Download Single-Phase Wax Deposition Experiments

Energy Fuels 2010, 24, 1069–1080
Published on Web 12/01/2009
: DOI:10.1021/ef900920x
Single-Phase Wax Deposition Experiments
Rainer Hoffmann* and Lene Amundsen
StatoilHydro ASA, Norway
Received August 25, 2009. Revised Manuscript Received November 5, 2009
The behavior of waxy crude oils in subsea production lines has been successfully investigated in a 2 in.
deposition flow loop. A North Sea waxy gas condensate was used to investigate wax deposition in
turbulent single-phase flow under different temperature and flow conditions. A reliable and accurate
procedure for determination of wax thickness and wax roughness from pressure drop, weight, and laser
measurements has been developed. The laser technique is a new and promising method to measure the
spatial distribution of wax thickness, which was not captured by the traditional pressure drop and weighing
methods. These experiments have led to an increased understanding of the mechanisms of wax deposition,
which is needed to develop more-accurate models based on physical effects. These models are then the basis
for a more accurate prediction of the rate of wax deposition in production lines. The main finding is that
molecular diffusion is indeed the central mechanism that steers wax deposition but that an accurate
quantitative description also needs to take the wax composition of the deposit and the effects of shear stress
into account. However, for higher oil temperatures it was found that the wax deposit’s structure changes
from the well-known smooth homogeneous type to a new irregular, patchy type. This deposit cannot be
described by the traditional diffusion models. In addition, the experiments were used to confirm that the
laboratory-scale measurement techniques that are typically used to determine wax appearance temperature do result in a temperature that coincides with the temperature where wax starts to deposit under
realistic flow conditions.
condensate flows through a test section where a surrounding
water annulus simulates the conditions subsea. Several experimental campaigns were performed where the influence of the
oil temperature, the cooling water temperature, and the flow
rate were investigated. The measurements included several
independent ways of determining the wax deposit thickness.
In addition, the resulting deposit composition was also analyzed to verify the assumption of some models that a constant
porosity and a single diffusion equation is sufficient to
describe the deposition process.
These experiments are used to identify the main physical
mechanisms that have to be included in a wax deposition
model. In a next step the aquired data will then be used to
quantitatively verify available models and simulation tools.
Introduction
Characterization of waxy oils and determination of deposition rate in production pipes is crucial in concept development
and engineering of new fields and for fields in operation. Wax
deposition can be an obstruction (show stopper) for development of new fields. For fields in operation, waxy oils can lead
to reduction in oil production, increased operational costs,
and HSE problems, and in some cases the pipeline can be
plugged by either wax deposits or a stuck pig. For all of the
wax control methods in use (pigging, pipeline insulation,
heating) the rate of wax deposition needs to be known in
advance to choose and design the appropriate control
method.
To predict wax deposition, models are being used that take
into account the properties of the gas condensate, the fluid
flow, and the pipeline. From the various mechanisms that
were discussed in the very first papers on pipeline wax deposition1 molecular diffusion is today considered to be the
dominant one. Since field data from production pipelines
are difficult to obtain (due to nonconstant conditions and
insufficient instrumentation2) the only way to validate the
basic assumptions of a model is to perform experiments in a
flow loop.
To this end a 2 in. flow loop was constructed at StatoilHydro Research Centre Porsgrunn where real waxy gas
Experimental Facilities
Wax Deposition Test Rig. The wax deposition test rig consists
of a flow loop where real crude oil or gas condensate is circulated
from a tank through the test section (see Figure 1). The test
section is 5.5 m long and is surrounded by an annulus that is
flooded by a concurrent water flow. The temperatures of oil and
water can be adjusted separately in the interval of 5-70 °C so
that all kinds of temperature conditions (temperature and
temperature gradient) at the inner pipe wall can be set.
The tank volume is 4000 L and has been chosen so that wax
depletion during an experiment is not an issue. An example may
illustrate this: If the tank is only half-filled (2000 L) with a very
low wax-content oil (2.5%) there is 50 L of wax available. If an
experiment is run where a wax deposit of 3 mm is built up (which
is a lot more than is usually obtained) about 2.7 L of wax are in
the deposit, so roughly 95% of the wax is still available in the
flow.
The rig can operate with real crude oils and gas condensates at
atmospheric pressure. The pump delivers a flow rate of 3-30 m3/h
*To whom correspondence should be addressed. E-mail: rahof@
statoilhydro.com.
(1) Burger, E. D.; Perkins, T. K.; Striegler, J. H. J. Pet. Technol. 1981,
36, 1075–1086.
(2) Labes-Carrier, C.; Rønningsen, H. P.; Kolnes, J.; Leporcher, E.
Wax deposition in North Sea gas condensate and oil systems: Comparison
between operational experience and model prediction. SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 2002.
r 2009 American Chemical Society
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pubs.acs.org/EF
Energy Fuels 2010, 24, 1069–1080
: DOI:10.1021/ef900920x
Hoffmann and Amundsen
Figure 1. Wax deposition test rig layout.
Table 1. Instrumentation of Test Rig
mass flow
instrument
accuracy
E&H Coriolis
Promass 63 F
(0.1% of reading
range
0-31 m3/h
differential
pressure
Rosemount
3051 cd2
(0.065% of
calibrated range
0-620 mbar
temperature
Rosemount
k-element
(0.5 °C
-100 to 1300 °C
Figure 2. Viscosity of test fluid at different shear rates.
which is monitored by Coriolis flow meters (see Table 1). The
piping consists of stainless steel with an inner diameter of 2 in.
The instrumentation for measuring wax thickness consists of:
(1) Pressure drop measurement across the test section. When
wax starts to deposit on the inner pipe wall of the test section the
effective diameter and wall roughness changes, which will result
in a change of the pressure drop. (2) Temperature measurements
of the oil flow before and after the test section. Since wax acts as
a thermal insulation the temperature difference across the test
section is a way of monitoring wax buildup. (3) A removable
part of the test section that can be used to visually inspect the
wax deposit, to determine its weight by weighing it, and to
retrieve wax sample for further lab analysis (GC, DSC, etc.).
