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Key parameters forecast model of injector wellbores during the dual-well sagd process
PETROLEUM EXPLORATION AND DEVELOPMENT Volume 39, Issue 4, August 2012 Online English edition of the Chinese language journal Cite this article as: PETROL. EXPLOR. DEVELOP., 2012, 39(4): 514–521.
RESEARCH PAPER
Key parameters forecast model of injector wellbores during the dual-well sagd process WU Yongbin1,*, LI Xiuluan1, SUN Xinge2, MA Desheng1, WANG Hongzhuang1 1. State Key Laboratory of Enhanced Oil Recovery, PetroChina Research Institute of Petroleum Exploration and Development, Beijing 100083, China; 2. PetroChina Xinjiang Oilfield Company, Keramay 834000, China
Abstract: Based on parameters forecast model of conventional horizontal injector wellbore, combined with coupling calculation of dual-tubing steam mass flow, the mass conservation equation, energy conservation equation and momentum conservation equation of steam flow within injector wellbore under different tubing combinations in preheating and production phases are formulated and the key parameters calculation model of dual-tubing injector wellbore is established. The temperature and pressure along the injector wellbore during the steam-assisted gravity drainage (SAGD) preheating phase of a SAGD well are calculated and compared with the downhole monitored data, which shows good match and verifies the accuracy of the model. Meanwhile, the model calculates that the minimal steam injection rate during SAGD preheating phase is 60 t/d, the longest horizontal length is 564 m under current configuration. Considering the current configuration has disadvantages of two sections of steam imbibition that may result in risk of section/point steam breakthrough at Point A during SAGD production phase, the combination of long tubing and short tubing is optimized: the short tubing is relocated 150 m from Point A and long tubing is located at Point B. Consequently, three sections of steam imbibition could be realized, and the risk of section/point steam breakthrough at Point A is effectively reduced. Key words: dual horizontal wells; SAGD; parallel-tubing; wellbore; temperature; steam quality; pressure
Introduction During the development of heavy oil reservoirs using Steam Assisted Gravity Drainage (SAGD) , the wellbore configuration of parallel tubing strings is generally used in injectors and producers. Injection by long tubing string and production by short tubing string are the typical processes during SAGD preheating phase by steam circulation, while during SAGD production phase, flexible injection and production schemes can be utilized like long tubing string injection, short tubing string injection, or dual string injection in injectors; long tubing string production, short tubing string production, or dual string production in producers, etc. Through flexible changes of tubing string combination for producers and injectors, the uniform development of steam chamber in horizontal section during SAGD process can be achieved [1]. As for producers, the conventional approach is mainly used to maintain downhole operation pressure to stabilize the steam-liquid level, therefore the regulation of producer is relatively simple and easy. While as for injectors, the steam properties along horizontal section are of great significance, since the low steam quality from the injector screener to the formation or
the non-uniform steam imbibition along horizontal section can always severely affect the steam chamber development and SAGD performance. Consequently, precise forecast of the key factors of steam along horizontal section during SAGD process is critical to optimizing the injector wellbore configuration, determining optimal injection parameters, and realizing uniform steam imbibition along horizontal section and efficient SAGD development. The parameter calculation model for steam injection wellbore of conventional horizontal wells is only feasible for processes of Cyclic Steam Stimulation or steam flooding in horizontal injectors with no tubing string in horizontal section but not feasible for the horizontal injector with dual tubing string. As for conventional horizontal injectors with no tubing strings in horizontal section, the steam flow in horizontal section is characterized as two types: linear flow along horizontal section and radial flow perpendicular to horizontal section from horizontal screener to the formation. While as for horizontal SAGD injectors with dual tubing strings, since the long tubing string lands at the toe (point B) and the short tubing lands at the heel (point A), therefore, the steam flow in long
Received date: 01 Aug. 2011; Revised date: 30 Mar. 2012. * Corresponding author. E-mail: [email protected] Foundation item: Supported by the National Science and Technology Major Project “Key Technologies for Heavy/Super-heavy Oil Reservoirs Development” (2011ZX05012). Copyright © 2012, Research Institute of Petroleum Exploration and Development, PetroChina. Published by Elsevier BV. All rights reserved.
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tubing string is a linear flow while after the steam comes out from the point B of long tubing string and flows into the annulus, the steam flow changes into the linear flow along the annulus and the radial flow perpendicular to the annulus into the formation, while the steam from the short tubing string flows into the annulus directly, and the steam flow is the linear flow along the annulus and the radial flow perpendicular to the annulus into the formation. Meanwhile, heat and mass transfer occur where the steam from the long tubing string and that from the short tubing string meet in the annulus, therefore the coupling calculation of heat and mass flow is necessary. Based on parameter forecast model of conventional horizontal injector wellbore, combined with coupling calculation of dual-tubing steam mass flow, the mass conservation equation, energy conservation equation and momentum conservation equation of steam flow within injector wellbore under different tubing combinations in preheating and production phases are formulated and the key parameter calculation model along dual-tubing injector wellbore are established. Using the real reservoir properties and parameters of SAGD wellbore configuration, the model formulated in this paper is used to calculate the changes of temperatures and pressures during SAGD preheating phase and make comparison with the real monitored temperature and pressure data. The precise match verifies the reliability of the model, after which, the lowest steam injection rate during SAGD preheating phase, the longest horizontal length under current wellbore configuration and the optimization of wellbore configuration are calculated by example.
