

orm

aliz

ed

Inte

ns

ity

Predicted NormalizedSignal Loss

Measured NormalizedSignal Loss

B-9

Tank DataTest bfL (cm): 28.3 Pump Data

Test qfL (cm/day) 24.039398 Time Pump rate

Intensity, Average, Box Car 150,10,2 (mL/min)Date 7/17/2007 935 7.25Time of tracer inject 1222 1050 7.2DTO center well (cm) 0 1223 7.1DTW center well (cm) 37.3Actual QfL (mL/min)= 7.2Diameter Well (cm) 5.08bwL (cm)= 37.3

bfL (cm)= 28.3

Actual qfL (cm/min)= 0.016694

Actual qwL (cm/min) 0.01527Average measured qfL (cm/min)= 0.016694alpha (unitless) 1.2060

Volume LNAPL in-well (cm3)= 378.004Co= 928.13

% flow though well= 20.50132

Test Data

TimeTime

elapsed Intensity

measurementStandard deviation

Ct/Co(pi)Right hand side of Equation 3.33

qwL, LNAPL flow in-well

qfL, LNAPL formation flow

w/o alpha

Predicted intensity

measurement

Actual intensity

normalized

Predicted intensity

normalizedActual minutes Intensity units unitless unitless unitless cm/min cm/min Intensity units unitless unitless1238 0 928.1300667 2.1492029 3.1416 3.1416 928.130 1.000 1.0001248 10 894.515381 2.2649129 3.0278 3.0278 0.01445 0.01905 892.603 0.964 0.9621257 19 865.5435926 2.6364821 3.0398 3.0398 0.01437 0.01893 861.851 0.933 0.9291308 30 833.9390469 2.7647508 3.0269 3.0268 0.01325 0.01746 825.563 0.899 0.8891316 38 804.3496087 5.0354704 3.0301 3.0301 0.01770 0.02333 800.281 0.867 0.8621325 47 776.4843333 3.2202697 3.0328 3.0328 0.01535 0.02024 772.710 0.837 0.8331334 56 752.633619 2.7824296 3.0451 3.0451 0.01362 0.01795 746.089 0.811 0.8041340 62 732.0611667 2.040951 3.0557 3.0557 0.01818 0.02396 728.952 0.789 0.785

Predicted Versus Actual Signal Loss

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 20 40 60 80

Time (min)N

orm

aliz

ed

Inte

ns

ity

Predicted NormalizedSignal Loss

Measured NormalizedSignal Loss

C-1

Appendix C Field Experiments

Appendix C.1 PMR Test Field Procedure Flow Chart

Initial field reconnaissance

Initial field reconnaissance

Office screening of study wells

Office screening of study wells

Initial setupInitial setup

no

1) Gauge wells (DTO-DTW)2) Insert C0 pipe3) Add tracer4) Mix tracer5) Scan

1) Gauge wells (DTO-DTW)2) Insert C0 pipe3) Add tracer4) Mix tracer5) Scan

1) Post DTO-DTW on geology-well completion diagrams2) Check screens relative to WT-OT fluctuations3) Identify wells of interest4) Estimate Ctracer for minimum 3x background at 580 nm4) Resolve materials for C0 and C100 controls

1) Post DTO-DTW on geology-well completion diagrams2) Check screens relative to WT-OT fluctuations3) Identify wells of interest4) Estimate Ctracer for minimum 3x background at 580 nm4) Resolve materials for C0 and C100 controls

1) Gauge all wells (DTO-DTW)2) Scan wells for background intensity3) Collect Product sample

Physical propertiesNAPL for standards @ 2-in wells

4) Collect water - Density

1) Gauge all wells (DTO-DTW)2) Scan wells for background intensity3) Collect Product sample

Physical propertiesNAPL for standards @ 2-in wells

4) Collect water - Density

Initial gaugingInitial gauging1) Scan C0, C100, Cwell, Cwell, C0, and

C100 (see details in scan procedure) 1) Scan C0, C100, Cwell, Cwell, C0, and

C100 (see details in scan procedure)

6) Insert C100 pipe6) Insert C100 pipe

yes

noTracer > 3X background?

yes

Tracer wellmixed?

