Introduction to Crude Oil Wax Crystallization Kinetics: Process Modeling

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Introduction to Crude Oil Wax Crystallization Kinetics: Process Modeling Mohammed I. Zougari* and Terry Sopkow DBR Technology Center/Schlumberger, 9450 17 AVenue, Edmonton, Alberta, Canada T6N 1M9

We developed a method for measuring and monitoring the crystallization kinetics of waxy crude oils under quiescent milieu. Using a setup based on a cross-polar microscope (CPM), coupled with a high-resolution, autoranging picoammeter, power meter connected to a light detector and a high-definition-high-resolution image processing, we have been able to capture wax particle growth from 1 micron and higher sizes. Both isothermal and non-isothermal kinetics processes were studied. Analysis of the continuous wax particles nucleation, as well as their growth process, of various oil samples from different geographical locations is presented. Results indicate some degree of similarities to trends observed in crystallization kinetics described by both Ozawa (Polymer 1971, 12, 150) for non-isothermal kinetics and Avrami (J. Chem. Phys. 1939, 7, 1103) for isothermal kinetics. Empirical models for both isothermal and non-isothermal crude oils crystallization cases are introduced. Introduction Crystallization1,2

is defined as the process of formation of a crystal (an ordered state) from a disordered (e.g., gas) or partially ordered (e.g., liquid) state. All crystallization processes consist of nucleation3 and crystal growth.4 The crystals nucleation can be categorized into two groups: first, the spontaneous nucleation that can be generated in isothermal5-7 conditions as a random event in the sample; and second, the time-dependent nucleation, which can happen at non-isothermal8 conditions in the occurrence of a cooling rate process at the same or nonaltered phase. After nucleation, the process of growth commences till the steady state is reached. Historically, isothermal and non-isothermal crystallization have been well-investigated for a wide variety of constituents. Avrami5-7 (isothermal crystallization) and later Ozawa8 (nonisothermal crystallization based on the mathematical derivation of Evans9) were among the pioneers of this subject study. They triggered an extensive crystallization analysis process that is still ongoing to the most detailed and specific extent. Wax precipitation, due to temperature drop, as described and processed in this paper, is a well-known phenomenon that has been thoroughly studied both chemically and thermodynamically. Generally, crude oils consist of numerous types of hydrocarbons10 such as paraffins, aromatics, and resins. Specifically, wax present in crude oils is primarily composed of n-paraffins,11 isoparaffins,12 cycloparaffins,13 and aromatics, which usually do not exceed 0.1% in refined waxes.14,15 The challenge with the waxy crude oils crystallization kinetics is its compositional complexity. Contrary to the general polymer or simple wax constituent crystallization process, the crude oils composition based on carbon numbers ranges from C1 to C100 or higher.16,17 Another issue that increases the complexity of the crude crystallization kinetics analysis is the fact that there are additional organics that may precipitates concurrently18 with the wax, such as asphaltenes and scales. These elements may alter the process of crystallization and, therefore, may mislead the studied process, particularly in the case of live oils. There is also the potential that nonorganic compounds may be present, such as contamination from mud and water, which may also lead to detection limitation. * Corresponding author. Phone: (780) 577-1321. Fax: (780) 4501668. E-mail: [email protected].