(4) A laser and a camera can be inserted into the rig to measure
the inner diameter and thus the deposit’s thickness optically.
Test Fluid. The used fluid for all experiments is a waxy
condensate from the North Sea. The main properties of this
fluid are: (1) density Foil =809 kg/m3 at 20 °C; (2) cloud point
(wax appearance temperature, WAT) TWAT ≈ 30 °C, depending
on the measurement technique; (3) pour point TPP ≈ 1 °C;
(4) wax content of ca. 4.5% using acetone precipitation technique (UOP Method 46-64); and (5) viscosity was measured in
a rheometer (Physica MCR 301) at different shear rates (see
Figure 2)
Experimental Procedure. An important precondition for repeatable stable experiments is a suitable experimental procedure. First, all wax in the rig is melted by running the rig at 60 °C
(i.e., well above WAT) for at least 6 h. Then both oil and water
temperature Toil, Twater are set to the desired oil target temperature. Flow rate versus pressure drop measurements are performed (see Figure 3) to verify that the pipe contains no wax
deposit prior to startup as expected and that all instrumentation
is performing correctly. Then Twater is quickly set down to the
target water temperature. Toil and Twater are kept within a range
of 0.2 °C of their target values and the flow rate within a range of
0.1 m3/h within its desired target value for the total experimental
time. After the experiment is finished the pipe is drained, the test
pipe is weighed, laser pictures are taken, and deposit samples are
collected for further analysis.
Figure 3. Determination of diameter and roughness from flow rate
variations.
the test section can be established that has to be solved
numerically
0
1
1:11 ! -2
D5 π2 Δp @
6:9Dπηoil
ε
!
A ¼
FðDÞ ¼
þ
0
- 1:8 log10
8Foil Q2 L
4QFoil
3:7D
ð1Þ
where Δp is the pressure drop, Foil is the oil density, Q is the
oil volume flow rate, L is the length of the differential
pressure measurement, ηoil is the viscosity of the fluid, and
ε is the roughness of the inner pipe wall.
The viscosity of the oil ηoil and the density Foil were
determined for the relevant temperature interval using a
Physica MCR 301 rheometer and an Anton Paar density
meter DMA 4500 M, respectively.
To determine the empty pipe diameter and roughness a
series of measurements were performed where the oil flow
rate was varied across the possible operational range (Qmin=
3 m3/h, Qmax = 30 m3/h), see Figure 3. Oil and water
temperature were both kept at 60 °C so that no precipitated
wax could disturb the measurements.
The measured data points were used for a nonlinear fit
using eq 1 to determine the diameter D and the roughness ε.
The found diameter of 52.56 mm fits very well with the
suppliers specification of Dinner = 52.5 mm. The found
roughness of 0 m means that for the relevant turbulence
Wax Thickness Measurement Methods
Pressure Drop. One way of determining the wax deposit
buildup is to measure the increase in pressure drop due to the
decrease of the pipe diameter. By using Haaland’s friction
factor correlation3 a relationship for the inner diameter D of
(3) Haaland, S. E. J. Fluids Eng. 1983, 105, 89–90.
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Energy Fuels 2010, 24, 1069–1080
: DOI:10.1021/ef900920x
Hoffmann and Amundsen
3
(Q = 21 and 25 m /h). Figure 5, left, shows the calculated
factor k for the exponent in eq 2 according to the measured
pressure drop change compared to an isothermal flow. In a
second series the oil temperature was kept constant at 40 °C
while the water temperature was varied from 35 to 60 °C. The
resulting factor k is shown in Figure 5, right.
The results show that the idea of correcting the friction
factor by the viscosity ratio seems to work but that Perry’s
numbers for the exponent are not applicable for our rig and
fluid. Actually, the plots in Figure 5 seem to suggest that the
exponent is not even constant for different temperature
combinations. However, since the variation is not too large
a fixed exponent of 0.07 was used for all further calculations
of wax thickness from pressure drop measurements. To give
an idea of the sensitivity of the thickness calculation on the k
exponent: Changing the k exponent by 0.01 will change the
calculated wax thickness by 0.7%.
Weight. An alternative way of determining the wax thickness is by measuring the weight increase of the pipe during
the deposition. To this end the removable part of the test
section is weighed several times during an experiment.
From the weight difference compared to an empty pipe the
wax thickness H can be calculated
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
mwax
H ¼ R - R2 Fwax πL
Figure 4. Determination of wax deposit roughness by variation of
oil flow rate.
regime (Remax =50 000) the wall roughness of the pipe is of
no significance. This does of course not imply that the same
assumption is valid for the wax deposit roughness. This
roughness is unknown a priori and has to be determined
during the deposition experiment.
To this end at regular intervals the oil flow rate was slightly
varied as examplified in Figure 4: Starting from the standard
flow rate (Qoil = 21 m3/h in Figure 4) the oil flow rate is
adjusted in two steps of ΔQoil=1 m3/h down to Qoil=19 m3/h
and then in four steps up to Qoil=23 m3/h for some minutes.
The reasoning behind this is that small rate variations for a
short period of time will not unduly disturb the wax deposition rate. However, by measuring the change in pressure
drop corresponding to the change in flow rate it is possible to
fit diameter and roughness using eq 1. So the procedure
shown in Figure 4 employs the same idea as used for an
empty pipe (see Figure 3). The underlying assumption is that
the wax thickness does not change significantly during the
short period of time it takes for performing the rate changes.
As will be shown below, different experimental conditions
can result in very different wax deposit roughness.
Equation 1 is only valid for an isothermal flow, that is, for
equal oil and water temperature. For the more realistic nonisothermal flow, the different wall temperature will lead to a
different oil viscosity in the vicinity of the wall. This will in
turn influence the fluid-wall drag forces and thus the
pressure drop. Perry4 suggests a correction of the friction
factor for non-isothermal flow depending on the ratio of the
viscosity in the bulk flow ηb and the viscosity near the wall ηw
k
η
fnon-isothermal ¼ fisothermal b
ð2Þ
ηw
where R is the inner (empty) pipe radius, mwax is the mass of
deposited wax, Fwax is the density of wax, and L is the length
of the removable test section [m].
