ARTICLE pubs.acs.org/EF
Asphaltene Deposition Measurement and Modeling for Flow Assurance of Tubings and Flow Lines Kamran Akbarzadeh,* Dmitry Eskin, John Ratulowski, and Shawn Taylor DBR Technology Center, Schlumberger, 9450, 17 Avenue, Edmonton, AB, Canada T6N 1M9 ABSTRACT: A recently developed asphaltene deposition model is tuned with some experimental data obtained in RealView, a high pressure deposition cell. The tuned model is validated with further experimental data. The lab-scale model is then extended to fieldscale tubings and flow lines, and the predicted deposition profile is qualitatively compared with field observations. Finally, an experimental protocol is developed for asphaltene deposition measurement and modeling for flow assurance of tubings and flow lines. The successful applications of RealView in investigating the impacts of shear, run time, residence time, pressure, chemical inhibitor, and surface roughness on the deposition of asphaltenes from five fluids from the Gulf of Mexico are also discussed.
’ INTRODUCTION The deposition of asphaltenes in well bores and transportation pipelines as a result of reduction in pressure or change in composition of the reservoir fluid has been a flow assurance concern for the oil and gas industry. The large capital and operating costs associated with prevention and remediation of deposits have created the need for improved methods of measuring and modeling for the optimization of system design and operations while minimizing the risk of deposition. Asphaltenes in crude oils that exhibit asphaltene precipitation and deposition behavior during primary depletion are typically undersaturated (saturation pressure < reservoir pressure).1 During reservoir production at a constant temperature, once pressure decreases to the asphaltene precipitation onset pressure, dissolved asphaltenes start to precipitate and potentially deposit in the wellbore region and flow lines. Typically, the amount of precipitated asphaltenes increases as the pressure decreases and reaches a maximum at the bubble-point pressure. Asphaltene precipitation is a thermodynamic process which is mainly a function of pressure, temperature, and fluid composition. Asphaltene deposition, on the other hand, is a much more complex process and also depends on flow shear rate, surface type and characteristics, particle size, and particlesurface interactions. Therefore, although asphaltene precipitation is a necessary condition for the formation of obstructions, it is not a sufficient condition for deposition. After precipitation, asphaltene particles must deposit and stick to a surface before they can become a flow assurance problem in straight flow lines. Where bends, valves, other restrictions, and large changes in flow rates occur, they may sediment without sticking in separators and heat exchangers in surface facilities. RealView, a high-pressure deposition cell based on the Taylor Couette flow principles, is a laboratory tool for generating organic solid deposits under a wide variety of operating conditions. This equipment has been used to measure the deposition rate of waxes and asphaltenes from live fluids under laminar and turbulent flow conditions.26 Although the high-pressure deposition cell is a capable tool in generating asphaltene deposits under a wide variety of operating conditions, the deposition rates obtained by this laboratory-scale r 2011 American Chemical Society
equipment cannot be directly applied to the field. A deposition model can, however, fill this gap and link the laboratory data to the field environment. Typically, the data are used to fine-tune and validate deposition models and thereby identify their parameters. The refined models are then used to predict deposition in the field. Recently, an asphaltene deposition model was developed by Eskin et al.79 The developed model has six parameters that need to be determined using experimental data. In this paper, an overview of the deposition model and RealView cell is provided. Then, the results of asphaltene deposition experiments with various oils for investigating the impacts of shear, run time, residence time, pressure, chemical inhibitor, and surface roughness on the deposition of asphaltenes are presented and discussed. Some of the lab-scale data are then used to tune and validate Eskin et al.’s deposition model for the Couette device (e.g., RealView). The identified parameters then become inputs to the asphaltene deposition pipe model in order to predict deposit thickness along wellbore tubing and transportation flow lines in the field. The deposition profile prediction is qualitatively compared with the field observations. Sensitivity analyses are performed to indicate the impacts of changes in model parameters on the deposit predictions. Through this exercise, the number of model parameters is reduced, and an experimental protocol is developed for conducting deposition experiments for modeling and simulation purposes.
’ DEPOSITION MODEL The asphaltene deposition model developed by Eskin et al.79 consists of three major modules: (1) particle precipitation module providing asphaltene particle concentration as a function of pressure, (2) particle size distribution module, and (3) particle transport module. A shear removal term is included in the particle transport module. Received: June 28, 2011 Revised: November 7, 2011 Published: November 07, 2011 495
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Figure 1. Schematic of the high-pressure deposition cell.
