LPET #580298 [LPET-2011-0171.R1], VOL 31, ISS 24
(September 10, 2013)
A Method for Calculating the Temperature Profile in Heavy Oil Wells With the Injection of Light Oil Diluent Y. Yu and K. Li
QUERY SHEET This page lists questions we have about your paper. The numbers displayed at the left can be found in the text of the paper for reference. In addition, please review your paper as a whole for correctness. Q1. Au: Confirm all author names and affiliations are correct. Q2. Au: Please provide department/faculty name for all affiliations. Q3. Au: Confirm correspondence address and author name are correct. Q4. Au: Do you mean Hasan and Kabir (1994)? Q5. Au: Add citation for Alves et al. (1992). Q6. Au: Please provide volume number and page range for Quan (1985). Q7. Au: Please provide volume number and page range for Willtite (1967).
TABLE OF CONTENTS LISTING The table of contents for the journal will list your paper exactly as it appears below: A Method for Calculating the Temperature Profile in Heavy Oil Wells With the Injection of Light Oil Diluent Y. Yu and K. Li
LPET #580298 [LPET-2011-0171.R1], VOL 31, ISS 24
(September 10, 2013)
Petroleum Science and Technology, 31:1–8, 2013 Copyright © Taylor & Francis Group, LLC ISSN: 1091-6466 print/1532-2459 online DOI: 10.1080/10916466.2011.580298
A Method for Calculating the Temperature Profile in Heavy Oil Wells With the Injection of Light Oil Diluent Y. Yu1 and K. Li2;3
Q1 Q2
1
Peking University, Beijing, China China University of Geosciences, Beijing, China 3 Stanford University, Palo Alto, California, USA
5
In this study, an analytical model was derived to determine the wellbore temperature profiles for heavy oil production assisted with the addition of light oil from the annulus in production wells. The derivation of the temperature profile model was conducted on the basis of energy balance between the formation and fluids flowing through each conduit in vertical wells. The temperature profiles in different cases were calculated using the proposed temperature model and the results were compared with the measured data. Sensitivity analysis was also conducted and the main factors that influence the temperature profiles were discussed.
10
2
Keywords: heavy oil production, light oil diluent, mathematical models, sensitivity analysis, wellbore temperature profile
15
1. INTRODUCTION In some heavy oil fields, oil can flow in the reservoirs but may not flow through the wellbore without taking measures such as heating or diluting with light oil. This is because of the high viscosity caused by low temperature around the wellbore close to surface. Tah oilfield is one of the ultra-deep and ultra-heavy oil reservoirs in China. It is also featured of high temperature 20 (130ı C) and high water salinity (over 100,000 ppm). Although the oil can flow in the reservoir easily, it cannot flow to the surface in many wells. The main reason may be because the viscosity of the crude oil increases greatly as the decreased temperature from the bottom to the upper part of the well. In Tah oilfield, one of the solutions to this problem was to inject light oil with much lower viscosity through the annulus to the crude oil in the tubing. This approach has been 25 being extensively applied in Tah oilfield and other oilfields in Xinjiang. Accurate prediction of the wellbore temperature profile is important to design the dilution. There have been many papers on the calculation of the temperature profiles in the wellbore but few in the cases in which light oil is injected from the annulus to mix with the produced crude oil in the tubing. The physical process and heat transfer in the case in which heavy oil is produced by adding light oil are similar 30 to those in gas-lift wells. However, there are some differences between the two cases. Ramey (1962) might have been the first to present a theoretical model to estimate fluid temperature as a function of well depth and production time. The model has been widely used Q3
Address correspondence to K. Li, China University of Geosciences (Beijing), China. E-mail:
[email protected]
1
LPET #580298 [LPET-2011-0171.R1], VOL 31, ISS 24
2
(September 10, 2013)
Y. YU AND K. LI
