MODEL CALCULATES WAX DEPOSITION FOR N. SEA OILS

June 18, 1990
A. Majeed, B. Bringedal, S. Overa Norsk Hydro Stabekk, Norway A model for calculation of wax formation and deposition in pipelines and process equipment has been developed along with a new method for wax-equilibrium calculations using input from TBP distillation cuts. Selected results from the wax formation and deposition model have been compared with laboratory data from wax equilibrium and deposition experiments, and there have been some field applications of the model.
A. Majeed, B. Bringedal, S. Overa
Norsk Hydro
Stabekk, Norway

A model for calculation of wax formation and deposition in pipelines and process equipment has been developed along with a new method for wax-equilibrium calculations using input from TBP distillation cuts.

Selected results from the wax formation and deposition model have been compared with laboratory data from wax equilibrium and deposition experiments, and there have been some field applications of the model.

NORTH SEA OILS

Crude oils from the North Sea contain a mixture of light and heavy hydrocarbon components. Typically, a stabilized oil may contain paraffinic, naphthenic, and aromatic components as heavy as C60. In addition, polars and asphaltenes may also be present.

The lighter components in the crude oil keep the heavier components in solution. This solubility depends very strongly on the temperature.

If the temperature of the oil is decreased, the solubility of the heavy hydrocarbons may be sufficiently reduced to cause precipitation of these components in the form of solid wax crystals. The polars and asphaltenes may also co-precipitate with the wax crystals.

The presence of wax crystals changes the flow behavior of the crude oil from Newtonian to non-Newtonian. The wax crystals usually lead to higher viscosity with increased energy consumption for pumping and a decreased capacity.

In addition, if the oil is cooled during transportation, the wax crystals tend to deposit on the colder pipewall. Wax deposits can lead to increased pipeline roughness, reduced effective diameter, more frequent pigging requirement, and potential blockage.

If these deposits get too thick, they can reduce the capacity of the pipeline and cause problems during pigging.

Wax deposition in process equipment may lead to more frequent shutdowns and operational problems. In extreme cases, wax crystals may also cause a crude oil to gel and lead to problems of restarting the pipeline.

For the present discussion, wax is understood to be solid hydrocarbons consisting of paraffin, naphthene, and aromatic components.

The discussion focuses on wax formation and deposition from stabilized oils only.

POTENTIAL SAVINGS

Great potential savings can be derived from accurate prediction of wax formation in offshore systems at an early phase in the project.

Knowledge of the magnitude of wax deposition can lead to reduction of insulation requirements for production and transportation systems. Conversely, problems with wax can be addressed in an early stage of a project so that sufficient thermal insulation is planned for instead of expensive chemical injection and loss in capacity or loss of availability.

Process heat loads can be reduced by increasing efficiency of heat transfer. Capacity reduction in heat exchangers can be overcome. This reduction results from blockage or vibration problems which in turn result from high velocity or flashing.

The size of export pumps and flow lines can be reduced by an accurate knowledge of the effect of wax formation on crude viscosity. The minimum pigging frequency can be determined if the amount of wax deposition can be estimated. In addition, problems related to start-up and shutdown can be solved cost effectively.

There are two main methods used for coping with wax-related problems: chemical or mechanical treatment.

Both of these methods have their disadvantages.

Chemical usage leads to increased operating expenses. For example, a 100-ppm dosage for a crude-oil rate of 30,000 standard cu m/day (scmd; about 200,000 b/d) leads to an increased operating expense of about $3 million/year.

Pigging the pipeline is useful for removing thin layers of wax only. A highly waxy crude may require frequent pigging to keep the wax accumulation manageable. A pigging operation often requires significant amounts of costly offshore man-hours. In addition, pigging of subsea completions is an intricate operation.

Norsk Hydro recognized the need for research and development on wax formation and deposition a few years ago. The company anticipated that the money spent in this area would be far outweighed by the money saved through improved process design as a result of the research. There have been several short-term achievements from these activities.

WHAT'S BEEN DONE

Holder and Winkler 1 studied cloud and pour points for binary mixtures of n-paraffins ranging from C20 to C28 They concluded that binary mixtures of n-paraffins crystallize both independently and as solid solutions. As the difference in molecular weight between the two paraffins decreases, co-crystallization predominates.

Bott and Gudmundsson 2 studied the deposition of paraffin wax from kerosine in cooled heat-exchanger tubes. They observed an asymptotic behavior of wax deposition and attributed it to the decrease in heat flux and increase of shear stress.