To determine wax deposition thickness by weighing it is
necessary to accurately determine the deposit’s density Fwax.
This measurement is performed using a gas displacement
pycnometer (Micromeritics AccuPyc 1330), which measures
the volume of a sample, independent of its structure, by
determining the volume of gas the sample displaces from the
sample cell.
The measurement procedure is as follows (see Figure 5):
The pressure in the sample cell Vcell and the expansion cell
Vexp is initially set to ambient pressure pa at ambient temperature Ta. Then the valve is closed and Vcell is filled with
measurement gas (Helium) up to a pressure p1. The gas
equation is
p1 ðVcell -Vsamp Þ ¼ nc RTa
where Vsamp is the volume of the sample in the sample cell,
Vcell is the volume of the sample cell, nc is the number of
moles of gas in the sample cell, R is the universal gas
constant, and Ta is the ambient temperature.
The equation for the expansion is
pa Vexp ¼ ne RTa
where ne is the number of moles of gas in the expansion cell.
When the valve is opened the pressure is lowered to p2
p2 ðVcell -Vsamp þ Vexp Þ ¼ nc RTa þ ne RTa
The factor k in the exponent is 0.11 for cooling and 0.17 for
heating according to Perry. To verify these numbers a series
of experiments with a clean pipe were performed where
different non-isothermal temperature combinations were
measured. These were chosen so that no disturbing wax
deposition could occur since the temperatures were always
kept well above WAT.
In a first series the water temperature was kept constant at
60 °C while the oil temperature was varied between 30 and
50 °C. The experiment was repeated at two different flow rates
This equation is used for the pycnometer measurement. Vcell
and Vexp are determined using calibration measurements.
The pressures are determined using difference pressure measurements against ambient pressure. It is essential to keep the
temperatures in the sample and expansion cell constant
during the measurement.
A pycnometer measurement was performed on a wax
deposit sample from an experiment with Qoil =21 m3/h and
two samples from an experiment with Qoil = 5 m3/h. Both
(4) Green, D. W.; Perry, R. H. Flow in Pipes and Channels, and NonIsothermal Flow; McGraw-Hill Book Company, 1963.
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Hoffmann and Amundsen
Figure 5. Influence of non-isothermal flow.
Figure 6. Schematic of pycnometer.
Figure 7. Laser-based thickness measurement;principle.
Table 2. Oil and Deposit Density Measurements
sample
wax
content
density
(g/cm3)
standard deviation
(g/cm3)
Qoil = 21 m3/h
Qoil = 5 m3/h, No. 1
Qoil = 5 m3/h, No. 2
33%
18%
18%
0.8996
0.8859
0.8827
0.0022
0.0011
0.0006
with calibration measurements for a series of clean pipes with
known diameters the deposit thickness can be determined.
The reason for using several calibration pipes with different
diameters was that the fish-eye lense of the camera shows
such a large distortion that no simple linear relationship
between the diameter observed by the camera and the real
diameter could be used.
To test the reliability of the method, measurements were
performed repeatedly first at the same position and afterward at different positions in the pipe. The standard deviation of the determined diameter was around 0.1% (both for
comparing measurements at the same position and for comparing measurements from different positions). A necessary
precondition, however, is to reduce mechanic vibrations
(e.g., due to operator movement in the vicinity of the rig)
that can be carried over to the mechanic support of the laser.
This leads to a blurred image, which makes precise image
recognition impossible.
It was found that it is not necessary to change the analysis
procedure depending on the refraction index of the deposit
or its roughness. The main challenge that was found is
measuring wax deposits with a high content of asphaltene.
The resulting deposit tends to absorb a significant part of the
red laser light so that determining the light circle on the
camera pictures can be difficult.
Temperature Difference. As the wax deposit builds up, the
heat transfer between oil flow and cooling water decreases
since wax has a rather low thermal conductivity compared to
steel and therefore acts as a thermal insulator. If the thermal
conductivity were known, the temperature drop of the oil
flow in the test section could be used to calculate the wax
thickness. However, measurements have shown that the
thermal conductivity of wax deposits is highly dependent
on the wax content. Since the wax content is also changing
over time (aging effect) no reliable way of determing the wax
thermal conductivity could be found yet. Therefore, the
experiments had Toil =20 °C, Twater =10 °C and an experimental duration of 100 h. Because of the different flow rate,
the deposits from the two experiments showed different wax
contents, which resulted in different deposit densities (see
Table 2). All samples were measured 10 times with resulting
standard deviations of less than 0.2%. The two samples from
the experiment with Qoil =5 m3/h showed almost the same
result (deviation of 0.3%).
Since the density difference between the two deposits from
low and high flow rate experiments is below 2% it was
decided to use a constant wax density of Fwax = 891 kg/m3
for the evaluation of the weight measurements.
Laser. Another deposit thickness measurement technique
that was tested is laser-based: A coaxial laser beam is
diverted by a 360° mirror toward the inner pipe wall, see
Figure 7, left. A camera mounted on the same mechanic
support takes a picture of the pipe, including the projected
laser beam, which will appear as a red circle, see Figure 7,
right. The diameter of this circle will decrease with an
increasing deposit thickness.
To derive the pipe diameter from the captured picture a
Matlab script is used (see Figure 8): First, the camera image
is read into Matlab. From the image center a number of
search rays is generated. Along each search ray the point of
maximum light intensity is determined to define the circle’s
coordinates. Some search rays will not return a result since
the mechanic support will always hide a part of the laser
beam.
Using these coordinates a nonlinear best fit is used to find
the circle’s center coordinates and diameter. By comparison
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Energy Fuels 2010, 24, 1069–1080
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Hoffmann and Amundsen
Figure 8. Laser image evaluation.
temperature drop was merely recorded to qualitatively check
that it corresponds with the other measurements.
