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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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
ii
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
iii
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
iv
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.
v
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
3 Theory ................................................................................................................................................ 16
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
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
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
ix
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
1
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
2
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.
3
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.
4
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)
5
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
6
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
7
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
8
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
9
(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
10
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.
11
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
12
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
13
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
14
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
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
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
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
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
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
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
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
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
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
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
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