An equation of state approach was employed for modeling particle precipitation/formation.10 The particle size distribution evolution in time was modeled using the population balance technique. In this model, particle aggregates were considered as fractal objects, and the population balance equations were solved for a wide range of particle sizes. The primary size of asphaltene particles was evaluated as several nanometers, while the biggest agglomerates reach sizes of tens of micrometers. The major empirical parameters used for the population balance model are the fractal dimension of particle aggregates and the particle particle collision efficiency, which determines the probability of an agglomerate formation at a single collision. The reported fractal dimension for asphaltene aggregates is between 1.5 and 1.9. In the current model, a fixed value of 1.6 was selected for all cases. It has been found that the collision efficiency strongly depends on the oil chemical composition and has very small values.7,8 The module for particle transport to the wall is based on a calculation of the particle flux to the wall, caused by the Brownian motion. The boundary condition is a zero particle concentration gradient at the wall that is explained by the very low probability of particle deposition at a single collision with the wall (the particlewall collision efficiency). Thus, the physics of particle transport is different from that modeled in the recent investigations on particle deposition where the diffusion caused by the particle concentration gradient in the wall vicinity was considered as the major transport phenomenon.7 Eskin et al. introduced the particlewall collision efficiency as a model parameter to determine the actual deposition rate. Note that the deposition rate is a function of particle size. To take into account the assumption that the relatively large particles do not deposit on the wall, a critical particle size was introduced as a model parameter, a first approximation of which is evaluated on the basis of the balance of a drag force and the van der Waals attraction force acting on a particle near the wall.7 A shear removal term was also considered as part of the transport module. Under highly turbulent flow conditions, the shear stress applied on the deposit layer may cause some of the already deposited asphaltenes to be removed. A practical application of the developed deposition model consists of two stages: (1) identification of the model parameters for a given oil composition in the range of expected pipe flow regimes on the basis of Couette device (e.g., RealView) experimental data and (2) calculation of the deposit layer thickness along
the tubing or pipeline. The proposed modeling technique demonstrates an accuracy sufficient for engineering purposes. Details about the model equations and parameters can be found elsewhere.8,9
’ EXPERIMENTAL DESIGN RealView Deposition Cell. The RealView deposition cell16 is a device capable of generating individual and/or combined wax and asphaltene deposit buildup under field conditions. The cell, which is based on TaylorCouette flow principles, was designed to simulate the hydrodynamic and thermal characteristics encountered in typical oilproduction lines. The rapid rotational movement of a spindle at the center of the device produces a fluid movement that in a regime of developed turbulence creates a flow field similar to that within a pipe.5,7 The RealView cell can operate in both batch and flow-through modes. A schematic of the deposition cell is shown in Figure 1. To initiate a test in the batch or closed system, the cell is initially filled with the parent stock tank oil (STO) of the sample. The STO is then displaced with live fluid, initially placed in a 1 L storage bottle, at reservoir temperature and at a pressure above its asphaltene onset pressure. The displacement continues until all STO (∼150 cm3) and some of the live oil that has made contact with it are removed. This step minimizes the compositional change of any fluid that was in the cell prior to the test. Next, the spindle is turned on and its rotational speed is set in such a way that the desired wall shear stress is achieved. The initially high pressure (above the asphaltene onset pressure) in this device is then reduced either abruptly or gradually to the desired test pressure, which is typically 100 psi above the bubble point of fluid where the maximum amount of precipitated asphaltenes exists in the fluid. Then, the batch test is run for a set time. When the run is completed, the oil inside the device is drained at the test pressure, and the generated deposit that formed on the cell wall is recovered with dichloromethane. After the solvent is evaporated, the residue is weighed. Its weight represents the total amount of deposit including occluded oil. The residue is then analyzed for asphaltene content using a modified IP-143 with n-heptane to determine the separate amounts of the asphaltene deposit and oil. The flow-through setup eliminates the batch system’s limitations for generating enough deposit from low-asphaltene-content samples. However, compared to the approximate 150 cm3 of oil needed for a batch test, a 4 h flow-through test with an oil flow rate of 3 cm3/min (50 min average residence time for fluid in the cell) will require approximately 900 cm3 of live fluid. Similar to the batch system, the first step in a flow-through test is to fill the cell with STO. The STO is then displaced with live fluid, initially 496
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Table 1. Characteristics of Asphaltenic GoM Crudes sample information
oil A
oil B
oil C
oil D
oil E
reservoir temperature (°C)
69
126
93
98
reservoir pressure (MPa)
71.7
103.4
103.4
103.4
98 103.4
GOR (m3/m3)
154
93
112
129
101
saturation pressure at Tres (MPa)
20.0
13.8
19.0
27.6
16.3
API°
33
33
29
26
24
asphaltene content (wt %)
1.6
1.7
4.5
4.7
13.3
asphaltene onset pressure @ Tres (MPa)
51.7
34.5
34.5
41.3
37.9
precipitated amount of asphaltenes in reference to live oil mass @ Tres and
0.69
0.26
0.49
0.72
3.28
viscosity (Pa s)
7.1e4
6.6e4
1.2e3
1.0e3
2.5e3
density (kg/m3)
700
714
742
780
800
slightly above bubble point (wt %)
Table 2. Test Matrix and Results of Deposit Analysis for RealView Batch Experiments corrected mass of Tfluid
pressure
rotational
asphaltene
wall shear
run time
de posi ted
deposition
test #
oil
(°C)
(MPaa)
speed (rpm)
Re
stress (Pa)
(hr)
asphaltenes(mg)
rate (g/m2/day)
1
A
69
20.68
720
16500
0.56
2
12.4
11.8
abrupt pressure drop
2
A
69
20.68
720
16500
0.56
2
16.8
16.0
gradual pressure drop