Similarly, water temperatures have been recorded since
the temperature drop in oil should correspond to a temperature increase in water. However, due to the higher heat
capacity of water the absolute temperature increase in water
is roughly a factor of two lower than the temperature drop in
oil. This increases the measurement uncertainties without
adding any additional information. Also, the water temperature difference cannot be used to calculate the wax thickness
without precise information about the wax deposit’s heat
conductivity.
Comparison of Methods. All of the described methods have
their specific advantages and disadvantages.
The pressure drop method can be performed online without interrupting the experiment and draining the rig. It is
therefore the only method available that manages to record
the development of the wax thickness over time. Unfortunately, this method is only available for single-phase flow
since the friction factor for multiphase flow is highly flow
regime dependent and no correlations for the friction exist
for multiphase flow that are as accurate as Haaland’s
correlation for single-phase flow.
The weighing of a small test section is a robust and reliable
method provided that the wax density has been measured
appropriately and the test section has been completely
drained for remaining oil. It can obviously only be performed when the experiment has been stopped and the rig fully
drained. Also the resulting wax thickness is an average over
the test section. If, for example, stratified oil-water flow
experiments were to be carried out, wax would only deposit
on the pipe wall in contact with the oil phase. This spatial
variation of the wax thickness cannot be captured by the
weighing method.
The laser-based optical method can at present only be
carried out when the experiment is interrupted and the test
section fully drained. In contrast to the weighing method, the
laser method should be able to detect also spatial variations
of the wax deposit. In a planned future modification the laser
will be changed from visible light to near-infrared at a
wavelength where oil is transparent it should also be possible
to carry out measurements without draining the test section.
Figure 9 shows a comparison of the results from the three
methods for a one-week experiment. The experiment was
interrupted two times in-between (at t=23 and 92 h) to carry
out weight and laser measurements in addition to measurements after the experiment was finished (t=190 h). As can be
seen in Figure 9 the results from the three methods show only
small deviations.
In this example the interruption of the experiment did
not lead to any problems. In some cases, however, the
Figure 9. Comparison of wax thickness measurement methods.
dp measurements showed disruptions after restarting
the experiment, which is suspected to result from gas
bubbles in the dp cell’s impulse lines. After several of
these incidents it was concluded to only run uninterrupted experiments. This results in smooth continuous
dp curves but removes the possibility of obtaining deposit
samples at different timesteps for investigating the change
in the deposit’s composition (aging). If aging is to be
investigated in more detail, a series of experiments with
increasing durations has to be carried out where each
experiment runs uninterrupted. This is obviously a very
time-consuming method and was not pursued in this
campaign.
Results for Constant Temperature Gradient
Motivation and Experimental Procedure. The standard
assumption about the driving mechanism for wax deposition
is that a temperature gradient from the bulk flow toward the
pipe wall causes a concentration gradient of dissolved wax
(see e.g., refs 5-7). This concentration gradient determines
the diffusion of wax molecules leading to a change in the wax
thickness h over time
dh
dC
¼D
dt
dr
ð3Þ
(5) Svendsen, J. A. AIChE J. 1993, 39, 1377–1388.
(6) Matzain, A. Multiphase Flow Paraffin Deposition Modeling; Ph.D.
Thesis, University of Tulsa, 1999.
(7) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. AIChE J.
2000, 46, 1059–1074.
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Energy Fuels 2010, 24, 1069–1080
: DOI:10.1021/ef900920x
Hoffmann and Amundsen
where D is the diffusion coefficient and dC/dr the concentration gradient. This concentration gradient can be split
into
dC
dC dT
¼
dr
dT dr
ð4Þ
where dC/dT represents the gradient of the wax solubility
curve of the fluid and dT/dr is the temperature gradient near
the pipe wall.
To measure only the influence of the wax solubility curve a
series of experiments was run in the test rig where the
temperature gradient dT/dr was kept constant but the absolute temperature was varied. So, the first experiment had an
oil temperature of Toil=10 °C and a cooling water temperature of Twater=5 °C, the next experiment had Toil=15 °C and
Twater =10 °C, and so on.
In a first series of experiments, the oil temperature was
increased for each experiment by 5 °C, starting at Toil=10 °C
for the first experiment. In the final experiment at Toil=35 °C
no wax deposition was detected at all (measured by pressure
drop, weighing, and laser). The oil flow rate was kept
constant at high level Qoil=21 m3/h. In a second series some
of the points were repeated at a low oil flow rate Qoil=5 m3/h
to measure the influence of shear forces on the wax thickness
and the influence of the flow rate on the deposit’s composition.
Wax Appearance Temperature (WAT) and Wax Solubility
Curve. Figure 10 shows the resulting wax thicknesses after
50 h as a function of the wall temperature for two different
flow rates. The temperature difference between oil and cooling water was always 5 °C. The wall temperature shown in
Figure 10 is the interface temperature between oil and steel at
the start of the experiment, that is, without any wax deposited. It was calculated by using the well-known equations
for heat transfer in turbulent flow.8
First, the total heat transfer coefficient Utot from oil to
water (for a clean pipe without wax deposit) is calculated
1
1
1
1
¼
þ
þ
Utot
hfilmoil hsteel hfilmwater
hsteel ¼
Doil
2ksteel
Doil þ 2dwax þ 2dsteel
ln
Doil þ 2dwax
0:33
hfilmwater ¼ 0:023Re0:8
water Prwater
0:8 0:33
hfilmoil ¼ 0:023Reoil
Proil
Reoil ¼
Figure 10. Influence of wall temperature at constant temperature
gradient.