Startup

no

yes

Initial-final C0-C100 within 1%?

1) Initiate periodic mix and scan(see details in scan procedure)

1) Initiate periodic mix and scan(see details in scan procedure)

Routine data collection

Routine data collection

C-2

Scanning

SetupSetup

Scan Well Scan Well

1) Turn on spectrometer and laptop2) Mix tracer in well using a down-hole bubbler3) Create file folders by day, well, and event4) Check probe

- blue light in 6 outer fibers- no oil inside-outside of reflectance probe

5) Place cable in C100

- Check spectrometer temp (green light)- Mark distance to oil-air interface- Adjust integration time so 480-510 ~ 50% of max.

6) Vertical scan to verify uniform tracer distribution (remix and repeat scan if not uniform)

7) Record LNAPL thickness8) Set data acquisition parameters (duration,…)

1) Turn on spectrometer and laptop2) Mix tracer in well using a down-hole bubbler3) Create file folders by day, well, and event4) Check probe

- blue light in 6 outer fibers- no oil inside-outside of reflectance probe

5) Place cable in C100

- Check spectrometer temp (green light)- Mark distance to oil-air interface- Adjust integration time so 480-510 ~ 50% of max.

6) Vertical scan to verify uniform tracer distribution (remix and repeat scan if not uniform)

7) Record LNAPL thickness8) Set data acquisition parameters (duration,…)

Sequentially scan C100 C0, Cwell, C0, C100 per steps below

Sequentially scan C100 C0, Cwell, C0, C100 per steps below

no

yes

Initial and final C0-C100 values within 1.5% ?

1) Enter filename of well-time-pipe (C0, C100 or Cwell)

2) Collect data and save data file3) Decon. probe and cable using ethanol or

isopropyl alcohol - Remove all visible oil- Be careful not to rotate the reflectance probe

1) Enter filename of well-time-pipe (C0, C100 or Cwell)

2) Collect data and save data file3) Decon. probe and cable using ethanol or

isopropyl alcohol - Remove all visible oil- Be careful not to rotate the reflectance probe

yesMove to next

wellMove to next

well

no

Additional wells to scan?

Check data Check data 1) Estimate QLNAPL per standard procedure2) Test data to resolve if the total flow through to the

well was less than 10% of the volume LNAPL3) Estimate t for a 5% loss

1) Estimate QLNAPL per standard procedure2) Test data to resolve if the total flow through to the

well was less than 10% of the volume LNAPL3) Estimate t for a 5% loss

C-3

Appendix C.2 Field Experiment Well Data

Well DateProduct Total

(gal)Product Delta

(gal)

Average Product RecoveryRate

(gal/day) (Calculated)

Water Total (gal)

Water Delta (gal)

Average Water RecoveryRate

(gal/day) (Calculated)

Water Recovery Rate

(gal/min) (Measured)