In the oil industry, modest work has been done to investigate the wax crystallization process, which is of significant importance in the deposition process. Senra19 evaluated the application of theOzawa8 theory for the non-isothermal crystallization of n-paraffins in solution and concluded that solution-based crystallization could be accurately predicted using the Ozawa theory only over a certain range of relative crystallinity. This range decreased as the cooling rate of the system increased. Bennema20 investigated the growth and morphology of paraffin crystals both theoretically and experimentally. His research was based on the growth of pure odd n-alkanes (CnH2n+2, n * 2n), over a range of chain lengths with 15 e n e 41, from solution under the influence of additives. He found good agreement between predictions based on the Ozawa theory and experimental data. Volkova21 studied the bulk n-paraffin crystallization process and reported experimental findings at slow crystallization rates. Liu22,23 studied long-chain n-paraffins crystallization and concluded excellent agreement between experimental data and theory. Jou24 ran a comparison of Johnson-Mehl-AvramiKologoromov kinetics with a phase model and concluded similitude between both. Zhang25 developed a new equation evaluating kinetics parameters. Several other authors, including Kong,26 Supaphol,27,28 Avila-Orta,29 Mitchell,30 and Gransy,31 to mention a few, studied non-isothermal crystallization of different materials such as aromatics and n-paraffin and concluded a very similar trend as defined by Ozawa model. Waheed32 constructed a crystallization model based on molecular dynamic simulation. Blyuss33 introduced an approach to study the phase change process using a master equation in which the state of the crystallizing material was described by a cluster size distribution function. A large number of authors reported isothermal and non-isothermal crystallization results, which all fall within the Avrami5 or Ozawa8 models. The objective of this work is to initiate a fundamental understanding of the crystallization process in waxy crude oils, including particle growth and size distribution, while crossing the thermodynamic boundary conditions (wax locus). We developed a simple yet reliable method to measure and monitor the crystallization kinetics of waxy crude oil both isothermally and non-isothermally. Subsequently, based on the obtained experimental results, empirical models for both isothermal and non-isothermal crude oils crystallization cases are introduced.

10.1021/ie061002g CCC: $37.00 © 2007 American Chemical Society Published on Web 01/26/2007

Ind. Eng. Chem. Res., Vol. 46, No. 4, 2007 1361 Table 1. Analyzed Oils Information

µ (cP) F (g/cm3) WAT wax %a

Gulf of Mexico oil sample (GOM)

African oil sample

Middle Eastern oil sample

Asian oil sample

South East Asian oil sample (SEA)

0.35 0.76 32 1.4

0.78 0.80 37 4.3

1.60 0.82 40 7.6

17.00 0.86 46 9.3

22.00 0.87 51.00 10.40

a Wax % is based on whole n-paraffin distribution using high-temperature gas chromatography (HTGC).

As a starting point, we will only be dealing with n-paraffin wax crystallization kinetics in this paper. Experimental Section Oil Samples. In this work, five samples from different geographical regions with different compositional characteristics were selected and analyzed. Table 1 presents the characteristics of each of the supplied oils. The samples used for testing purposes were identified to be average available waxy light crude oils. It is of interest to evaluate the crystallization process of oils with low wax contents not only for study but also, as importantly, to validate the overall performance of the detection and measurement techniques and tools used. Figure 1 shows a comparison between compositions of all fluids based on the high-temperature gas chromatography (HTGC). The HTGC analysis shows a higher concentration of n-alkane carbon numbers in the South East Asian (SEA) oil sample compared to the Gulf of Mexico (GOM) sample. Moreover, the SEA, the Middle Eastern, and the African oil samples exhibit a particular dual-peak behavior distribution as well as a lower light-end concentration in carbon numbers. Comparing the concentration of n-alkanes in the oils with their wax content confirms that, the higher the concentration of n-alkanes in oil, the higher is their wax content. This concentration behavior has an apparent effect on the wax kinetics, as will be subsequently shown. Wax Detection and Measurement Device. A Linkam heating/cooling system, which delivers a cooling rate ranging from 0.01 to 30 °C/min with 0.01 °C/min increment step was used for this study. The available cooling rate mimics a wide range of transport process in the pipelines, where the temperature drops from reservoir conditions to the considered environment at a rate as low as 0.02 °C/min. The actual setup operating temperature ranges from -120 to 100 °C. The system is closed, insulated, and cooled by both a Peltier device and liquid nitrogen when extreme cooling is required (below -20 °C). Dry nitrogen gas is purged through the main chamber to avoid any vapor or condensate sticking to the pass-through windows. The sample placed in a crucible is heated/cooled through a stage attached to the Peltier device for direct heating/cooling. The Linkam device is coupled with a microscope that can be adjusted at magnifications of 10× and 50×. The magnification can even be expanded to 100× or higher. The total diameter covered by the 10× lens is ∼500 µm with a depth of view of ∼10 µm. A high-resolution, autoranging picoammeter, power meter model 1830C coupled with a model 818-SL detector are used to measure the transmitted light through the wax particles. A 640 × 480 and 8 bit camera is used to take pictures at a rate up to 30 f/s. All the cited components are connected to a computer through a data-acquisition system that processes the signal and the images and delivers the selected results in forms of data, graphs, and sets of images or video stream.

