Effect of gaseous CO2 on superheated steam flow in wells

Engineering Science and Technology, an International Journal 20 (2017) 1579–1585

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Effect of gaseous CO2 on superheated steam flow in wells Fengrui Sun a,b,⇑, Yuedong Yao a,b, Xiangfang Li b a b

State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum – Beijing, 102249 Beijing, PR China College of Petroleum Engineering, China University of Petroleum – Beijing, 102249 Beijing, PR China

a r t i c l e

i n f o

Article history: Received 8 July 2017 Revised 24 September 2017 Accepted 6 October 2017 Available online 27 October 2017 Keywords: CO2 EOR Effect of CO2 Real gas model Superheated steam Wellbore hydraulics Sensitivity analysis

a b s t r a c t In this paper, a novel model is proposed for estimating pressure and temperature in wellbores when CO2 and superheated steam (SHS) are co-injected. Firstly, a model comprised of mass, energy and momentum conservation equations are developed. Then, Coupled with real gas model and heat transfer model in formation, a comprehensive model is established. The mass, momentum and energy balance equations are solved simultaneously with finite difference method on space and the iteration method. Finally, sensitivity analysis is conducted. Results show that (a). In order to obtain a higher superheat degree, a higher injection temperature and a lower mass fraction of CO2 are suggested. (b). Superheat degree decreases with increasing injection pressure or with increasing mass fraction of CO2. (c). Superheat degree increases with increasing mass flow rate. (d). Superheat degree decreases with increasing mass fraction of CO2. Ó 2017 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction Carbon dioxide injection for heavy oil recovery has been proved effective by huge of field practices [1–3]. The effective use of CO2 has alleviated the greenhouse effect and improved economic efficiency in the petroleum industry [4–12]. On the other hand, thermal injection (usually saturated steam) is another effective method for heavy oil recovery [13–20]. In order to make full use of advantages of both CO2 and thermal fluid, CO2 is always injected into oil layer accompanied with thermal fluid. However, practicing engineers are now facing the difficulty of how to estimate the pressure and temperature at well-bottom when CO2 and SHS are coinjected. In the late 1950’s, focusing on gas production well, Lesem et al. [21] developed an analytical model for estimating temperature at well-bottom. Moss et al. [22] presented a mathematical model to analyze the distribution of hot water temperature in wellbores. Ramey [23] developed an steady-state model to predict heat transfer rate of single-phase fluid in wellbores. However, in his model, kinetic energy and friction loss were both neglected, which brought some error. Based upon Ramey’s work, Willhite [24] presented an improved method on heat transfer coefficient calculation. Satter [25] further extended the single-phase model ⇑ Corresponding author at: State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum – Beijing, 102249 Beijing, PR China. E-mail address: [email protected] (F. Sun). Peer review under responsibility of Karabuk University.

developed by Ramey to two-phase condition. However, these early studies were based on the assumption that pressure is unchanged along the vertical wellbore. Later, taking pressure drop caused by shear stress into consideration, Holst et al. [26] gave the distribution of pressure in the vertical wellbore. Neglecting the slippage between vapor and liquid phases, in 1969, Earlougher [27] and Hagedorn et al. [28] presented models for pressure calculation in saturated steam injection well. Taking slippage into consideration, Fontanilla et al. [29] presented an improved model to estimate steam quality based on Beggs et al.’s [30] work. Based on previous works, Farouq Ali [31,32] and Wooley [33] presented numerical models for predicting distribution of pressure of saturated steam in complex wellbores. Based on modified Ramey’s model, Sagar et al. [34] gave a model to calculate temperature distribution of saturated steam in deviated wellbores. Considering the coupling between wellbore and formation, Stone et al. [35,36] presented a numerical model based on energy and momentum equations. With consideration of multi-phase flow in reservoir, Livescu et al. [37– 39] presented an improved model based on Stone et al.’s works. Taking both axial and radial heat flow in formation into consideration, Bahonar et al. [40] presented a numerical model to predict pressure of saturated steam in wellbores during the downward flow process. Xiong et al. [41] improved the calculation accuracy of heat loss rate in horizontal wellbores, which was further improved by You et al. [42,43]. However, all of these previous works were focused on the single-component flow of saturated steam in wellbores with no discussion on the effect of other components on profile of pressure.

https://doi.org/10.1016/j.jestch.2017.10.003 2215-0986/Ó 2017 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Nomenclature g hfluid pfluid Q fluid qfluid;out qfluid;in r ai T fluid;out

v fluid

wfluid z

the gravitational acceleration, m/s2 Specific enthalpy of the mixed fluid, J/kg pressure of the mixed fluid in wellbores, Pa heat transfer rate from the mixed fluid to formation, J/s the heat transfer rate per unit depth at the outlet of the segment, W/m the heat transfer rate per unit depth at the inlet of the segment, W/m inside radius of the inner tubing, m the temperature at outlet of the segment, K flow velocity of the mixed fluid in wellbores, m/s mass flow rate of CO2 coupled with SHS in wellbores, kg/s well depth, m

Barelli et al. [44] studied the effect of CO2 on the profiles of pressure and steam quality in wellbores. Fidan [45] developed a numerical model focusing on heat transmission, pressure drop and steam quality when saturated steam and non-condensable gases are co-injected. Rafael et al. [46] presented an improved model which can predict pressure distribution when saturated steam and solvent are co-injected. However, these works were focused on the effect of CO2 and N2 on saturated steam pressure along the wellbores with no discussion on SHS condition. In recent years, Zhou et al. [47], Xu et al. [48], Fan et al. [49] developed early models for predicting pressure and temperature of SHS in single-tubing wells. However, there models meet limitations in high injection rate condition. Therefore, Sun et al. [3,15,19,50,51] developed improved numerical models to estimate SHS pressure and temperature in wellbores. However, these models cannot analyze the effect of CO2 on SHS pressure and temperature. Sun et al. [16] presented a numerical model for analyzing flow behaviors of multi-component thermal fluid in perforated horizontal wellbores. However, the constant mass flow process in vertical wellbores is quite different from the variable mass flow process in horizontal wellbores. Sun et al. [17] presented a complex numerical model for multi-component thermal fluid flow in concentric dual-tubing wells. In their work, heat exchange between inner tubing and annuli was taken into consideration. However, the wellbore structure of single-tubing wells is quite different from that of concentric dual-tubing wells. In this paper, a novel model based on mass, energy and momentum conservation equations was developed to analyze the effect of CO2 on SHS pressure and temperature in vertical wellbores. This paper has mainly two contributions to the existing body of literature: (1). A numerical model is presented to predict the distributions of pressure and temperature when CO2 and SHS are coinjected. (2). Effect of CO2 on the profiles of pressure and temperature under various injection conditions is discussed in detail. This model can be used to analyze the effect of CO2 on distributions of pressure and temperature in SHS injection wells for oil field. 2. Model description 2.1. General assumptions The wellbore structure is shown in Fig. 1. The model is established based on the assumptions listed below: (1) The injection parameters (pressure, temperature and mass flow rate) at well-head are steady-state.

Subscripts a inner tubing i inside wall of the tubing fluid the mixture of CO2 and SHS f friction loss Greek letter h the well angle from vertical, rad qfluid density of the mixed fluid, kg/m3 sf the shear stress in the vertical wellbores, N

Fig. 1. Horizontal section of the vertical wellbores [3,15,51].

(2) Heat transfer rate from thermal fluid to the outside wall of the cement sheath is steady-state. (3) Heat transfer rate in formation is transient-state. (4) Thermal parameters of formation are independent from well depth. 2.2. Mathematical model There does not exist mass transmission between wellbore and formation, the mass conservation equation in wellbores can be expressed as:

@ðqfluid v fluid Þ @wfluid ¼0 ¼ pr 2ai @z @z

ð1Þ

where wfluid is the mass flow rate of CO2 coupled with SHS in wellbores, kg/s; r ai is the inside radius of the inner tubing, m; qfluid is the density of the mixed fluid, kg/m3; v fluid is the flow velocity of the mixed fluid in wellbores, m/s; z denotes the well depth, m. The total heat loss from wellbore to formation is equal to the energy change of the mixed fluid. The energy balance equation can be expressed as:

dQ fluid dhfluid d ¼ wfluid  wfluid dz dz dz

v 2fluid 2

! þ wfluid g cos h

ð2Þ

where Q fluid denotes the heat transfer rate from the mixed fluid to formation, J/s; hfluid denotes specific enthalpy of the mixed fluid, J/ kg; g is the gravitational acceleration, m/s2; h denotes the well angle from vertical, rad.

