A Cubic Equation of State for Reservoir Fluids

Transcription

1 6th IASME/WSEAS International Conferene on HEAT TRANSFER, THERMAL ENGINEERING and ENVIRONMENT (HTE'08) Rhodes, Greee, August 0-, 008 A Cubi Equation of State for Reservoir Fluids AMIR AHMAD SHIRAZIMANESH, MOHSEN EDALAT Oil and Gas Center of Exellene, Department of Chemial Engineering University of Tehran Enghlab Ave., Tehran, P.O.Box: IRAN Abstrat: - In this study we derived a new ubi of state with a hard sphere repulsive term proposed by Hajipour and Edalat [18]. The parameters of the new are alulated using ritial properties and aentri fator. By using the repulsive term in the new liquid density of fluids an be aurately predited. Sine parameter is onsidered to be a linear funtion of aentri fator this of state an simply be applied to heavy hydroarbons and petroleum frations. The proposed of state predits vapor pressure of pure omponents as well as vapor-liquid equilibria properties of fluids within aeptable auray. The new of state predits vapor pressure more aurate than other ommonly used s of state suh as Guo-Du and Peng-Robinson s for reservoir fluids. This of state predits liquid density of normal alkanes from C 1 to C0 in the range T r = with the mean average absolute deviation of less than 1 %. Key-Words: - Cubi of state, Reservoir fluids, Vapor pressure, Saturated liquid density, Saturated vapor density, Temperature dependant ompressibility fator 1 Introdution Cubi s of state are ommonly used in reservoir simulation. Although it has been shown that, subjet to use of a proper alpha funtion, all ubi s of state an produe nearly the same auray of pure omponent vapor pressure and mixture vapor-liquid phase equlibria [1-4], the predition of volumetri properties is different from one to another. Three different strategies have been proposed to derease the deviations observed in the predited volumetri properties. 1. Inreasing the number of parameters whih are assumed to be temperature dependant [5-8].. Modifiation of the form of of state. 3. Using additional substane dependant parameters [9-10]. However the results indiate that ubi s of state require at least three parameters for a reasonable representation of both vapor and liquid volumes [11-1]. Also, the works of many researhers [13-16] showed that the optimum value of ompressibility fator of substane is not equal to the experimental ritial ompressibility of the fluids. As a matter of fat, mathing the ompressibility fator of an of state to the real ritial ompressibility fator of ompounds may impair the performane of in some regions of PVT spae [17]. In this artile, we propose a new four parameter ubi of state. All of the parameters of the new are alulated by T, P and aentri fator (Subsript denotes ritial property). The new ubi of state The of state proposed in this work has the following form: RT ( v 0.85 b) a d P vv ( b) vv ( ) vv ( b)( v) (1) a a () f ( T ) f ( T ) (3), r,1 r 5 4 3,1 1 1 r 1 1 r 1 1 r 11 r 11 r , 1 r 1 r 1 r 1 r 1 r f a T b T T d T e T f f a T b T T (4) (5) d T e T f and T r is redued temperature, is aentri fator and R is the universal gas onstant. The universal onstants used in s (4-5) are showed in table (1). In the development of the new, we used a simplified hard sphere of state proposed by Hajipour and Edalat [18] as the referene repulsive term beause as implied by several authors [19-0], use of a proper repulsive term has a signifiant ISSN: ISBN:

2 6th IASME/WSEAS International Conferene on HEAT TRANSFER, THERMAL ENGINEERING and ENVIRONMENT (HTE'08) Rhodes, Greee, August 0-, 008 effet on the improvement of predited liquid densities. A somewhat similar form has been proposed by Chien et.al. [0], but in the development of the new, in addition to hanges made to the repulsive and attrative terms, a different approah has been applied. Using the Abbot s method [1] and taking Z and b as the input parameters, the following s is obtained b (6) (7) Table 1 Constants used in s (4) and (5) a a b b d d e e f 1 0 f 1 a b b b a b d (8) P a a (9) RT P b b (10) RT P (11) RT P d d (1) RT In (6-7), denotes the apparent ritial ompressibility fator whih is taken as an input parameter and is alulated using the following f,( T ),1( ) r f T r (13) e f,1 a1 b1 1T 1 exp 1 r d Tr (14) f e, a b 1Tr d exp Tr 1 (15) Values of universal onstants used in s (14-15) are showed in table. The ovolume parameter (i.e. b ), whih is another input parameter in (1), is alulated as follows b RT P (16) It should be mentioned that the oeffiient has been obtained by a trial and error proedure to minimize observed deviations of vapor density. Table Constants used in s (14) and (15) a a b b d d e e 1 3 Results and Disussion 3.1 Pure fluid alulations In this setion a omparison between the results obtained using the new and those of two well known EOSs (Equations of State) are presented. All the vapor pressure, liquid density, aentri fator and ritial properties data used in the omparison were taken from DIP projet 801 []. Vapor density data are taken from two aurate of state [3,4]. Sine existing values of aentri fator in referenes, differs from on to another, in order to maintain onsisteny, we obtained the aentri fators of ompounds by using the vapor pressure s of the DIP. All the alulated AARDs (Average Absolute Relative Deviations) observed for eah ompounds has been obtained by omparing to experimental points that starts from T r =0.45uptoT r =0.99with redued temperature inrements whih is equal to 0.01, exept for those ompounds that their triple point temperatures are above the T r = Saturated liquid density Saturated liquid density of 43 pure omponents are ompared with experimental data as well as the preditions given by the 1, and the well known (Peng-Robinson) [5] and (Guo-Du) [6] s of state. Among 43 omponents, the new predits the saturated liquid density of 4 omponents better than all the other EOSs. The results obviously show the superiority of the new in omparison to the other above mentioned s. (Table (1) in Appendix (1)) 3.3 Saturated vapor density Sine aurate vapor density data are rarely found in the literature, we limited the number ompounds studied in this setion to 11 important reservoir fluids. As it an be seen in table (3) the new gives lower average deviations of vapor density than the, s of state. ISSN: ISBN:

3 6th IASME/WSEAS International Conferene on HEAT TRANSFER, THERMAL ENGINEERING and ENVIRONMENT (HTE'08) Rhodes, Greee, August 0-, 008 Table 3 Comparison of observed deviations for predited vapor density Component No. of points new AAD (%) AAD (%) AAD (%) C C C n-c n-c n-c n-c n-c n-c n-c n-c grand average Vapor pressure In table (1) of Appendix 1, the predited vapor pressures of 43 ompounds are ompared with the experimentalresultsaswellasthevaluespredited by the above mentioned s of state. One an see the overall superiority of the new. 4 Conlusion There are a few s of state that in their development, the ritial ompressibility fator has been assumed to be an input temperature dependant parameter, suh as EOS [5], PT (Patel and Teja) EOS [0] and more reently ER (Esmaeilzade and Roshanfekr) EOS [7]. The results obtained by the proposed in this artile, whih has been developed by the same assumption, shows that this approah reates a very flexible EOS that an predit muh better volumetri properties. However as it has been shown in the previous setion, the auray of results obtained using this method, espeially in the near ritial region, an impair overall apability of the due to improper mathing of the method and the form of EOS. Our obtained results, whih is obviously superior to two famous [5] and [6] s, show that this defiieny does not exist in the new and in fat the new is augmented onformity of the above mentioned method and general form of an of state. Referenes: [1] Twu, C.H., Coon, J.E., Cunningham, J.R., A new ubi of state, Fluid phase equilibria, Vol.75, 199, pp [] Twu, C.H., Coon, J.E., Cunningham, J.R., An approah for the extension of a 3-parameter ubi of state to heavy hydroarbons, Fluid phase equilibria, Vol.104, 1995, pp [3] Twu, C.H., Coon, J.E., Cunningham, J.R., A generalized alpha funtion for a ubi of state. Part.1. Peng-Robinson, Fluid phase equilibria, Vol.105, 1995, pp [4] Twu, C.H., Coon, J.E., Cunningham, J.R., A generalized alpha funtion for a ubi of state. Part.. Redlih-Kwong, Fluid phase equilibria, Vol.105, 1995, pp [5] Kumar, K.H., Starling, K.E., The most general density-ubi of state: Appliation to pure non-polar fluids. Industrial and engineering hemistry fundamentals, Vol.1, 198, pp [6]Adahi,Y.,Sugie,H.,Developmentofafive parameter ubi of state, Fluid phase equilibria, Vol.8, 1986, pp [7] Chu, J.Z., Zuo, Y.X., Guo, T.M., Modifiation of the Kumar-Starling five parameter ubi of state and extension to mixtures, Fluid phase equilibria, Vol.77, 199, pp [8] Lin, H.M., Chen, J.T., Ming, J.L., A ubi perturbed hard-hain of state, Fluid phase equilibria, Vol.16, 1996, pp [9] Trebble, M.A., Bishnoi, P.R., Development of a new four parameter ubi of state, Fluid phase equilibria, Vol.35, 1987, pp [10] Adahi, Y., Lu, B.C.Y., A four parameter of state, Fluid phase equilibria, Vol.11, 1983, pp [11] Adahi, Y., Lu, B.C.Y., Sugie, H., Three parameter ubi s of state, Fluid phase equilibria, Vol.13, 1983, pp [1] Cismondi, M., Mollerup, J., Development and appliation of a three parameter RK- of state, Fluid phase equilibria, Vol.3, 005, pp [13] Shmidt, G., Wenzel, H., A modified van der waals type of state,, Chemial engineering siene, Vol.35, 1980, pp [14] Patel, N.C., Teja, A.S., A new ubi of state for fluids and fluid mixtures, Chemial engineering siene, Vol.37, 198, pp [15] Valderrama, J.O., Cisternas, L.A., A ubi of state for polar and other omplex ISSN: ISBN:

4 6th IASME/WSEAS International Conferene on HEAT TRANSFER, THERMAL ENGINEERING and ENVIRONMENT (HTE'08) Rhodes, Greee, August 0-, 008 mixtures, Fluid phase equilibria, Vol.9, 1986, pp [16] Valderrama, J.O., A generalized Patel-Teja of state for polar and nonpolar fluids and their mixtures, Journal of hemial engineering of japan, Vol.3, No.1, 1990, pp [17] Sengers, J.V., Kayser, R.F., Peters, C.J., White, H.J., Equations of state for fluids and fluids mixtures, Elsevier, 000. [18] Hajipour, S., Edalat, M., A new two parameter ubi of state, Journal of phase equilibria and diffusion, Vol.xxx, 008, pp. xxx (published online). [19] Mohsen-Nia, M., Moddaress, H., Mansoori, G.A., Sour natural gas and liquid of state, Journal of petroleum siene and engineering, Vol.1, 1994, pp [0] Lin, H.M., Kim, H., Guo, T.M., Chao, K.C., Cubi hain of rotators of state and VLE alulations, Fluid phase equilibria, Vol.13, 1983, pp [1] Abbott, M.M., Cubi s of state, AIChE journal, Vol.19, No.3, 1973, pp [] Daubert, T.E., Danner, R.P., Sibul, H.M., Stebbins, C.C., DIP Data Compilation of Pure Compound Properties, Projet 801, Publi Release, Design Institute for Physial Property Data, AIChE, 001. [3] Span, R., Wagner, W., Equation of state for industrial appliations, International journal of thermophysis, Vol.4, 003, pp [4] Starling, K.E., Fluid thermodynami properties of light petroleum systems, Gulf publishing ompany, [5] Peng, D.Y., Robinson, D.B., A new two onstant ubi of state, Industrial and engineering hemistry fundamentals, Vol.15, No.1, 1976, pp [6] Guo, T.M., Du, L., A three parameter ubi of state for reservoir fluids, Fluid phase equilibria, Vol.5, 1989, pp [7] Esmaeilzade, F., Roshanfekr, M., A new ubi of state for reservoir fluids, Fluid phase equilibri, Vol.39, 006, pp ISSN: ISBN:

5 6th IASME/WSEAS International Conferene on HEAT TRANSFER, THERMAL ENGINEERING and ENVIRONMENT (HTE'08) Rhodes, Greee, August 0-, 008 Appendix 1 Table 1 Values of AADs (%) obtained for predited saturated liquid density ( ) and vapor pressures ( ). Component No. of points new new C C C n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c i-c 4 H i-c 5 H neopentane methylpentane methylpentane ylohexane methylylohexane ethylene propylene butene pentene hexene heptene Ar N O H S CO CO CH 3 Cl CHCl CCl grand average ISSN: ISBN: