Copyright 2005, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the 2005 SPE International Symposium on Oilfield Chemistry held in Houston, Texas, U.S.A., 2 – 4 February 2005. This paper was selected for presentation by an SPE Program Committee following review of information contained in a proposal submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to a proposal of not more than 300 words; illustrations may not be copied. The proposal must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435. Abstract At some thermodynamic conditions, asphaltenes flocculate into larger, almost spherical particles that have a specific gravity of 1.05 to 1.10. Work is cited here that indicates that asphaltene stable colloids exist in oil as very minute particles and that their pre-flocculation sizes are in the range of about 10 to 15 Å. This corresponds to 334 and 1,128 molecular weight respectively, assuming asphaltene spherical colloids and an experimentally determined asphaltene density of 1.06 g/cm3. The reason for this high specific gravity of asphaltene particles compared to the rest of the molecules of oils is that they consist mostly of asphaltenes and resins, the heaviest constituents of oils. Roughly, resins have specific gravities of 0.95 to 1.0 and asphaltenes 1.1 to 1.2. Because of their high specific gravity asphaltene particles settle by the force of gravity in storage systems where the convection currents and shear forces are minimal. Some of these particles are large enough to overcome the convection currents and shear forces and settle in large separators and occasionally in large pipes due to Stoke’s law effects, especially at elbows changing the direction of flow where the particles impinge against the pipe wall and are temporarily halted. Wax precipitation often results in the formation of sub-micron wax spherical particles that also settle under the influence of gravity. Although paraffin waxes have specific gravities around 0.8 to 0.85, field waxes have higher specific gravities, usually higher than 0.9, because they usually co-precipitate with asphaltenes and resins, if present. Hence, in oils that contain asphaltenes and resins, precipitating waxes do settle by gravity. It has been shown that asphaltenes and resins are considered responsible for causing the formation of amorphous spherical wax crystal particles rather than wax needle crystals. Both flocculated asphaltene particles and crystallized wax particles agglomerate to form very large micron-level particles whose molecular weights run in the

hundreds of thousands or millions. These large particles settle fairly quickly in storage systems. This paper presents a modeling methodology for the simulation of sedimentation of asphaltene and wax particles in both onshore and offshore storage systems. The asphaltene and wax particle size distribution is usually available from microscopic observations, filtration, and thermodynamic models. The sedimentation calculation is done by assuming that the particles have settled and are at gravimetric equilibrium. Two examples are presented: one 1,000,000-barrel FPSO case and one 250,000-barrel oil storage tank case. Both the FPSO and the tank had lost a substantial fraction of their capacity due to accumulation of asphaltene and wax sludge. Introduction Fundamental research with asphaltenic systems was first published by Richardson1. Richardson, in the late 19th to early 20th century, studied the colloidal chemistry of Trinidad asphaltenes using the ultra-microscope and other techniques. In the 1920's and 30's, while working for the Government Road Laboratory in Holland, Nellensteyn2 was the first to propose the colloidal structure of bitumens, as depicted in Figure 1.

Figure 1: Colloidal Structure of Oils and Bitumens

(Prior to Asphaltene Flocculation)

SPE 92958

Quantification of Asphaltene and Wax Sludge Build-up in Crude Oil Storage Facilities Kosta J. Leontaritis, SPE, AsphWax Inc.

2 [SPE 92958]

Nellensteyn called the asphaltene nuclei of Figure 1 ultra-microns or microns and the outside shell of resins as the protective bodies; the combined entity he called a micelle. He wrote that, "...The stability of these systems in the first place depends upon the relation between the micelles and the medium. Changes in this stability caused by flocculative and peptizing agents are known as the phenomena of the reversible flocculation. Flocculated micelles may be re-peptized by peptizing agents, as long as the micelles remain in tact, but if the micelle itself is destroyed, it cannot be re-peptized directly by peptizing agents; in this case irreversible flocculation takes place." Nellensteyn thought that the ultra-microns or microns were graphitic carbon. The currently held view is that the asphaltene nuclei consist of molecules that are highly polar (i.e., organic acids and/or bases) and that they contain hydrogen and hetero-atoms (i.e., N, S, O), in addition to carbon. In the Prinos Field3, analysis of the asphaltene fraction of the oil showed that it contained highly carbonaceous substances (sometimes called carboids) that were not soluble even in benzene or carbon disulfide. A few years later, Pfeiffer and Saal4, gave the following description for the existence of asphaltenes and resins in these systems, "...In the asphaltic bitumens, the asphaltenes are centers of micelles which are formed by adsorption, and perhaps partly by absorption, of part of the maltenes on the surfaces or in the interiors of asphaltene particles. When the entire system contains sufficient constituents for the formation of the outer region of the micelles, the asphaltenes are fully peptized and able to move through the bitumen as freely as the viscosity of the inter-micellar phase permits...If, however, there is a shortage of asphaltic resins, part of the forces causing the formation of the micelle are not compensated by adsorption of asphaltic resins and the micelles will be subjected to mutual attraction." Pfeiffer and Saal thought of the existence of asphaltenes and resins as depicted in Figure 1. Katz et al.5 pioneered the use of electron microscopy in search of the colloidal asphaltene particles by studying thin films of asphalt and oil. These films were free of particles 65Å in diameter and larger. However, numerous particles appeared when suspensions of asphalt in benzene and/or petroleum ether were examined. Their conclusion was that, if the colloidal asphaltene particles exist in native asphalt and oil, their size must be less than 65Å, which was the resolution of their electron microscope. At the same time Katz's group was using electron microscopy, Preston6 (another student of Dr. Katz’s) was investigating ultra-centrifugation as a possible means of finding, separating, and quantifying the colloidal asphaltene particles. His results indicated that asphaltene particles were present in three crude oils and may be force-sedimented (or ultra-centrifuged out of suspension) from any sample of the three crude oils prepared with or without solvent. He also found that centrifuging of pure oils was completely reversible and those particles sedimented by high centrifugal force nearly all returned to their original state of dispersion upon removal of the centrifugal field. The lower size limit of the un-flocculated

asphaltene particles Preston separated in his ultra-centrifugation experiments was 11 Å, which, at a density of 1.06 g/cc that he determined, corresponds to a spherical particle with molecular weight of 448. The higher size limit of the flocculated asphaltene particles Preston separated in his ultra-centrifugation experiments was approximately 40 Å, which corresponds to a spherical particle with molecular weight of 21,500. Ray et al.7 performed similar ultra-centrifugation experiments at 80,000g centrifugal fields on crude oils ranging from 18° to 46° API gravity. They were able to sediment out of the oils studied asphaltic particles of colloidal dimensions ranging from 30 to 65Å. Other smaller particles in crude oil that may be asphaltic in character were also suspected. They proposed that the dimensions of the colloidal particles, in their natural state in petroleum obtained through their ultracentrifuge studies, is essentially the same as those obtained in their analytical studies. The asphaltene particles they separated in their ultra-centrifugation experiments had an average spherical particle molecular weight of 30,000, diameter 40 Å, and density of 1.22 g/cc. Neumann et al.8 using a technique called ultra-filtration, among others, determined that asphaltenes and resins are poly-dispersed, re-suspendable, spherical, and oleophilic micelle colloids. They are oleophilic because they are stably dispersed in hydrocarbons. They are re-suspendable because, after separation by ultra-filtration, they can again be colloidally dispersed. They are poly-dispersed because during multistage ultra-filtration they are progressively held back on filters with different pore sizes. And they are spherical because even solutions with relatively high concentrations (e.g., 10%) form low-viscosity oils and not highly viscous gels. Furthermore, ultramicroscopic surveys show almost globular particles. Every colloid consists of several molecules. The ultra-filtration of several oils showed that no filtration is achieved using filters with an average pore diameter >350Å. Successively, smaller diameter filters separate varying (i.e., increasing) amounts of residue. With a filter of 50Å pore-diameter all colloids can be separated from the oil. Neumann et al. determined that it is the colloids that cause a black-brown coloration in oils and their residual fractions.

Figure 2: Asphaltene Particles Photographed After Flocculation at 500X (The inserted text sizes are directly below the particle)

[SPE 92958] 3

All of the work cited above indicates that asphaltene stable colloids exist in oil as very minute particles. The above data indicate that their pre-flocculation sizes are in the range of about 10 to 15 Å. This corresponds to 334 and 1,128 molecular weight respectively, assuming asphaltene spherical colloids and an asphaltene density of 1.06 g/cm3. After flocculation, asphaltene particles emerge that are visible even by naked eye. Figure 2 shows flocculated asphaltene particles at 500x magnification. Field and laboratory data indicate that the crystallization of crude oil heavy molecules is primarily driven by a decrease in temperature9, whereas flocculation of crude oil molecules is primarily driven by a decrease in pressure10. Flocculation can and does occur at high temperatures, but it has only little sensitivity to temperature. Crystallization occurs at lower temperatures, but it has only little sensitivity to pressure. Hence, the two mechanisms of organic deposition have diametrically opposite sensitivities to temperature and pressure. The asphaltene deposition envelope (ADE) and wax deposition envelope (WDE) demonstrate succinctly these pressure-temperature relations and sensitivities10. Hence, one can determine the deposition mechanism from the deposition envelope alone. Furthermore, one would surmise that these two different mechanisms of solid formation and deposition should lead to solid deposits that have different compositions11. Since flocculation results from destabilization of asphaltene-resin micelles and their subsequent aggregation into larger particles, one would expect that organic deposits resulting from flocculation should be rich in asphaltenes and resins, hence of higher specific gravity. In wax crystallization, in general, larger molecules lose kinetic energy and crystallize first. Any large n-paraffin molecules present would crystallize together with large asphaltene and resin molecules and possibly along with asphaltene-resin micelles, heavy aromatics, and heavy naphthenes. Hence, in general, organic deposits caused by flocculation should contain primarily asphaltenes and resins, whereas organic deposits caused by crystallization should contain a mixture of all type of heavy molecules present in the oil, including n-paraffins in the C20 to about C75 range. Asphaltenes, as defined by separation with the conventional solvents, co-precipitate from oil with the normal paraffins as the oil cools. Since cooling reflects a lowering in the kinetic energy of the molecules and asphaltene micelles present in the oil, it is evident that asphaltene micelles when they are in tact behave like large molecules themselves. This is primarily due to the interactions of the alkyl groups attached on the resin and asphaltene molecules with the normal paraffins. The crystallization of crude oil heavy molecules as the temperature drops is apparently a molecular-thermodynamic phenomenon caused by van der Waals type attractive forces. Hence, asphaltene micelles precipitate from the oil along with other heavy molecules as the temperature drops by forming amorphous crystals. It is evident then that this mechanism of asphaltene precipitation is not due to asphaltene flocculation as described earlier but it is rather due to conventional “molecular-thermodynamic” crystallization. Three crystalline

forms of wax are generally recognized, i.e., plate form, needle form, and mal or imperfect crystal formations12. Nelson13 suggests that the crystalline behavior of wax stocks is dependent upon the properties of the crystallizing medium. That is if the oil is viscous (usually because it contains high amount of resins and asphaltenes), the crystals will be small and spherical and thus an amorphous wax results, see Figure-3.

Figure 3: Amorphous Wax Particles Photographed at 50X. The oil contains asphaltenes and resins. Particle sizes vary from approximately 0.001 to 40 µ. If the oil is fluid, the crystals are large and needle or plate like and a pressible type of wax results, as shown in Figure-4.

Figure 4: Needle-like Wax Particles. The oil does not contain asphaltenes and resins. Needle and plate crystals from paraffinic oils can grow to large sizes.

4 [SPE 92958]

In addition, he believed that bituminous or high-boiling materials inhibit crystallization of wax. Typical wax psd have been estimated from centrifugation settling curves to range from 2 micron to 8 micron radius using Stoke’s Law19. The median of the estimated wax psd’s ranged from 2 micron to 6 micron radius. It is noted, however, that the particles in the above centrifugation tests had plenty of time to aggregate and form larger complexes (chemically untreated waxes do interact with each other) which may have biased the above estimates towards higher medians. Since asphaltene and most field wax particles are spherical, their sedimentation characteristics can be approximated fairly accurately using Stoke’s law or a similar theory. The asphaltene and wax particle size distribution (psd) must of course be determined prior to addressing the sedimentation of the particles. In this paper, we will only be concerned with the sedimentation characteristics of particles of known psd, be it asphaltenes or waxes. The psd can be obtained via experiment or simulation. There are asphaltene and wax models that provide a theoretical framework for correlating particle psd to thermodynamics14, 17, 18. Relevant Sedimentation Theory There are several good textbooks that cover colloidal chemistry15, 16 which the reader may use as a reference to the concepts presented here. A solution is called colloidal if some of the constituents exist in it as aggregates of molecules rather than single molecules. Colloidal solutions or suspensions can exist in all phase combinations of gas, solid, or liquid for the suspension medium and the suspended materials. Colloidal solutions or suspensions with very fine particles have some properties that are similar to those of true solutions, however, they continue to have properties particular to colloidal solutions such as: turbidity, refraction and reflection of light, Brownian motion, etc. Crude oils seem to fall in this category. In colloidal systems the particle size of the dispersed phase may vary anywhere from 1.0 nm to 1000 nm. In crude oils the size of the original asphaltene particles in suspension is apparently less than 65 Å or 6.5 nm5. The lower limit of the molecular size of colloidal systems comes by considering the fact that upon further granulation of a substance a solution no longer contains aggregates of molecules but the molecules themselves. Therefore, the lower particle size limit of a colloidal solution depends largely on the size of the individual molecules that make up the colloidal particles. There is relative difficulty in establishing the limits of some colloidal systems because the individual molecules that make up the particles are not identical. Such systems are called poly-disperse colloidal systems and one example of them is the asphaltene particles in oil. The asphaltene sub-units that make up the particles are not identical because of the variety of ways that the elements that comprise them can bond with each other. The derivation of the required equations to calculate the sizes of the suspended and sedimented particles in colloidal systems is presented next.

A. Stoke's Law Spherical particles tend to settle under the influence of gravity in quiet fluid mediums. The gravity force is given by:

34 ( )3g p p fF r gπ ρ ρ= −

1 Stoke’s law gives the frictional fluid force that resists the fall of particles:

6f pF rπ µυ= 2

The gravitational force causing the particle fall is constant. The frictional force resisting the fall is a function of the velocity, as shown in equation 2 above. When the values of Fg and Ff are equal a limiting velocity of fall is obtained. Equating equations 1 and 2 one obtains this limiting velocity as:

22 ( )9

pp f

g rυ ρ ρ

µ= −

3 It is important to remember that in the derivation of the above equation, the following restrictions apply:

1. The gravitational force is taken as constant 2. The sedimenting particles are considered to be

spheres 3. There is no diffusion or hindered settling. That is the

settling of the particles is not influenced by the presence of other particles or molecules.

4. There are no convection currents present in the fluid. Limitations 3 and 4 were imposed in the derivation of Stoke’s Law, equation 2. B. Sedimentation Equilibrium Another mathematical approach to the settling of colloidal particles, bypassing Stoke’s Law, can lead to other useful equations. In this derivation the effects of convection currents are neglected and the particles are considered to be settling under the influence of gravity and diffusing upwards under the influence of the concentration gradient produced. These two forces are always in effect and the resulting two microscopic processes go on indefinitely. However, when they exactly neutralize each other, no macroscopic change will be perceptible, and a state of equilibrium is achieved. Thus, at any level in the oil mixture the amount settling under equilibrium conditions must equal the amount diffusing upwards across this same level. The flux due to settling, because of the gravity force, is given by:

g cυΨ = 4

Where: υ is the settling velocity, and c is the concentration at the given level. The settling particles are under the influence of two forces the gravity force, Fg, and the resulting opposing and equal friction

[SPE 92958] 5

force, Ff. Fg, is given by equation 1. Another form of equation 1 is:

(1 )fg p

pF m gρ

ρ= − 5

Where: mp, mass of single particle The resulting opposing and equal friction force, Ff, is given by:

2 31 2 3 ...........fF ϕ υ ϕ υ ϕ υ= + + +

6

For small settling velocities, such as in the case of settling colloidal particles, all the nonlinear terms of Ff are negligible. Combining equations 4, 5, and 6 one gets:

1(1 ) /fg p

pm g cρ ϕρΨ = −

7 Fick's first law of diffusion gives the upward flux, due to diffusion:

( )dcDh∂

Ψ = −∂ 8

Where: D, is the diffusion coefficient

h, is height As mentioned, at equilibrium the two fluxes shown in equations 7 and 8 must be equal and opposite, hence:

1(1 ) / ( )fp

p

cm g c Dh

ρ ϕρ∂

− = −∂ 9

Rearranging and integrating yields the following:

( ) 1ln 1 /fp ref

ref p

c m g h h Dc

ρϕ

ρ

= − − −

10

This expression gives us the equilibrium distribution of the settling colloidal particles in the fluid. Einstein's law of diffusion15, 16 is:

1D k Tϕ = 11 Where: k, is the Boltzmann constant

T, is temperature Combining equations 10 and 11 gives:

( )ln 1 /fp ref

ref p

c m g h h k Tc

ρρ

= − − −

12

This equation is more convenient to use for determining equilibrium particle distributions because it does not require knowledge of the diffusion and friction coefficients. Equation 12 can be transformed in completely macroscopic terms by multiplying both m and k by Avogadro's number NA to get the molecular weight MW of the particles and the universal gas

constant R:

( )ln 1 /fref

ref p

c MW g h h RTc

ρρ

= − − −

13

Where:

• ( ) 34

3 A p pMW N rπ ρ= 14

• NA is Avogadro's number 6.0225x1023 • g is gravity acceleration constant, 980.665 cm/sec2

• R is universal gas constant, 82.057 (cm3-atm)/gmole-°K)

• T is temperature in °K For a set of particle sedimentation criteria, equations 13 and 14 yield the critical particle size (or critical particle molecular weight, MWcrit,), which is the smallest particle that settles under the force of gravity. The sedimentation criteria are a specified particle concentration change c/cref at a specified height change h-href. They specify how quickly the concentration of sedimented particles drops off as the container is ascended. A sharp change in the concentration of settled particles occurs at the interface of the settled phase with the supernatant fluid. This is indeed a somewhat arbitrary decision of the observer because the concentration of the particles of a given size changes smoothly when the container is ascended. Hence, what one may call interface of asphaltene and supernatant liquid phases is dependent on what one defines the sedimentation criteria to be. With enough experience one can determine a good set of sedimentation criteria, as shown later in the two case histories. It is apparent that settled particles are much closer to each other than suspended particles, which are above the interface. The settled particles are packed or compacted to some degree as defined by the packing factor, discussed later in section D. It is also apparent that within the settled phase the packing factor of the particles is a function of height in the container due to the overburden. Hence, one can only talk of an ‘average packing factor’. C. Particle Size Distribution To compute the fraction of settled and suspended particles at sedimentation equilibrium, the total amount of asphaltene and/or wax particles and their particle size distribution is required. As mentioned previously, particle sizes can be determined experimentally. However, there are asphaltene and wax phase behavior simulators that can calculate the total amount and size distribution of the asphaltene and/or wax particles17, 18. There is experimental and modeling evidence that supports the idea that asphaltene and wax particles are gamma distributed. This is partly due to the fact that the Gamma Distribution provides high flexibility in representing such data. The Gamma Distribution is given below.

6 [SPE 92958]

( ) ( )αβ α

βα

Γ=

−−x

exxf1

15

Where: α and β are constants related to the mean and standard deviation and are always greater than 0 σ ≡ standard deviation, σ2 = αβ2 µ ≡ mean, µ = αβ Γ(α) is the gamma function given by the formula:

( ) ∫∞ −−=Γo

tdtet 1αα 16

Note that for x ≤ 0 always f(x) = 0. Existing data indicate that σ and µ of the asphaltene and wax particle size distribution are a function of the thermodynamics of the system. D. Particle Packing Factor As discussed previously, the settled particles are much closer to each other than the suspended particles, which are above the interface. Also, the packing factor of the particles, which are below the interface, is a function of height in the container, because the overburden weight of the particles and liquid causes them to be compacted. Hence, one can only talk of an ‘average packing factor’. This section addresses the packing process of asphaltene and/or wax particles as they settle in storage systems. The void space in the settled asphaltene particle mass is filled with suspension medium, which in crude oil cases is a liquid. This liquid is part of the total precipitate and needs to be accounted for when estimating the total amount of precipitate (or settled mass) under gravity settling. The fraction of total volume occupied by the particles is called the Packing Factor (PF). The packing factor is the opposite of porosity. Porosity refers to the fraction of void volume. Hence, PF is equal to one minus Porosity. For spherical asphaltene and/or wax particles, the packing factor can be calculated for different packing arrangements that the particles may have. Given the volume of the settled average size individual asphaltene and/or wax particles, the packing factor can be used to calculate the volume of the total settled mass or precipitate under gravitational forces. The PF is defined as15, 16:

1 PVolume of ParticlePacking Factor PF orosityVolume of Unit Cell

≡ ≡ = − 17

i. PF for a Body-Centered Cubic (BCC)