1 1.1
Parameter calculation model along wellbore Basic assumptions
During dual-horizontal well SAGD process, the basic assumptions for horizontal injector wellbore with two tubing strings (Fig. 1) are as follows: (1) The oil formation where horizontal injector locates is flat (dip angle: 0) in structure and homogeneous in reservoir properties with unique pay zone thickness and infinite drainage area; (2) Short tubing string lands at point A and long tubing string lands at point B in horizontal section; (3) Parameter calculation starts from point A and the effects of tubing coupling and screener hanger on steam heat loss are not considered. The heat transfer from the wellbore to the
Fig. 1 Wellbore configuration of dual-tubing horizontal injectors during SAGD process
outer edge of screener is steady-state while the heat transfer from the outer wall of the screener to the formation is non-steady state. (4) Parameters of the steam quality, injection pressure, injection steam rate at point A are constants and known constants. Based on the assumptions above and the conventional mass conservation equation, energy conservation equation and momentum conservation equation of steam flow in horizontal injectors [2], the three equations of steam flow within dual string injector wellbores under different tubing combinations during preheating and production phases of SAGD are established. 1.2
Mass conservation equation
As for a random micro-segment in horizontal wellbore of conventional horizontal injectors, the basic mass conservation equation for steam flow is [2]: wU 'vsx 't Adx m 't vis dx't (1) wt 1.2.1
SAGD preheating phase by steam circulation
The mass conservation equation for steam flow in horizontal wellbore during SAGD preheating phase is discussed in two cases: (1) The steam is injected down the long tubing string and travels back to the surface through the short tubing string. Since under this condition no steam flows into the formation in the long tubing string, the vis is 0, therefore the mass conservation equation for steam flow in the long tubing string is: wU 'vsx 't Aldx m 't 0 (2) wt (2) The steam flows out of the long tubing string at point B and flows to point A through the annulus. since under this condition part of steam flows into the formation under pressure difference between the annulus and the formation, the vis does not equal to 0, therefore the mass conservation equation for steam flow in the annulus is: wU 'vsx 't Aa dx m 't vis dx't (3) wt 1.2.2
SAGD production phase
The mass conservation equation for steam flow in horizontal wellbore during SAGD production phase is discussed in three cases: (1) Only long tubing string injection. The mass conservation equation for steam flow in the long tubing string fulfills the equation (2), while the mass conservation equation for steam flowing out from the string at point B into the annulus and then enters into the formation fulfills the equation (3). (2) Only short tubing string injection. The steam flows into the annulus at point A directly, and then enters into the formation along horizontal section; therefore the mass conservation equation fulfills the equation (3).
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(3) Dual tubing string injection simultaneously. In this case, as for a random micro-segment in horizontal wellbore, the steam from the short tubing string flows into this random micro-segment in the annulus from point A with the mass flow velocity vsxs, and the steam from the long tubing string flows into this random micro-segment in the annulus from point B with the mass flow velocity vsxl, therefore during a unit time, the mass difference of steams flowing in and out of the random micro-segment is expressed as: x L x 'vsxt ' vsxs vsxl ' ª vss ³ viss dx vsl ³ visl dx º (4) «¬ »¼ 0 0 Put the equation (4) into the equation (3) and acquire the mass conservation equation of steam flow at a random micro-segment in the annulus during simultaneous dual string steam injection as follows: wU 'vsxt 't Aa dx m 't visdx't (5) wt
1.3
Energy conservation equation
The energy conservation equation of steam flow in horizontal wellbore of conventional horizontal wells is expressed as: during a unit time, the incremental formation energy per unit length equals to the energy loss of the steam itself per unit length minus the friction energy loss per unit length and the heat loss per unit length [2], which is expressed as follows: § v v2 · d ¨ vsx hm sx m ¸ 2 § 2 ¹ dQ v v · dW (6) ¨ vis hm is r ¸ © 2 ¹ dx dx dx © 1.3.1
ª v § 1 dT 1 · dp 1 dvsx º vm vsx « sx ¨ ¸ » A T p p x A U U m dx ¼ d d ¹ ¬ m©
SAGD preheating phase
The energy conservation equation for steam flow in horizontal wellbore during SAGD preheating phase is discussed in two cases: (1) No steam flows into the formation from the long tubing string, therefore, vis and vr equal to zero, and the energy conservation equation in the long tubing string is: § v v2 · d ¨ vsxhm sx m ¸ 2 ¹ dQ dW © (7) 0 dx dx dx (2) Steam flows out from the long tubing string at point B into the annulus and enters into the short tubing string at point A, therefore the energy conservation equation for steam flow in the annulus fulfills the equation (6). 1.3.2
(2) Only short tubing string injection. The steam flows into the annulus at point A directly, and then enters into the formation along horizontal section; therefore the energy conservation equation fulfills the equation (6). (3) Dual tubing string injection simultaneously. In this case, as for a random micro-segment in the annulus, the flow velocity of the steam from short tubing string flows into this random micro-segment is vms, and the flow velocity of the steam from long tubing string flows into this random micro-segment is vml, which is in the opposite direction with vms. Therefore the value of the steam flow rate vm in this random micro-segment is the absolute difference between the vml and vms. Since the steam mass flow rate at a random micro-segment in the annulus is expressed as the equation (4), and the steam mass imbibition rate of the formation per unit length equals to the steam from the dual tubing strings , therefore the energy conservation equation in the annulus for steam injection from the dual tubing strings simultaneously is: ª v v v2 º dW « viss visl hm iss isl r » 2 ¬ ¼ dx 2 ª v v v º d «vsxt hm sxt ms ml » 2 ¬« ¼» dQ (8) dx dx According to the steam energy loss equation and PVT phase equation, the equation (6) can be converted into: dh dp dQ dW § vm2 vr2 · dvsx ¨ ® w vsx ¸ dx dx © 2 ¹ dx ¯ dp dx
SAGD production phase
The energy conservation equation for steam flow in horizontal wellbore during SAGD production phase is discussed in three cases: (1) Only long tubing string injection. The energy conservation equation for steam flowing in the long tubing string fulfills the equation (7), while the energy conservation equation for steam flowing into the annulus from the long tubing string at point B and then entering into the formation fulfills the equation (6).