Rewater ¼
vwater ¼
cpoil ηoil
koil
voil ¼
m_ oil
π
FD2oil
4
ð9Þ
ðD2waterouter -D2waterinner Þ
Dwaterouter
ln
Dwaterinner
Dwaterouter -Dwaterinner
Dwatereff ¼
ð10Þ
Using this total heat transfer coefficient Utot and the heat
transfer coefficient hfilmoil, which describes the heat flow from
the bulk oil flow toward the inner pipe wall, the pipe wall
temperature can be determined as
ð5Þ
Twall ¼ Toil -
Utot
ðToil -Twater Þ
hfilmoil
ð11Þ
Using this set of equations it is also easy
to estimate the
dT temperature gradient at the pipe wall dr which will be used
later on
ð6Þ
dT hfilmoil
¼
ðToil -Twall Þ
dr koil
ð12Þ
Several interesting observations can be made from these
results. One is that wax deposition was found to start somewhere in the interval between 27.5 and 32.5 °C. It is instructive to compare this WAT derived under real flow conditions
with the various small-scale lab tests that are used typically to
determine WAT: (1) DSC: As an oil sample cools below its
cloud point wax crystals are formed. This results in a small
amount of heat being produced and therefore a slight rise in
the temperature of the sample. During a DSC analysis, the
heat flow between two small aluminum pans is measured
very accurately. One pan is empty and the other pan contains
a small amount of oil. The DSC apparatus measures the
difference in the temperature of the two pans. As the wax
appearance temperature is reached, the pan containing oil
cools at a slightly slower rate than the empty pan, which is
ð7Þ
Foil voil Doil
ηoil
Proil ¼
4m_ water
2
Fwater πðDwaterouter -D2waterinner Þ
ð8Þ
ðD2waterouter þ D2waterinner Þ -
kwater
Dwaterinner
koil
Doil
Fwater vwater Dwatereff
ηwater
(8) Kays, W. M.; Crawford, M. E. Convective Heat and Mass Transfer; McGraw-Hill: New York, 1987.
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Energy Fuels 2010, 24, 1069–1080
: DOI:10.1021/ef900920x
Hoffmann and Amundsen
Figure 11. Comparison of wax deposition in rig with wax precipitation in DSC.
exhibited as an inflection in a cooling curve.9 For the fluid
used here the WAT determined by DSC was 29 ( 1.5 °C. (2)
NIR: The NIR wax onset method is based on the observation
that there is a sharp increase in light absorption or attenuatin
in the near-infrared region at the onset of wax crystallization.
This is due to the formation of light-scattering wax crystals.10
For the fluid used here the WAT determined by NIR was
27 ( 1 °C. (3) Microscopy: The appearance of wax crystals is
determined optically in a microscope using cross-polarized
light.11 For the fluid used here the WAT determined by
microscopy was 30 ( 1 °C. (4) Rheometer: The precipitation
of wax results in a change of the fluid’s viscosity. The onset of
this deviation can be detected using a statistical method
described in ref 12. For the fluid used here the WAT
determined by rheometer was 31 ( 0.5 °C.
To summarize, it can be concluded that it is possible to use
small-scale lab methods to determine a wax appearance
temperature that agrees well with the temperature at which
wax starts to deposit in a real flow loop. The small spread in
the resulting WAT for the various measurement techniques
is due to the different sensitivities of the techniques and does
not necessarily reflect different physical conditions.
Another interesting application for the measured wax
thicknesses is to check the validity of the assumption of
molecular diffusion as the main mechanism that is steering
wax deposition (see eq 3). Since the temperature gradient
dT/dr has been constant for all the experiments, the wax
deposition should follow the wax solubility curve. Figure 11
shows a comparison of the measured wax thicknesses (at Qoil
= 21 m3/h) with the amount of wax that precipitated in a
DSC instrument at comparable temperatures. The two
curves show a remarkable similarity, indicating that wax
solubility and thus also wax diffusion are indeed a major
parameter for wax deposition.
Wax Deposit Composition. To determine the composition
of the wax deposit, gas chromatography (Hewlett-Packard
Figure 12. Comparison of wax deposit compositions (Q = 21 m3/h,
Toil - Twater = 5 °C).
6890A GC) is used. Figure 12 shows a comparison of the
composition of the deposits that were retained from the
experiments at high flow rate (Q=21 m3/h). The figure also
shows the composition of the waxy fluid. Compared to the
fluid, the deposits show a significant peak ranging from
about C25 to C45. This peak represents the accumulated
waxy components in the deposit. Comparing the chromatographs of the deposits from different temperatures shows
that the wax peak size is growing significantly for higher
temperatures and shifting its center toward heavier carbon
fraction. This is in line with the visual observations of the
deposit where the wax layer for higher temperatures was
found to be thinner (see Figure 10) but also harder than for
lower temperatures. This growing hardness will probably be
the result of a combination of the two effects: the increase of
the amount of wax in the deposit and the change of the wax
composition toward heavier hydrocarbons.
The reason why the wax composition changes toward
heavier hydrocarbons for higher temperatures is probably
related to the solubility of the various wax components. For
the lower temperatures most of the heavier hydrocarbons
have already precipitated in the oil bulk flow. Since the
mostly accepted theory in the wax community is that wax
deposition is only possible by dissolved wax molecules but
not by precipitated wax crystals, these heavier hydrocarbons
are not available for wax deposition at lower temperatures.
At higher temperatures where these heavier hydrocarbons
(9) Coutinho, J. A. P.; Goncalves, C.; Marrucjo, I. M.; Pauly, J.;
Daridon, J.-L. Fluid Phase Equilib. 2005, 233, 28–33.
(10) Leontaritis, K. J. Cloud point and wax deposition measurement
techniques. SPE International Symposium on Oilfield Chemistry, Houston,
Texas, 2003.
(11) Zougari, M. I.; Sopkow, T. Ind. Eng. Chem. Res. 2007, 46, 1360–
1368.
(12) Sch€
uller, R. B.; Tande, M.; Almøy, T.; Sæbø, S.; Hoffmann, R.;
Kallevik, H.; Amundsen Annu. Trans. Nordic Rheol. Soc. 2009, 17, 191–
197.