They also observed that a decrease in flowrate and temperature slowed the wax deposition rate, while a greater wax concentration increased the wax-deposition rate. They concluded that the mechanism of wax deposition is controlled by cohesive forces between the wax particles and the fluid behavior within the boundary layer.

Bern 3 studied wax deposition in North Sea submarine crude-oil pipelines. They found that the laminar boundary layer controlled the rate of wax deposition. They assumed molecular diffusion and shear dispersion as the two important mechanisms for wax deposition.

They expected molecular diffusion to be the dominant process at higher temperatures and heat fluxes, whereas shear dispersion dominates at lower temperatures and low heat fluxes. Tests on stabilized Forties crude oil indicated that molecular diffusion is the predominant mechanism for wax deposition at sealine conditions.

Burger 4 investigated mechanisms of wax deposition in the Trans-Alaska Pipeline.

It was found that only a small part of potentially precipitable hydrocarbons will actually deposit under favorable conditions. Molecular diffusion, shear dispersion, and Brownian diffusion were identified as mechanisms for wax deposition.

It was concluded that molecular diffusion, through the laminar sublayer, was the dominant mechanism at higher temperatures and high flux conditions. It was also concluded that little or no wax deposition occurs under conditions of zero or negative heat flux.

Weingarten and Euchner 5 reported experiments developed to measure wax formation conditions for live oils. They expressed their results using the "ideal-solution" theory. They found that sloughing was not related to transition from laminar to turbulent flow.

Sifferman 6 reported the flow properties of U.S., Indonesian, and Libyan waxy crude oils. He concluded that the pour point is insufficient to indicate the flow properties of a crude oil and that viscosity and gel strength should also be considered.

Viscosity is needed for pressure-drop calculations; gel strength is needed to calculate start-up pressure.

Asperger 7 predicted wax buildup in a 24-in. cold, deepsea oil-loading pipeline. The study concluded that wax buildup will get harder with time as heavier components diffuse towards the cold pipewall. Use of heavy external thermal insulation to reduce wax problems was suggested.

Hartley and Jadid 8 reported various laboratory tests for assessing the wax-related properties of the North Sea's Troll oil. They concluded that untreated crude will deposit wax upon cooling, but the effects can be reduced with wax modifiers or periodic pigging. In this case, full insulation of the flow line was not recommended for economic reasons.

Several field experiences with wax deposition are reported.

Marshall 9 reported severe wax deposition in a North Sea Valhall subsea crude-oil pipeline over a period of many years.

Howes 10 reported a decrease of production rate and pressure in the North Sea's Ness subsea installation, which was attributed to wax deposition at low transport temperatures.

Tuttle 11 reported wax problems in U.S. oil fields in south Louisiana, Utah, and Michigan. Tuttle also refered to wax problems in oil fields in China, India, and the Soviet Union.

IDENTIFYING PROBLEMS

The oil industry uses several standard test methods for identifying potential wax problems.

  • The wax content is determined by UOP method 4664. This method is based on precipitation of wax with acetone followed by filtration.

  • Pour point is measured by the ASTM D-97-66 method.

  • Cloud point is determined using ASTM D-97-57; or a modification of this method is used to determine the wax appearance or disappearance point.

Unfortunately, these standard test methods give very little quantitative information about oil composition or wax deposition rates from the crude oil.

We conducted an experimental program for identification of paraffin, naphthene, and aromatic content of stabilized oils from selected North Sea fields. This experimental program was undertaken by DB Robinson & Associates, Edmonton, and the actual analyses were done at Alberta Research Council.

The results from these analyses were semi-quantitative because of the assumptions and approximations in the treatment of the mass spectrometric data. The analyses provided molecular weight vs. composition data up to about C60. These data formed a good basis for a compositional equilibrium model, which is necessary for a molecular diffusion wax-deposition model.

A schematic of the oil analysis method is shown in Fig. 1.The stabilized oil was divided into a naphtha, mid-distillate, and residue cut with a spinning-band distillation.

The naphtha cut was analyzed by gas chromatography and mass spectrometry (GC/MS) with electron impact. The asphaltenes were first separated from the residue by n-pentane precipitation. The mid-distillate and residue cuts were separated into saturate, aromatic, and polar fractions by a silica/alumina column chromatographic method.

The saturate and aromatic fractions of the mid-distillate were analyzed by GC/MS with N20 chemical ionization (CI). The residue saturate fraction was analyzed by solids probe MS with CH4 CI. The residue aromatic fraction was analyzed by solids probe MS with N20 CI-Results from oil analyses are shown in Fig. 2.

EQUILIBRIUM MODEL

The equilibrium model presented by Erbar 12 is used here. The calculation is performed by imposing material and equilibrium K-value constraints. The overall material balance must be satisfied as shown in Equation 1 (box).

The material balance for each of the n components in the feed must be satisfied. This yields n-1 independent equations of the following form:

The mole fraction in the feed (z) is experimentally obtained from the oil analysis.

The equilibrium K-values for each component in the feed describe the relationship between the wax mole fraction and the mole fraction in the oil (Equation 3).

The K-value is calculated for each component with the method given by Won 13 14 using the calculation found in Equation 4.

The activity coefficient for each component is estimated from the solubility parameter using Equations 5a, 5b, 5c, and 5d.

The equilibrium calculation involves the solution of Equation 6 for material balance and K-value.

HEAT TRANSFER, DEPOSITION MODEL

The deposition model is based on work reported by Bern and Burger .3 4

The deposition mechanism is assumed to be molecular diffusion. The equilibrium concentration of dissolved wax decreases with decreasing temperature.

The radial temperature gradient therefore sets up a radial concentration gradient of dissolved wax, with decreasing concentration towards the wall.

The flux of dissolved wax molecules towards the wall is then given by Equation 7.

The model assumes that all the wax molecules that diffuse to the wall deposit and form a wax layer which is not removed by shear forces from the fluid. The concentration of dissolved wax vs. temperature, and hence dx/dT, is calculated from the equilibrium calculation. The temperature gradient is calculated from the inlet and outlet temperatures.

The diffusivity is as a first approximation assumed equal for all the different components.

The flux is calculated for all the components that are given in the oil analysis. The total flux is the sum of the fluxes of each component. In our model, the deposition is assumed to be only from molecules that precipitate on the wall.

No deposition is assumed from the solid particles, such as wax crystals, that may have precipitated away from the wall. The concentration of these wax crystals is higher towards the wall, which leads to a larger crystal diffusion rate away from the wall.

The net effect of crystal diffusion is to give a reduction in the wax-deposition rate resulting from entrainment of dissolved wax molecules away from the wall. In our model, neglecting crystal diffusion, therefore, gives a conservatively high value for the wax-deposition rate.

The heat-transfer calculation includes the convection from oil to inside of the wax (if present) or tubing, conduction through the wax layer (if present), and conduction through coatings and insulation (if present).

The calculation is partly transient, as it calculates the time-dependent heat transfer which decreases due to increase of wax layer. The transient effect as a result of tubing walls heating up, coating, and insulation vs. time is not included.

The overall heat-transfer coefficient (U) is calculated by Equation 8.

The plastic viscosity (up) at wall temperature is assumed to be a function of the temperature only. A Guzman-Andrade function is assumed:

up = A exp (B/T)

where: A and B are constants, and T is the absolute temperature.

The plastic viscosity is the inclination of the shear stress vs. shear rate curve above shear rates that give a constant slope. It is assumed that the Guzman-Andrade function is also valid after the wax starts to precipitate. This assumption is taken from Barry. 15

The plastic viscosity at two temperatures is required for the evaluation of constants A and B.

The Nusselt number (Nux) is calculated as follows:

Nux = 0.023 Rey0.8 Pr0.3

The Reynolds and Prandtl numbers are evaluated at the bulk temperature.

The value of the minimum Nusselt number is taken to be 4.

For laminar flow the Nusselt number is calculated as:

Nux = 1.86 (Re Pr ID/x)'13

where:

ID Inside diameter

x Distance from the entrance

u Plastic viscosity

Verification The wax equilibrium model was verified with experimental data on binary mixtures of n-heptane which contained 1, 2, or 3 wt % of tetracosan (n-C24H50), triacontan (n-C30H62), or hexatriacontan (n-C36H74)

The experiments were carried out in a Bohlin VOR viscometer with a double-gap concentric cylinder. The oil mixture was cooled at a constant rate of 0.1 C./min. The wax formation point was determined to be the temperature at which the viscosity increased by more than a factor of 2.

The experimental results for n-heptane with 1, 2, and 3 wt % n-C36H74 are shown in Fig. 3.

The wax formation points for these three binary mixtures calculated from the equilibrium model are also shown for comparison.

The equilibrium model generally predicts the wax formation temperature of all the binary mixtures studied to within 2-40 C.

The freezing point of pure n-C36H74 is about 750 C. We were very encouraged by the ability of the model to predict the depression in the pure component freezing point of about 40-50 C. with such accuracy. The temperature predictions from the model are consistently lower than those from viscosity measurements.

We have also verified the wax-equilibrium model against experimental data for a North Sea oil.

The oil sample was cooled and centrifuged at high speed for several days.

This experiment was performed at 0, 5, 1 0, 15, and 200 C. The oil was then drained and the wax sample collected and weighed.

The results from this experiment are compared with the calculations from the wax equilibrium model in Fig. 4. The model accurately predicts the wax formation point of this oil. The amount of insoluble wax as a function of temperature also agrees well with the experimental measurements.

These experiments are very difficult to perform at high temperatures, where the amount of wax formation is very low. In addition, the quality of data from such experiments depends on the ability to separate oil from wax.

The results should be used with caution if oil entrainment in the wax is significant. We were, nevertheless, very pleased with the ability of the equilibrium model to handle such a complex oil mixture.

The wax-deposition model was verified with experiments performed in a laboratory flow loop. A schematic of this flow loop is shown in Fig. 5.

The test section was 1 m long, and diameters of 6, 9, or 12 mm could be selected. A 2.5-1. oil sample was circulated at about 50 1./min. The oil and water temperatures were varied between 5 and 30 C.

The wax-deposition rate was obtained by weighing the test section at various time intervals during the experiment. We tried to maintain a constant water temperature in order to achieve a high heat-transfer rate on the water side. We also kept a co-current oil-water flow in order to obtain similar entrance effects on inlet and outlet. The flow regime was kept laminar because it required reasonably small oil samples.

The results from selected experiments are shown in Fig. 6. We have also plotted the results from our model.

The initial wax-deposition rate calculated by the model agrees well with the measurements for the high heat-flux conditions where molecular diffusion is the predominant mechanism. The model takes into consideration that it is not possible to have fully developed flow in a 1-m test section with laminar flow.

We could assume a fully developed velocity profile but not a fully developed temperature profile due to cooling in the test section. Therefore, we have taken into account the entrance effects in development of the laminar boundary layer.

We were encouraged with the results of the model, especially in view of all the assumptions. The low heat-flux conditions (Fig. 6d) are underpredicted because there is no shear dispersion term in the model.

The wax-deposition model gives conservative results and does not predict the asymptotic time-dependent behavior shown by the experimental data. We believe the difference could be due to several assumptions in the model. We have not modeled the depletion of the wax amount from the oil.

This effect could be significant if large amounts of wax are deposited from our sample. We have assumed the thermal conductivity of the wax and oil to be the same. With laminar flow the thermal insulation effect of the wax layer in the model is therefore very small.

APPLICATIONS

The wax formation and deposition model has been applied to the calculation of wax formation and deposition in an offshore crude-oil pipeline. This study was performed at an early phase in an offshore project.

The crude oil, containing appreciable amounts of insoluble wax at seabed temperatures, was exported at about 20 C. higher than its wax formation temperature. The objective of the study was to select the flow line diameter and insulation requirements for a subsea flow line to transport about 14,000 scmd (90,000 bo/d) of the crude oil.

The wax-deposition rates for the uninsulated flow line are shown in Fig. 7a. Wax deposition starts when the crude oil is cooled to less than the wax-formation temperature and stops when the seabed temperature is reached.

The distance in the flow line between these two temperature limits was almost independent of the flowrate in this case. The wax-deposition rate was proportional to the flowrate because higher Reynolds numbers give high heat fluxes and lead to more wax deposition.

The wax-deposition rates for the insulated flow line are given in Fig. 7b. This figure shows an increasing and then decreasing rate of wax deposition.

At low flowrates the effect of the insulation is minimal. The oil cools to less than the wax-formation temperature and eventually reaches seabed temperature.

As the flowrate is increased, the distance in the flow line between the wax-formation temperature and seabed temperature increases as well as the heat-transfer rate due to higher Reynolds number. This leads to an increase in wax deposition.

At very high flowrates, the oil is no longer cooled to seabed temperature at the exit of the flow line. This causes a decrease in the wax-deposition rate. It was concluded that an insulated flow line should be used in order to avoid very frequent pigging and excessive pressure drop with loss in production capacity and availability.

The wax formation and deposition model has also been applied to a 28-in., 116-km subsea flow line transporting about 40,000 scmd (250,000 bo/d) of a waxy crude oil. The model predicts a significant amount of wax deposition in the flow line.

The calculated wax deposition profile after one week is shown in Fig. 8.

The flow line is regularly pigged, about once a week. The total amount of wax collected in the pig receiver in a year is about 8 tons, which averages 150 kg/week. A large amount of the oil bypasses the pig, and this oil resuspends the wax in front of the pig back into the oil flow.

