PVTpetro: A COMPUTATIONAL TOOL FOR ISOTHERM TWO- PHASE PT-FLASH CALCULATION IN OIL-GAS SYSTEMS

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1 PVTpetro: A COMPUTATIONAL TOOL FOR ISOTHERM TWO- PHASE PT-FLASH CALCULATION IN OIL-GAS SYSTEMS A. M. BARBOSA NETO 1, A. C. BANNWART 1 1 University of Campinas, Mechanical Engineering Faculty, Energy Department Petroleum Division for contact: aneto@dep.fem.unicamp.br ABSTRACT The aim of this work is to show a computational tool capable of carrying out isothermal two-phase PT-flash using a multicomponent approach. PVTpetro consists of a compositional PVT simulator and it was developed to predict phase behavior and thermodynamic properties of hydrocarbon mixtures. One of the modules of this program is two-phase PT-flash, used for oil and gas systems. This is based on the modelling of vapor-liquid equilibria using cubic equations of state (EoS). Rachford-Rice equation was implemented, allowing the quantity and composition of each existing phase to be determined, whereas, for compressibility factor and fugacity of distributed components in each phase, SRK and PR EoS were applied. Results were compared to commercial simulators, so that the generated responses presented similar results. 1. INTRODUCTION Exploration and production in offshore reservoirs often mean working under extreme and complicated conditions. In this sense, phase behavior modeling of oil-gas systems is very important from an economical and environmental point of view. Phase equilibria calculations form the basis of a large range of petroleum and chemical engineering applications, such as compositional reservoir simulation, miscibility studies, wellbore and pipe flow and separation processes (Gaganis and Varotsis, 2014). When strong compositional effects are in system, these calculations are applied in fluid thermodynamic modeling (Qui, et al., 2014). In these cases, compositional simulation allows a more realistic description of component transfer between phases (Wei et al., 2011). Moreover, prediction of thermodynamic properties and phase behavior becomes more accurate and reliable. Flash calculations and multiphase equilibria algorithm are necessary to determine the number of phases in equilibrium, compositions and quantity of each phase and their proprieties. Thus, the use of a computational tool capable of characterizing an oil-gas system in distinct pressure and temperature conditions is essential. Barbosa Neto (2015) developed a compositional PVT simulator, which predicts the phase behavior at PT conditions using phase calculations based on cubic Equations of State (EoS). The program is commonly used to study phase equilibria applied to petroleum fluids. Based on this context, the main aim of this work is to show a software capable of carrying out an isothermal two-phase PT-flash using a compositional approach.

2 2. PHASE EQUILIBRIA MODELING To obtain a compositional approach in an oil-gas system, an algorithm including isothermal two-phase PT-flash and Vapor-Liquid Equilibrium (VLE) was needed. A PVTpetro simulator, developed by Barbosa Neto (2015), is capable of evaluating the phase behavior of multicomponent systems and was used in this work. The algorithm implemented in PVTpetro considers the existence of two phases: oil and gas, in equilibrium. Thermodynamic modeling of these phases was based on the VLE theory using phi-phi approach, according to Danesh (1998). In order to do this, the equality of the component fugacity in the existing phases was used as the criteria for equilibrium (Michelsen, 1982; Ahmed, 2007), as shown in Equation 1 for the LVE. f il = f iv ; i = 1, N c (1) Superscripts, L and V are indexes of the oil and gas phases, respectively; f [bar] represents fugacity and N c corresponds to the number of components. In terms of multicomponent systems of hydrocarbons, fugacity depends on pressure p [bar] and temperature T [K], as well as phase composition (x, y) (Michelsen and Mollerup, 2007), as shown in Equation 2: f il = f i(t, p, x) f iv = f i(t, p, y) (2) 2.1. Flash Calculation Flash calculation problems consider that feed stream, with global composition represented for a set of molar fractions (z i ), contains one mol of chemical species that do not react. Thus, Equations 3 and 4, respectively, give global and component balance equations for two phases in equilibrium. L + V = 1 Lx i + Vy i = z i (3) (4) In Equations 3 and 4, L is the moles number of liquid, with molar fraction x i ; V is the moles number of vapor, with molar fraction y i. These equations can be combined resulting in Equation 5: Vy i + (1 V)x i = z i ; i = 1, N c (5) Substituting the definition of equilibrium ratio (K i = y i x i ) and solving for x i and y i using Equation 5, results in: x i = y i = z i 1 V + VK i K i z i 1 V + VK i (6) (7)

