Multi-Solid Model Modified to Predict Paraffin Precipitation

MULTI-SOLID MODEL MODIFIED TO PREDICT PARAFFIN PRECIPITATION

Ciencia, Tecnología y Futuro

MULTI-SOLID MODEL MODIFIED TO PREDICT PARAFFIN PRECIPITATION IN PETROLEUM FLUIDS AT HIGH TEMPERATURES AND PRESSURES

Juan-Carlos-M. Escobar-Remolina1*, Wilson Barrios-Ortiz2 and Gildardo Santoyo-Ramírez3

1, 2 Ecopetrol S.A. - Superintendencia de Yacimientos, Bogotá, Colombia 3 Gems Ltda, Bucaramanga, Santander, Colombia

(Received April 2, 2008; Accepted November 25, 2009)

thermodynamic structure has been modified in order to calculate cloud point, fluidity and amount of pre- Acipitated wax under a wide range of temperature conditions, composition, and high pressures. The model is based on a combination of ideal solution concepts, fluid characterization, and formation of multiple solid phases using Cubic State Equations. The experimental data utilized for testing the prediction capacity and potentiality of a model exhibit different characteristics: continuous series synthetic systems of heavy alkanes, discontinuous series,

and dead or living petroleum fluids with indefinite fractions such as C7+, C10+, C20+, and C30+. The samples were taken from the literature, petroleum fluids from the main Colombian reservoirs, and some samples of Bolivian fluids. Results presented in this paper show the minimum standard deviations between experimental data and data calculated with a model. This allows a progress in decision-making processes for flow assurance in reservoirs, wells, and surface facilities in the petroleum industry.

Keywords: multi-solid model, paraffin precipitation, high pressure and temperature, flow assurance.

* To whom correspondence may be addressed

CT&F - Ciencia, Tecnología y Futuro - Vol. 3 Núm. 5 Dic. 2009 35 JUAN-CARLOS-M ESCOBAR-REMOLINA et al.

n el presente trabajo se ha modificado una estructura termodinámica para el cálculo del punto de Enube, de fluidez y cantidad de cera precipitada en un amplio rango de condiciones de temperatura, composición y altas presiones. El modelo se fundamenta en una combinación de los conceptos de solución ideal, caracterización del fluido y de formación de fases sólidas múltiples empleando ecuaciones de estado cúbicas (EDEC). Los datos experimentales usados para probar la capacidad de predicción del modelo y su potencialidad tienen características variadas: sistemas sintéticos de series continúas de alcanos

pesados, series discontinuas y fluidos del petróleo vivo y muerto con fracciones indefinidas como C7+, C10+,

C20+, y C30+. Las muestras se tomaron de la literatura, fluidos de petróleos de los principales yacimientos Colombianos y algunas muestras de fluidos Bolivianos. Los resultados que se presentan en este trabajo muestran desviaciones mínimas entre los datos experimentales y los calculados con el modelo. Lo anterior permite por tanto, un avance en la toma de decisiones para aseguramiento del flujo en yacimiento, pozos y facilidades de superficie en la industria petrolera.

Palabras Clave: modelo multi-sólido, precipitación de parafinas, elevadas presiones y temperaturas, aseguramiento del flujo.

36 CT&F - Ciencia, Tecnología y Futuro - Vol. 3 Núm. 5 Dic. 2009 MULTI-SOLID MODEL MODIFIED TO PREDICT PARAFFIN PRECIPITATION

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CT&F - Ciencia, Tecnología y Futuro - Vol. 3 Núm. 5 Dic. 2009 37 JUAN-CARLOS-M ESCOBAR-REMOLINA et al.

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CT&F - Ciencia, Tecnología y Futuro - Vol. 3 Núm. 5 Dic. 2009 MULTI-SOLID MODEL MODIFIED TO PREDICT PARAFFIN PRECIPITATION

Table 1. Composition of oils used in this research work as taken from the literature

CT&F - Ciencia, Tecnología y Futuro - Vol. 3 Núm. 5 Dic. 2009 JUAN-CARLOS-M ESCOBAR-REMOLINA et al.