§ dh dh · dp dq °½ vsx ¨ s w ¸ vsx hs hw ¾ p p x d d d dx ¿° © ¹
(9)
N1 vsx hs hw
(10)
where
§ dh dh · dp vsx ¨ s w ¸ © dp dp ¹ d x 2 dQ dW vm vr2 dvsx dhw dp vsx dx dx 2 dx dp dx N2
N3
ª v § 1 d T 1 · dp 1 dvsx º vm vsx « sx ¨ ¸ » ¬ AUm © T dp p ¹ dx AUm dx ¼
(11)
(12)
The edge conditions of q x 0 q0 and p x 0 p0 are substituted into the equation (9) to solve the first-order ordinary differential linear equations, and the equation of the steam quality along the annulus is formulated in the case of long tubing string injection and short tubing string production during SAGD preheating phase, and only long or short tubing string injection during SAGD production phase: § N ·ª N §N · N º q exp ¨ 2 x ¸ « 3 exp ¨ 2 x ¸ q0 3 » (13) N2 »¼ © N1 ¹ «¬ N2 © N1 ¹ Similarly, the equation of the steam quality along the annulus is deduced by solving the equation (8) in the case of steam
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injection from the dual tubing strings simultaneously during SAGD production phase: § N ' ·ª N ' §N ' · N 'º q exp ¨ 2 x ¸ « 3 exp ¨ 2 x ¸ q0 3 » (14) N2 ' ¼» © N1 ' ¹ ¬« N2 ' © N1 ' ¹ where
N1 ' vsxt hs hw
(15)
§ dh dh · dp N2 ' vsxt ¨ s w ¸ © dp dp ¹ dx
(16)
2 dQ dW vms vml vr dvsxt dhw dp vsxt dx dx 2 dx dp dx 2
N 3c
ª v § 1 dT 1 · dp 1 dvsxt º vms vml vsxt « sxt ¨ ¸ » A T d p p d x A U Um dx ¼ ¹ ¬ m© 1.4
(17)
Momentum conservation equation
The pressure of the wet steam along horizontal section for a conventional horizontal well is [2]: dv W 2vm is c dp 1 d x dx (18) dx A § 1 dT 1 · vm vis 1 ¨ ¸ © T dp p ¹ A 1.4.1 SAGD preheating phase
The momentum conservation equation for steam flow in horizontal wellbore during SAGD preheating phase is discussed in two cases: (1) The vis equals to zero during SAGD preheating phase, therefore the pressure loss of steam along long tubing string is: dp Wc c (19) dx Aldx
dom time point can be obtained by solving the equation (22) . 1.4.2
The momentum conservation equation for steam flow in horizontal wellbore during SAGD production phase is discussed in three cases: (1) Only long tubing string injection. The pressure along the long tubing string fulfills the equation (21), while when the steam flows into the annulus from the long tubing string at point B and enters into the formation along the annulus, the pressure distribution fulfills the equation (22). (2) Only short tubing string injection. The steam flows into the annulus from point A directly and enters into the formation along the annulus; therefore the momentum conservation equation fulfills the equation (18). The pressure distribution along the annulus in this case is obtained by solving the equation (18): 2 v v § dT pc · ʌDcx § vmx vmx 1 · pc p0 ms iss ¨ ln ¸ f cc U m ¨ ¸ (23) Aa © T p0 ¹ 8 Aa © 2 ¹ (3) Steam injection from the long and short tubing strings simultaneously. The pressure distribution in the long tubing string fulfills the equation (21). Since the steam flow velocity at a random micro-segment along the annulus equals to the absolute velocity of steam from the long tubing string minus that from the short tubing string and the steam imbibition in this segment equals to the total imbibition of steam from the long and short tubing strings, therefore the pressure distribution in the annulus is formulated as follows: v v (v v ) § dT pc · pc p0 ms ml iss isl ¨ ln ¸ Aa T p 0 ¹ ©
f ccU m