6802.04

38

34

342

33

3

==

≡π

π

r

rxPF

ii. PF for a Face-Centered Cubic (FCC)

7405.04322

24

344

3

3

==

≡xr

rxPF π

π

iii. PF for a Simple-Cubic Structure (SCS)

( )52.0

23

4

3

3

=

≡r

r

PF

π

A limited number of studies indicate that asphaltene particles pack in a sub-SCS arrangement with a PF = 0.15 to 0.52. But as discussed earlier in section B, because the settling is done under the force of gravity without any compaction, one can only talk of an ‘average packing factor’ because the packing factor is a function of height in the container. Also, because the asphaltene and wax particles are poly-dispersed, the larger particles settle first and thus get packed more tightly. Sedimentation Modeling In this section, an application of the previous concepts, equations, and modeling methodology for the simulation of sedimentation of asphaltene and wax particles in storage systems is presented. Two field examples are discussed: a 250,000-barrel of oil storage tank and a 1,000,000-barrel FPSO. A. Case History - 250,000-Barrel Tank i. Prinos Field The case presented here is a 250,000-barrel crude oil storage tank used for temporary storage of asphaltenic Prinos crude oil3. The Prinos field suffered major subsurface and surface asphaltene problems during primary production3. The tank was used as a surge tank to temporarily store crude oil prior to off-loading it to crude oil tankers. Reference 3 gives a description of the Prinos field but some information is presented next for clarity. The Prinos Field was discovered in early 1974. Following development drilling and construction of the production facilities the first producing well was opened in July 1981. The producing formation is the middle Miocene sandstone with shale barriers in-between at a depth of 8600 feet and with a pay zone varying from 200 to 300 feet thick covering an area of about 6 square kilometers. The reservoir consists mainly of 4 different pay zones separated by shale barriers all in a dome configuration. The original reservoir pressure was 5,730 psig. The bubble point of the crude oil ranges from 1,100 to 1,250 psig. The GOR ranges from 800 to 900 SCF/BBL depending on the geographical location within the field. The oil is under-saturated intermediate base crude with a gravity of about 28 degree API. It is sour crude containing approximately 40% by weight H2S at the wellhead. The reservoir temperature is 262 °F. An analysis of the average

[SPE 92958] 7

reservoir effluent is given in Table 1.

Component Mole %H2S 35.64CO2 3.80N2 0.19C1 8.96C2 3.36C3 4.65

I-C4 1.07n-C4 3.10I-C5 2.37n-C5 1.80C6 3.65C7+ 31.41

Total 100.00

Prinos Oil Composition

Table 1: Prinos Oil Composition From the first day of production asphalt deposits were observed in the tubing, separators, pumps, strainers and other locations. Asphaltenes were simply everywhere. The Prinos asphaltene problem initially was so severe that it was thought it would kill the project economically. The company took a number of steps to alleviate the problem and to a good extend was successful in doing so. The first hint that there was accumulation of asphaltene deposits in the tank came about when after about six months of operation the operators observed that the tank was filling up much faster than originally. Subsequent level measurements and careful examination of the data showed that the tank had indeed accumulated a very thick deposit at the bottom. Since these particles need a quiet medium without convection currents and shear forces to settle and build-up, it was decided to install mixers, heating, and circulation capability to remedy the problem. This indeed solved the problem. ii. Sedimentation Equilibrium Simulation The asphaltene-informed reader is aware of the reversibility or irreversibility issue surrounding asphaltene flocculation. This issue has to do with the question of whether asphaltenes that flocculate from oil due to a thermodynamic change would de-flocculate and return to their original state if the original thermodynamic conditions were reinstated. Some Prinos oil data indicated that asphaltene flocculation was irreversible to some extent. From the author’s experience, in general, about 20% of the cases have exhibited some asphaltene irreversibility. However, there is currently no evidence that the actual sedimentation of asphaltene particles in tanks is affected by asphaltene flocculation reversibility or irreversibility. The nature of the asphaltene particles and their particle size distribution and packing factor may be different in each case but the sedimentation methodology presented here would be applicable. Also, once the particles form at some thermodynamic conditions during the flow of oil, the particles can and do separate from their original liquid due to their mobility difference. In general, flowing oil will not dissolve existing separated particles. Hence, these particles will settle when given a chance.

Recall that the sedimentation criteria are that a specified particle concentration change c/cref occurs at a specified height change h-href. The author has determined the following sedimentation criteria for defining the position of the interface of asphaltene and supernatant liquid phases: c/cref = 1.0x10-3

h-href = 1.0x10-2 cm to 1.0x10-3 These sedimentation criteria may change slightly in the future when more sedimentation data are available. Other model constants may change as well. Given the above set of particle sedimentation criteria, equations 13 and 14 will yield the critical particle radius (or critical particle molecular weight, MWcrit) which is the smallest particle that settles. The Prinos oil data relevant for these equations are: Stock Tank Oil Density = 0.887 g/cc Asphaltene Density = 1.06 g/cc Average Tank temperature = 62 °F All calculations for the Prinos oil 250,000 BPD tank case are summarized in Tables-4 and -5. The critical particle molecular weight, MWcrit, is calculated using equation 13 as 44,604. The critical particle radius is calculated using equation 14 as 51.1 Å or 0.00511 micron. Hence, all particles with radius equal or greater to 0. 00511 micron will settle in the tank at sedimentation equilibrium. If the asphaltene particle size distribution is known, a rather simple integration from a particle radius of 0.00511 micron to infinity will give us the fraction of the incoming asphaltene particles that settle in the tank. iii. Particle Size Distribution As mentioned previously, the theoretical considerations of this topic are not covered in this paper due to space limitations. However, this topic has been covered in the past14, 17, 18. The thermodynamic colloidal model of asphaltene or T-C Model14,

18 was utilized here to calculate the particle size distribution (psd) of the asphaltene particles and perform the integration of the psd from a particle radius of 0.00511 micron to infinity. One may obtain the asphaltene psd from other asphaltene models or even from experiment and continue the sedimentation calculations as described here. That is the T-C Model is not a prerequisite to this sedimentation modeling approach. According to the T-C Model, using the critical particle radius of 0.00511 micron, the fraction of the incoming asphaltene particles that settle in the tank is calculated to be 0.001824 lbs of asphaltene settled per lb of stock tank oil. The asphaltene psd is shown in Table 2. It is important to remember that, although the sedimentation calculation is done at tank conditions, the asphaltene psd calculation is recommended at the thermodynamic state where the asphaltene particle size is at its maximum. And that is the bubble point of the reservoir oil at the prevailing temperature, unless the oil is flashed through a choke from a pressure higher than the BP (but lower than asphaltene flocculation pressure). In that case, the T-C Model calculation is done at

8 [SPE 92958]

the choke upstream pressure and temperature. The basic idea here is that the particles, once flocculated, have no chance due to flow and mobility differences to come in contact with their original liquid and de-flocculate.

Dia., Micron Gamma Density0.002051 2.38E-020.010604 5.48E-020.025195 1.22E-010.044529 1.63E-010.066889 1.64E-010.090288 1.37E-010.112648 1.02E-010.131982 6.95E-020.146572 4.35E-020.155126 2.28E-020.181220 4.87E-020.281509 4.35E-020.452573 5.21E-030.679253 1.79E-040.941414 2.79E-061.215763 3.06E-081.477924 3.64E-101.704604 6.98E-121.875668 2.95E-131.975957 3.19E-14

Asphaltene Particle Size Distribution

Table 2: Prinos Oil Asphaltene Particle Size Distribution iv. Particle Packing Factor and Tank Build-up The oil flow to the tank was varying between 25,000 to 40,000 BPD. This converts to between 7,758,146 to 12,413,033 lbs/day of oil. Given the above 0.001824 lbs of asphaltene settled per lb of stock tank oil, the above flow rate yields 14,151 to 22,641 lbs/day of settled asphaltene, see Tables-4 and -5. At a density of asphaltene of 1.06 g/cc, the above converts to 38.1 to 61.0 BPD of settled asphaltene. With an estimated packing factor of 0.20, the above converts to 190.8 to 305.2 BPD of settled asphaltene sludge (this includes interstitial oil). Finally, this translates from 69,638 to 111,421 Bbls of settled asphaltene sludge in a year. For such a small fraction of asphaltenes settling, the material balance builds up fairly rapidly to an average of about 90,000 Bbls of asphaltene sludge yearly. The company had estimated that the tank had lost about half of its storage capacity, i.e., 125,000 barrels, to asphaltene accumulation in one and a half years of operation. The model in this case predicts 90,000 barrels for one year plus ½*90,000 barrels for half year which is 135,000 barrels of sludge build-up. Considering that no effort was made to tweak the model, this result is remarkable. B. Case History – 1,000,000-Barrel FPSO i. Far East Field In the early 90’s, Asphwax was hired to work on a serious offshore wax deposition problem in the Far East which we will call “Far East Project” for the purposes of this paper. The oil company was producing two fields through two separate offshore production and processing facilities into a floating production, storage, and offloading vessel (FPSO). Far East oils are notorious for their wax deposition propensity. A lab investigation had concluded that Oil A would pose mild and

Oil B would not pose any wax deposition problems during production. The operator in the Far East Project designed the facilities according to the above recommendation with Oil A assumed to cause and Oil B to not cause wax problems. At the time AsphWax was invited to work on this project, the facilities had been producing for a few years. The situation in the field, however, was that Oil A was causing no wax problems whereas Oil B was causing wax problems. The FPSO had lost an estimated half of its storage capacity to wax deposition caused from oil B. Regardless of the real reason for the erroneous recommendation from the lab investigation, the problems in the field came as a surprise, in reverse of expectations, and of higher severity. ii. Sedimentation Equilibrium Simulation Given the previous set of particle sedimentation criteria, as per equation 18, equations 13 and 14 will yield the critical particle radius (or critical particle molecular weight, MWcrit), which is the smallest particle that settles. The Far East Project oil data relevant for these equations are: Stock Tank Oil Density = 0.849 g/cc Wax Deposit Density = 0.94 g/cc Average Tank temperature = 75 °F All calculations for the 1,000,000 BPD oil FPSO case are summarized in Tables-4 and -5.

