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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: DOI:10.1021/ef900920x
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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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(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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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 1072
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: DOI:10.1021/ef900920x
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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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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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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.
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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.
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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.
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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
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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.
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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.
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