The edge condition is: p x 0 p0 and the IJcƍ can be calculated using the equation as follows:
W cc
fc Um
ʌDdx § vm x vmx 1 · ¨ ¸ 8 © 2 ¹
2
(20)
The edge condition above and the equation (20) are put into the equation (19) to solve the differential linear equation as follows: p
p0 fc Um
ʌDx § vm x vmx1 · ¨ ¸ 8 Al © 2 ¹
2
(21)
The steam pressure along long tubing string during SAGD preheating phase can be obtained by solving the equation (21). As for the exit point of the long tubing string (point B), since the vmx=vmx+1=vmB, therefore the pressure at point B is : pB=p0 fcȡmʌDLvmB2/8Al. (2) Transforming the coordination system taking the point B as the origin of coordinates to calculate the coupling pressure along the annulus, therefore the p x 0 pB . The pB is put into the equation (18) to solve the first-order ordinary differential equation to obtain the steam pressure pƍ along the annulus: pc
pB
vmlvisl § dT pc · ʌDcx § vmx vmx 1 · ln ¸ fccUm ¨ ¨ ¸ Aa © T pB ¹ 8 Aa © 2 ¹
2
(22)
The pƍ from SAGD circulation preheating phase to a ran-
SAGD production phase
1.5
ʌDcx § vmsx vmsx 1 vmlx vmlx 1 · ¨ ¸ 8 Aa © 2 ¹
2
(24)
The calculation of the unknown variables
(1) The calculation of the wet steam density. The method of Beggs-Brill [3,4] is used to calculate the wet steam density. Firstly, the flow type is determined according to the fluid flow velocity and the flow diameter in the horizontal section, and then, the wet steam density is calculated according to the flow type. (2) The steam imbibition vis in a random micro-segment in horizontal wellbore can be calculated as follows [58]: vis Um Is ps pi Jliq (25) (3) The calculation of the friction coefficient fc between the steam and the inner wall of the long tubing string. The fc is a function of the Reynolds number of steam (Res=Dvmȡm/ȝ) and the relative roughness of the inner wall of the long tubing string (ǻ=İ/D) [913]. When Resİ2 000, fc=54/Res; when Res>2 000, fc=[1.142 lg(ǻ+21.25 Res0.9)]2. Similarly, the friction coefficient fcƍ between the steam and the inner wall of the screener is expressed as: fcƍ=[1.142 lg(ǻƍ+21.25 Resƍ 0.9)]2, in which Resƍ=Dƍvmȡm/ȝ and ǻƍ=İ/Dƍ. (4) The heat transfer calculation between the random mi-
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cro-segment and the formation. The equation of heat loss from the inner wall of the long tubing string to the formation for the steam in a random micro-segment of the long tubing string is: dQ Tl Te (26) dx R While in the annulus, the heat loss of steam from the inner wall of the screener to the formation in a random micro-segment is: dQc Ta Te (27) dx Rc Equations (26) and (27) can be used to calculate the steam heat loss during SAGD preheating phase and SAGD production phase with different combinations of injection and production tubing strings. The total thermal resistance from the inner wall of the long tubing string to the formation is: 1 ª 1 f (t ) ln(rso / rsi ) º R (28) « » 2ʌ ¬ hrlo Oe Os ¼ The total thermal resistance from the inner wall of the screener to the formation is: 1 ª f (t ) ln(rso /rsi ) º Rc (29) « » 2ʌ ¬ Oe Os ¼ where
2.1
Fig. 3 Comparison of the calculated temperature and monitored temperature for Well A-1
culated results agree precisely with the monitored data with only 0.2% of pressure error and 0.19% of temperature error, which validates the reliability of the model.