Table 2. Composition of Bolivian Crude oils used in the research work

Feeding composition (% molar) Component LCS-11 LCS-5 LCS-14H PIS-7H P10

C2 0,834 0,827 0,000 0,840 0,000 C3 0,569 1,128 0,582 0,573 1,141 C4 0,432 0,428 0,441 0,435 0,433 C5 0,348 0,345 0,356 0,350 0,349 C6 2,754 2,729 1,252 1,233 1,227 C7 5,811 5,758 4,861 5,055 5,031 C8 6,801 6,739 6,714 6,614 7,994 C9 6,014 5,959 6,361 6,057 5,821 C10 5,719 5,668 5,848 5,761 6,104 C11 5,052 5,006 5,166 5,258 5,234 C12 4,926 4,881 5,037 5,272 5,093 C13 4,847 4,945 5,102 5,170 5,146 C14 4,861 4,817 5,239 5,161 5,137 C15 4,727 4,805 4,958 5,006 4,861 C16 4,428 4,388 4,644 4,689 4,553 C17 3,811 3,882 4,114 4,052 4,034 C18 3,728 3,695 3,916 3,756 3,738 C19 3,172 3,144 3,244 3,292 3,181 C20 2,737 2,803 2,892 2,849 2,744 C21 2,605 2,667 2,752 2,711 2,611 C22 2,236 2,216 2,371 2,336 2,242 C23 1,979 2,039 2,104 2,073 1,984 C24 1,819 1,803 1,860 1,833 1,824 C25 1,600 1,586 1,636 1,685 1,604 C26 1,468 1,454 1,572 1,478 1,472 C27 1,413 1,400 1,445 1,423 1,416 C28 1,232 1,221 1,260 1,306 1,235 C29 1,129 1,119 1,155 1,137 1,132 C30+ 12,948 12,552 13,117 12,596 12,659

CT&F - Ciencia, Tecnología y Futuro - Vol. 3 Núm. 5 Dic. 2009 MULTI-SOLID MODEL MODIFIED TO PREDICT PARAFFIN PRECIPITATION Table 3. Oil Composition taken from the literature and used in this research work Table

CT&F - Ciencia, Tecnología y Futuro - Vol. 3 Núm. 5 Dic. 2009 JUAN-CARLOS-M ESCOBAR-REMOLINA et al. 0,072 0,326 0,312 0,662 0,944 0,852 3,720 93,111 H8-13 0,020 0,187 0,229 0,394 0,627 0,492 2,459 95,593 0,086 0,521 0,644 1,269 1,960 1,600 5,825 U9-11 U13-12 88,095 0,059 0,323 0,333 0,709 1,108 1,015 4,858 91,594 0,025 0,228 0,293 0,560 0,953 0,798 3,490 93,654 XC19-9 BC25-10 0,090 0,611 0,704 1,579 2,210 1,969 6,406 86,432 Q6-7 K5-8 0,090 0,611 0,704 1,579 2,210 1,969 6,406 86,432 0,056 0,283 0,369 0,775 1,381 1,211 5,444 90,481 Feeding composition (% molar) 0,013 0,237 0,451 0,782 1,594 1,157 4,760 T27-5 T32-6 91,170 0,007 0,103 0,200 0,398 0,890 0,739 3,681 93,990 YD29-4 Table 4. Composition of Colombian Crude Oils used in this research work Table 0,039 0,207 0,240 0,500 0,723 0,621 2,835 94,890 YB28-2 C3-3 0,020 0,139 0,174 0,351 0,653 0,565 2,784 95,316 S26-1 0,066 0,314 0,323 0,680 1,121 1,020 4,926 91,550 C2 C3 C4 C5 C6 i-C4 i-C5 C7+ Component

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CT&F - Ciencia, Tecnología y Futuro - Vol. 3 Núm. 5 Dic. 2009 JUAN-CARLOS-M ESCOBAR-REMOLINA et al.