Oil Oil Oil OilCapacity Flow Rate Density Density Mass Rate

Case barrels BPD g/cc lbs/gal lbs/dayTank 250,000 25000 0.887 7.39 7758146Tank 250,000 40000 0.887 7.39 12413033FPSO 1,000,000 110000 0.849 7.07 32673425FPSO 1,000,000 130000 0.849 7.07 38614048 Table 4: FPSO and Prinos Case Data Settled Particles Settled Particle Particle Settled Particle Settled Settledper Weight Oil Particles Density Density Particles Packing Phase Phaselbs/lb lbs/day g/cc lbs/gal BPD Factor BPD bbl/year

0.001824 14151 1.06 8.83 38.2 0.20 190.8 696380.001824 22641 1.06 8.83 61.1 0.20 305.3 1114210.001114 36398 0.94 7.83 110.7 0.25 442.7 1615890.001114 43016 0.94 7.83 130.8 0.25 523.2 190968

Table 5: FPSO and Prinos Case Data (Continue from Table-4) The critical wax particle molecular weight, MWcrit, is calculated using equation 13 as 77,070. The critical particle radius is calculated using equation 14 as 63.8 Å or 0.00638 micron. All particles with radius equal or greater to 0.00638 micron will settle in the FPSO at sedimentation equilibrium. iii. Particle Size Distribution Since this is a wax crystallization case, AsphWax’s WAXModel was utilized to calculate the wax particle size distribution (psd). Also, some wax particle size distribution data was obtained with cross polar microscopic measurements on forming wax particles. This technology is now available from some fluid service companies. The data from the CPM

[SPE 92958] 9

can be fitted to a gamma distribution function to yield the wax crystal psd. The WAXModel calculated a critical particle radius of 0.00638 micron. The fraction of the incoming wax crystal particles that settle in the FPSO was calculated to be 0.001114 lbs of waxes settled per lb of stock tank oil. The wax particle psd is shown in Table 3.

Dia., Micron Gamma Density0.000053 5.60E-090.000276 1.50E-070.000657 1.44E-060.001161 5.91E-060.001744 1.53E-050.002354 2.87E-050.002936 4.22E-050.003440 4.96E-050.003821 4.57E-050.004044 2.99E-050.030137 1.08E-010.138757 7.87E-010.324031 1.04E-010.569541 1.50E-030.853479 5.66E-061.150618 1.16E-081.434556 2.50E-111.680066 1.04E-131.865340 1.37E-151.973960 7.38E-17

Asphaltene Particle Size Distribution

Table 3: Prinos Oil Asphaltene Particle Size Distribution iv. Particle Packing Factor and FPSO Build-up The oil flow to the FPSO was varying between about 110,000 to 130,000 BPD. This converts to between 32,673,425 to 38,614,048 lbs/day of oil. Given that 0.001114 lbs of wax settled per lb of stock tank oil, the above flow rate yields 36,398 to 43016 lbs/day of settled wax particles, see Tables-4 and -5. At a density of wax of 0.94 g/cc, the above converts to 110.7 to 130.8 BPD of settled wax. With an estimated packing factor of 0.25, the above converts to 442.7 to 523.2 BPD of settled wax sludge (this includes interstitial oil). Finally, this translates from 161,589 to 190,968 BBLS of settled wax sludge in a year. The company had estimated that the FPSO had lost about half of its storage capacity to wax accumulation in three years of operation. Conclusions and Recommendations This paper presented concepts and a modeling methodology for the simulation of sedimentation of asphaltene and wax particles in FPSOs, tanks, and other storage systems. It was shown that build-up of asphaltene and wax particles, generally known as crude oil sludge, can be predicted with the modeling methodology presented here. The following conclusions can be made:

1. The size of colloidal asphaltene particles in native asphalt and oil was determined to be less than 65Å. The lower size limit of the un-flocculated asphaltene particles Preston separated in his ultra-centrifugation experiments was 11 Å, which, at a density of 1.06 g/cc that he determined, corresponds to a spherical particle with molecular weight of 448. The higher size limit of the flocculated asphaltene particles

Preston separated in his ultra-centrifugation experiments was approximately 40 Å, which corresponds to a spherical particle with molecular weight of 21,500.

2. Centrifuging of pure oils is completely reversible and those particles settled by high centrifugal force nearly all return to their original state of dispersion upon removal of the centrifugal field.

3. The data indicate that their pre-flocculation sizes are in the range of about 10 to 15 Å. This corresponds to 334 and 1,128 molecular weight respectively, assuming asphaltene spherical colloids and an asphaltene density of 1.06 g/cm3. After flocculation, asphaltene particles emerge that are visible even by naked eye.

4. Wax precipitation often results in the formation of sub-micron wax spherical particles that also settle under the influence of gravity. Although paraffin waxes have specific gravities around 0.8 to 0.85, field waxes have higher specific gravities, usually higher than 0.9, because they co-precipitate with asphaltenes and resins, if present.

5. Typical wax psd have been estimated from centrifugation settling curves to range from 2 micron to 8 micron radius using Stoke’s Law19. The median of the estimated wax psd’s ranged from 2 micron to 6 micron radius. The particles in the centrifugation tests had plenty of time to aggregate and form larger complexes (chemically untreated waxes do interact with each other) which may have biased the above estimates towards higher medians.

6. Both flocculated asphaltene particles and crystallized wax particles agglomerate and form very large micron-level particles whose molecular weights run in the hundreds of thousands or millions. These large particles settle fairly quickly in storage systems.

7. Relevant theory dealing with the simulation of particle settling was presented here, as follows:

a. Stoke's Law b. Sedimentation Equilibrium c. Particle Size Distribution (Gamma

Distribution) d. Particle Packing Factor

8. Two case-histories were presented, as follows: a. 250,000-Barrel Onshore Tank b. 1,000,000-Barrel FPSO

9. The company had estimated that the FPSO had lost about half of its storage capacity to wax accumulation in three years. In the 250,000 Bbl tank case, the company had estimated that the tank had lost about half of its storage capacity to asphaltene accumulation in two years. Although the available data for modeling were meager, the reported field build-up rates match fairly well with the calculated rates in each case.