§ 2 Dt · f (t ) ln ¨¨ ¸¸ 0.29 © rso ¹
2
Fig. 2 Comparison of the calculated pressure and monitored pressure for Well A-1
Model validation and application
2.2
Model validation
A SAGD injector A-1 in a SAGD pilot test area is used as an example to calculate the pressure and temperature distribution along the long tubing string and the annulus during SAGD preheating phase using the model formulated in this paper. The parameters of the horizontal wellbore are as follows: the horizontal length is 460 m, the well is completed with 177.8 mm (7 in) slotted screener, the inner and outer diameters of the screener are 166.8 mm and 177.8 mm respectively and the heat conductivity is 0.993 W/(m·K), the diameters of the short long tubing strings are 73 mm (2 7/8 in) and 88.9 mm (3 1/2 in)respectively, the inner diameters of the short and long tubings are 62 mm and 77.9 mm respectively, the absolute roughness and the thermal conductivity of the short and long tubing strings are 0.000 05 m and 0.8 W/(m·K) respectively, and 7 thermocouples and piezometers are even distributed along the annulus. Other parameters in the calculation are as follows: the formation temperature is 19 qC, the thermal conductivity of the formation rock is 1.73 W/(m·K), the formation thermal diffusivity is 0.004 m2/hm. During SAGD preheating phase, the steam injection rate is 100 t/d, the downhole steam quality at point A is 60%, the steam injection pressure is 2.5 MPa and the steam temperature is 224 qC. Figs. 2 and 3 are the calculated and monitored results of pressure and temperature along the long tubing string and the annulus of Well A-1. And Figs. 2 and 3 indicate that the cal-
Model applications
The model formulated in this paper is used to calculate the lowest steam injection rate during SAGD preheating phase and the longest horizontal length, and to optimize the wellbore configuration during SAGD production phase according to the reservoir properties and the parameters of the current wellbore configurations of Well A-1. 2.2.1 The calculation of the lowest steam injection rate during SAGD preheating phase
During SAGD preheating phase, the steam is required to have a certain degree of steam quality at Point A when the steam flows from the long tubing string into the annulus at Point B and enters into the short tubing string at Point A so as to ensure the uniform preheating effect in the horizontal section. If the steam quality is zero at Point A, the fluid is water and the liquid holdup at Point A will happen because of in-sufficient power of fluid to flow up from the bottom of the short tubing string to the wellhead. And long-term liquid holdup at Point A will cause preferential heat communication between the injector and the producer in the horizontal section around Point A [14,15], which will cause the steam breakthrough during SAGD production phase. Therefore, the key of determining the lowest steam injection rate is to ensure that the steam quality of the steam flowing back to Point A is above zero. Under the current wellbore configuration of Well A-1, assuming that the steam quality at the entrance of the long
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tubing is 60%, the steam quality along the annulus at the steam injection rates of 0.46 kg/s(40 t/d), 0.69 kg/s(60 t/d), 0.93 kg/s(80 t/d), 1.16 kg/s(100 t/d) is calculated (Fig. 4). The calculation results reveal that when the steam injection rate is 60 t/d, the steam quality of the steam flowing back from the annulus to Point A is 0.2%, while further reducing the steam injection rate to 40 t/d, the fluid flowing back along the annulus to Point A is the hot water with no steam quality, therefore the lowest steam injection rate during SAGD preheating phase is 60 t/d. 2.2.2 The calculation of the longest horizontal length in SAGD process
According to the successful experiences of the foreign SAGD projects, the highest pressure difference along the annulus should not exceed 0.05 MPa during SAGD production phase so as to ensure the uniform steam imbibition along the horizontal section [15,16]. Therefore under conditions of 177.8 mm (7 in) slotted screener completion, 300t/d steam injection rate, and 2.5MPa steam injection pressure at point A, the pressure difference is calculated in the annulus of different horizontal lengths in three cases of wellbore configuration: no long tubing string, 73 mm (2 7/8 in) long tubing string and 88.9 mm (3 1/2 in) long tubing string (Fig. 5). The calculation results reveal that in the case of no long tubing string in horizontal section, the longest horizontal length that fulfills the pressure difference of 0.05 MPa can reach 1500m, when 73 mm (2 7/8 in) long tubing string runs into the horizontal section, the longest horizontal length is 751 m and when 88.9 mm (3 1/2 in) long tubing string runs into the horizontal section, the longest horizontal length is 564 m. therefore under current wellbore configuration and 460m horizontal length, the steam injection rate 300 t/d can fulfill the requirement of highest pressure difference lower than 0.05 MPa. 2.3 Optimization of injector wellbore configuration in SAGD production phase
The injector wellbore configuration of short tubing string landing at point A and long tubing string landing at point B is
Fig. 4 Steam quality along the long tubing string and the annulus under different steam injection rates
Fig. 5 Relationships between pressure difference in horizontal section and the horizontal length in the case of no long tubing string, 73 mm long tubing string and 88.9 mm long tubing string
extensively used in the current SAGD pilot test area (Fig. 6a). The production performance shows that the steam chamber develops better at point A and point B, even the steam channeling and steam breakthrough occur nearby at point A and point B in some SAGD wells, while no steam chamber or steam chamber develops poorly in the middle of the horizontal section. In order to improve the steam chamber development in horizontal section so as to enhance the tapping efficiency of the formation in the horizontal section, the model formulated in this paper is used to calculate the steam mass rate along the annulus in two cases of wellbore configuration: short tubing string lands at point A and long tubing string lands at point B (Fig. 6a) ( Case 1); short tubing string lands at 150 m behind point A and long tubing string lands at point B (Fig. 7a) (Case 2). According to the field data, the steam rate of the long tubing string is 100t/d while the steam rate of the short tubing string is 150t/d, which means that the proportion of the steam injection rate between the long tubing string and the short tubing string is 2:3. Using the wellbore configuration data and the steam injection data above, the calculation results of steam mass flow rate along the annulus indicate that in Case 1, the steam mass rate from point A and point B into the middle of the horizontal section becomes smaller and smaller gradually because of the steam imbibition in the horizontal section, and the steam mass imbibition rate along the entire horizontal section is distributed as two sections (Fig. 6b). While as for Case 2, the steam from the short tubing string is divided into two portions under the pressure difference between the exit point of the short tubing string and other parts of the horizontal section, one portion of steam flows towards the heel and the other portion of steam flows towards the middle section. Therefore the steam mass imbibition rate along the entire horizontal section is distributed as three sections (Fig. 7b). by using the optimized wellbore configuration (Case 2), the steam from the short tubing string is effectively divided and the steam mass rate is reduced at the exit of the short tubing string, therefore the steam imbibition along the horizontal section is more uniform and the risk of the steam breakthrough at point A can be effectively reduced. And the
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monitored data and verifying the reliability of the model. Meanwhile, the model is used to calculate the minimal steam injection rate during SAGD preheating phase is 60 t/d, the longest horizontal length is 564 m under current configuration. The current configuration has disadvantages of two sections of steam imbibition resulting in risk of section/point steam breakthrough at point A during SAGD production phase, so the combination of long tubing string and short tubing string is optimized: the short tubing string lands at 150 m behind point A and long tubing string lands at point B. Consequently, 3 sections of steam imbibition can be realized, and the risk of section/point steam breakthrough at point A is effectively reduced.
Nomenclature Fig. 6 Wellbore configuration and steam mass flow rate along the annulus before optimization
Fig. 7 Wellbore configuration and steam mass flow rate along the annulus after optimization
wellbore configuration of Case 2 has been recommended as the injector wellbore configuration for the extended SAGD pilot test.
3
Conclusions
Based on the parameter forecast model of conventional horizontal injector wellbore, combined with coupling calculation of dual-tubing steam mass flow, the mass conservation equation, energy conservation equation and momentum conservation equation of steam flow within injector wellbore under different tubing combinations in preheating and production phases are formulated and the key parameter calculation model along the dual-tubing injector wellbore are established. Take the reservoir properties and injector wellbore configurations of a SAGD pilot test area as an example, the changes of temperature and pressure along the injector wellbore during SAGD preheating phase are calculated, showing that the simulation data has a good match to the downhole
L—Horizontal length between point A and point B, m; vsx—Steam mass flow rate in a random micro-segment in the horizontal section, kg/s; t—Time, s; A—Cross section area in the horizontal section for conventional horizontal wells, m2; x—Location of a random point A along the horizontal wellbore, m; ȡm—Fluid density in the micro-segment, kg/m3; vis—Steam mass imbibition rate in the horizontal section per unit length, kg/s; Al—Cross section area of the long tubing string, m2; Aa—Cross section area of the annulus, m2; vsxt—Steam mass flow rate in the random micro-segment of annulus in the case of the dual string injections, kg/s; vsxs—Steam mass flow rate in a random micro-segment of the annulus in the case of only short tubing string injection, kg/s; vsxl—Steam mass flow rate in a random micro-segment of the annulus in case of only long tubing string injection, kg/s; vss—Steam mass flow rate in the short tubing string, kg/s; viss—Mass imbibition rate of the formation to the steam per unit length from the short tubing, kg/s; vsl—Steam mass flow rate in the long tubing string, kg/s; visl—Mass imbibition rate of the formation to the steam per unit length from the long tubing, kg/s; hm—Heat enthalpy of steam, J/kg; vr—Flow velocity of steam into the formation, m/s; W—Power the friction has done in a unit time, W; vm—Flow velocity of steam in the random micro-segment, m/s; Q—Heat loss of steam in a unit time, W; vms—Flow velocity of steam from the short tubing string into a random micro-segment of the annulus, m/s; vml—Flow velocity of steam from the long tubing string into a random micro-segment of the annulus, m/s; T—Temperature of wet steam in a random micro-segment, qC; hw—Heat enthalpy of the condensed water in the random micro-segment, J/kg; p—Pressure of wet steam in a random micro-segment, Pa; hs—Heat enthalpy of the dry steam in a random micro-segment, J/kg; q—Steam quality in a random micro-segment,%; q0—Steam quality at point A in the wellbore, %;
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p0—Steam pressure at point A in the wellbore, Pa; IJc—Shear friction between the fluid in the wellbore and the inner wall of the screener, N; IJcƍ—Shear friction between the fluid and the inner wall of the long tubing string, N; fc—Friction coefficient between wet steam and the inner wall of the long tubing string, dimensionless; D—Inner diameter of the long tubing, m; vmx—Steam flow velocity at a random micro-segment of dx in the wellbore, m/s; vmx+1—Steam flow velocity at a random micro-segment of dx+1 in the wellbore, m/s m/s; pB—Steam pressure at point B, Pa; vmBüSteam flow velocity at poing B, m/s; pƍ—Steam pressure at point in the wellbore where the distance from point B is x, Pa; fcƍ—Friction coefficient between wet steam and the inner wall of the screener, dimensionless; Dƍ—Inner diameter of the screener, m; vmsx—Flow velocity of steam from the short tubing string at a random micro-segment of dx in the annulus, m/s; vmsx+1—Flow velocity of steam from the short tubing string at a random micro-segment of dx+1 in the annulus, m/s; vmlx—Flow velocity of steam from the long tubing string at a random micro-segment of dx in the annulus, m/s; vmlx+1—Flow velocity of steam from the long tubing string at a random micro-segment of dx+1 in the annulus, m/s; Is—Steam imbibition index of the formation per unit horizontal length, m1; ps—Average steam injection pressure, Pa; pi—Initial reservoir pressure before steam injection, Pa; Jliq—Liquid production index of the formation, m3/(Pa·s); ȝ—Wet steam viscosity in the annulus, Pa·s; İ—Absolute roughness of the inner wall of the screener, m; Tl—Steam temperature at a random micro-segment of the long tubing string, K; Te—Formation temperature outside of the random micro-segment, K; R—Total heat resistance from inner wall of the long tubing string to the formation, (m·K)/W; Qƍ—Heat loss of steam in a random micro-segment of annulus in a unit time, W; Ta—Steam temperature in a random micro-segment of annulus, K; Rƍ—Total heat resistance from inner wall of the annulus to the formation, (m·K)/W; h—Convective heat transfer coefficient of the long tubing, W/(m2·K); rlo—Outer radius of the long tubing, m; Ȝe—Thermal conductivity of the formation, W/(m·K); rso—Outer radius of the screener, m; rsi—Inner radius of the screener, m; Ȝs—Thermal conductivity of the screener, W/(m·K); Į—Thermal diffusivity of the formation, m2/s.
dual-well SAGD heat circulation. Journal of Southwest Petroleum University: Science & Technology Edition, 2010, 32(4): 103–108. [2]
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[10] Clark H P, Ascanio F A, Kruijsdijk C V, et al. Method to improve thermal EOR performance using intelligent well technology: Orion SAGD field trial. SPE 137133, 2010. [11] Zhang Yufeng, Wu Xiaodong, Zhang Yumin, et al. Two-phase closed thermosyphon (TPCT) decreases heat loss of liquid within heavy oil wellbores. Petroleum Exploration and Development, 2011, 38(2): 228–232. [12] Guan Wenlong, Xi Changfeng, Chen Yaping, et al. Fireflooding technologies in post-steam-injected heavy oil reservoirs. Petroleum Exploration and Development, 2011, 38(4): 452–462. [13] Bao X, Chen Z J, Wei Y, et al. Geostatistical modeling and numerical simulation of the SAGD process: Case study of an Athabasca reservoir with top water and gas thief zones. SPE 137435, 2010. [14] Klemin D, Pimenov V, Rudenko D. Development of effective numerical model for heavy oil production using steam-assisted gravity drainage. SPE 117387, 2008. [15] Li P, Chalaturnyk R J. History match of the UTF Phase: A project with coupled reservoir geomechanical simulation. PETSOC, 2009, 29(01): 29–35. [16] Li Zhaomin, Lu Teng, Tao Lei, et al. CO2 and viscosity
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RESEARCH PAPER
Key parameters forecast model of injector wellbores during the dual-well sagd process WU Yongbin1,*, LI Xiuluan1, SUN Xinge2, MA Desheng1, WANG Hongzhuang1 1. State Key Laboratory of Enhanced Oil Recovery, PetroChina Research Institute of Petroleum Exploration and Development, Beijing 100083, China; 2. PetroChina Xinjiang Oilfield Company, Keramay 834000, China
Abstract: Based on parameters forecast model of conventional horizontal injector wellbore, combined with coupling calculation of dual-tubing steam mass flow, the mass conservation equation, energy conservation equation and momentum conservation equation of steam flow within injector wellbore under different tubing combinations in preheating and production phases are formulated and the key parameters calculation model of dual-tubing injector wellbore is established. The temperature and pressure along the injector wellbore during the steam-assisted gravity drainage (SAGD) preheating phase of a SAGD well are calculated and compared with the downhole monitored data, which shows good match and verifies the accuracy of the model. Meanwhile, the model calculates that the minimal steam injection rate during SAGD preheating phase is 60 t/d, the longest horizontal length is 564 m under current configuration. Considering the current configuration has disadvantages of two sections of steam imbibition that may result in risk of section/point steam breakthrough at Point A during SAGD production phase, the combination of long tubing and short tubing is optimized: the short tubing is relocated 150 m from Point A and long tubing is located at Point B. Consequently, three sections of steam imbibition could be realized, and the risk of section/point steam breakthrough at Point A is effectively reduced. Key words: dual horizontal wells; SAGD; parallel-tubing; wellbore; temperature; steam quality; pressure
Introduction During the development of heavy oil reservoirs using Steam Assisted Gravity Drainage (SAGD) , the wellbore configuration of parallel tubing strings is generally used in injectors and producers. Injection by long tubing string and production by short tubing string are the typical processes during SAGD preheating phase by steam circulation, while during SAGD production phase, flexible injection and production schemes can be utilized like long tubing string injection, short tubing string injection, or dual string injection in injectors; long tubing string production, short tubing string production, or dual string production in producers, etc. Through flexible changes of tubing string combination for producers and injectors, the uniform development of steam chamber in horizontal section during SAGD process can be achieved [1]. As for producers, the conventional approach is mainly used to maintain downhole operation pressure to stabilize the steam-liquid level, therefore the regulation of producer is relatively simple and easy. While as for injectors, the steam properties along horizontal section are of great significance, since the low steam quality from the injector screener to the formation or
the non-uniform steam imbibition along horizontal section can always severely affect the steam chamber development and SAGD performance. Consequently, precise forecast of the key factors of steam along horizontal section during SAGD process is critical to optimizing the injector wellbore configuration, determining optimal injection parameters, and realizing uniform steam imbibition along horizontal section and efficient SAGD development. The parameter calculation model for steam injection wellbore of conventional horizontal wells is only feasible for processes of Cyclic Steam Stimulation or steam flooding in horizontal injectors with no tubing string in horizontal section but not feasible for the horizontal injector with dual tubing string. As for conventional horizontal injectors with no tubing strings in horizontal section, the steam flow in horizontal section is characterized as two types: linear flow along horizontal section and radial flow perpendicular to horizontal section from horizontal screener to the formation. While as for horizontal SAGD injectors with dual tubing strings, since the long tubing string lands at the toe (point B) and the short tubing lands at the heel (point A), therefore, the steam flow in long
Received date: 01 Aug. 2011; Revised date: 30 Mar. 2012. * Corresponding author. E-mail: [email protected] Foundation item: Supported by the National Science and Technology Major Project “Key Technologies for Heavy/Super-heavy Oil Reservoirs Development” (2011ZX05012). Copyright © 2012, Research Institute of Petroleum Exploration and Development, PetroChina. Published by Elsevier BV. All rights reserved.