3
A
69
20.68
3360
77000
6.8
2
9.5
9.1
4
A
69
20.68
720
16500
0.56
2
16.9
16.1
5
A
69
20.68
3360
77000
6.8
2
5.9
5.6
6
A
69
20.68
3360
77000
6.8
2
9.9
9.4
repeat of test #3
7
B
82
12.27
780
13100
0.64
1
12.3
23.5
run time effect
8 9
B B
82 82
12.27 12.27
780 780
13100 13100
0.64 0.64
2 4
9.6 15.2
9.1 7.3
base run run time effect
purpose
shear effect chemical effect150 ppm repeat of test #3
10
B
82
12.27
780
13100
0.64
8
19.0
4.5
run time effect
11
B
126
14.48
780
18100
0.56
2
8.4
8.0
run time and temperature
12
B
126
14.48
780
18100
0.56
6
13.4
4.3
13
C
93
20.34
1020
13500
1.09
1
9.3
17.7
run time effect
14
C
93
20.34
1020
13500
1.09
1
6.7
12.8
gradual pressure drop
15
C
93
20.34
1020
13500
1.09
2
14.1
13.5
run time effect
16 17
C C
93 93
20.34 20.34
1020 1020
13500 13500
1.09 1.09
4 8
12.1 20.6
5.8 4.9
run time effect run time effect
18
D
98
29.65
780
13360
0.69
2
29.4
28.0
19
D
98
29.65
780
13360
0.69
6
59.5
18.9
run time effect
20
D
98
35.85
780
13360
0.69
2
21.3
20.3
pressure effect
abrupt pressure drop
base run
21
E
98
17.03
2100
14100
4.8
1
51.2
97.7
run time effect
22
E
98
17.03
2100
14100
4.8
2
56.8
54.2
abrupt pressure drop
23
E
98
17.03
2100
14100
4.8
2
53
50.6
gradual pressure drop
24
E
98
17.03
2100
14100
4.8
6
55.6
17.7
run time effect
the test. Two pumps are used to control the flow in and out of the cell and thereby regulate the pressure. The flow-through rate is low; therefore the mean fluid residence time in the RealView cell is long enough to treat this device as an ideal mixer. After completion of each test, the remaining fluid in the cell is pushed out by helium while the spindle is still rotating. This minimizes the settlement of asphaltenes on the bottom cap. The deposited material is removed and analyzed as explained earlier. The flow-through system provides valuable information about the deposition process because the collected deposit mass is usually much higher than that in the batch system. This is because during the
placed in a 1 L storage bottle, at reservoir temperature and at a pressure above its asphaltene onset pressure. The displacement continues until all STO (∼150 cm3) and some of the live oil that has made contact with it are removed. Fresh fluid is then flowed at a set rate into the top of the cell, forcing the live fluid to exit the cell through the drilled hole in the bottom cap. An empty bottle receives the live fluid at high pressure once it exits the cell. The spindle is then turned on at a specified rotational speed, and the pressure of the system is reduced to that of the test pressure, which is normally 100 psi above the bubble point of the fluid. The pressure, temperature, rotational speed, and flow rate are controlled throughout 497
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498
A
A
A
A
34 35
36
37
38
39
B
B B
B
B
B
C
C
C
C
C
C
45
46 47
48
49
50
51
52
53
54
55
56
B
A A
33
44
A
32
B
A
31
A
A
30
43
A
29
42
A
28
A A
A
26 27
40 41
A
A A
25
oil
test #
93
93
93
93
93
93
126
126
126
126 126
126
126
126
69
69 69
69
69
69
69
69 69
69
69
69
69
69
69
69 69
69
(°C)
Tfluid
3
3
3
3
3
3
3
3
3
3 10
3
3
3
3
3 3
3
3
3
3
3 10
3
10
15
10
6
3
3 3
20.34
20.34
20.34
20.34
20.34
20.34
14.48
27.58
14.48
14.48 14.48
14.48
14.48
780
20.68
20.68 20.68
20.68
20.68
55.16
55.16
20.68 20.68
20.68
20.68
20.68
20.68
20.68
20.68
20.68 20.68
20.68
(MPaa)
(cm3/min)
3
pressure
flow rate
6000
3000
2100
1500
1020
720
780
780
780
3600 780
2100
1500
18100
3360
720 1800
720
720
720
3360
720 3360
720
720
1200
1200
1200
3360
1200 1800
720
(rpm)
speed
rotational
79500
39700
27800
19900
13500
9550
18100
18100
18100
83300 18100
48600
34700
0.56
71000
16500 38000
16500
16500
16500
71000
16500 71000
16500
16500
25300
25300
25300
71000
25300 38000
16500
Re
22.09
6.80
3.71
2.09
1.09
0.69
0.56
0.56
0.56
7.80 0.56
3.02
1.70
4.0
6.76
0.56 2.34
0.56
0.56
0.56
6.76
0.56 6.76
0.56
0.56
1.17
1.17
1.17
6.76
1.17 2.34
0.56
stress (Pa)
wall shear
4.0
4.0
4.4
4.0
4.0
4.0
1.8
4.0
2.0
4.0 1.3
4.0
4.0
50
3.6
4.3 4.0
4.0
3.9
3.9
4.3
8.8 1.6
2.5
1.3
0.8
1.6
2.3
4.0
3.6 4.0
4.3
(hr)
run time
Table 3. Test Matrix and Results of Deposit Analysis for RealView Flow-Through Experiments
50
50
50
50
50
50
50
50
50
50 15
50
50
56.9
50
50 50
50
50
50
50
50 15
50
15
10
15
25
50
50 50
50
cell, min
time in the
average residence
26.8
37.1
143
31.5
36.7
62.0
30.7
36.1
30.6
37.7 24.6
38.3
41.3
27.1
27.2
76.0 22.0
25.0
26.1
14.4
2.6
426.0 18.1
32.3
35.2
17.7
22.6
37.2
35.0
34.9 23.0
80.0
asphaltenes (mg)
deposited
corrected mass of asphaltene
12.8
17.7
6.2
15.0
17.5
29.6
32.5
17.2
29.2
18.0 36.7
18.3
19.7
27.1
14.5
33.5 10.5
11.9
12.7
7.0
1.1
92.4 21.6
24.7
50.4
42.2
26.9
30.9
16.7
18.5 11.0
35.5
(g/m2/day)
deposition rate
shear
shear
pressure shear
shear, residence time,
base run
shear
repeat of test #55
pressure
run time
shear residence time
shear
shear
time, pressure
time, run
shear, residence
repeat of test #34
repeat of test #31 repeat of test #33
effect, 500 ppm
chemical inhibitor
effect, 150 ppm
chemical inhibitor
pressure, shear
pressure, shear
run time residence time, shear
run time
residence time, shear
residence time
residence time
residence time
shear
shear, residence time shear
shear, run time
purpose
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a
499
C
C C
C
C
C
C
C
C
D
D
D
57
58 59
60
61
62
63
64a
65a
66
67
68
98
98
98
93
93
93
93
93
93
93 93
93
(°C)
3
3
3
3
3
3
3
3
3
3 3
29.65
29.65
29.65
20.34
20.34
20.34
20.34
20.34
27.58
20.34 20.34
20.34
(MPaa)
(cm3/min)
10
pressure
flow rate
3120
1560
780
1020
1020
1020
1020
1020
1500
1020 1020
1020
(rpm)
speed
rotational
53500
26700
13400
13500
13500
13500
13500
13500
17600
13500 13500
19900
Re
7.25
2.23
0.69
1.09
1.09
1.29
1.29
1.29
2.20
1.09 1.09
2.09
stress (Pa)
wall shear
4.0
4.0
4.0
4.1
4.1
2.7
4.0
4.0
4.0
2.0 6.0
1.3
(hr)
run time
50
50
50
50
50
50
50
50
50
50 50
15
cell, min
time in the
average residence
113.0
144.9
109.6
56.0
29.8
95.5
75
121.4
24.1
37.8 89.4
34.2
asphaltenes (mg)
deposited
corrected mass of
The reported deposited masses in tests 64 and 65 are based on the improved deposit analysis methodology discussed in the Appendix.