Table 5. Constants of Equation (10) and correction factor for critical pressure

3F &ULWLFDO7HPSHUDWXUH 7F $FHQWULFIDFWRUȦERLOLQJ -4 M T f (13) Δ Cpi 0,2557Mi 4,4245*10 i i WHPSHUDWXUH 7E DQGVSHFL¿FJUDYLW\ Ȗ EDVHGRQKXQ- GUHGVRIH[SHULPHQWDOGDWDDQGFRUUHODWLRQVWDNHQIURP f [=] cal/mol, f [=] WKHOLWHUDWXUHDQGGDWDEDVHVIRULQVWDQFH1,67 5LD]L :KHUH¨Cpi > @FDOPRO.¨hi Ti and $O6DKKDI DVVKRZQLQEquation 10 K, and MiLVWKHPROHFXODUZHLJKWLQJPRO 7DEOHǻLVDQ\RIWKHDERYHPHQWLRQHGSURSHUWLHVDQG LVDIXQFWLRQRIWKHPROHFXODUZHLJKWMi.

RESULTS AND ANALYSIS

Crude oils presented in Table 1 Fusion properties 7KH:37RIWKHQLQHRLOVVKRZQLQ7DEOHDVWDNHQ )XVLRQSURSHUWLHVDUHQHFHVVDU\IRUWKHFDOFXODWLRQ IURPWKHOLWHUDWXUHZDVFRPSDUHGWRWKHPRGL¿HGPRGHO RISXUHVROLGIXJDFLW\Equation 7. 7KHVHDPRXQWV SUHVHQWHGLQWKLVSDSHU DQGWRRWKHUPRGHOVFRPPRQO\ KDYHEHHQHYDOXDWHGXVLQJGLIIHUHQWSURFHGXUHVLQFOX XVHGLQWKHFDOFXODWLRQRIWKHVROLGOLTXLGHTXLOLEULXP GLQJ31$DQDO\VLVLQIRUPHUSXEOLFDWLRQV7KLVZRUN WDNHVWKHFRUUHODWLRQVSURSRVHGE\(VFREDU5HPROLQD 7DEOHFRPSDUHVWKHPRGL¿FDWLRQWRRWKHUZHOONQRZQ PRGHOVVXFKDV/LUD*DOHDQDet al.,9DIDLH6DIWL et al.,7KHDYHUDJHDEVROXWHGHYLDWLRQSHUFHQWDJH EHWZHHQWKHH[SHULPHQWDO:37YDOXHDQGWKHYDOXHFDO- f 15760,33 (11) Ti 370,12 0,002403Mi FXODWHGZLWKWKHPRGHOVZDVIRXQG 7KHFDOFXODWHG

Mi ( :37WRJHWKHUZLWKWKHPRGHO$$'DUHVKRZQLQ7DEOH 139,67exp (0,008546 M i $FFRUGLQJWR7DEOHLQJHQHUDOWHUPVWKHPRGL¿HG PRGHOLVEHWWHUWKDQWKHIRUPHUPRGHO7KLVPRGHOKDV DQ$$'YDOXHWKDWGRHVQRWH[FHHGUHJDUGLQJWKH Δ h f 0,107834 M T f (12) i i i H[SHULPHQWDOPRGHO7KHUHLVQRGLIIHUHQFHIRUPDQ\RI

CT&F - Ciencia, Tecnología y Futuro - Vol. 3 Núm. 5 Dic. 2009 MULTI-SOLID MODEL MODIFIED TO PREDICT PARAFFIN PRECIPITATION

Table 6. Average Absolute Deviation (AAD) for experimental WPT and the values calculated with other models and this work.

Crude oil WPTExp. (K) Modified model Lira-Galeana, 1996 Vafaie-Safti, 2000

Oil 1 304,15 304,00 305,9 Oil 10 314,15 314,33 316,0 321,0 Oil 11 295,15 295,10 299,3 Oil 12 305,15 306,00 301,2 311,0 Oil 15 308,15 307,95 309,5 310,0 Bim 13 312,81 312,90 Mixture C 297,35 298,90 Mixture 1 303,35 303,90 Mixture 5 307,05 307,00 AAD (%)a all models _ 0,1350 0,8606 1,5660 AAD (%) this workb _ 0,1350 0,0934 0,1336

i=n aDAP% = (100/n) TPC /TPC ∑i=1 cali expi bOnly experimental points for each model are considered.