3 The value of V can be determined by the solution of the non-linear Rachford-Rice equation (Rachford-Rice, 1952). Equation 8 was obtained from Equations 6 and 7. N c f(v) = (y i x i ) = z i(k i 1) 1 V + VK i i=1 N c i=1 = 0 (8) Newton-Raphson method with 10 6 tolerance, as shown in Figure 1, was applied to solve Equation 8. Furthermore, negative flash concept was implemented in this step The Cubic Equations of State Compressibility factor of the phases oil and gas, as well as the fugacity for each component in each phase of the mixture were determined using cubic EoS, such as Soave-Redlich-Kwong (1972) (SRK) and Peng-Robinson (1978) (PR) equations. They are presented in the following way, respectively (Soave, 1972; Peng and Robinson, 1976): p = p = RT V b RT V b aα(t) V(V + b) a(t) V(V + b) b(v b) (9) (10) After some algebraic operations and thermodynamic concept applications, Equations 9 and 10 can be rewritten in their cubic form relating to phase compressibility factor (Z) (Ahmed, 2007): Z 3 Z 2 + (A B B 2 )Z AB = 0 (11) Z 3 (1 B)Z 2 (A 2B 3B 2 )Z (AB B 2 B 3 ) = 0 (12) The A and B parameters are presented as: A = a m p (RT) 2 (13) B = b mp RT (14) For each equation, terms a m and b m have specific definitions that are accessible in Danesh (1998) and Ahmed (2007). Expression for fugacity was obtained using SRK and PR EoS with van der Waals classical mixing rules (Ahmed, 2007) as shown in Equations 15 and 16, respectively: ln f i p = b i b (Z 1) ln(z B) + A B [a i a b i b + 1 ] ln { Z Z + B } (15)

4 ln f i p = b i b (Z 1) ln(z B) + A B 2.3. VLE Algorithm [a i a b i b + 1 ] ln { Z + (1 2)B Z + (1 + 2)B } (16) Figure 1 shows a vapor-liquid equilibrium flowchart that illustrate your computation procedure in two loops. In the internal loop, Rachford-Rice s equation was solved to carry out a flash calculation. The determination of Z factor and fugacity using cubic EoS and the VLE convergence were performed in the external loop. Start Given: input data and thermodynamic properties (T, P, z i, MW, T ci, P ci, V ci, Z ci, ω i ) f Calculation (Rachford-Rice) Estimate K i, using Wilson s correlation Calculate V f Calculation Newton s Method V n+1 = V n f f Erro > 10 6 Calculate x i and y i Set-up EoS PR for Liquid Set-up EoS PR for Vapor Compute Z L Compute Z V Compute f Li Compute f Vi Upgrade of K i K i n+1 = K i n f L i f Vi n No N c f 2 L i 1 < 10 12? f Vi i=1 Yes Print V, L, x i, y i, Z L, Z V, K i End Figure 1 Vapor-liquid equilibrium algorithm flowchart using isothermal two-phase flash calculations and cubic equations of state. Successive substitution method was used to obtain problem convergence (Michelsen and Mollerup, 2007). In addition, PVTpetro simulator performs a stability analysis module that applies the tangent plan criterion to ensure Gibbs energy minimization.

5 3. RESULTS AND DISCUSSION As a way to validate flash and VLE calculations in PVTpetro, a petroleum multicomponent composition with molar fraction z i, as shown in Table 1, was selected to be studied. Barbosa Neto (2015) describes the properties of each component. In order to evaluate the performance of the algorithm implemented, some simulations at a large range of pressure and temperature were performed using PVTpetro and compared to the Hysys and WinProp simulator predictions, available at Unicamp. Table 1 presents, in a comparative form, results of the molar compositions for oil and gas phases after flash calculation performed at p = 150 bar and T = K using PR EoS. Table 1 Molar composition of the oil (x i ) and gas (y i ) phases of fluid composition analysed for flash calculation at p = 150 bar and T = K, using PR EoS Comp. z i (%) (Feed) x i (%) (PVTpetro) x i (%) (Hysys) y i (%) (PVTpetro) y i (%) (Hysys) Erro - x i (%) Erro - y i (%) CO N C C C i-c n-c i-c n-c C C C C C C C C C C C C C C C

6 Table 1 shows values of relative error between the PVTpetro and Hysys results for oil and gas phase compositions. The majority of errors are in the % range, which indicates a satisfactory agreement between solutions of the simulators. Furthermore, analyzing phase behavior, it was observed that the oil phase represents 55.73% of the system. This phase is characterized by a hydrocarbon liquid phase, which is rich in light components (C1 C7), about 73%, and with an % C20 + pseudo component. On the other hand, the gas phase occupies 44.27% of the system with about 99% of light components, mostly methane ( %). This information on phase equilibrium is essential in multiphase flow compositional simulators (Gaganis and Varotsis, 2014). Computed results of equilibrium constant (K i ), for mixture components, are displayed in Figure 2 and compared with the values determined using the WinProp. The algorithm was evaluated at pressure 150 bar and at temperature K, using SRK EoS. The dashed line in graph at K i = 1, means that the component quantity is equal in both phases in equilibrium. Equilibrium Constant - K i 3,0 2,5 2,0 1,5 1,0 SRK EoS K i (PVTpetro) K i (Wimprop) K i = 1 0,5 0,0 CO 2 N 2 C 1 C 2 C 3 I-C 4 Components N-C 4 I-C 5 N-C 5 C 6 Figure 2 Equilibrium constant of the mixture components, at p = 150 bar and T = K, using SRK EoS in both PVTpetro ( ) and WinProp ( ). It is possible to check in Figure 2 that the PVTpetro results matched well with the commercial simulator solution. Since K i > 1 for components N2 and C1, these are concentrated in the gas phase. As expected for this operational condition evaluated, the heavier components tend to remain in the oil phase, as shown by the simulated data. In the specific case of CO2 and C2, K i values are close to 1, but with higher concentrations in the liquid phase. Figures 3a and 3b show the oil fraction curves with the pressure for two different temperatures ( and K). The PVTpetro results, using SRK EoS and PR EoS, were compared to Hysys and WinProp, respectively, showing a good agreement between the solutions. Curves presented similar behavior for both EoS. As pressure decreases, existence of two distinct regions was noted. Firstly, only the liquid phase existed, because all the gas is solubilized in oil due to high pressure conditions. This occurred up until reaching the bubble pressure and beginning the gas release. For SRK EoS, bubble pressure values were verified at 253 bar and 234 bar, and for PR EoS, they were C 7 C 8 -C 20