oil
test #
Tfluid
Table 3. Continued asphaltene
53.9
69.1
52.3
26.3
13.9
67.0
3.6
57.9
11.5
36.1 28.4
51.4
(g/m2/day)
deposition rate
shear
shear
shear
simdist analysis
repeat of test #60 -
30 μm, run time chemical inhibitor, 200 ppm
surface roughness-
smooth
surface roughness-
30 μm
surface roughness-
pressure
run time run time
residence time
purpose
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Energy & Fuels constant influx of a fresh fluid no or minimal depletion occurs in the flow-through system. To confidently employ RealView for deposition studies, it was important to show that the deposition conditions in a pipeline can be imitated in the RealView device. A detailed description of the similitude between the two systems from both fluid dynamics and particle transport points of views can be found elsewhere.79 Deposition Experiments. Precipitation and deposition experiments were carried out in such a way that the results could be used for asphaltene deposition modeling purposes. Some experiments were designed to help in model tuning, while others were designed on the basis of the deposition model output to validate model predictions. The designed experiments are explained in three steps as follows. Step 1: Batch Runs. As the first step, it was decided to conduct some deposition tests in the RealView batch system to study how deposit grows over time and if depletion takes place at a certain run time. It should be noted that the amount of deposit obtained in the batch system needs to be more than 20 mg to be acceptable. On the basis of some simple calculations, if the amount of deposited asphaltenes is less than 20 mg, the deposit is still limited to the first layer of asphaltenes adsorbed on the metal. In such a case, it is recommended that the data not be interpreted for practical purposes. Nevertheless, the data may be used for modeling purposes to estimate the particleparticle collision efficiency as well as the critical particle size. Step 2: Gradual versus Sudden Pressure Decrease. In a typical batch run, the pressure of the system is reduced abruptly from reservoir pressure to the test pressure (e.g., slightly above the bubble-point pressure). This quick pressure drop usually takes approximately 10 min. But what if the system pressure is reduced gradually from asphaltene onset pressure to the test pressure over a certain period of time (e.g., test run time), which normally happens in actual pipelines? Would this impact the kinetics of asphaltenes’ formation and growth and eventually their deposition rate? This question guided us to design some tests with a gradual pressure decrease in the RealView batch system and later compare the results with the abrupt pressure decrease tests under the same running conditions. Step 3: Flow-Through Runs. As will be discussed later, the batch deposition tests provided inconclusive results, and therefore we decided to switch to flow-through deposition experiments. As mentioned earlier, the flow-through system provides valuable information about the deposition process because the collected deposit amount is usually higher than that in the batch system. Therefore, deposited asphaltenes are not limited to the adsorbed layer anymore; that is, asphaltene asphaltene layers are formed. The flow-through experiments were designed to cover shear, residence time, pressure, run time, asphaltene inhibitor, and surface roughness effects. A combination of batch tests and flow-through tests was selected for tuning the asphaltene deposition model, which will be discussed in the Experimental Protocol section Oil Samples. Five STO samples, A to E, all from the Gulf of Mexico (GoM) were used for the deposition studies in this work. All five samples were asphaltenic crudes with low to high asphaltene contents. The STO samples were recombined with synthetic gases to make live oil samples representative of their bottomhole fluids from the composition and gas to oil ratio (GOR) perspectives, although the asphaltene contents of the supplied STOs might be less than the asphaltene contents of the bottomhole fluids originally sampled under reservoir conditions. Table 1 summarizes some characteristics of the recombined fluid samples. Test Matrix. Overall, 68 RealView deposition experiments were carried out for the purposes of this work. Out of these 68 runs, 24 were run in the batch system and the rest in the flow-through system. Tables 2 and 3 show the running conditions as well as the purpose of each test in the batch and flow-through systems, respectively.
ARTICLE
Figure 2. Results of batch deposition experiments for samples A to E.
’ EXPERIMENTAL RESULTS AND DISCUSSION Tables 2 and 3 show the results of deposition experiments for batch and flow-through runs, respectively. The deposition rate was defined as follows: depositionrate ¼
mad Ac t
ð1Þ
where mad is the corrected mass of deposited asphaltenes, Ac is the surface area of the cell, and t is the total run time. The procedure for calculating the corrected mass of deposited asphaltenes is explained in the Appendix. Batch Runs. Figure 2 shows the amounts of deposited asphaltenes over time for samples A to E. As shown, except for samples D and E, the amounts of deposited asphaltenes were 20 mg or less; that is, their deposition was limited to adsorption on the metal. For samples D and E, however, sufficient amounts of deposit were obtained mainly due to high asphaltene contents of the oils and the presence of numerous depositing asphaltene particles in the fluids. The second observation from batch runs for samples B, C, and E was the growth of deposit at the beginning and then flattening at longer run times. The main reason was due to depletion of depositing asphaltenes. However, depletion here is not compositional-based but mechanical; that is, over time the particles in the fluid grow to a critical size above which they do not tend to deposit.8,9 For sample D, an increase in deposition over time is expected to continue until depletion starts to overcome the deposition, at which point flattening of the deposition profile takes place. The third observation was that the gradual pressure decrease did not have a big impact on the deposition of asphaltene particles compared to the sudden pressure decrease. This is possibly due to the fast kinetics of asphaltene formation and growth independent of depressurization rate under shear. Flow-Through Runs. Shear Effect. Shear-effect studies represent the changes in either production rate or pipe inner diameter for design purposes. Generally, the higher the Reynolds number, the higher the shear stress on the deposit and the lower the deposition rate. Average fluid velocity, pipe inner diameter, fluid density, and fluid viscosity impact the Reynolds number and therefore the wall shear stress. 500
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Figure 4. Effect of residence time of the fluid in the cell on the asphaltene deposition rate from samples A, B, and C.
regarding the deposit amount at low shear for sample D until this run is repeated. In sum, shear has a significant impact on the deposition rate of asphaltenes, and controlling the production rate in the field can help in controlling asphaltene deposition. A field that normally produces oil at high production rates with little or no asphaltene deposition cannot be guaranteed against asphaltene deposition issues when the production rate declines. Residence Time Effect. As a result of limited fluid volume and arbitrary testing duration, a calculated deposition rate based on testing time and total deposit amount may not reflect the true deposition rate in the field. In production systems, since the tubing is in contact with “fresh” fluid at all times, contact time between tubing and a fluid at a given pressuretemperature condition can be seen as zero.2 On the basis of this understanding, a series of deposition tests at different residence times were performed to evaluate “apparent deposition rate”. Residence time is defined as the ratio of the RealView cell volume (i.e., 150 cm3) to the flow rate of the fluid passing through the cell. As shown in Figure 4, the shorter the residence time, the higher the apparent deposition rate. Such test results were extrapolated to zero residence time, and the estimated deposition rates under production conditions for oils A, B, and C were approximately 50, 40, and 70 g/m2/day at their prescribed pressure, temperature, and flow rate. It should be noted that a shorter residence time corresponds to a faster flow of fluid in the cell and therefore a shorter test run time for the same volume of fluid used. That is why, despite the lower deposit mass obtained at shorter residence times, the deposition rate is higher due to a shorter run time compared to the longer residence time test. The residence time tests can also help in investigating the kinetics of asphaltenes deposition. The bigger the difference between the deposition rate at a short residence time and that at a longer residence time, the faster the kinetic of deposition. As such, according to Figure 4, the kinetics of deposition for oil C is faster than that for oil A. The kinetics of deposition for oil B on the other hand is slower than that for oil A. The faster the kinetics of deposition, the quicker the depletion of fluid of depositing asphaltenes might be at longer residence times. However, depletion in deposition is not exclusively a compositional
Figure 3. Effect of shear on the mass of asphaltenes deposited from samples (a) A and B and (b) C and D.