Nomenclature rp= radius of particle ρp= density of particle ρf= density of fluid

10 [SPE 92958]

g= acceleration due to gravity, 980.665 cm/sec2 µ= viscosity of fluid υ= velocity of fall of particle c= particle concentration at the given level Fg= gravity force Ff= frictional force mp= mass of single particle φi= friction coefficient D= diffusion coefficient h= height k= Boltzmann constant T= temperature, °K MW= molecular weight NA= Avogadro's number 6.0225x1023 R= universal gas constant, 82.057 (cm3-atm)/gmole-°K) α= Gamma Distribution Constant β= Gamma Distribution Constant σ= Gamma Distribution standard deviation M= Gamma Distribution Mean PF= packing factor

Subscripts p= particle ref= reference f= fluid g= gravity

Superscripts t= integration variable, Eqn-16 Acknowledgements This paper is dedicated to the memory of Professor Donald L. Katz of the Chemical Engineering Department at the University of Michigan, Ann Arbor, and of his student Floyd W. Preston. Dr. Katz’s work on this topic has been pivotal in recognizing the colloidal and particular nature of asphaltenes and determining their particle size distribution before and after flocculation. Dr. Ali Mansoori, my Ph.D. advisor, and I visited Dr. Katz in May of 1988 to discuss his views and enormous research on asphaltenes. Dr. Katz remarked about his colloidal approach to asphaltenes that “…I provided the ingredients and you baked the cake”. He gave me the unpublished Thesis of Floyd W. Preston with the request to publish some material on their behalf. I promised to the late Dr. Katz to do so and, although belatedly, this paper fulfills my promise. References

1. Richardson., “Modern Asphalt Pavement,” New York, 1905, J. Phys. Chem. 19, 241 (1915).

2. Nellensteyn, F. J., “The Colloidal Structure of Bitumens,” The Science of Petroleum, Oxford University Press, vol. 4, 2760, (1938).

3. Bleakly, W. B., “Prinos Field Offers Challenges,” Petroleum Engineer International, March 15, 1984.

4. Pfeiffer, J. P. and Saal, R. N.J., Asphaltic Bitumen as a Colloid System, J. Phys. Chem 44, 139. (1940).

5. Katz, D. L. and Beu, K. E., “Nature of Asphaltic Substances,” Ind. of Engin. Chemistry, 37, p. 195 (1945).

6. Preston, W. F., “Ultracentrifuge Investigation of Crude Oil,” M.S. Thesis, 1947, University of Michigan, Ann Arbor, Michigan.

7. Ray, B. R., Witherspoon, P. A., and Grim, R. E., “A Study of the Colloidal Characteristics of Petroleum Using the Ultracentrifuge,” J. Phys Chem. 61, 1296, (1957).

8. Neumann, H. J., Paczynska-Lahme, B., and Severin, D., “Composition and Properties of Petroleum,” Ferdinand Enke Publishers, Stuttgart, Germany, (1981).

9. Won, K.W., “Continuous Thermodynamics for Solid-Liquid Equilibria : Wax Formation from Heavy Hydrocarbon Mixtures,” Paper 27A presented at AIChE Spring National Meeting. Houston, TX. March 26, (1985).

10. Leontaritis, K.J., "The Asphaltene and Wax Deposition Envelopes," The Symposium on Thermodynamics of Heavy Oils and Asphaltenes, Area 16C of Fuels and Petrochemical Division, AIChE Spring National Meeting and Petroleum Exposition, Houston, Texas, March 19-23, 1995.

11. Soldan, A., Campagnolo, E., and Leontaritis, K. J., "Wax Crystallization vs. Asphaltene Flocculation. Different Organic Deposition Mechanisms Supported by Analysis of Field Deposits." The Symposium on “Heavy Organic Deposition in Gas and Oil Systems,” Area 16c of Fuels and Petrochemical Division, AIChE Spring National Meeting and Petroleum Exposition, Houston, Texas, March 9-13, 1997.

12. Ferris, S. W. and Cowles, H. C., "Crystal Behavior of Paraffin Wax". Industrial and Engineering Chemistry, November 1945, p. 1054.

13. Nelson, W. L., Chemical Engineering Series: Petroleum Refinery Engineering McGraw-Hill Book Company, Inc., New York (1936).

14. Leontaritis, K. J.: "Asphaltene Deposition: A Thermodynamic-Colloidal Model,” Ph.D dissertation, University of Illinois, Chicago, Illinois, (March, 1988).

15. van Olphen, H., “Introduction to Clay Colloid Chemistry,” The Science of Petroleum, Oxford University Press, vol. 4, 2760, (1938).

16. Mysels, K. J., “Introduction to Colloid Chemistry,” Robert E. Krieger Publishing Company, Huntington, New York, 1978.

17. AsphWax, Inc., petroleum industry wax course, "Wax Deposition Modeling", 1994 to present.

18. AsphWax, Inc., petroleum industry asphaltene course, "Asphaltene Deposition Modeling", 1994 to present.

19. Burger, E. D., Perkins, T. K., and Striegler, J. H., “Studies of Wax Deposition in the Trans Alaska Pipeline,” J. Petr. Tech., June, 1075 (1981).