R-91 05/03/07 62690 2059 15407800 698800 19

R-91 06/08/07 65184 2494 69.28 16576500 1168700 22.54 22.67

R-91 07/09/07 67182 1998 64.45 17541200 964700 21.61 21

R-91 08/09/07 68407 1225 39.52 18453900 912700 20.45 17.33

R-91 09/06/07 68754 347 12.39 19227800 773900 19.19 21.33

R-91 09/27/07 69230 476 22.67 19887700 659900 21.82 23

R-91 10/25/07 69406 176 6.29 20434400 546700 13.56 12

R-91 11/21/07 71201 1795 66.48 21196600 762200 19.60 15.33

R-91 11/29/07 71517 316 39.50 21384200 187600 16.28 18

R-93 05/03/07 43477 1587 14378100 270100 7.33

R-93 06/08/07 46321 2844 79.00 15154200 776100 14.97 14

R-93 07/09/07 48492 2171 70.03 15703400 549200 12.30 23

R-93 08/09/07 51915 3423 110.42 16176900 473500 10.61 12

R-93 09/06/07 54642 2727 97.39 16626400 449500 11.15 16

R-93 09/27/07 55662 1020 48.57 16785500 159100 5.26 8

R-93 10/25/07 58605 2943 105.11 17295900 510400 12.66 15

R-93 11/21/07 60616 2011 74.48 17749900 454000 11.68 9

R-93 11/29/07 61225 609 76.13 17846300 96400 8.37 9.33

This data was provided by ENSR

Well ID Easting Northing

TOC Elevation

Ground Elevation

Top of Screen Elevation Status

Current Survey Date

Construction Diagram

45 Unknown No113 761863.98 794556.13 5118.01 5118.38 5111.38 Current 3/31/2006 YesPZ-333S 767239.90 794981.93 5120.27 Current 12/11/2003 NRPZ-334S 767226.55 794997.95 5119.91 Current 12/11/2003 NoPZ-335S Unknown NoPZ-341S 767265.30 794999.02 5120.29 Current 12/11/2003 NRPZ-342S 767287.84 794998.31 5120.08 Current 12/11/2003 NRR-91 766397.07 794497.31 5122.40 Current YesR-93 766136.67 794551.63 5119.07 Current YesTW-416 (MW-416) 766155.15 794552.00 5121.73 Current 6/28/2004 YesTW-418 (MW-418) 766176.31 794552.35 5122.80 5122.80 Current 6/28/2004 YesTW-419 766387.11 794497.84 5123.05 Current 6/28/2004 YesTW-420 766377.15 794496.83 5121.76 Current 6/28/2004 Yes

Provided by ENSR

C-4

Appendix C.3 First Field Experiment Data Reduction

Well Name TW-419 bwL 0.28 ft

D 0.166666667 ftdate

Tracer added: 10/27/07 12:00 PM 0 100

Date time-well mixedElapsed Time

(days)

Elapsed Time from Last test

(d) C0 (intensity)C100

(intensity) WS (intensity) Slope InterceptWS Percent

(%) cumlative Normalizedratio of

C100/C0 Ct/Co(pi)RHS eqn

3.33

QwL

ft3/day

QwL

ft3/day qwL ft/yr10/27/2007 10/27/07 12:12 PM 0.00 0.00 503.3830324 1989.1678 1831.038525 14.86 503.38 89.36 395.1610/27/2007 10/27/07 2:20 PM 0.10 0.10 618.3233571 2154 1999.621933 15.36 618.32 89.95 348.3610/27/2007 10/27/07 5:35 PM 0.23 0.14 671.2081053 2248.8296 1867.091426 15.78 671.21 75.80 0.84 335.04 2.648 2.648 0.0071 2.59334 55.5710/28/2007 10/28/07 8:07 AM 0.84 0.61 579.6898667 2258 1459 16.78 579.69 52.39 0.74 389.52 2.324 2.324 0.0026 0.96511 20.6810/28/2007 10/28/07 12:50 PM 1.03 0.20 607 2255 1098 16.48 607.00 29.79 0.75 371.50 2.352 2.352 0.0079 2.87047 61.51

Well Name TW-420 bwL 0.57 ftD 0.166666667 ft

dateTracer added: 10/27/07 12:00 PM 0 100

Date time-well mixedElapsed Time

(days)

Elapsed Time from Last test

(d) C0 (intensity)C100

(intensity) WS (intensity) Slope InterceptWS Percent

(%) cumlative Normalizedratio of

C100/C0 Ct/Co(pi)RHS eqn

3.33

QwL

ft3/day

QwL

ft3/day qwL ft/yr10/27/2007 10/27/07 12:25 PM 0.00 0.00 503.3830324 1989.1678 1739.887773 14.86 503.38 83.22 395.1610/27/2007 10/27/07 2:20 PM 0.10 0.10 618.3233571 2154 1855.268453 15.36 618.32 80.55 0.97 348.36 3.037 3.051 0.0037 1.3605 14.3210/27/2007 10/27/07 5:35 PM 0.23 0.14 671.2081053 2248.8296 1840.86136 15.78 671.21 74.14 0.92 335.04 2.892 2.879 0.0077 2.80046 29.4810/28/2007 10/28/07 8:07 AM 0.84 0.61 677 2350 1807 16.73 677.00 67.54 0.92 347.12 2.884 2.886 0.0017 0.61068 6.4310/28/2007 10/28/07 12:50 PM 1.03 0.20 607 2255 1620 16.48 607.00 61.47 0.92 371.50 2.905 2.906 0.0048 1.73448 18.26

Well Name TW-416 bwL 0.61 ftD 0.166666667 ft

dateTracer added: 10/27/07 12:00 PM 0 100

Date time-well mixedElapsed Time

(days)

Elapsed Time from Last test

(d) C0 (intensity)C100

(intensity) WS (intensity) Slope InterceptWS Percent

(%) cumlative Normalizedratio of

C100/C0 Ct/Co(pi)RHS eqn

3.33

QwL

ft3/day

QwL

ft3/day qwL ft/yr10/27/2007 10/27/07 1:00 PM 0.00 0.00 345 983.29089 1277.4438 6.38 345.00 146.08 285.0110/27/2007 10/27/07 3:00 PM 0.13 0.12 324.460931 1015 1142 6.91 324.46 118.39 0.77 312.83 2.407 2.408 0.025 9.12737 89.77710/27/2007 10/27/07 6:00 PM 0.25 0.13 360 1115 1020.071983 7.55 360.00 87.43 0.74 309.72 2.320 2.320 0.028 10.2361 100.6810/28/2007 10/28/07 8:45 AM 0.86 0.61 419.5221875 1148.2896 940.1014286 7.29 419.52 71.43 0.86 273.71 2.717 2.716 0.0029 1.07347 10.55910/28/2007 10/28/07 1:13 PM 1.05 0.19 358.337 1045.1832 673 6.87 358.34 45.81 0.78 291.68 2.462 2.459 0.0156 5.7013 56.078

Well Name TW-418 bwL 0.65 ftD 0.166666667 ft

dateTracer added: 10/27/07 12:00 PM 0 100

Date time-well mixedElapsed Time

(days)

Elapsed Time from Last test

(d) C0 (intensity)C100

(intensity) WS (intensity) Slope InterceptWS Percent

(%) cumlative Normalizedratio of

C100/C0 Ct/Co(pi)RHS eqn

3.33

QwL

ft3/day

QwL

ft3/day qwL ft/yr10/27/2007 10/27/07 1:00 PM 0.00 0.00 345 983.29089 1344.098884 6.38 345.00 156.53 285.0110/27/2007 10/27/07 1:52 PM 0.08 0.08 324.460931 929.56391 1262 6.05 324.46 154.94 286.4910/27/2007 10/27/07 6:00 PM 0.25 0.17 360 1115 1326.753605 7.55 360.00 128.05 0.83 309.72 2.596 2.596 0.0143 5.23535 48.32610/28/2007 10/28/07 8:45 AM 0.86 0.61 419.5221875 1148.2896 1345.769 7.29 419.52 127.10 0.99 273.71 3.122 3.122 0.0001 0.05232 0.482910/28/2007 10/28/07 1:13 PM 1.05 0.19 358.337 1045.1832 1122.559753 6.87 358.34 111.27 0.90 291.68 2.821 2.821 0.0078 2.84066 26.221

C-5

Appendix C.4 First Field Experiment Calculations

Tim Smith1-22-2008Calculating discharge measured from PMR tests during October 27-28, 2007 Casper field work.