1075
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: DOI:10.1021/ef900920x
Hoffmann and Amundsen
Figure 13. Definition of wax content from GC results.
are still in solution they start to contribute significantly to the
wax deposit. The reason why the wax composition at these
higher temperatures no longer includes the same amount of
lighter hydrocarbons must be due to the fact that at these
temperatures the wall temperature is so high that the lighter
heavycarbons cannot form wax crystals at the pipe wall. To
summarize, the condition for a certain carbon fraction to
participate in the deposition process is that it needs to be in
solution at the bulk temperature but it also needs to crystallize at the wall temperature.
As can be seen from the chromatographs that the deposit
found on the inner pipe never consists entirely of wax but is
always a combination of wax and oil, where oil is entrapped
in the wax network. The amount of oil in the deposit is often
called porosity (P) in the literature and is an important
parameter since the included oil will increase the thickness
of the deposit compared to a hypothetical deposit consisting
only of wax. Typically, wax deposition models enhance the
basic diffusion eq 3 by including the porosity13
dh
1
dC
¼
D
ð13Þ
dt
1 -P
dr
Figure 14. Deposit wax content depending on wall temperature and
flow rate.
experiments were run at 5 days except the one for Twall=17.5
°C and Qoil = 5 m3/h, which was run for 11 days. The
conclusions that can be drawn from the results shown in
Figure 14 are: (1) Wax content increases for deposits obtained at higher wall temperatures. (2) Wax content is higher
for higher flow rates. (3) Wax content is increasing with time.
The wax content for Twall=17.5 °C and Qoil=5 m3/h is higher
than the next one at Twall = 22.5 °C due to the longer
experimental runtime.
The higher wax content coincides with the observation of
harder wax deposit for all three cases (higher wall temperature, higher flow rate, and longer experimental runtime).
Some of the experiments were repeated and the difference
of the measured wax content for equal experimental conditions was found to be below 5%.
Results for Constant Cooling Temperature
To test these models against the experimental data it is
therefore important to define the amount of oil/wax in the
deposit. The method used here is based on the deposit’s GC
data. Figure 13 shows a typical chromatogram of a wax
deposit.
The peak including the wax components starts at C24 (see
Figure 13), where the measured weight fractions start to
deviate from the exponential decline typically seen in waxfree oils. The problem is to define which amount of
the components heavier than C24 are due to the wax in
the deposit and which of them are due to the included oil in
the deposit. The method used here is to fit an exponentially
declining curve based on the measurements from C10 to C20,
that is, in a region where no wax components should occur.
This curve is assumed to describe the pure oil. Only the area
above this curve (marked dark gray in Figure 13) is assumed
to include wax. So the wax content of a deposit is calculated
by integrating the area between the wax peak and the
exponential fit.
Figure 14 shows the resulting wax content for the deposits
from various wall temperatures at low and high flow rate. All
Experimental Procedure. In a real subsea application the
cooling medium of the pipeline (i.e., seawater and sea bed)
has approximately constant temperature, whereas the fluid
in the pipeline typically starts at high temperatures and is
cooled down in the pipeline until it reaches the same temperature as the surrounding seawater.
Therefore, a second series of experiments was run with
constant cooling temperature Twater = 10 °C, which is the
lowest cooling temperature that can be kept stable in the rig
during summer times and various oil temperatures, ranging
from Toil = 15 °C up to Toil = 50 °C. At Toil = 50 °C the
resulting wall temperature is around 30 °C where wax
deposition was found to cease in the previous serious of
experiments (see Figure 10). The oil flow rate was kept
constant at Qoil=21 m3/h for all experiments. Unfortunately,
no wax content measurements are available for these experiments.
Wax Structure. Figure 15 shows the pressure drop increase
over time for the various experiments. Unfortunately, it is
not possible to show the wax thickness for each experiments
since some of the experiments showed highly irregular
deposits (see below) that make the calculation of wax thickness from pressure drop impossible. For each experiment
the oil bulk flow temperature Toil and the inner pipe
wall temperature Twall are specified in Figure 15. Twall is
(13) Hovden, L.; Rønningsen, H. P.; Xu, Z. G.; Labes-Carrier, C.;
Rydahl, A. Pipeline Wax Deposition Models and Model for Removal of
Wax by Pigging: Comparison between Model Predictions and Operational
Experience; Multiphase Technology: Banff, Canada, 2004.
1076
Energy Fuels 2010, 24, 1069–1080
: DOI:10.1021/ef900920x
Hoffmann and Amundsen
curves for oil temperatures up to Toil = 30 °C show a
continuous rising trend with no sign of reaching an asymptotic state. In contrast to this, the curve for Toil=40 °C, Twall
=24.7 °C becomes asymptotic for t > 100 h. However, the
fluctuations of the pressure drop are much higher here than
those that are usually observed. When the deposit was
inspected visually after the experiment was finished it
showed a very different structure then is usually observed.
Figure 17 shows a comparison of the wax that was deposited at Toil =20 °C, which was smooth and homogeneous,
and the one that was deposited at Toil = 40 °C. This wax
showed a highly irregular structure where spots of wax with
diameters of some millimeters were surrounded by areas of
bare steel.
Determination of the hydraulic roughness of this deposit
by flow rate variation (see Figure 3) showed a roughness
around 40 μm, whereas the smooth deposits that are usually
obtained show a roughness below 5 μm. The experiment at
Toil=40 °C was repeated to ensure the validity of the results.
More experiments were carried out with variation of the oil
and water temperature to find out more about the onset of
this different type of deposit. It seemed like that there is a
gradual onset of this phenomenon for high oil temperatures
Toil > 30 °C (i.e., Toil ≈ TWAT) and high oil-water temperature differences Toil - Twater > 20 °C.
A possible explanation for this deposit structure is that at
the high wall temperatures the adhesion force between the
wax layer and the steel pipe is so low that wax is periodically
removed from the pipe wall due to the turbulent shear force.
That means that the overall amount of wax stays constant
over time but that the actual topology changes constantly.
That would also explain the high fluctuation in the pressure
drop measurements.
A conclusion of this observation is of course that the
classical diffusion-based models are not suitable to represent
this type of deposition. So, care has to be taken when
performing a simulation of a real subsea production pipeline
on how the simulation results for the first kilometers after
WAT has been passed are evaluated. A classical molecular diffusion-based model will probably overestimate
wax deposition in this region.
Figure 15. Influence of oil temperature at constant cooling temperature.
Figure 16. Concentration gradient as a function of temperature.
calculated for the start of the experiment where no wax was
yet deposited, that is, at the interface of oil and steel.
Several observations can be made from Figure 15: (1)
Pressure drop (and thus wax thickness) increases fastest for
the lowest wall temperatures. This is consistent with the
solubility curve that shows the highest gradient in this low
temperature region. One exception is the curve for Toil =
20 °C, Twall=14.4 °C: This curve rises faster at the start of the
experiment than any other curve, including the one with
lower wall temperature (Toil =15 °C, Twall =12.1 °C). This
can be partly explained by not only looking at the solubility
curve but also at the total concentration gradient dC/dr =
(dC/dT)/(dT/dr). This is plotted in Figure 16 and shows a
clear peak at about Twall ≈ 17 °C. This curve has been derived
by multiplying the gradient of the solubility curve (measured
in the DSC)
by the temperature gradient at the inner pipe
Results for Varying Oil Flow Rate
Motivation. Since the results shown above indicated a significant influence of the oil flow rate (see Figures 10 and 12)
a separate series of experiments was run where the oil flow rate
was varied from 5 to 25 m3/h . This corresponds to a variation
of the shear stress τ from 5 to 89 Pa.
1
τ ¼ f Foil v2oil
2
where f=0.315Re-0.25 is the Blasius friction factor,14 Foil is the
oil density, and voil is the oil velocity. The shear rate dv/dy varies
from 444 to 7420 s-1.
dv
1
F
¼ fv2 oil
dy 8 oil ηoil
Twall and the temperature
wall dT
dr . The inner wall temperature
where ηoil is the oil viscosity. The temperatures of oil
and water were kept constant at Toil =20 °C and Twater =10
°C. Due to the varying flow rate, the inner steel wall temperature Twall, calculated by eq 11, varies from 12.2 to 15.2 °C.
gradient at the inner wall dT
dr are calculated by eqs 11 and 12,
respectively. (2) The curve for Toil =25 °C, Twall = 16.8 °C
shows instabilities for t > 100 h, which was caused by
nonstable experimental conditions (the experiment was
stopped several times to obtain deposit samples). (3) The
(14) Blasius, H. Z. Ver. Dtsch. Ing. 1912, 56, 639–643.
1077
Energy Fuels 2010, 24, 1069–1080
: DOI:10.1021/ef900920x
Hoffmann and Amundsen
Figure 17. Comparison of smooth (Toil = 20 °C) and rough (Toil = 40 °C) deposit.
Figure 18. Deposit thickness depending on flow rate (Toil = 20 °C,
Twater = 10 °C).
Table 3. Deposit Thickness Depending on Flow Rate (Toil = 20 °C,
Twater = 10 °C, t = 65 h)
flow rate Qoil (m3/h)
Figure 19. Comparison of wax thickness with concentration
gradient.
deposit thickness (mm)
5
10
15
21
25
approximated by the Colburn analogy15
1.55
0.92
0.75
0.62
0.53
0:33
hoil ¼ 0:023Re0:8
oil Proil
koil
Doil
where Reoil is the Reynolds number of the turbulent oil flow,
Proil is the Prandtl number of the oil, koil is the heat
conductivity of the oil, and Doil the diameter of the oil pipe.
The dependence on the Reynolds number explains why the
heat transfer coefficient rises with increasing flow rate and
thus in turn also the temperature gradient and the concentration gradient.
A pure diffusion-based model can therefore not explain
the decreasing wax thickness for increasing flow rates. Two
additional effects are necessary to explain this behavior: the
different wax content in the deposit and the effect of increasing shear stress.
The wax content’s deposit changes significantly for different flow rates. Higher flow rates result in a higher wax
content, leading to a more compact wax deposit. To model
this behavior an additional set of equations needs to be
introduced that describes the (time-changing) wax content
of the deposit.16 To visualize the amount of the effect,
Figure 19 shows also the calculated thickness of pure wax
Wax Deposition Thickness. Figure 18 shows the resulting
wax thickness for the experiments with varying oil flow rate.
A clear trend is visible that indicates thinner wax deposits for
increasing flow rates, confirming the findings shown already
in Figure 10.
The problem is that this behavior cannot be explained
by a diffusion model. Figure 19 compares the measured
wax thickness after 50 h for the various flow rates with
the calculated concentration gradient dC/dr = (dC/dT)/
(dT/dr), which is the steering factor in a diffusion model
(see Section ). As can be seen in Figure 19, the concentration
gradient increases with increasing flow rate whereas the
measured deposit thickness decreases.
The main reason is that the temperature
gradient in the
is
given
by
vicinity of the inner pipe wall dT
dr
Twall
dT hoil
¼
ðToil -Twall Þ
dr Twall
kwax
(15) Chilton, T. H.; Colburn, A. P. Ind. Eng. Chem. Res. 1934, 26,
1183–1187.
(16) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. R. Aging
and Morphological Evolution of Wax-Oil Gels During Externally Cooled
Flow Through Pipes. Second International Conference in Petroleum Phase
Behaviour and Fouling, Copenhagen, Denmark, 2000.
where hoil is the inner convective heat transfer coefficient,
kwax is the heat conductivity for the wax layer, Toil is the
temperature of the oil in the bulk flow, and Twall the oil/wall
interface temperature. The heat transfer coefficient can be
1078
Energy Fuels 2010, 24, 1069–1080
: DOI:10.1021/ef900920x
Hoffmann and Amundsen
The discontinuity of the gas chromatography curves in
Figure 20 at around C50 is due to the used measurement
technique. To perform measurements of solid deposits in GC
it is necessary to dilute the deposit 1:100. A side effect is that
the heavier hydrocarbons are no longer detectable with an
acceptable accuracy.
Since the temperature conditions for all experiments were
kept constant, the wax peak in the composition of the wax
samples is almost at the same carbon number for all experiments. Only a slight shift toward lower carbon numbers can
be detected for the wax peak at the lowest flow rate (Qoil =
5 m3/h). The explanation for this is that the oil/steel interface
temperature depends on the oil’s convective heat transfer
coefficient. For the lowest flow rate this results in a significantly lower wall temperature (Twall=11.9 °C for Qoil=5 m3/h)
than for the higher flow rates (Twall=14.4 °C for Qoil=21 m3/h).
This lower wall temperature leads to a wax peak at lower
carbon numbers (see Figure 12).
Figure 20. Deposit composition depending on flow rate (Toil = 20 °C,
Twater = 10 °C).
Conclusions and Outlook
The wax deposition experiments in the flow loop using
North Sea gas condensate showed that it is possible to obtain
stable repeatable data on both wax deposit thickness and
composition. The results were confirmed by repetition of the
experiments and the wax thickness measured by three independent measurement techniques (pressure drop, weight, and
laser). The laser measurement technique is a new technique
that will also be very valuable when continuing with multiphase experiments, as it can also measure the spatial distribution along the circumference.
One important result from these flow loop experiments is to
show that the WAT value that is measured using various smallscale lab measurement techniques is indeed representative for the
temperature where wax starts to deposit in a real turbulent flow.
Another conclusion from the experimental results is that,
indeed, molecular diffusion seems to be the dominant mechanism for wax deposition for most of the temperatures
studied. So any model that attempts to describe the process
will have to use a diffusion equation as the main building
block. However, the results from different flow rates and
different experimental runtimes also showed clearly that the
wax content cannot be considered as an independent, constant
parameter. So a useful model will also have to include a set of
equations describing the wax content or even needs to be
compositional, that is, to treat the various wax components
independently. In addition there is the open issue of modeling
the effect of shear stripping. Currently there is no model based
on first-principles available so this will probably have to
remain an empirical term as in ref 6.
However, for certain temperature conditions (high oil temperature and low wall temperature) a new type of deposit
structure was found that was rough and irregular compared
to the otherwise smooth and homogeneous deposits. This new
type of deposit cannot be described by a diffusion-based model.
Having managed to acquire high-quality reliable data a
natural next step will be to test available wax deposition
simulation tools like Olga2,21 or the Michigan wax deposition
model22 against these data.
by multiplying the total deposit thickness with the measured
wax content of the deposit. This shows that for the flow rate
increase from 5 to 10 m3/h the pure wax thickness does
indeed increase according to the increasing concentration
gradient. For even higher flow rates, however, the pure wax
thickness starts to decrease again. The assumption is that this
is mainly an effect of the increasing shear stress at the fluiddeposit interphase.
These effects of increasing shear stress at increasing flow
rates have often been discussed in the literature.17-20 The
possible explanations are either that the increasing shear
stress makes it more difficult for new wax molecules to
adhere to the already existing wax deposit or that the shear
stress removes parts of the already deposited wax. No
conclusion has been reached yet on the dominant mechanism and therefore no suitable model is available to incorporate these effects in a prediction tool. It should also be
noted that shear stress is highly dominant on the pipe
diameter, so to reach a better understanding it would
also be necessary to perform experiments with test pipes of
different diameters.
Wax Deposition Composition. The change in wax content
in the wax deposit for varying flow rates is clearly reflected in
the changing composition from the samples taken after each
experiment (see Figure 20). The area under the wax peak is
increasing with increasing flow rates, which explains the
harder and thinner deposit. Only the curves for Qoil = 15
and 21 m3/h seem to be almost equal, but this is due to the
fact that the experiment at 21 m3/h had to be stopped after
100 h whereas all the other experiments were run for about
140 h. So the assumption is that, if the 21 m3/h experiment
had been allowed to run further on, the aging effect would
have increased its wax peak accordingly.
(17) Hernandez, O. C.; Sarica, C. Effect of Flow Regime, Temperature
Gradient and Shear Stripping in Single-Phase Paraffin Deposition. 11th
International Conference Multiphase '03, San Remo, Italy, 2003.
(18) Matzain, A.; Zhang, H.-Q.; Volk, M.; Redus, C. L.; Brill, J. P.;
Apte, M. S.; Creek, J. L. Multiphase flow wax deposition model.
Engineering Technology Conference on Energy, New Orleans, Louisiana,
2000.
(19) Venkatesan, R. The Deposition and Rheology of Organic Gels;
Ph.D. Thesis, University of Michigan, 2004.
(20) Singh, P. Gel Deposition on Cold Surfaces; Ph.D. Thesis, University
of Michigan, 2000.
(21) Rygg, O. B.; Rydahl, A. K.; Rønningsen, H. P. Wax deposition in
offshore pipeline systems. BHRG Multiphase Technology Conference,
1998.
(22) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. R.
AIChE J. 2001, 47, 6–18.
1079
Energy Fuels 2010, 24, 1069–1080
: DOI:10.1021/ef900920x
Hoffmann and Amundsen
Regarding the next experimental campaign, several possible routes are open: (1) One option is to repeat parts of the
experiments with a different crude oil to avoid drawing all
conclusions from a single fluid. Preferrably, a heavier crude oil
should be used that also shows a higher pour point so that
gelling effects will be more visible when operating at low
temperatures. (2) A series of experiments with identical
temperatures and flow rates but different runtimes should
be carried out to gather more-reliable data on the effect of
aging. (3) By repeating some of the experiments with a new test
section at a different diameter, the effect of shear stripping
could be investigated in more detail. Since production pipelines usually have considerably larger diameters than the
typical 2 in. that is used for flow loops it is especially important
to learn about the scale-up laws that apply to wax deposition
models. (4) Also, since most production streams consist not
only of single-phase oil flow but contain also water and/or gas,
the test rig will be modified so that two-phase flow experiments using oil and water mixtures can also be performed.
This will open up a whole new set of parameters since the flow
regime (stratified-wavy, dispersed, etc.) will have considerable
influence on the wax deposition.
1080