Figure 1. HTGC n-paraffins concentration comparison between analyzed oils.

Measurement Procedure. The processed sample volume ranges from 0.1 to 1 µL, which is small yet representative enough for this analysis, as will be shown through testing repeatability and particle growth magnitude. This volume range is first selected to avoid both particle cohesion and Brownian motion due to crystal particles size and shape; furthermore, the used volume is dictated by the detection limits. The sample, which is contained in the crucible, is enclosed within a controlled device that allows 3-D movement of the sample. For this analysis, all the oils are taken directly from the original flashed bottom-hole (live) oil sample and stored at either 35 °C above the available measured live wax appearance temperature (WAT) if available or a maximum of 80 °C, whichever is applicable. During the testing, heating and cooling processes can be repeated several times with the same sample in order to cover a wide range of cooling rates and avoid compatibility and reproducibility issues. To reduce and minimize any secondary precipitation from other organics or inorganics, we first opted for a stock tank oil or dead oil (no gas phase) analysis. Theory Crude Oils Crystallization Complex Kinetics Modeling: Non-isothermal Kinetics. The Ozawa model is expressed by eq 1,

(

Χr(T,λ) ) 1 - exp -

)

K(T) λn

(1)

where Xr(T) is the relative crystallinity, K(T) is the Ozawa crystallization rate function, n is the Ozawa exponent, and λ is the cooling rate. Equation 1 can be rewritten in an extended form34-37 for non-isothermal kinetics as formulated by eq 2:

[

(

Xr(T,λ) ) 1 - exp -C1∆T exp -

C2 T∆T

2

)( ) ] ∆T n λ

(2)

The relative crystallinity or relative change of phase, Xr(T,λ), depends on temperature, cooling rate, Ozawa exponent, and C1 and C2 parameters. Knowing that for eq 2 to converge ∆Tn+1 must be positive, adjustment needs to be made to the equation to avoid divergence. Hypothetically, if we consider the crystallization process as cumulative, then the crystallinity expression for two normal paraffins should be written as

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Xr(T,λ) )

(

[

1 - exp -(C1a + C2a)∆T exp -

)( ) ]

(C1b + C2b) ∆T n (3) λ T∆T2

Hammami38-40 analyzed the crystallinity of C25 + C28 and C44 + C50 compounds. He found acceptable agreement with the theoretical modeling procedure as described by eq 2. For complex systems, similar crude oils constituted numerous components; if we apply the same cumulative procedure and ignore any cross terms, the crystallinity can be expressed as

Xr(T,λ) )

[

m

1-

∏ i)1

( )( ) ]

m

exp -Cia∆T

∏ i)1

exp -

Cib

∆T

T∆T2

λ

n

(4)

(

K(θ) ) C′1n exp φ)

C′2n (θ + C′3n)θ

)

2

θn+1, θ )

(

T - Tmin , Tmax - Tmin

)

Tmax - Tmin n λ , C′1n ) C′1(Tmax - Tmin ) , λeff λeff C′2n )

C′2

Tmin , and C′ ) 3n (Tmax - Tmin)3 (Tmax - Tmin )3

In the above equations, θ is defined as the normalized temperature, φ is the normalized cooling rate, and λeff is the effective cooling rate that represents the highest cooling rate at which the earliest wax particle would appear (WAT). Any cooling rate slower than λeff would show the same WAT and same kinetics profile. In many cases, we found λeff ≈ 0.1 °C/ min. Results and Discussion

or

Xr(T,λ) )

[

1 - exp -

( )( ) ] m

m

Cia∆T exp ∑ i)1

Cib ∑ i)1

∆T

T∆T2

λ

n

(5)

where m represents the number of pure-compound normal paraffins available in the analyzed oil. Unfortunately, there is no available data for complex systems that would confirm the above modeling approach described by eq 4 or 5. Moreover, the above mechanism does not take into consideration any effect or interaction of other available oil constituents such as isoparaffins and other nonparaffinic elements. Therefore, at this stage of the analysis, we made the following assumptions, which simplify the preliminary modeling procedure: 1. The crystallization process in crude oil is cumulative; that m m C Cia ) C′1 ∑i)1 is, ∑i)1 ib ) C′ 2. 2. Only crystallization of n-paraffins is considered. In other words, no isoparaffin or cycloparaffin crystallization is taken into account. 3. No other precipitation such as asphaltene or scales occurs. 4. Because of the compositional gradient of the waxy crude oils, equilibrium (maximum) temperature is taken to be Tmax ) 80 °C assuming that, at this temperature, all the waxes/nparaffins are melted or dissolved. 5. No growth exists beyond Tmin ) -110 °C. Upon applying these assumptions, eq 5 becomes

[

(

Xoil(T,λ) ) 1 - exp -C′1 ∆T exp -

C′2 T∆T

)( ) ]

2

∆T n λ

(6)

where ∆T ) T - Tmin. At this stage of the study, C1′ and C2′ are empirically defined. For mathematical modeling simplicity and adaptation, eq 6 was rearranged into the following dimensionless (or normalized) format,

(

Xoil(θ,φ) ) 1 - exp where

)

K(θ) φn

(7)

The produced signal in the measuring device represents the actual light output extracted from the light transmittance through the oil and formed crystal particles. The signal is then processed, generating a graph that shows either the transmitted light through the detector or the total measured wax surface from the image processing, or what we will report later as absolute crystallinity, as a function of temperature and/or time. The light transmittance represents the amount of available crystals as a function of temperature and time. When there are no crystals, there is no transmittance. Figure 2a illustrates the actual light power in watts. The images are independently analyzed using in-house software that measures the total surface occupied by the wax particles. Figure 2b illustrates some of the images taken during the SEA oil sample cooling at 1 °C/min. Reproducibility and Compatibility Validation. One of the most important factors that may affect the output signal is the sample homogeneity. Therefore, a systematic analysis was performed to evaluate the wax crystallization reproducibility using different portions from the same oil sample. Results show excellent profile reproducibility as provided by Figure 2a. Four subsamples from the same oil sample were used for this analysis, where a cooling rate of 20 °C/min was applied. The reproducibility in this particular reported case, and for all other analyzed samples, was excellent. This preliminary analysis led to the validation of the sample preparation procedure as well. As mentioned earlier, because of the Brownian motion, although minimized by sample containment, there is still the potential of particles moving out of the field of view, especially at very low temperature. This phenomenon caused some noise effects, as observed in Figure 2a. Cooling-Heating Cycle. Figure 3 shows a cooling/heating cycle of crystallization process for the GOM oil sample. The heating followed the cooling process instantaneously to close the cycle. The lower curve represents the cooling, and the higher curve represents the heating. The wax dissolving or melting is a slower process. Analysis and Wax Crystallization Kinetics Investigation. The data will be presented in the following two formats: (i) power transmittance, which will be referred to as absolute crystallinity, and (ii) normalized power transmittance, which will be referred to as relative crystallinity. First, the SEA oil sample, as shown in Figure 4, was tested at the following selected cooling rates: 0.5, 1.0, 2.0, 5.0, and 10.0 °C/min. From the provided data, a similar qualitative trend of the light response is observed as seen in polymers and/or the n-paraffins crystallization. The crystallinity equilibrium, as

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Figure 2. (a) Crystallization process: reproducibility validation. (b) SEA oil sample image from kinetics test with cooling rate of 1 °C/min.

shown, is very dependent on the cooling rate. The faster the cooling rate, the lesser is the crystallinity. The crystallization process speed, as mentioned earlier, is very slow when compared to the normal paraffins crystallization. Figure 5 demonstrates the normalized measured LPD crystallinity of the SEA oil sample. The crystal growth is very slow yet very much dependent on the cooling rate, as observed in the case of polymers or normal paraffins. The growth depends on the composition strength and wax concentration. We know from high-temperature gas chromatography that the SEA

n-paraffin peaks are located around C27 and C55 with the distinction of a broad carbon number distribution. The second series of wax crystallization tests were performed on the GOM oil. Results as shown in Figures 6 and 7 for both absolute crystallinity and relative crystallinity, respectively, indicate the same trend as observed for the SEA sample, with the distinction of lower light power transmittance. This can be explained by the lesser wax content in the GOM oil and the noticeable regular gap between profiles as cooling rate increases. For the GOM oil sample, the performed cooling rates were 1,

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Figure 3. Crystallization process: cooling/heating cycle for GOM oil sample.

Figure 6. Absolute crystallinity of GOM: from 1.0 to 20 °C/min.

Figure 4. Absolute crystallinity of SEA: from 0.5 to 10 °C/min.

Figure 7. Relative crystallinity of GOM: from 1.0 to 20 °C/min.

Figure 5. Relative crystallinity of SEA: from 0.5 to 10 °C/min.

2, 4, 6, 8, 10, 15, and 20 °C/min. For a 20:1 ratio in cooling rate, the amount of total crystallized particles or entities was twice that of the SEA oil sample. As previously mentioned for the SEA oil sample, the cooling rate has a strong effect on the crystallization process both qualitatively and quantitatively. It should also be reiterated that the process of crude oil crystallization is contingent on the composition of the processed crude oil. The light-end chemical compounds (C1-C7) of the original oil play an important role in defining the crystallinity process of the oil heavy ends from C14 to higher carbon number. For instance, if an oil sample is heated enough to a level where some or all of the light-end components are evaporated, then the outcome of the cooling (at any rate) will be different from a similar sample of the same oil where no or less light ends were lost. This fact just adds to the complexity of the empirical model of the

Figure 8. Absolute crystallinity of African oil: from to 20 °C/min.

crystallization process of the crude oil. Brown41 reported similar observations. The crude oils composition is very complex, heterogeneous, and limited in crystallinity. Therefore, it should not be surprising that the cooling process can go beyond usual (below ambient) conditions to achieve equilibrium or steady state. From Figures 4 and 6, it can be concluded that the procedure of crystallization of crude oil follows the same qualitative trend of polymer or pure n-paraffin compounds crystallization. Similar to polymers, the cooling rate has an apparent consequence on both growth speed and wax growth density. Figures 8 and 9, 10 and 11, and 12 and 13 show, respectively, the absolute and then relative crystallinity for the African, Middle Eastern, and Asian oils recorded at a cooling rate of 1-20 °C/min. Furthermore, Figure 14 shows relative crystallinity of several oils with different chemical compositions,

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Figure 9. Relative crystallinity of African oil: from 1.0 to 20 °C/min.

Figure 12. Absolute crystallinity of Asian oil: from 1.0 to 20 °C/min.

Figure 10. Absolute crystallinity of Middle Eastern oil: from 1.0 to 20 °C/min.

Figure 13. Relative crystallinity of Asian oil: from 1.0 to 20 °C/min.

Figure 11. Relative crystallinity of Middle Eastern oil: from 1.0 to 20 °C/min.

thermodynamic properties, and wax contents. The profiles show the randomness of the response to a single cooling rate of 1 °C/min. All the analyzed oils seem to exhibit the same behavior in response to cooling rate with different crystallization speeds. As mentioned earlier, the crude oil wax kinetics exhibits some unusual behavior, including slow response to cooling rates, very low crystallinity, narrow band crystallization rate, and remarkable low-temperature steady state or equilibrium state. Non-Isothermal Kinetics Model Validation. Following the above analysis, the next step was to test the existing crystallization theories associated with the crude oil nucleation and growth. The approach was to acquire the Ozawa crystallization rate function K(T) and the Ozawa exponent n parameters using

Figure 14. Relative crystallinity for several oil samples for a cooling rate of 1 °C/min.

the Ozawa model for non-isothermal crystallization kinetics. After laborious attempts, it was concluded that the original Ozawa theory could not be used for crude oil wax crystallization. Alternatively, a benchmark between the modified crude oil wax crystallization model represented by eq 7 and experimental data was then performed. The benchmark was carried out using the proposed oil samples. Results show good agreement between the modified model expressed by eq 7 and the experimental data, as presented in Figures 15-19. All benchmarked samples produced very satisfactory results with an error associated with the testing procedure, setup limitation, and actual modeling procedure not exceeding 15%. Consequently, we carried out a benchmark of eq 7 against several other oils non-isothermal crystallization response experimental data, and the results revealed similar trend and accuracy.

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Figure 18. Crystallinity model validation of Middle Eastern oil sample. Figure 15. Crystallinity model validation of SEA oil sample.

Figure 16. Crystallinity model validation of GOM oil sample.

Figure 19. Crystallinity model validation of Asian oil sample.

Figure 17. Crystallinity model validation of African oil sample. Figure 20. Isothermal absolute crystallinity of GOM oil with 1 h hold.

Isothermal Crude Oil Wax Kinetics. Analysis related to isothermal crystallization kinetics was performed on the GOM and SEA oil samples. The study revealed consistent kinetics response. The tests were performed such that a high cooling rate (20 °C/min) with a maximum temperature drop step of 5 °C was applied to minimize or avoid non-isothermal kinetics effects. Tests were performed from 50 to 20 °C with 1 h hold. Figures 20 and 21 show the response from the GOM oil sample and Figures 22 and 23 show the response from the SEA oil samples, as isothermal absolute and relative crystallinity or total crystal growth at isothermal conditions, respectively. Data analysis confirmed the exponential form of the growth. However, after laborious attempts to apply the Avrami model, it did not yield any acceptable benchmark. Therefore, we investigated other alternatives. When normalizing the time, the data from

the GOM and SEA oils kinetics produced the following new isothermal crystallization kinetics model,

XIsothermal(θ) ) XIso-max(1 - exp(-A × θ0.5))

(8)

Xr-Isothermal(θ) ) 1 - exp(-A × θ0.5)

(9)

or

where Xisothermal(θ) is the actual isothermal crystallinity, Xr-isothermal(θ) is the relative isothermal crystallinity, Xiso-max is the steady-state isothermal absolute crystallinity, θ ) (t/thold), and A is a parameter computed experimentally and defined for the SEA oil sample as A ) -0.2Thold + 9.3 and for the GOM

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model was introduced based on an upgrade of the Ozawa model, with some parametrical modifications. The initial benchmark of the introduced model against the experimental data revealed good agreement. Isothermal crude oil wax kinetics experimentation and modeling was also introduced, and the preliminary modeling benchmark revealed similitude with the existing Avrami isothermal kinetics model. Although nucleation and growth of crude oil wax strongly depend on temperature, pressure, composition, and potentially production rate, it is still unclear how the nucleation and later the growth of nucleates under flow would affect the crude oil transport process and particularly the crude oil wax deposition problem and rheological behavior. Figure 21. Isothermal relative crystallinity of GOM oil with 1 h hold.

Figure 22. Isothermal absolute crystallinity of SEA oil for 1 h hold.

Figure 23. Isothermal relative crystallinity of SEA oil with 1 h hold.

oil sample as A ) -0.08Thold + 7.3 with a maximum error or deviation of 7%. Evidently, the parameter A ) -aThold + b is specific to an individual oil and, therefore, has to be evaluated through experimental data. Equation 10 represents a practical isothermal crude oil wax crystallization model formulated as follows:

Xr-Isothermal ) 1 - exp(-(aThold + b) × θ0.5)

(10)

Conclusion Introduction to crude oil wax nucleation and growth (isothermal and non-isothermal kinetics) analysis under a quiescent environment was discussed. Non-isothermal kinetics analyses using several crude oil samples from different geographical locations were performed. The study showed profiles similitude between crude oils wax kinetics and those observed from polymers and single n-paraffins compounds with an apparent slower kinetics for crude oils. A crude oil wax crystallization

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ReceiVed for reView July 31, 2006 ReVised manuscript receiVed December 1, 2006 Accepted December 12, 2006 IE061002G