in petroleum industry. However, the model is only applicable to single-phase flow. The approach reported by Satter (1965) improved Ramey’s model by honoring the effect of phase change 35 during steam injection. There have been many modified temperature models for two-phase flow in wellbore. Sagar et al. (1991) considered kinetic energy and Joule-Thompson expansion effects. Hasan and Kabir (1996) reported a mechanistic model for circulating fluid temperature. Hasan Q4 et al. (1996) presented a model to compute the temperature profiles for gas-lifting wells. In this study, an analytical two-phase model was proposed to calculate the fluid temperature 40 in the wellbore for heavy oil production assisted by the addition of light oil. The heat-transfer coefficient in the proposed model was not given as a constant. Instead, it was inferred from other parameters using the model proposed by Manabe et al. (2003). 2. THEORY Reverse injection was adopted in the production of heavy oil in Tah oilfield. That is, light oil was injected from the top to the bottom through the annulus and flew back up from the tubing. For vertical wells, the mathematical model for the temperature profiles can be expressed in Appendix Eqs. (A-7) to (A-11). To calculate the temperature profile, one main challenge is to calculate the heat transfer coefficients in both the tubing and annulus, thus one needs to study the fluid dynamic there. In the case of Tah oilfield, the Reynolds number of fluid flow in the annulus is less than 1000. So it is reasonable to assume a laminar flow in the annulus. The convective heat-transfer coefficient in the annulus is constant. For the tubing, the two-phase model presented by Manabe et al. (2003) is used. Another difficult is to consider the effect of injected light oil on the viscosity change of the fluid in turbing. The mathematical model for inferring the viscosity of the mixture oil (heavy crude oil with injected light oil) should be determined. More than 100 groups of experiments were conducted using a rotational viscometer to measure the viscosities of the mixture oil from 30ı C to 120ı C. Those data were compared to that predicted by the double-log viscosity model (Quan, 1985) lg lg.mix / D
1 x lg lg.l / C lg lg.h /; 1Cx 1Cx
45
50
55
60
(1)
where x is the volume ratio of light oil to heavy oil, mix, l , and h are viscosities of the mixture, the light oil, and heavy oil, respectively. The results showed the viscosity data of the mixture calculated by Eq. (1) were consistent with those measured. Therefore Eq. (1) was used in our calculation. 3. TEMPERATURE CALCULATION
65
The proposed models (Eqs. [A-7] to [A-11]) were used to calculate the temperature profiles of a self-flowing well in Tah oilfield, where the mixing point was at the bottom. All the relevant data are shown in Table 1. We compared the model results with the temperature data measured in this Tab1 well. As shown in Figure 1, the calculated temperature data in the tubing match with the measured Fig1 temperature satisfactorily, except for the data point at the wellhead. Sagar (1991) observed similar 70 phenomenon and explained this might be due to the measurement error. This has not been verified yet. One can also see that the temperature in the annulus changes so quickly near the wellhead that it almost became equal to the formation temperature at the depth below about 2,000 m, which might be because of the heat loss from the injected light oil to the formation.
LPET #580298 [LPET-2011-0171.R1], VOL 31, ISS 24
(September 10, 2013)
CALCULATING TEMPERATURE PROFILE IN HEAVY OIL WELLS
3
TABLE 1 Wellbore, Formation, and Fluid Data Well depth, m Wellhead pressure, MPa Bottomhole temperature, ı C Surface formation temperature, ı C Injection temperature of light oil, ı C Production time, days Tubing radius, m Casing radius, m Wellbore radius, m Density of heavy oil, kg/m3 Density of light oil, kg/m3 Production rate, m3 /day Volume fraction of gas in oil, m3 /m3 Volume ratio of light to heavy oil, m3 /m3 Thermal diffusivity of formation, m2 /h Thermal conductivity of formation, W/(m ı C) Thermal conductivity of cement, W/(m ı C)
5,500 2.98 123.44 20 80 7 0.038 0.089 0.15 980 830 74.7 25.3 0.8 0.0037 2.4 1.74
4. SENSITIVITY STUDY The effects of the temperature of the injected light oil on the temperature profiles in the wellbores are shown in Figure 2. As expected, calculated temperatures change significantly near the wellhead. The temperatures in both the tubing and the annulus increase with the increase of injection temperature. But there is even no difference in temperature profiles in the tubing at the depth
FIGURE 1 Calculated fluid temperature profiles in the tubing (with a comparison to the measurements) and the annulus. (color figure available online)
75
Fig2
LPET #580298 [LPET-2011-0171.R1], VOL 31, ISS 24
4
(September 10, 2013)
Y. YU AND K. LI
FIGURE 2 Temperature profiles calculated with different injection temperatures. (color figure available online)
below about 500 m. This also happens to the temperatures in the annulus below about 1,000 m. We speculated that the heat loss in the annulus happens so quickly that the temperature in the annulus drops close to the formation temperature about 1,000 m below the wellhead, as shown in Figure 1. The effect of the production rate on temperature profiles was also investigated. With a fixed ratio of light oil to heavy oil, the production rate was changed to 10 times and 0.1 times as it was, which was 74.7 m3 /day. In Figure 3, significant changes can be seen in the temperature profiles. For the annulus, because the ratio of light oil to heavy oil is fixed, the mass flow rate in the annulus is 10 times greater when the production rate is 10 times greater. The light oil flows too fast to have sufficient heat exchange with the formation. So the temperature in the annulus at shallow depth is much higher than that in the formation. At deeper depth where heat flux is from the formation to the annulus, the temperature in the annulus remains much lower than that in the formation because of the same mechanism. In contrast, when the mass flow rate is only 0.1 times as it was, fluid flows so slow that it changes heat sufficiently with formation, so even near the wellhead, temperature in the annulus is almost the same as that in the formation. The same mechanism can be used to explain the significant changes in the temperature profiles in the tubing. Figure 4 shows the influence of the volume ratio of the light oil to heavy oil. The ratios of 0.4, 0.8, and 2.0 were used. As the ratio of the light oil to heavy oil increases, mass flow rates in the annulus increase. Although the change is not significant, temperature profiles in the annulus have the same trend as seen in Figure 3. In the tubing, with fixed production rates of heavy oil, there are two major parameters affected by the change in ratio of the light oil to heavy oil: the viscosity of the mixture and the total mass flow rate in the tubing. As the ratio of the light oil to heavy oil increases, the viscosity of the mixture decreases. This will lead a decrease in the fluid temperature in the tubing. At the same time, as the ratio of the light oil to heavy oil increases, the total mass flow rates in the tubing will increase. As shown in Figure 3, the temperature in the tubing will
80
85 Fig3
90
95 Fig4
100
105
LPET #580298 [LPET-2011-0171.R1], VOL 31, ISS 24
(September 10, 2013)
CALCULATING TEMPERATURE PROFILE IN HEAVY OIL WELLS
FIGURE 3
Temperature profiles calculated with different mixing ratio. (color figure available online)
FIGURE 4 Temperature profiles calculated with different production rates. (color figure available online)
5
LPET #580298 [LPET-2011-0171.R1], VOL 31, ISS 24
6
(September 10, 2013)
Y. YU AND K. LI
increase significantly. Figure 4 shows the latter effect plays a decisive role. Temperature in the tubing increases with the ratio of light oil to heavy oil, especially at shallow depth. 5. CONCLUSIONS The following conclusions may be drawn according to the present study. 1. An analytical temperature model was derived for heavy oil production wells assisted with 110 the addition of light oil. With certain reasonable assumptions, the calculation procedure is simple and the model results match with measured temperature data satisfactorily. 2. The accuracy to calculate the viscosity of the mixture of the light and heavy oil in the tubing was important to predict the temperature profiles and our experimental data demonstrated that the double-log viscosity model works satisfactorily in calculating the viscosity of the 115 mixture. 3. The parameters, including the viscosity of the injected light oil, the production rate, and the ratio of the light oil to heavy oil, have significant impact on temperature profiles in the tubing, especially at the depth near the wellhead in vertical production wells. However, the influence of the temperature of the injected light oil was limited in the cases studied, 120 especially at the deep depth. REFERENCES Alves, I. N., Alhanatl, F. J. S., and Shoham, O. (1992). A unified model for predicting flowing temperature distribution in wellbores and pipelines. SPE Prod. Eng. 7:363–367. Hasan, A. R., and Kabir, C. S. (1994). Aspects of wellbore heat-transfer during two-phase flow. SPE Prod. Eng. 9:211–216. 125 Hasan, A. R., Kabir, C. S., and Ameen, M. M. (1996). A mechanistic model for circulating fluid temperature. SPE J. 1:133–144. Manabe, R., Wang, Q., and Zhang, H. Q. (2003) A mechanistic heat-transfer model for vertical two-phase flow. SPE 84226, SPE Annual Technical Conference and Exhibition, Denver, Colorado, October 5–8. 130 Quan, Z. X. (1985). Computation of mixture of heavy and light oils. J. Oil Gas Transport. 4. Ramey, H. J. Jr. (1992). Wellbore heat transmission. J. Pet. Technol. 14:427–435. Sagar, R. K., Doty, D. R., and Schmidt, Z. (1991). Predicting temperature profiles in a flowing well. SPE Prod. Eng. 6:441–448. Satter, A. (1965). Heat losses during flow of steam down a wellbore. J. Pet. Technol. 17:845–851. Willtite, G. P. (1967). Overall heat-transfer coefficients in steam and hot water injection wells. J. Pet. Technol. 607. 135
Q5
Q6
Q7
APPENDIX A The schematic of the wellbore heat-transfer while mixing light oil is shown in Figure 5. Ramey’s Fig5 (1962) assumptions were adopted in this study: (a) heat flows radically in the wellbore and (b) heat travels much faster in the wellbore than that in the formation. In the case studied, light oil was injected through the annulus and it was also assumed that the 140 light oil injected is noncompressible. Based on the previous works (Ramey, 1962; Willtite, 1967; Hasan and Kabir, 1994), the energy balance equation can be written as d Tt D dZ
At .Tt
d Ta D dZ
At wt .Tt wa
Ta /
g C FC ; Cpt
Ta / C Aa .Ta
(A-1) Te /:
(A-2)
LPET #580298 [LPET-2011-0171.R1], VOL 31, ISS 24
(September 10, 2013)
CALCULATING TEMPERATURE PROFILE IN HEAVY OIL WELLS
FIGURE 5
7
Schematic of the heat transfer in wellbore. (color figure available online)
Here: 2 rt Ut ; Cpt wt rc ke Ua 2 Aa D ; Cpa wa f .t/Ua rc C ke At D
(A-3) (A-4)
where the subscripts a, t, c, and e refer to variables for the annulus, tubing, cement, and formation, respectively. T is the temperature, g is the acceleration of gravity, r is the radius, Cp is the specific 145 heat of fluid, w is the mass flow rate, k is the thermal conductivity, and U is the overall heat transfer coefficient. FC is a result of Joule-Thompson effect estimated by Sagar’s (1991) empirical equation and f .t/ is the transient heat-conduction time function for the formation introduced by Ramey (1962). In this study where the mixing point is at the bottom of the well, the boundary conditions are 150 (only for vertical wells): Z D 0; Tt D Tbh ;
(A-5)
Z D H; Ta D Ti n ;
(A-6)
where H is the well length, Ti n is the temperature of the injected light oil at the wellhead. If the wellbore is divided into many elements, and a constant temperature in each element is assumed, the physical properties of the fluids are the same in an individual element. So the analytical solutions of the previous equations are expressed as follows: 155
Tt
Te D C1 e 1 Z C C2 e 2 Z
Ta
Te D C1 e 1 Z C C2 e 2 Z
wt At Mt C Aa Mt C AgG wa C ; Aa At wt At Mt C AgG C1 1 e 1 Z C C2 2 e 2 Z C gG wa C C ; Aa At At
(A-7)
(A-8)
LPET #580298 [LPET-2011-0171.R1], VOL 31, ISS 24
8
(September 10, 2013)
Y. YU AND K. LI
where AD 1
wt At Aa ; wa p Aa ˙ A2a C 4Aa At ; 1;2 D 2 g Mt D C FC : Cpt
(A-9) (A-10) (A-11)
Here, C1 and C2 are parameters needed to be decided by the boundary condition.
NOMENCLATURE Cp f .t/ g gG k p r t T Tbh Ti n U v w x Z h l mix
specific heat of fluid transient heat-conduction time function of formation gravity constant geothermal gradient thermal conductivity pressure radius production time temperature bottomhole temperature of formation injection temperature of light oil overall heat-transfer coefficient flow rate mass flow rate volume ratio of light oil to heavy oil depth viscosity of heavy oil viscosity of light oil viscosity of the mixture of heavy and light oil
160
165
170
175
Subscripts a t c e t
annual tubing cement formation tubing
180