The wax amount that is removed from the flow line is therefore inaccurately known. This comparison highlights the difficulties in verification of this model with field data and underscores the need for controlled laboratory experiments.

TBP INSTALLATION

The wax-equilibrium model requires a very detailed oil analysis as input data.

There are many oil samples for which such a detailed oil analysis is not available. We have therefore developed a new method for providing the input to the wax-equilibrium model from a true boiling point (TBP) distillation.

This method has an additional advantage in that it allows use of the same hypothetical components found in the vapor-liquid equilibrium (VLE) models. Further testing and refining of this technique are ongoing, A brief outline of the method and some preliminary results are presented here.

The freezing points for each cut from a TBP distillation on a crude oil have been measured. The distillation and freezing point data are shown in Fig. 9.

The crude oil has been characterized with ten hypothetical components using the method by Johannesen.16 An average freezing point temperature has been calculated for each hypothetical component. This temperature is used in the wax-equilibrium model.

The wax-equilibrium curve was then calculated and compared with results for the same oil with a detailed oil-analysis input. The comparison is shown in Fig. 10. There is a remarkable agreement between results from the two calculations. Further verification for this method for different crude oils i s planned.

ACKNOWLEDGMENT

The authors acknowledge the experimental work done at Norsk Hydro Research Center, Porsgrunn, and the contributions of coworkers E. Stange and M. N. Lingelem. We also appreciate Norsk Hydro's permission to publish this article.

REFERENCES

  1. Holder, G. A., and Winkler, J., "Wax Crystallization from Distillate Fuels," Part 1, J. Inst. of Petr., Vol. 51, p. 499, July 1965.

  2. Bott, T.R., and Gudmundsson, J. S., "Deposition of Paraffin Wax from Kerosene in Cooled Heat Exchanger Tubes," Can. J. of Chem. Eng., 55, August 1977.

  3. Bern, P.A., Withers, Y. R., and Cairns, R. J. R., "Wax Deposition in Crude Oil Pipelines," European Offshore Petroleum Conference & Exhibition, London, Oct. 21-24, 1980.

  4. Burger, E. D., Perkins. T. K., and Striegler, J. H., "Studies of Wax Deposition in the Trans Alaska Pipeline," J. Petr.Tech., June 1981.

  5. Weingarten, J. S., and Euchner, J. A., "Methods for Predicting Wax Precipitation and Deposition," SPE 15654, 61st Annual Technical Conference & Exhibition, New Orleans, Oct. 5-8, 1986.

  6. Sifferman, T. R., "Flow Properties of Difficult To Handle Waxy Crude Oils," J. Petr. Tech., August 1979.

  7. Asperger, R. G., Sattler, R. E., Tolonen, W. J., and Pitchford, A. C., "Prediction of Wax Buildup in 24 Inch Cold, Deep Sea Oil Loading Line," SPE 10303, 1981.

  8. Hartley, R., and bin Jadid, M., "Use of Laboratory and Field Testing To Identify Potential Production Problems in the Troll Field," SPE 15892, SPE European Petroleum Conference, London, England, Oct. 20-22, 1986.

  9. Marshall, G. R., "Cleaning of the Valhall Offshore Oil Pipeline," OTC 5743, 20th Annual OTC, Houston, May 2-5, 1988.

  10. Howes, J., "Mobil Overcomes Wax Problem on Ness," The Oilman, January 1989.

  11. Tuttle, R., "High Pour Point and Asphaltic Crude Oils and Condensates," J. Petr. Tech., June 1983.

  12. Erbar, J. H., "Three Phase Equilibrium Calculations," Proceedings of Fifty-Second Annual GPA Convention, 1973.

  13. Won, K. W., "Continuous Thermodynamics for Solid-Liquid Equilibria: Wax Formation from Heavy Hydrocarbon Mixtures," A1ChE Spring National Meeting, Mar. 24-28, 1986.

  14. Won, K. W., "Thermodynamics for Solid Solution Liquid Vapor Equilibria: Wax Phase Formation from Heavy Hydrocarbon Mixtures," 4th International Conference on Fluid Properties and Phase Equilibria, Denmark, May 11-16, 1986.

  15. Barry, E. G., "Pumping Non-Newtonian Waxy Crude Oils," J. Inst. Petr., Vol. 57, p. 554, March 1971.

  16. Johannesen, S. O., and Stange, E., "HYPO*S A Program for Heavy Ends Characterization," Proceedings of Sixty-Fifth Annual GPA Convention, 1986.

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