WKHÀXLGVVWXGLHGLQWKLVZRUN(YHQWKRXJKWKHDWPRV RIWKHGLVDGYDQWDJHVRIWKHYLVFRPHWU\PHWKRGWKH¿UVW SKHULFSUHVVXUHLVWKHYDOXHXVHGLQFDOFXODWLRQVGDWD SDUDI¿QFU\VWDOVFDQEHIRUPHGDWKLJKHUWHPSHUDWXUHVLQ DQGUHVXOWVVKRZDPRGHOLPSURYHPHQWWKDWLVFRQVLVWHQW WKLVFDVHDERYH& . 'XHWRWKLVFRPSOLFD- ZLWKIRUPHUPRGHOV,WLVDOVRVWURQJDQGFRPSHWLWLYHLQ WLRQWKHQH[WVWHSZDVWRSUHGLFWWKH:D[3UHFLSLWDWLRQ WKLVW\SHRIFRPSOH[SKHQRPHQD 3RLQWV :37 DVZHOODVSUHFLSLWDWLRQDQGFU\VWDOOL]DWLRQ UDWHVIRU%ROLYLDQFUXGHRLOVZLWKWKHLPSURYHGYHUVLRQ Crude oils presented in Table 2 RIWKHPRGHO7KHREMHFWLYHRIWKLVZDVÀRZDVVXUDQFH DQGFRRSHUDWLRQLQGHFLVLRQPDNLQJSURFHVVHVUHJDUGLQJ 7DEOHVKRZVWKHFRPSRVLWLRQ PRODU RIFUXGH oil production. RLOÀXLGVIURP%ROLYLDQUHVHUYRLUVWKDWZHUHDQDO\]HG DW0$*&23,&3$VPHQWLRQHGDERYHWKHÀXLGLW\ SRLQWV$3,JUDYLW\%6:YDOXHVZHUHPHDVXUHGWRDOORI 3DUDI¿QFRPSRXQGVRI%ROLYLD/&6 WKHVH%ROLYLDQFUXGHRLOV7KH\ZHUHDOVRVXEPLWWHGWR )LJXUHVKRZVWKHXQL¿HGFXUYHIRUSUHFLSLWDWLRQ UKHRORJLFDOWHVWVLQRUGHUWRGHWHFWWKHFORXGSRLQWRU:37 FU\VWDOOL]DWLRQFORXGDQGÀXLGLW\SRLQWIRUWKHVDPSOH E\YLVFRPHWU\7KHYLVFRPHWU\WHFKQLTXHFRQVLVWVLQWKH /&6,WLVZRUWKPHQWLRQLQJWKDWWKLVSUHFLSLWDWLRQ FRQVWUXFWLRQRIDYLVFRVLW\ORJDULWKPYDOXHJUDSKDJDLQVW SURSHUW\XQL¿FDWLRQLVDQHZFRQFHSWDSSOLHGWRWKLVZRUN WKHLQYHUVHYDOXHRIWKHDEVROXWHWHPSHUDWXUH7KH1HZ- 7KHFXUYHVKRZVDFORXGSRLQWRI. & DQG WRQLDQÀXLGSURSHUW\DWKLJKWHPSHUDWXUHLVXVHG VWUDLJKW - OLQH 2QFHWHPSHUDWXUHGHFUHDVHVDQGPLQXWHZD[FU\WDOV :37FRXOGQRWEHGHWHUPLQHGE\H[SHULPHQWDOUKHRORJL SUHFLSLWDWHWKH1HZWRQLDQÀXLGSURSHUW\LVORVWDQGD FDODQDO\VLV7KLVYDOXHLQGLFDWHVWKDWSUHFLSLWDWLRQIRUWKLV GHYLDWLRQZLWKUHJDUGWRWKHVWUDLJKWOLQHLVREVHUYHG7KLV FUXGHRLOLVLQLWLDWHGE\WKHKLJKPROHFXODUZHLJKWSDUDI¿Q SRLQWRIFKDQJHUHSUHVHQWVWKH:37)LJXUHVKRZVDQ PROHFXOHV DURXQGJPRO WKXVJHQHUDWLQJWKH¿UVW H[DPSOHIRUHDFK%ROLYLDQFUXGHRLOVDPSOHVVWXGLHG,Q VROLGFRUHVWKDWMRLQRWKHUSUHFLSLWDWLQJFRPSRXQGV SUH )LJXUHWKHZD[SUHFLSLWDWLRQSRLQWLVQRWFOHDU7KH VHQWLQJUHDWHUDPRXQW DVWHPSHUDWXUHORZHUVWRSURGXFH :37FRXOGQRWEHHVWLPDWHGHLWKHULQWKHYLVFRVLW\WHVWV WKHRSHUDWLRQSUREOHPVDWWKHNQRZQWHPSHUDWXUHYDOXHV DSSOLHGWRWKHUHVWRIWKHFUXGHRLOVDPSOHV7KLVLVRQH LQWKHSURGXFWLRQSLSHOLQHVDQGVXUIDFHIDFLOLWLHV