F. Sun et al. / Engineering Science and Technology, an International Journal 20 (2017) 1579–1585

An arbitrary segment of the vertical wellbore showing various forces acting on this segment used for mathematical analysis is shown in Fig. 2. Thirdly, the momentum balance equation can be expressed as:

pr2ai dpfluid ¼ qfluid pr2ai g cos hdz  sf  pr2ai dðqfluid v 2fluid Þ

ð3Þ

where sf denotes the shear stress in the vertical wellbores, which is discussed in detail in Appendix C. 3. Numerical solution of the mathematical model In this paper, the established model is solved by numerical method. The energy and momentum balance equations are represented as difference equations, as shown below:

f ðpfluid;out Þ ¼ pr 2ai ðpfluid;out  pfluid;in Þ qfluid;out þ qfluid;in  pr2ai g cos h Dz þ sf 2 þ pr2ai ðqfluid;out v 2fluid;out  qfluid;in v 2fluid;in Þ

ð4Þ

where pfluid;out and qfluid;out denote the outlet pressure and density of the mixed fluid, respectively; pfluid;in and qfluid;in denote the inlet pressure and density of the mixed fluid, respectively; Dz is the length of the segment; v fluid;out and v fluid;in denote the flow velocity of the mixed fluid at the outlet and inlet of the segment, respectively.

f ðT fluid;out Þ ¼

qfluid;out þ qfluid;in ðhfluid;out  hfluid;in Þ þ wfluid 2 ! Dz 2 2 d v fluid;out v fluid;in  wfluid g cos h þ wfluid  Dz 2 2

ð5Þ

where qfluid;out and qfluid;in denote the heat transfer rate from the mixed fluid to formation per unit depth at the outlet and inlet of the segment, respectively, W/m; hfluid;out and hfluid;in denote the specific enthalpy of the mixed fluid at the outlet and inlet of the segment, respectively. Given the fact that the injection parameters at well-head are known, pressure and temperature at outlet of the first segment can be calculated using Eqs. (4) and (5) with iteration method. Then, this pair of pressure and temperature are input for the inlet

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of the second segment and another iteration begins. Finally, distributions of pressure and temperature along the entire vertical wellbore are obtained. 4. Results and discussions 4.1. Injection temperature In this section, effect of injection temperature on the profiles of thermophysical properties of the mixed fluid is discussed in detail. Different injection temperature (590, 610 and 630 K) are input into the model under the condition that the injection pressure and mass flow rate are kept unchanged. Besides, in order to study the effect of mass fraction of CO2 on the profiles, different mass fraction of CO2 (CO2: SHS = 10%: 90%, 30%: 70% and 50%: 50%) are added for comparison, as shown in Fig. 3. Fig. 3(a) shows that: (a). the pressure gradient increases with increasing injection temperature when the mass fraction of CO2 is kept unchanged. This is because the density of the mixed fluid decreases with increasing injection temperature, which caused the increase of flow velocity. As a result, the shear stress increases which causes larger pressure drop. (b). the pressure gradient decreases with increasing mass fraction of CO2 when injection temperature is kept unchanged. This is because the molecular weight of CO2 is larger than that of SHS. Accordingly, the density of the mixed fluid increases with increasing mass fraction of CO2, which causes decrease of flow velocity. Consequently, the pressure gradient decreases with increasing mass fraction of CO2. Fig. 3(b) shows that: (a). temperature of the mixed fluid increases with increasing injection temperature. However, the temperature gradient is almost constant. (b). temperature of the mixed fluid decreases with increasing mass fraction of CO2. As shown in Fig. 3(c), the change rule of superheat degree is similar to that of temperature. Fig. 3(d) shows the effect of mass fraction of CO2 on temperature and superheat degree at well-bottom when injection temperature at well-head is 590 K. It is found that both temperature and superheat degree at well-bottom decrease with increasing mass fraction of CO2. Consequently, in order to obtain a higher superheat degree, a higher injection temperature and a lower mass fraction of CO2 are suggested. However, the increase of injection temperature leads to the increase of cost and the decrease of mass fraction of CO2 reduces the oil displacement efficiency. Therefore, practicing engineers are suggested to weigh the advantages and disadvantages before determining the parameters of steam injection with help of the model. In fact, CO2 is used to increase the fluidity of heavy oil through miscible displacement but not heating heavy oil to a higher temperature, as shown in Fig. 3(e). Fig. 3(e) shows that the enthalpy of the mixed fluid decreases significantly with increasing mass fraction of CO2. 4.2. Injection pressure

Fig. 2. Force analysis of fluid in an arbitrary segment of the vertical wellbore.

In this section, effect of injection pressure on the profiles of thermophysical properties of the mixed fluid is discussed in detail. Different injection pressure (3, 4 and 5 MPa) are input into the model under the condition that the injection temperature and mass flow rate are kept unchanged. Besides, in order to study the effect of mass fraction of CO2 on the profiles, different mass fraction of CO2 (CO2: SHS = 10%: 90%, 30%: 70% and 50%: 50%) are added for comparison, as shown in Fig. 4. Fig. 4(a) shows that: (a). The pressure increases with increasing injection pressure. (b). The pressure increases with increasing mass fraction of CO2. Fig. 4(b) shows that: (a). The temperature increases with increasing injection pressure. (b). The temperature decreases

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Fig. 3. Effect of injection temperature and mass fraction of CO2 on the profiles of thermophysical properties of the mixed fluid in wellbores.

with increasing mass fraction of CO2. Fig. 4(c) shows that: (a). Superheat degree decreases with increasing injection pressure. (b). Superheat degree decreases with increasing mass fraction of CO2. Fig. 4(d) further shows that the enthalpy of the mixed fluid decreases with increasing mass fraction of CO2. Therefore, in order to obtain a higher superheat degree at well-bottom, a lower injec-

tion pressure and a smaller mass fraction of CO2 are suggested. However, as mentioned above, a smaller mass fraction of CO2 cannot take full use of the advantages of CO2 in miscible or immiscible displacement for heavy oil recovery. Besides, a lower injection pressure may cause smaller amount of the mixed fluid injected into the oil layer, which leads to worse heating effect. Conse-

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Fig. 4. Effect of injection pressure and mass fraction of CO2 on the profiles of thermophysical properties of the mixed fluid in wellbores.

quently, practicing engineers are suggested to weigh the advantages and disadvantages before determining the parameters of steam injection with help of the model.

4.3. Mass flow rate In this section, effect of mass flow rate on the profiles of thermophysical properties of the mixed fluid is discussed in detail. Different mass flow rate (100, 150 and 200 t/d) are input into the model under the condition that the injection temperature and pressure are kept unchanged. Besides, in order to study the effect of mass fraction of CO2 on the profiles, different mass fraction of CO2 (CO2: SHS = 10%: 90%, 30%: 70% and 50%: 50%) are added for comparison, as shown in Fig. 5. Fig. 5(a) shows that the pressure decreases with increasing mass flow rate when the mass fraction of CO2 is kept unchanged. This is because the shear stress increases with increasing mass flow rate, which causes more friction loss. Fig. 5(b) shows that the temperature increases at first but turns to decrease with increasing mass flow rate when the mass fraction of CO2 is kept unchanged. This is because when mass flow rate is very small, effect of heat loss on fluid temperature is obvious. However, the pressure drop gradually becomes the dominant factor on temperature drop with increasing mass flow rate.

Fig. 5(c) shows that (a). The superheat degree increases with increasing mass flow rate when the mass fraction of CO2 is kept unchanged. (b). The superheat degree decreases with increasing mass fraction of CO2 when the mass flow rate is kept unchanged. Fig. 5(d) shows that (a). The effect of mass flow rate on enthalpy is negligible. (b). Enthalpy of the mixed fluid decreases rapidly with increasing mass friction of CO2.

5. Conclusions In this paper, a numerical model is developed to analyze the effect of CO2 on the profiles of thermophysical properties of the CO2 and SHS mixture in wellbores. Effect of CO2 and the injection parameters on distributions of pressure and temperature are discussed in detail. Some meaningful conclusions are listed below: (a) In order to obtain a higher superheat degree, a higher injection temperature and a lower mass fraction of CO2 are suggested. (b) Superheat degree decreases with increasing injection pressure or with increasing mass fraction of CO2. (c) Superheat degree increases with increasing mass flow rate. (d) Superheat degree decreases with increasing mass fraction of CO2.

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Fig. 5. Effect of mass flow rate and mass fraction of CO2 on the profiles of thermophysical properties of the mixed fluid in wellbores.

Acknowledgements The authors wish to thank the State Key Laboratory of Offshore Oil Exploitation (2015-YXKJ-001). This work was also supported in part by the National Natural Science Foundation Projects of China (51490654), and the National Science and Technology Major Projects of China (2016ZX05042 and 2016ZX05039).

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Appendix A. Supplementary data [9]

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