Figure 3a and b show the effect of shear on the deposited mass of asphaltenes from oils A to D. For oil A, the experiments were performed at 69 °C, 20.68 MPa, and a flow-through rate of 3 cm3/ min. As shown, the amount of deposited asphaltenes dropped from approximately 80 mg at low shear (i.e., 0.56 Pa representing 318 m3/day field production) to approximately 35 mg at high shear (i.e., 6.8 Pa representing 1272 m3/day field production). Similar trends were observed for samples B and C. Shear experiments were run at 126 °C, 14.48 MPa, and a flow-through rate of 3 cm3/min for sample B and at 93 °C, 20.3 MPa, and a flow-through rate of 3 cm3/min for sample C. The total run time was approximately 4 h for all runs. The slope of deposit reduction from low shear to mid shear was sharper for samples A and C compared to sample B. This may represent the strength of the deposit in resisting against shear removal in regards to sample B. Unlike the other three samples discussed above, the amount of deposited asphaltenes from sample D at low shear was less than that at higher shears. Typically, it is expected to have more deposit at lower shears. However, if the flocculation tendency is high, the particles may get big enough under a low shear environment and therefore lose their tendency for deposition. This is speculation only, and no conclusion can be made 501
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Figure 5. Effect of run time on the amount of deposited asphaltenes from sample A to C.
Figure 6. Effect of pressure on the amount of deposited asphaltenes from samples B and C.
phenomenon; it is mainly caused by the particles growing so large that they are not capable of sticking to the wall. Our experiments have shown that when the oil, which has deposited part of its asphaltenes in a flow-through test, is collected at high pressure and high temperature, reconditioned at reservoir conditions for five days, and then reused for a deposition experiment, a deposition rate close to the deposition rate obtained by fresh original fluid would be obtained. This indicates that depletion of the asphaltene particle deposition is not necessarily due to a scarcity of depositing asphaltenes but mainly due to growing to a critical size, above which asphaltene particles no longer tend to deposit. The residence time tests are useful in validating the predicting capability of the RealView asphaltene deposition model. Run Time Effect. The effect of run time in a batch system was discussed earlier. It was concluded that over time the deposit growth reduces and eventually stops mainly due to the growth of asphaltene particles to a critical size, above which they do not tend to deposit any more. This is what we call depletion. In the flow-through system, however, depletion is expected to be minimized due to a continuous flow of fresh oil through the cell over a period of time. Therefore, a linear increase in the deposit mass would be expected. Figure 5 compares the growth of asphaltene deposited mass with time for samples A to C. In all three cases, the asphaltene deposit mass increased with time. In the case of oil C, the amount of deposited asphaltenes obtained for a 4 h run seems off-trend. The results of conducting flow-through runs at different run times can also be used for both tuning and validation of the RealView deposition model as discussed later. Pressure Effect. The quantity (concentration) of precipitated asphaltenes increases when the pressure is reduced from the asphaltene onset pressure to the bubble point. On the other hand, smaller particles that have a higher tendency for deposition appear at pressures close to the asphaltene onset pressure. Therefore, it is important to investigate the impact of pressure on the deposition of asphaltenes in live fluids. Figure 6 shows approximately a 16% reduction in the amount of deposited asphaltenes from sample B and a 23% reduction from sample C by running the tests at 6.9 MPa below their detected onset pressures rather than running them at slightly
above their bubble points. This expected outcome can be explained as follows. Despite a smaller mean size for asphaltene particles at higher pressure, their concentration in the fluid and their residence time in the cell would play more important roles in the deposition process. As such, the closer the pressure to the asphaltene onset pressure, the less the amount of deposited asphaltenes would be. The tests run for sample A above its detected onset pressure at 69 °C showed a negligible amount of asphaltene deposition (see tests #36 and 37 in Table 3). Chemical Inhibitor Effect. Asphaltene inhibitors are polymeric dispersants that have been developed to prevent asphaltene flocculation. It is believed that inhibitors interact with asphaltenes and do not let them come together and form bigger aggregates. Despite a reduction in the size of asphaltene aggregates, the injection of asphaltene inhibitors does not guarantee a reduction in the asphaltene deposition rate. In fact, if an asphaltene inhibitor shows a better interaction with the surface (e.g., metal, sand), deposition may not reduce. Rather, it may even increase due to the smaller size of the asphaltene particles and more frequent particle interactions with the surface. Therefore, conventional tests such as ADT or flocculation tests may not be helpful in identifying the most effective inhibitor. Representative deposition experiments, on the other hand, may show the real impact of inhibitors. It is worth noting that for deposition experiments with inhibitors, the desired inhibitor was added to the sample at a reservoir temperature and pressure, and the treated sample was conditioned prior to the deposition experiments. Figure 7 shows that the amount of deposited asphaltenes from sample A in the flow-through system reduced from approximately 80 mg (deposition rate of 35.2 g/m2 day) to approximately 26 mg (deposition rate of 12.7 g/m2 day) when using 150 ppm of inhibitor. This means an inhibitor efficiency of 67%. Increasing the concentration of the inhibitor in oil from 150 ppm to 500 ppm, however, did not improve the efficiency of the inhibitor. In contrast, the inhibitor did not show any improvement in the batch system. The main reason is that the amount of deposited asphaltenes in the batch system is typically very low and limited to the adsorbed layer on the metal surface, and therefore the 502
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Figure 7. Effect of asphaltene inhibitor on the amount of deposited asphaltenes from sample A in both batch and flow-through systems.
Figure 8. Effect of surface roughness on the deposition tendency of asphaltenes from sample C (T = 93 °C, P = 20.3 MPaa, shear stress ∼1.2 Pa, flow rate = 3 cm3/min).
injection of inhibitor would not make much difference and would be limited to the error range. Another asphaltene inhibitor was tested on sample C. The results showed that the amount of deposited asphaltenes reduced from 56 mg with the blank oil to 30 mg with the sample treated with 200 ppm of inhibitor. This indicates approximately a 50% efficiency. Surface Roughness Effect. The RealView cell wall has an average roughness of 8 μm. In order to investigate the effect of surface roughness on the deposition tendency of asphaltenes, two metal inserts that fit the cell were manufactured: one with an average roughness of 30 μm and the other with a “smooth” surface. Figure 8 shows the amounts of asphaltenes deposited on the regular cell, rough surface, and smooth surface with time. Approximately 50% more deposit was generated with the rough insert compared to the regular cell. In contrast, a negligible amount of asphaltene deposit was formed on the smooth surface. This may indicate the importance of surface roughness in the deposition process. The rougher the surface, the higher the sticking efficiency of particles with the metal surface. For field applications, however, with the deposit buildup over time, the roughness of the surface is determined by the asphaltene deposit layer formed on the wall, and therefore after production for some time, it would not be important any more.
The net or actual deposition mass flux, qa, is then calculated as7 qa ¼ ksr q0
ð3Þ
where q0 is the overall deposition mass flux in the absence of shear removal. All six parameters are determined using the experimental data. Our main purpose is to reduce the number of parameters from six to two by fixing four parameters using the available experimental data for various oils. The following is our approach to doing so: • Determine all six parameters by tuning the RealView deposition model with one set of experimental data for one of the fluids. • Perform a sensitivity analysis to find out less sensitive parameters. • Reduce the number of parameters by fixing less sensitive parameters and tune the model with experimental data for other fluids. • Assess the validity of model predictions with fewer parameters (preferably two) using the experimental data that were not used for tuning purposes It should be noted that, due to a lack of enough oil sample, no repeatability testing was performed. As such, the error range of RealView asphaltene deposition experiments is not known at this stage. Model tunings and calculations in this work have been performed with the assumption that all of the experimental data are representative unless otherwise noted in the text or indicated on the plots. Whether model predictions are in the range of error or not is not known, and therefore it will not be discussed. Determine Model Parameters. The experimental data for oil C were used to tune the model and determine all six parameters. A two-step process was used for this purpose. First, the results of batch experiments (see Figure 2) and flow-through experiments (see Figure 5) were used to estimate particleparticle collision efficiency, particle-wall collision efficiency, and particle critical size. Figures 9 and 10 show the outcome of model tuning in the absence of the shear removal term. The average absolute deviation (AAD) of model calculations from experimental data points is 14% in Figure 9 and 28% in Figure 10. In the second step, the model was tuned with shear removal data. For this purpose, a ksr was determined for matching each
’ MODEL TUNING AND VALIDATION As explained earlier, an engineering asphaltene deposition model was developed to link the RealView experimental data, obtained in the lab, to production tubings on the field scale. In the absence of shear removal, the developed deposition model by Eskin et al.8,9 has three parameters: particleparticle collision efficiency,α; particle-wall collision efficiency, γ; and critical particle size, dcr. For details regarding the development of the model and the equations involved, please refer to Eskin et al.79 The shear removal term, ksr, in this report is an empirical equation with three parameters: b n ksr ¼ a þ ð2Þ τw where a, b, and n are the parameters and τw is wall shear stress. 503
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Figure 9. Model tuning with batch deposition data for sample C. Figure 11. Estimated ksr vs wall shear stress for sample C.
Table 4. Estimated Model Parameters for Sample C deposition model parameter
estimated value for sample C
particleparticle collision efficiency, α
7.0 105
particle-wall collision efficiency, γ particle critical size, dcr
3.7 106 100 nm
shear removal parameter, a
0.4625
shear removal parameter, b
0.2764
shear removal parameter, n
1.1
Figure 10. Model tuning with flow-through deposition data for sample C.
deposition point for oil C shown in Figure 3. A plot of ksr vs wall shear stress was then plotted as shown in Figure 11. The shear removal term in eq 2 was then fitted with the points in Figure 11, and its parameters were estimated. Table 4 summarizes all six model parameters for oil C. Figure 12 shows modeling results with the tuned model for the effect of shear on the deposition of asphaltenes from oil C. The calculated AAD for this case was 32% mainly because one of the experimental data points seems to be off. Perform Sensitivity Analysis. Once the model parameters for sample C were estimated by tuning the model with some experimental data, a sensitivity analysis was performed to assess the sensitivity of each parameter on performance of the model. Figures 1315 show the impact of changing one parameter at a time on the calculated amount of deposited asphaltenes in batch and flow-through systems for sample C. As shown, the model is not that sensitive to changes in critical size especially in regard to the flow-through system. Therefore, we decided to keep this parameter fixed at 100 nm for deposition calculations for other samples. Changes in particlewall collision efficiency, however, make a difference. The model is sensitive to changes in particleparticle
Figure 12. Modeling results for the effect of shear on deposition from sample C.
collision efficiency as well but to a lesser extent compared to particlewall collision efficiency. Since the model is more sensitive to particlewall collision efficiency and since this parameter is more controlling in the deposition process, we decided to fix the particleparticle collision efficiency at 8 105 for other oil samples and only consider the particlewall collision efficiency as the tuning parameter. Finally, changes in the power of the shear removal term (parameter n in eq 2) indicated that this parameter could also be used as a tuning parameter for modeling shear removal effects. 504
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Table 5. Estimated parameters for samples A, B, D, and E oil sample parameter particlewall
A
B 6
D 6
E 5
4.9 10
6.7 10
1.33 10
1.02 105
1.1
0.55
1.0
1.0
collision efficiency, γ power n in shear removal term
Figure 13. Sensitivity analysis for modeling of sample C in the batch system.
Figure 16. Model predictions for sample A: shear effect at 3 cm3/min flow rate; AAD = 21%. Figure 14. Sensitivity analysis for modeling of sample C in the flowthrough system.
required. One experiment is recommended to be performed at low shear (lower limit of turbulent flow regime in RealView) where the shear removal term is not in effect. This way the particlewall collision efficiency can be estimated by matching the data point at low shear. The second experiment is recommended to be performed at mid shear or high shear (or the shear that is representative of the maximum production rate in the field). By matching this data point, the parameter n in the shear removal term can be estimated. Table 5 summarizes the two estimated parameters for samples A, B, and D. For sample E, only parameter γ was determined from available batch data. No flow-through experiments at high shear were available to determine parameter n for this oil. As such, n was assumed to be unity. The results of calculations will be demonstrated in the next section. Validate. Once the two parameters were identified for each oil sample, the rest of the measured data points were predicted using the tuned model. Figures 1618 compare experimental data with predicted values for sample A in regard to shear effect (T = 69 °C, P = 20.68 MPa, run time ∼4 h, and flow-through rate = 3 cm3/min), residence time effect (T = 69 °C, P = 20.68 MPa, and rotational speed = 1200 rpm), and shear effect with a different flow-through rate (T = 69 °C, P = MPa, run time ∼1.3 h, and flow-through rate = 10 cm3/min), respectively. As shown, the predicted values were in good agreement with experimental values. The AAD between calculated values and experimental values in Figures 1618 are 21%, 10%, and 20%, respectively.