CT&F - Ciencia, Tecnología y Futuro - Vol. 3 Núm. 5 Dic. 2009 JUAN-CARLOS-M ESCOBAR-REMOLINA et al.

0,100

0,010

0,001 3.150000 3.250000 3.350000 3.450000 3.550000 3.650000 1000/T(K)

Figure 1. Rheological curve for the LCS-11 crude oil sample. No WPT is detected Y axis = Apparent viscosity

Figure 2. Precipitation and crystallization curve for the crude oil sample LCS-11. The WPT and Fluidity point are indicated Left Y axis = % weight; Right Y axis = % crystallized weight; X axis = Temperature (K)

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Table 7. Wax precipitation temperatures measured and calculated in this work (modified model) at different saturation pressure values

Saturation WPT Saturation WPT WPTC Pressure WPTC Pressure Oil pressure Exp. DT pressure Exp. Cal. DT (bar) al. (°C) Oil (bar) (bar) (°C) (bar) (°C) (°C) 1 29 120 31 32 -1 10 332 420 16 20 -4 15 32 34 -2 200 20 22 -2 1 34 35 -1 100 25 25 0 25 26 27 -1 1 28 31 -3 2 317 320 24 24 0 11 378 420 24 26 -2 100 26 27 -1 200 27 28 -1 50 28 30 -2 100 34 35 -1 20 28 28 0 50 39 42 -3 10 29 32 -3 25 40 43 -3 1 34 36 -2 1 42 42 0

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New Model 22

16 050100 150 200 250 300 350 400 450

Figure 3 Effect of pressure on wax precipitation temperatura for Oil 10. Comparison with the improvement (saturation pressure of 25 bars) Y axis = wax precipitation temperature (ºC); X axis = pressure (bar)

&UXGHRLOVDPSOHVLQ7DEOH FRPSDULVRQZDVPDGHZLWKVDPSOHV6DQG<% 7DEOHVKRZV&RORPELDQFUXGHRLOPL[WXUHV ,QWKLVFDVHWKHGLIIHUHQFHLVDQG& .DQG IURPRQHRIWKHPDLQ&RORPELDQUHVHUYRLUV:37ZDV . UHVSHFWLYHO\ 7DEOH ,QDGGLWLRQ7DEOH GHWHUPLQHGXVLQJWKHPLFURVFRSLFWHFKQLTXH6LPXODWLRQ VKRZVWKHPD[LPXPDPRXQWRISUHFLSLWDWHGZD[$3, UHVXOWVZLWKWKLVPRGHODUHSUHVHQWHGLQ7DEOH7KHPDU- ZHLJKWDQGVSHFL¿FJUDYLW\RIWKH&IUDFWLRQIRUHDFK sample studied. JLQRIHUURUEHWZHHQFDOFXODWHGYDOXHVDQGH[SHULPHQ- WDOO\IRXQGYDOXHVIRUÀXLGLW\SRLQWWHPSHUDWXUH )7 LV& . 6DPSOHVDUHFKDUDFWHUL]HGZLWK WKHNQRZQSURSHUWLHVRIWKH&IUDFWLRQ7KHDYHUDJH SK\VLFDOSURSHUWLHVIRXQGIRUWKHSVHXGRFRPSRQHQWV CONCLUSIONS RIWKLVIUDFWLRQLQFOXGHWKHIROORZLQJPROHFXODUZHLJKW VSHFL¿FJUDYLW\ERLOLQJWHPSHUDWXUHIXVLRQDQGHQWKDOS\ WHPSHUDWXUHFDORUL¿FFDSDFLW\DFHQWULFIDFWRUWHPSHUD- Ɣ $QLPSURYHPHQWWRDPXOWLVROLGWKHUPRG\QDPLF ture and critical pressure. PRGHOIRUSDUDI¿QSUHFLSLWDWLRQZDVGHYHORSHGLQWKLV ZRUNGHVFULELQJWKLVSKHQRPHQRQDWKLJKSUHVVXUH and temperature values in petroleum reservoirs. Pre- )RUWKH)7FDOFXODWLRQWKHSUHFLSLWDWLRQUDQJHRIWKH GLFWLRQVPDGHZLWKWKLVPRGL¿FDWLRQZHUHFRPSDUHGWR carbon number C 36ZDVXVHGZKLFKZDVFDOFXODWHGE\ H[SHULPHQWDOGDWDIRUGLIIHUHQWFUXGHRLOVDPSOHVDQG - RYHUO\LQJWKHÀXLGLW\SRLQWWHPSHUDWXUHVIRXQGH[SHUL VLPLODUUHVXOWVZHUHREWDLQHGZLWKSHUFHQWDJHVEHORZ PHQWDOO\LQHDFKSDUDI¿QSUHFLSLWDWLRQJUDSKFRUUHV $QDO\VHVZLWKWKLVLPSURYHGPRGHOIDFLOLWDWH SRQGLQJWRWKHVDPSOHVRIWKH&RORPELDQFUXGHRLO GHFLVLRQPDNLQJSURFHVVHVXQGHUGLIIHUHQWFLUFXP- ZHOOV)RUDOORLOZHOOVWKH:37WKUHVKROGEHJLQVLQWKH VWDQFHVIRUÀRZDVVXUDQFHDWSHWUROHXPORFDWLRQV carbon number C DQGWKHÀXLGLW\SRLQWRFFXUVLQ&36. )XUWKHUPRUHFRPSDULVRQVWRRWKHUFRPPRQO\XVHG - 1RUPDOSUHVVXUHDQGWHPSHUDWXUHYDOXHVZHUHDOVRFDO PRGHOVZHUHHVWDEOLVKHG7KHPRGL¿FDWLRQUHVXOWHG FXODWHGIRUFUXGHRLOVDQGIRULQVWDQFHDQH[SHULPHQWDO LQEHWWHUSUHGLFWLRQVZLWKUHJDUGWRWKHFDOFXODWHG

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Table 8. Comparison of this work results to the experimental data. Some properties for Colombian crude oil simulation are also shown

TPC (°C) TF (°C ) Wax. Max °API MW C30+ G.E C30+

Calc. Exp. Calc. Exp. % 60/60°F g/mol S26-1 52,0 52,0 19,0 18,0 2,0 42,6 587,861 1,047 YB28-2 61,6 55,6 25,6 27,0 4,3 37,3 594,263 1,000 C3-3 53,2 51,0 15,2 18,0 3,3 42,7 571,688 0,732 YD29-4 54,9 52,8 26,2 27,0 4,8 38,8 569,313 0,919 T27-5 58,2 55,0 25,8 27,0 4,4 38,9 588,311 0,967 T32-6 52,2 51,2 20,2 18,0 2,5 39,9 578,158 1,327 Q6-7 55,9 53,6 24,0 24,0 3,5 42,0 583,634 0,987 K5-8 54,0 54,8 18,8 21,0 5,0 39,1 587,713 0,947 XC19-9 53,2 53,8 30,5 27,0 3,2 39,5 584,773 0,941 BC25-10 57,0 53,4 24,6 27,0 3,3 40,9 580,485 0,964 U9-11 55,1 55,6 27,0 27,0 5,3 41,2 588,179 0,892 U13-12 55,0 54,2 24,4 27,0 3,5 38,8 586,442 0,933 H8-13 55,0 53,2 25,0 27,0 3,8 39,6 576,570 0,933

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