7 observed at 257 bar and 282 bar, respectively at K and K. Below these pressures, the system becomes two-phase and the oil fraction curve decreases Oil Fraction (%) = K (SRK - Hysys) (a) = K (SRK - PVTpetro) = K (SRK - Hysys) = K (SRK - PVTpetro) Pressure (Bar) = K (PR - Wimprop) Figure 3 Molar fraction of oil phase as a function of pressure, at and K (a), SRK EoS in the PVTpetro and Hysys (b) PR EoS in the PVTpetro and WinProp. Oil Fraction (%) (b) = K (PR - PVTpetro) = K (PR - Wimprop) = K (PR - PVTpetro) Pressure (Bar) Similarly, Figures 4a and 4b present gas fraction as a function of the system pressure for two different temperature ( and K) using SRK and PR EoS, respectively = K (SRK - PVTpetro) = K (SRK - Hysys) = K (SRK - PVTpetro) = K (SRK - Hysys) = K (PR - PVTpetro) = K (PR - Wimprop) = K (PR - PVTpetro) = K (PR - Wimprop) Gas Fraction (%) Gas Fraction (%) Pressure (Bar) (a) Figure 4 Molar fraction of the gas phase as a function of the pressure, at and K (a), SRK EoS in the PVTpetro and Hysys (b) PR EoS in the PVTpetro and WinProp. Gas curves presented the same behavior for both EoS, equivalent to oil curves. These curves 0 Pressure (Bar) (b)

8 existed only in the two-phase region below bubble pressure, where the gas was released from oil. Other physical analyses on system were related to temperature influence. In Figures 3 and 4, it was observed that temperature modified phase behavior, changing the bubble pressure and the intensity, with which the gas is released from the oil phase. However, the gas quantity at p = 1 bar is the same. 4. CONCLUSIONS The isothermal two-phase PT-flash and LVE modules of the PVTpetro simulator showed compatible solutions with the commercial thermodynamic packages (Hysys and WinProp) for analyzed fluid at all investigated conditions. From a thermodynamic point of view, both SRK and PR EoS presented similar performance in the LVE algorithm. Small numeric and qualitative differences in phase behavior were verified between the cubic EoS. Errors in magnitude order of % were obtained in flash calculation to determine oil and gas phase compositions. Therefore, PVTpetro is a software which could be used to analyze the two-phase PT-flash and LVE in oil-gas systems in the petroleum and chemical industry. 5. REFERENCES AHMED, T. Equations of State and PVT Analysis: Applications for Improved Reservoir Modeling. Houston: Gulf Publishing Company, BARBOSA NETO, A. M. Desenvolvimento de um Simulador PVT Composicional para Fluidos de Petróleo. Dissertação de Mestrado, FEM/Unicamp. Campinas, DANESH, A. PVT and Phase Behaviour of Petroleum Reservoir Fluids. Amsterdam: Elsevier, GAGANIS, V.; VAROTSIS, N. An integrated approach for rapid phase behavior calculations in compositional modeling. J. of Petroleum Science and Engineering, v. 118, p , MICHELSEN, M. L. The isothermal flash problem. Part II. Phase-Split calculation. Fluid Phase Equilibria, v. 9, p , MICHELSEN, M. L.; MOLLERUP, J. M. Thermodynamic Models: Fundamentals & Computational Aspects. 2. ed. Holte: Tie-Line Publications, PENG, D. Y.; ROBINSON, D. B. A new two-constant equation of state. Industrial & Eng. Chemistry Fundamentals, v. 15, n. 1, p , QIU, L.; WANG, Y.; JIAO, Q.; WANG, H.; REITZ, R. Development of a thermodynamically consistent, robust and efficient phase equilibrium solver and its validations. Fuel, v.115, p.1-16, RACHFORD, H. H.; RICE, J. D. Procedure for use of electrical digital computers in calculating flash vaporization hydrocarbon equilibrium. JPT, v. 195, n. 19, p , SOAVE, G. Equilibrium constants from a modified Redlich-Kwong equation of state. Chemical Engineering Science, v. 27, p , WEI, Y.; CHEN, Z.; SATYRO, M.; DONG, C.; DENG, H. Compositional simulation using the advanced Peng-Robinson equation of state. Paper SPE, n , 2011.