Simulation Studies of Temperature and Pressure Distribution in Carbon Dioxide Injection Well

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1 Simulation Studies of Temperature and Pressure Distribution in Carbon Dioxide Injection Well Baojian-Du 1,2*, Linsong-Cheng 1,2 Jingchen-Ding 1,2 1 Department of Petroleum Engineering, China University of Petroleum (Beijing), Beijing, China 2 MOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, China *Corresponding author, Baojian-Du, PhD student, Department of Petroleum Engineering, China University of Petroleum (Beijing), 18 Fuxue Road, Changping Dist., Beijing, , China, ABSTRACT This paper analyzes the phase characteristics and physical properties of carbon dioxide under geological conditions. And based on these analyses, this paper deduces the distribution of temperature and pressure in CO 2 injection well. Phase change has also been taken into account. Numerical model of temperature and pressure distribution in CO 2 injection well has been established as well. To test and verify this model, this paper takes an actual well as example and calculates the temperature and pressure distribution. Finally, a sensitivity analysis has been carried out to describe the temperature and pressure distribution under the influence of several parameters. KEYWORDS: CO 2 injection well; temperature distribution; pressure distribution; example application; sensitivity analysis INTRODUCTION Enhance oil recovery (EOR) by CO 2 flooding has caught considerable attention in the oil industry since its appearance several decades ago. In recent years, an increasing number of countries are running CO 2 injection programs so as to satisfy the demand for environmentally friendly society and to gain long-term benefits. So far, CO 2 flooding has become one of the most significant methods of oil recovery (Li Shilun et al., 2001)

2 Vol. 19 [2014], Bund. F 1468 The bottom-hole pressure and temperature of CO 2 injection well are both crucial factors for all the CO 2 injection schemes because they are decisive factors of miscible displacement. So it is very important for engineers to know the temperature and pressure distribution in CO 2 injection wells. However, CO 2 belongs to non-hydrocarbon, the physical and chemical properties of CO 2 are totally different from natural gas. From well head to the bottom, there will be phase change of CO 2. CO 2 in the injection well may be liquid, gas or supercritical fluid. CO 2 has different physical properties in different phase behavior. The traditional method has not taken phase change into account, and therefore the result will be inaccurate. This paper analyzes the carbon dioxide phase characteristics and physical properties under geological conditions by taking phase change into account. Based on energy conservation equation and wellbore heat transmission equations proposed by Ramey, this paper deduces the distribution of temperature and pressure in CO 2 injection well. And then, a carbon dioxide injection wellbore temperature and pressure distribution model has been established. The model is developed with VB language as well. And then, a sensitivity analysis has also been carried out to describe the temperature and pressure distribution under the influence of several parameters. PRESSURE DISTRIBUTION MODEL Based on energy conservation, the equation of pressure gradient in the injection well is: dp 2 sin dv ρ = ρg θ ρv f v (1) dz dz 2D where P is pressure, MPa; g is acceleration due to gravity, 9.8m/s 2 ; ρ is density of gas, kg/m 3 ; v is flow rate of gas, m/s; z is vertical depth of injection well, m. In formula (1), the three parts in the right side are gravity loss, acceleration pressure loss and frictional loss of the injection media. The acceleration pressure loss is mainly depended on the change of flow rate. Compared to the total energy loss, acceleration pressure loss is negligible during the practical gas injection proceed. θ is the wellbore inclination angle from horizontal degrees, we can calculate it by using the vertical depth and horizontal displacement of the injection well. Q 1000Gt Gt v = A = π D = ρd ρ (2)

3 Vol. 19 [2014], Bund. F 1469 where A is the cross-sectional area of the flow, 2 A = π D, m 2. Gt is injection rate, m/s. 4 There are several ways to calculate gas deviation factor, such as empirical formulas, state equation, type curve matching method, and table lookingup method etc. For programming calculation, type curve matching method and table lookingup method are not realistic. After analyzing and comparing several empirical formulas and state equations, we find that P-R state equation is the optimum method to calculate the deviation factor of CO 2 (Peng D et al.,1976) Z (1 B) Z + ( A 3B 2B) Z ( AB B B ) = 0 (3) Under the given temperature and pressure, we can calculate the corresponding deviation factor by using formula (3)(Figure 1). Figure 1: Deviation factor of CO 2 under different temperature/pressure Density of CO 2 in different phase varies considerably. So firstly we should ascertain the phase behavior of CO 2 in the wellbore before calculating the density of CO 2. In recent years, people mainly use equations of state (EOS) to predict CO 2 phase behavior. After comparing EXP-RK, SRK, PR, and PT EOS, we find that EXP-RK and PR EOS have a higher precision. In this paper, we use PR EOS to ascertain the phase behavior and calculate the density. CO 2 densities under different pressure and temperature are showed in Figure 2.

4 Vol. 19 [2014], Bund. F 1470 Figure 2: Density of CO 2 under different temperature/pressure According to experimental data, Chung summarized a method to estimate gas viscosity (GUO Xu-qiang et al.,1999). The calculation error is less than 5%. In this study, we use this method to calculate viscosity. 1/ ( MTc) η = η* (4) 2/3 Vc where η is viscosity, mpa.s; M is molecular weight; Tc is critical temperature, K; Vc is critical volume, cm 3 /mol. Friction factor is the friction resistance gradient produced by the friction between fluid and pipe wall. We can use the empirical formulas (J J Xiao et al.,1990 ; Wang Mikang et al.,1997) to calculate the friction factor of gas. 1 e = lg( + ) (5) 0.9 f D Re Where Re is Reynolds number, Re (4). ρvd =. The viscosity can be calculated with the method in µ After all the parameters above have been ascertained, we can use formula (1) to calculate the pressure distribution and bottom-hole pressure through iterative method. First, we divide the whole well depth into several parts. From well head to bottom, we calculate the bottom pressure

5 Vol. 19 [2014], Bund. F 1471 of each part and make it the initial pressure of the next part, the rest may be deduced by analogy. Finally we can get the bottom-hole pressure. In order to improve the accuracy of calculation, we can increase the number of parts and shorten the length of each part. In this study, the length of each part is 50m. TEMPERTURE DISTRIBUTION MODEL In the practical CO 2 injection schemes, the injected CO 2 is in liquid state with a temperature of -35 ~-20. Since the temperature is different from the formation, there will be heat exchange between the injected CO2 and the reservoir. As a result, the temperature of injected CO 2 will change. Taking injection time and injection rate into account, we calculate the temperature distribution through wellbore heat transmission theory (Ramey et al., 1962). T ( H,) t ah T aa ( t aa T ) e ( H/ A) = o + 0 (6) where GC t [ K+ f() t ru to to] A = π ru K to to When calculating the value of A, the most important part is getting the value of overall heat transfer coefficient Uto. In the practical CO2 injection schemes, annuluses are full of fluid (water or crude oil). So we have to calculate the density, viscosity, expansion coefficient, thermal conductivity and heat capacity of the fluid under different temperature. These parameters are easy to calculate with the methods presented in reference (Wan Renfu et al., 1977). After all the parameters above have been ascertained, we can calculate Uto through iterative method. Then we can get the value of A. Finally, we can obtain the temperature under corresponding depth with formula(6). After the numerical model of pressure and temperature distribution has been established, we have developed the model with VB language to make it easier to calculate. EXAMPLE APPLICATION In this study, we take an actual CO 2 injection well F-4 presented in reference (Zhang Chuanru et al., 1999) (well head pressure 6.5 MPa) as example and calculate. By using the numerical model and VB program established before, we have obtained the deviation factor (Z), density, and viscosity of CO 2 in the injection wellbore, then the pressure and temperature under different well depth are obtained as well (Table 1, Figure 3, and Figure 4).

6 Vol. 19 [2014], Bund. F 1472 Pressure (MPa) Actual Value Figure 3: Pressure Distributions in Well F-4 Temperature ( ) Actual Value Calculated Value Figure 4: Temperature Distributions in Well F-4 Table 1: Well F-4 Temperature and Pressure Pressure(MPa) Temperature( ) Well Actual Calculated Actual Calculated Depth(m) Error Error Value Value Value Value % % % % % % % % % %

7 Vol. 19 [2014], Bund. F % % % % % % % % Average Error 0.82% Average Error 2.02% From Table 1, Figure 3, and Figure 4 we can see that the calculated value of temperature/pressure is close to the actual value of well F-4. The biggest error of pressure is 2.34% and the average error is 0.82%. The biggest and the average error of temperature are 5.22% and 2.02% respectively. So the results are accurate and reliable. So this numerical model can fully satisfy the demand of engineering calculation and field production. SENSITIVITY ANALYSIS Finally, sensitivity analysis has been carried out to study the change of wellbore pressure and temperature under different injection rate and injection temperature. The results are showed as follows. Temperature ( ) 10t/d 20t/d 30t/d 40t/d 50t/d Figure 5: Wellbore Temperature Distributions under Different Injection Rates Figure 5 shows the wellbore temperature distributions under different injection rates. From figure 5. we can see that as the injection rate increases, there is a slight increase in the wellbore temperature. When the well depth is below 300m, with the increase of well depth, the temperature increase rapidly; and then when the well depth is more than 300m, the temperature is still increase but the growth rate become lower. Figure 6 shows the wellbore pressure distributions under different injection rates. It is clear that the wellbore pressure increases with the increase of injection rate. And the bigger the injection rate is, the higher growth rate of wellbore pressure will be.

8 Vol. 19 [2014], Bund. F 1474 Pressure (MPa) 10t/d 20t/d 30t/d 40t/d 50t/d Figure 6: Wellbore Pressure Distributions under Different Injection Rates Figure 7 shows the wellbore temperature distributions under different injection temperatures. It is obvious that wellbore temperature increase as the well depth increase. When the well depth is below 200m, injection temperature has a great influence on wellbore temperature; while the well depth is more than 200m, the impact of injection temperature decreases and finally become negligible. Temperature ( ) Figure 7: Wellbore Temperature Distributions under Different Injection Temperatures Figure 8 shows the wellbore pressure distributions under different injection temperatures. Calculated data shows that the bottom-hole pressure decreases with the increase in injection temperature, but the difference is too small to see in the curve. So injection temperature has a negligible influence on wellbore pressure.

9 Vol. 19 [2014], Bund. F 1475 Pressure (MPa) Figure 8: Wellbore Pressure Distributions under Different Injection Temperatures CONCLUSION 1. Through the analysis of special physical properties of CO 2, and taking phase change into behavior, this paper obtains the calculating method of physical parameters (density, viscosity, deviation factor) of CO Based on energy conservation, a carbon dioxide injection well bore temperature and pressure distribution model has been established. The model is verified with the actual data as well. Result shows that the calculated value and actual value are in good agreement. 3. A sensitivity analysis has been carried out to describe the temperature and pressure distribution under the influence of several parameters. The results show that the injection temperature and injection rate have some influence on wellbore temperature and pressure. REFERENCES 1. Li Shilun, Zhang Zhengqing, and Ran Xinquan. Enhance Oil Recovery By Gas Injection. Chengdu: Sichuan Science and Technology Press,p , Peng D, Robinson D.B. A new two-constant equation of state. Industrial and Engineering Chemistry Fundamentals, Vol.15, p.54, 1976, 3. GUO Xu-qiang, RONG Shu-xia, YANG Ji-tao et al. The viscosity model based on PR equation of state [J]. Acta Petrolei Sinica, Vol.20, p56, J J Xiao & Brill. A Comprehensive Mechanistic Model for Two Phase Flow in Pipelines. SPE20631, p167, 1990

10 Vol. 19 [2014], Bund. F Wang Mikang. Two-Phase Frictional Pressure Drop And Single-Phase Friction Factor In Pipes. Journal of The University of Petroleum, Vol.21, p52, Ramey H J. Wellbore heat transmission.jpt, Vol.14,p427, Wan Renfu, Luo Yingjun. Oil Recovery Handbook. Beijing: Petroleum Industry Press, p178, Zhang Chuanru, Yu Shaoyong. Testing and evaluation method of CO2 well. Beijing: Petroleum Industry Press,p245, , EJGE

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