Figure 15. Sensitivity analysis for modeling of sample C in regard to shear effect.
The other two parameters (i.e., a and b) in the shear removal term were fixed. Reduce Number of Parameters. In the previous step, four out of six parameters were suggested to be fixed. The two tuning parameters are particlewall collision efficiency, γ, and the power n in the shear removal term (eq 2). In order to determine these two parameters for a specific oil sample, at least two experimental deposition data points are 505
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Figure 17. Model predictions for sample A: residence time effect at 1200 rpm rotational speed; AAD = 10%.
Figure 19. Model predictions for sample B: shear effect at 3 cm3/min flow rate; AAD = 3%.
Figure 18. Model predictions for sample A: shear effect at 10 cm3/min flow rate; AAD = 20%.
Figure 20. Model predictions for sample B: run time effect; AAD = 4%.
Figures 19 and 20 compare experimental data with model predictions for sample B in regard to shear effect and run time effect, respectively. Again, predicted values are in good agreement with measured values in spite of fixing four parameters and tuning the model with only two parameters. The AADs between calculated and experimental values in Figures 19 and 20 are 3% and 4%, respectively Figure 21 compares the results of the model for sample C with the measured values. For this case, the tuned model underpredicted the experimental data for 15 min residence time (or 10 cm3/min flow-through rate). The calculated AAD is 19%. Figure 22 compares experimental data with model calculations for sample D in regard to shear effect. As explained earlier, for sample D, the parameter n was considered unity and the model was tuned with the experimental point at 7.25 Pa shear only. The reason for this was a low amount of deposited asphaltenes at low shear. As shown, the model predicted the mid shear point very well. The calculated AAD was 33%. Figure 23 compares experimental data with model predictions for sample D in the batch system. The model prediction was in
Figure 21. Model predictions for sample C for 15 min residence time, AAD = 19%.
very good agreement with the 6 h data point but overpredicted the 2 h data point. The calculated AAD was 23%. 506
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Figure 22. Model results for sample D- shear effect at 3 cm3/min flow rate, AAD = 33%.
Figure 24. Model results for sample E: batch system, AAD = 3%.
Figure 23. Model results for sample D: batch system, AAD = 23%. Figure 25. Computed deposit thickness distributions along vertical tubing.
Figure 24 compares experimental data with model predictions for sample E in the batch system. Due to a lack of flow-through data, parameter n was assumed unity, and only the particle surface interaction parameter was used as a tuning parameter. As shown, the model results are in good agreement with the rest of the experimental data. The calculated AAD was 3%. In sum, the deposition model once tuned with two experimental data points can be used to predict the deposited amount of asphaltenes under other operating conditions at least for the oil samples in this study. Since all five samples in this study were from GoM, it is believed that the two-parameter model can be used for predicting asphaltene deposition from other GoM oil samples. For oils outside of GoM, some experimental data may be required to validate the predictability of the model once it is tuned with two data points.
we illustrate a deposition model performance in a depleting reservoir producing oil A through vertical 2.500 -diameter tubing. Details of the deposition model for the flow line and related examples can be found elsewhere.15 The flow line model parameters are the ones obtained for sample A and presented in Tables 1 and 5. For the sake of simplicity, the bottomhole pressure was assumed to drop linearly by 1000 psi during one year of production. A change in the bottomhole pressure results in a shift of the asphaltene onset location in the tubing during production. The initial mean flow velocity was assumed to be 0.7 m/s. Figure 25 shows the deposit layer profiles, computed for the different operation times of three months, six months, and one year. A qualitative agreement of the modeled deposit profiles with those reported by Haskett and Tartera16 is obvious. Note that this comparison is justified only for the tubing region, where the pressure exceeds the bubble point pressure during the entire operation time. The abrupt decrease in the deposition profile takes place when the bubble point pressure is reached in the tubing.
’ FROM REALVIEW TO FLOW LINE Once model parameters are determined using the RealView experimental data, the deposition model for the flow line can be employed to predict asphaltene deposit formation in vertical production tubings and transportation pipelines. In this section, 507
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fluid due to pressure reduction, grow to a critical size, above which they do not tend to deposit. • Shear has a significant impact on the deposition rate of asphaltenes. Controlling the production rate in the field can help in controlling the asphaltene deposition. • Unlike batch experiments, in flow-through experiments, the amount of deposit grew continuously over time, mainly due to fresh oil passing through the deposition cell. • The deposition rate of asphaltenes at pressures closer to the asphaltene onset pressure is smaller than that at pressures closer to the bubble point pressure. • Chemical inhibitors’ effectiveness on reducing the deposition of asphaltenes could be observed with the flow-through system. • Surface roughness impacts the rate of asphaltene deposition in the RealView system. More deposit was generated using the rough surface compared to the smooth surface. Through a three-step process, a recently developed asphaltene deposition model was tuned with experimental data, and the number of parameters was reduced from six to two for the oils under study. The two variable parameters are particle surface collision efficiency and parameter n in the shear removal term. On the basis of the experimental data and modeling results, an asphaltene deposition experimental protocol was therefore developed. The proposed experimental protocol consists of a minimum of three deposition experiments: two for tuning the model and one for validation. The simulation results for deposition of asphaltenes in vertical production tubings were qualitatively compared with field observations reported by Haskett and Tartera.16 The results of simulations based on the tuned model with representative experimental data can help in better design of production tubings and transportation pipelines in the field and therefore saving capital and operating expenses.
No deposition calculation was performed in the two-phase region (i.e., below bubble point).