Round 1 Round 2 Round 3 Radius from Recovery Well LNAPL Well Thickness0.12 days 0.61days 0.20 days (rw) (bwL)

qwL qwL qwL

Area Well ID Dates ft/yr ft/yr ft/yr (ft) (ft)R91 TW-419 10-27 to 10-28 55.6 20.7 61.5 10.00 0.28R91 TW-420 10-27 to 10-28 29.5 6.4 18.3 19.9 0.57R93 TW-416 10-27 to 10-28 100.7 10.6 56.1 18.33 0.61R93 TW-418 10-27 to 10-28 48.3 0.5 26.2 30.66 0.65

Notes:1. The units are for a flux through the well (L3/(T-L2))--not through the formation2. No attempt to calculate a flow convergence factor, alpha, was made3. No attempt to include LNAPL formation thickness was made4. Round 2 occurred over a longer time period, and tracer may have been completely displaced from the well at some intervals.* The data point from over night was ommited due to waiting too long between mixing events

Measured LNAPL discharge rate through the well, using the measured LNAPL flow rates, and thedistance between the monitoring well and the LNAPL recovery well

Well TW-419 Well TW-420 Well TW-416 Well TW-418

rad419 10 ft rad420 19.9 ft rad416 18.33 ft rad418 30.66 ft

bL419 0.28 ft bL420 0.57 ft bL416 0.61 ft bL418 0.65 ft

q1419 55.6ft

yr q1420 29.5

ft

yr q1416 100.7

ft

yr q1418 48.3

ft

yr

q2419 61.5ft

yr q2420 18.3

ft

yr q2416 56.1

ft

yr q2418 26.2

ft

yr

Where:rad = distance from recovery well (L)bL = LNAPL thickness in monitoring well (L)

q = LNAPL flux rate through the well (L/T)

Q1419 π 2 rad419 bL419 q1419 20.034gal

day Q2419 π 2 rad419 bL419 q2419 22.16

gal

day

Q1420 π 2 rad420 bL420 q1420 43.061gal

day Q2420 π 2 rad420 bL420 q2420 26.712

gal

day

Q1416 π 2 rad416 bL416 q1416 144.895gal

day Q2416 π 2 rad416 bL416 q2416 80.721

gal

day

Q1418 π 2 rad418 bL418 q1418 123.869gal

day Q2418 π 2 rad418 bL418 q2418 67.192

gal

day

C-6

Also, the flow convergence factor of 0.91 measured by Iltis (2007) for a 0.03 slotted PVC well

α 0.91

Q1419α

Q1419

α

22.015gal

day Q2419α

Q2419

α

24.351gal

day

Q1420α

Q1420

α

47.319gal

day Q2420α

Q2420

α

29.354gal

day

Q1416α

Q1416

α

159.225gal

day Q2416α

Q2416

α

88.704gal

day

Q1418a

Q1418

α

136.12gal

day Q2418α

Q2418

α

73.837gal

day

Average measured LNAPL discharge rate from the two well clusters

QR91ave

Q1419 Q1420 Q2419 Q2420

427.992

gal

day

QR93ave

Q1416 Q1418 Q2416 Q2418

4104.169

gal

day

Actual LNAPL recovery rates reported from ENSR

QR91act 37.42gal

day QR93act 85.24

gal

day

The averaged measured LNAPL discharge rate through the well must be correlated to thedischarge rate of the recovery well using the flow convergence factor.

αR91

QR91ave

QR91act0.748 αR93

QR93ave

QR93act1.222

Or the α values can be calculated at each well for eachmeasurement

α1420

Q1420

QR91act1.151 α1419

Q1419

QR91act0.535

α2420

Q2420

QR91act0.714 α2419

Q2419

QR91act0.592

α1418

Q1418

QR93act1.453 α1416

Q1416

QR93act1.7

α2416

Q2416

QR93act0.947

α2418

Q2418

QR93act0.788

C-7

Appendix C.5 Second Field Experiment Data Reduction and Calculations

Well Name Well 45 Gipps bwL 0.25 ft 2.85 0

D 0.2375 ft effective dimeter for well 45 0.177205 0.018435 0.15877042date

Tracer added: 10/28/07 9:30 AM 0 100

Date time-well mixed

Elapsed Time (days)

Elapsed Time from Last test

(d) DTO DTWLNAPL

ThicknessC0

(intensity)C100

(intensity)WS

(intensity) Slope InterceptWS Percent

(%) cumlative Normalizedratio of

C100/C0 Ct/Co(pi)RHS eqn

3.33 QwL ft3/day QwL ft

3/day qwL ft/yr

10/28/2007 10/28/07 9:40 AM 0.01 0.00 20.10 20.35 0.25 390.89 1278.07 1264.16 8.87 390.89 98.43 326.9611/15/2007 11/15/07 9:35 AM 18.00 18.00 nm nm 0.31 291.00 992.71 1067.09 7.02 291.00 110.60 1.12 341.14 0.00 3.530 3.142 0 0 012/5/2007 12/5/07 12:50 PM 38.14 20.14 20.20 20.51 0.31 235.00 789.00 779.71 5.54 235.00 98.32 0.88 335.74 0.10 2.750 2.750 8.51515E-05 0.03108 0.422143

12/19/2007 12/19/07 9:15 AM 51.99 13.85 20.21 20.56 0.35 346.66 1094.00 1118.71 7.47 346.66 103.31 1.05 315.58 0.00 3.301 3.142 0 0 01/4/2008 1/4/08 10:15 AM 68.03 16.04 20.14 20.45 0.31 614.66 1758.69 1784.35 11.44 614.66 102.24 0.99 286.12 0.01 3.108 3.107 7.52278E-06 0.002746 0.033032

Well Name PZ-334s Gipps bwL 0.48 ftD 0.166666667 ft

dateTracer added: 10/28/07 9:30 AM 0 100

Date time-well mixed

Elapsed Time (days)

Elapsed Time from Last test

(d) DTO DTWLNAPL

ThicknessC0

(intensity)C100

(intensity)WS

(intensity) Slope InterceptWS Percent

(%) cumlative Normalizedratio of

C100/C0 Ct/Co(pi)RHS eqn

3.33 QwL ft3/day QwL ft

3/day qwL ft/yr

10/28/2007 10/28/07 9:40 AM 0.01 0.00 19.74 20.26 0.52 390.89 1278.07 811.95 8.87 390.89 47.46 1.00 326.9610/27/2007 11/15/07 9:35 AM 18.00 18.00 nm nm 0.65 291.00 992.71 579.79 7.02 291.00 41.16 0.87 341.14 0.10 2.724 2.724 0.000104924 0.038297 0.35351312/5/2007 12/5/07 12:50 PM 38.14 20.14 19.84 20.49 0.65 235.00 789.00 426.64 5.54 235.00 34.59 0.86 335.74 0.11 2.707 2.707 9.76102E-05 0.035628 0.328871

MORE TRACER ADDED12/5/2007-Tracer added 12/5/07 3:50 PM 38.26 0.00 19.84 20.49 0.65 235.00 789.00 735.85 5.54 235.00 90.41 1.00 335.74 - - - - - -

12/19/2007 12/19/07 9:15 AM 51.99 13.73 19.83 20.50 0.67 346.66 1094.00 903.159 7.47 346.66 74.46 0.82 315.58 0.14 2.588 2.588 0.000188257 0.068714 0.6153491/4/2008 1/4/08 10:15 AM 68.03 16.04 19.78 20.34 0.56 614.66 1758.69 1333.29 11.44 614.66 62.82 0.87 286.12 0.10 2.737 2.743 9.67849E-05 0.035327 0.378498

Well Name PZ-335s Gipps bwL 0.52 ft

D 0.166666667 ftdate

Tracer added: 10/28/07 9:30 AM 0 100

Date time-well mixed

Elapsed Time (days)

Elapsed Time from Last test

(d) DTO DTWLNAPL

ThicknessC0

(intensity)C100

(intensity)WS

(intensity) Slope InterceptWS Percent

(%) cumlative Normalizedratio of

C100/C0 Ct/Co(pi)RHS eqn

3.33 QwL ft3/day QwL ft

3/day qwL ft/yr

10/28/2007 10/28/07 9:40 AM 0.01 0.00 20.03 20.55 0.52 390.89 1278.07 846.42 8.87 390.89 51.35 1.00 326.9611/15/2007 11/15/07 9:35 AM 18.00 18.00 nm nm 0.49 291.00 992.71 535.41 7.02 291.00 34.83 0.68 341.14 0.26 2.131 2.131 0.000193203 0.070519 0.863512/5/2007 12/5/07 12:50 PM 38.14 20.14 20.18 20.67 0.49 235.00 789.00 371.94 5.54 235.00 24.72 0.80 335.74 0.16 2.523 2.523 0.000104962 0.038311 0.469116

MORE TRACER ADDED12/05/2007-Tracer added 12/5/07 3:50 PM 38.26 0.00 20.18 20.67 0.49 235.00 789.00 814.46 5.54 235.00 104.60 1 335.74 - - - - - -

12/19/2007 12/19/07 9:15 AM 51.99 13.73 20.18 20.67 0.49 346.66 1094.00 896.00 7.47 346.66 73.51 0.70 315.58 0.24 2.208 2.208 0.000233626 0.085273 1.0441631/4/2008 1/4/08 10:15 AM 68.03 16.04 20.13 20.51 0.38 614.66 1758.69 1259.56 11.44 614.66 56.37 0.84 286.12 0.13 2.627 2.633 8.38817E-05 0.030617 0.483423

Well Name Well 113 Op. Area bwL 0.5 ft 3.892745

D 0.324395376 ft effective dimeter for well 113 0.330597 0.018435 0.31216217date

Tracer added: 10/28/07 10:30 AM 0 100

Date time-well mixed

Elapsed Time (days)

Elapsed Time from Last test

(d) DTO DTWLNAPL

ThicknessC0

(intensity)C100

(intensity)WS

(intensity) Slope InterceptWS Percent

(%) cumlative Normalizedratio of

C100/C0 Ct/Co(pi)RHS eqn

3.33 QwL ft3/day QwL ft

3/day qwL ft/yr

10/28/2007 10/28/07 10:40 AM 0.01 0.00 9.40 9.90 0.50 212.10 821.66 824.71 6.10 212.10 100.50 1.00 387.3911/15/2007 11/15/07 10:38 AM 18.01 18.00 nm nm 0.58 171.03 660.28 646.23 4.89 171.03 97.13 0.97 386.06 0.03 3.036 3.036 8.95286E-05 0.032678 0.17368112/5/2007 12/5/07 3:25 PM 38.20 20.20 9.60 10.18 0.58 123.24 499.72 438.11 3.76 123.24 83.64 0.87 405.49 0.11 2.720 2.720 0.000319059 0.116456 0.618957

12/19/2007 12/19/07 10:45 AM 52.01 13.81 9.50 9.90 0.40 192.17 718.88 700.99 5.27 192.17 96.60 0.99 374.09 0.00 3.125 3.125 1.26477E-05 0.004616 0.0355771/4/2008 1/4/08 10:15 AM 67.99 15.98 9.37 9.75 0.38 585.40 2133.36 2074.87 15.48 585.40 96.22 1.00 364.43 0.00 3.130 3.130 7.25274E-06 0.002647 0.021475

4/17/2008 4/17/2008 10:45 172.01 104.02 9.31 9.70 0.39 173.691 700.956 608.4433 5.27 173.69 82.45 0.86 403.56 0.11 2.711 2.711 4.25242E-05 0.015521 0.122684