’ EXPERIMENTAL PROTOCOL Previously, we could reduce the number of model parameters from six to two for the oil samples under this study. As such, only two experimental data points would be required to tune the asphaltene deposition model. The following is the proposed experimental protocol for conducting asphaltene deposition experiments and simulation. 1. Regardless of the field operating conditions, the first flow-through experimental data point should be designed in such a way that the calculated Reynolds number in RealView is a number between 10 000 and 13 000. This is called the low shear point, where the shear removal effect is usually zero. Particlewall collision efficiency can be estimated by tuning the model with this experimental point. 2. The second flow-through experimental point is designed in such a way that the maximum production rate in the field is mimicked. This point is used to tune the model for parameter n. 3. A third experiment is recommended to validate model predictions. It could be running the flow-through experiment for a longer period of time, at a different shear, or with a different flow-through rate. It could also be a batch run, if preferred. 4. The estimated model parameters are then used to simulate deposition in the wellbore, tubing, or transportation pipeline under field conditions using the flow line model. It should be noted that the suggested experimental protocol is based on the assumption that the two-parameter model can be used for various oils. If an oil outside of GoM is used, more experiments may be necessary in case the two-parameter model cannot be validated. In such a case, all six parameters may need to be determined using sufficient experimental data. For conducting any deposition study, the following experiments are necessary prior to the design of deposition experiments: 1. Asphaltene content of the oil 2. Saturation pressure of the fluid at the temperature at which deposition tests will be performed (typically reservoir temperature) 3. Asphaltene onset pressure of the fluid at the same temperature as in step 2 4. Postfiltration of precipitated asphaltenes at the desired pressure (typically 100 psi above the saturation pressure) and temperature to determine the amount of precipitated asphaltenes for modeling purposes 5. Special care should be taken to make recombined fluids as representative as possible of the bottomhole fluid sample (in case enough bottomhole fluid does not exist to cover all of the flowthrough experiments)
’ CONCLUSIONS A total of 68 deposition experiments on five fluids from GoM were carried out. Through these experiments, the effects of shear, run time, residence time, pressure, chemical inhibitor, and surface roughness on the deposition of asphaltenes were investigated. The following main conclusions were drawn from the available experimental data: • Most of batch experiments resulted in asphaltene deposit amounts of less than 20 mg. Although the deposit amount increased over time, the deposit growth rate slowed down at longer running times due to the depletion of depositing asphaltenes. • The depletion of depositing asphaltenes occurs over time because asphaltene nanoparticles, originally formed in the
’ CONVERSION FACTORS °API bbl/d °C cm3 cm3/min cP g/cm3 g/m2/d h min mg ppm psi MPa scf/bbl
141,500/(131.5 + °API) 1.84 106 273.15 + °C 106 1.6 108 103 103 1.1 108 3600 60 106 106 6.894757 103 0.1781071
= kg/m3 = m3/s =K = m3 = m3/s = Pa.s = kg/m3 = kg/m2/s =s =s = kg = m3/m3 = kPa = kPa = m3/m3
’ APPENDIX Asphaltene Deposit Analysis Methodology. Once the deposited material is rinsed with dichloromethane, the solution is submitted for analysis. Figure A.1 shows the deposit analysis methodology applied for this report. First, dichloromethane is 508
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Energy & Fuels removed from the rinse using rotavap. The residue is then weighed. This residue is called the whole deposit, and its mass is represented by mt. The asphaltene content of the whole deposit is then obtained using a modified IP-143 technique. Briefly, 40-fold high-purity nheptane was added to the residue, and the mixture was heated to reflux at approximately 75°C and an atmospheric pressure for 2 h. The precipitated asphaltenes are then filtered while the mixture is still hot. The filter is then washed using a Soxhlet extractor to remove the non-asphaltenic materials absorbed on the asphaltenes and on the filter. The washing is performed at approximately 75°C and atmospheric pressure until the solvent is clear. Asphaltenes are then extracted from the filter and weighed. The asphaltene content is then calculated. The total asphaltene mass from the whole deposit is represented by mat. The total asphaltene mass is composed of asphaltene mass related to the occluded oil and the deposited asphaltene mass. Therefore, the total asphaltene mass needs to be corrected. For this purpose, first the mass of maltenes, mm, is determined: mm ¼ mt mat Then, the mass of occluded oil, mo, is determined: mm mo ¼ 1 xa =100 where xa is the asphaltene content of the production oil (the dead oil drained at the end of the run) in wt %. Next, the mass of asphaltenes related to the occluded oil, mao, is calculated: mao ¼ mo
xa 100
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Finally, the corrected asphaltene deposit mass, mad, is determined: mad ¼ mat mao With this method, typically over 85% of occluded oil is obtained. However, the field deposits normally show approximately 50% occluded oil and 50% solid deposit. In order to get more representative results, the asphaltene deposit methodology was improved using a neutral solvent as pre-rinse and simulated distillation analysis.
’ AUTHOR INFORMATION Corresponding Author
*Phone: 1-780-577-1341. Fax: 1-780-450-1668. E-mail:
[email protected].
’ ACKNOWLEDGMENT The authors would like to thank the following individuals for their contributions: Jose Zacharia and Abdel Kharrat for the development of the asphaltene deposit analysis methodology, Sajjad Hussain and Camila Vega for determining the asphaltene contents of the deposits, and Paul Church and Jessica Saulnier for performing RealView experiments. ’ NOMENCLATURE a = Parameter in the shear removal term Ac = Surface area of the cell ∼0.0107 m2 b = Parameter in the shear removal term ksr = Shear removal coefficient mm = Mass of maltenes mat = Total mass of c7-asphaltenes in the deposit mo = Mass of occluded oil mao = Mass of asphaltenes related to occluded oil mad = Corrected mass of deposited asphaltenes mt = Total mass of deposit n = Parameter in the shear removal term P = Pressure qa = Reynolds number = 2πrsωFo(ri rs)/μo t = Total run time T = Temperature xa = Asphaltene content of drained oil, wt % α = Particleparticle collision efficiency γ = Particlewall collision efficiency τw = Wall shear stress AAD% = Average absolute deviation = 100 (ABS(experimental calculated)/experimental) ’ REFERENCES (1) Akbarzadeh, K.; Hammami, A.; Kharrat, A.; Zhang, D.; Allenson, S.; Creek, J.; Kabir, S.; Jamaluddin, A.; Marshall, A. G.; Rodgers, R. P.; Mullins, O. C.; Solbakken, T. Asphaltenes- Problematic But Rich in Potential. Oilfield Review, Summer 2007. (2) Akbarzadeh, K.; Ratulowski, J.; Lindvig, T.; Davies, T.; Huo, Z.; Broze, G.; Howe, R.; Lagers, K. The Importance of Asphaltene Deposition Testing in the Design and Operation of Subsea Pipelines. SPE 124956-PP. SPE Annual Technical Conference and Exhibition, New Orleans, LA, October 47, 2009. (3) Akbarzadeh, K.; Ratulowski, J.; Eskin, D.; Davies, T. The Importance of Wax Deposition Measurement in the Simulation and Design of Subsea Pipelines. SPE 115131. SPE Annual Technical Conference and Exhibition, Denver, CO, September 2124, 2008.
Figure A.1. Deposit analysis methodology. 509
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dx.doi.org/10.1021/ef2009474 |Energy Fuels 2012, 26, 495–510