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tubing string is a linear flow while after the steam comes out from the point B of long tubing string and flows into the annulus, the steam flow changes into the linear flow along the annulus and the radial flow perpendicular to the annulus into the formation, while the steam from the short tubing string flows into the annulus directly, and the steam flow is the linear flow along the annulus and the radial flow perpendicular to the annulus into the formation. Meanwhile, heat and mass transfer occur where the steam from the long tubing string and that from the short tubing string meet in the annulus, therefore the coupling calculation of heat and mass flow is necessary. Based on parameter forecast model of conventional horizontal injector wellbore, combined with coupling calculation of dual-tubing steam mass flow, the mass conservation equation, energy conservation equation and momentum conservation equation of steam flow within injector wellbore under different tubing combinations in preheating and production phases are formulated and the key parameter calculation model along dual-tubing injector wellbore are established. Using the real reservoir properties and parameters of SAGD wellbore configuration, the model formulated in this paper is used to calculate the changes of temperatures and pressures during SAGD preheating phase and make comparison with the real monitored temperature and pressure data. The precise match verifies the reliability of the model, after which, the lowest steam injection rate during SAGD preheating phase, the longest horizontal length under current wellbore configuration and the optimization of wellbore configuration are calculated by example.
1 1.1
Parameter calculation model along wellbore Basic assumptions
During dual-horizontal well SAGD process, the basic assumptions for horizontal injector wellbore with two tubing strings (Fig. 1) are as follows: (1) The oil formation where horizontal injector locates is flat (dip angle: 0) in structure and homogeneous in reservoir properties with unique pay zone thickness and infinite drainage area; (2) Short tubing string lands at point A and long tubing string lands at point B in horizontal section; (3) Parameter calculation starts from point A and the effects of tubing coupling and screener hanger on steam heat loss are not considered. The heat transfer from the wellbore to the
Fig. 1 Wellbore configuration of dual-tubing horizontal injectors during SAGD process
outer edge of screener is steady-state while the heat transfer from the outer wall of the screener to the formation is non-steady state. (4) Parameters of the steam quality, injection pressure, injection steam rate at point A are constants and known constants. Based on the assumptions above and the conventional mass conservation equation, energy conservation equation and momentum conservation equation of steam flow in horizontal injectors [2], the three equations of steam flow within dual string injector wellbores under different tubing combinations during preheating and production phases of SAGD are established. 1.2
Mass conservation equation
As for a random micro-segment in horizontal wellbore of conventional horizontal injectors, the basic mass conservation equation for steam flow is [2]: wU 'vsx 't Adx m 't vis dx't (1) wt 1.2.1
SAGD preheating phase by steam circulation
The mass conservation equation for steam flow in horizontal wellbore during SAGD preheating phase is discussed in two cases: (1) The steam is injected down the long tubing string and travels back to the surface through the short tubing string. Since under this condition no steam flows into the formation in the long tubing string, the vis is 0, therefore the mass conservation equation for steam flow in the long tubing string is: wU 'vsx 't Aldx m 't 0 (2) wt (2) The steam flows out of the long tubing string at point B and flows to point A through the annulus. since under this condition part of steam flows into the formation under pressure difference between the annulus and the formation, the vis does not equal to 0, therefore the mass conservation equation for steam flow in the annulus is: wU 'vsx 't Aa dx m 't vis dx't (3) wt 1.2.2
SAGD production phase
The mass conservation equation for steam flow in horizontal wellbore during SAGD production phase is discussed in three cases: (1) Only long tubing string injection. The mass conservation equation for steam flow in the long tubing string fulfills the equation (2), while the mass conservation equation for steam flowing out from the string at point B into the annulus and then enters into the formation fulfills the equation (3). (2) Only short tubing string injection. The steam flows into the annulus at point A directly, and then enters into the formation along horizontal section; therefore the mass conservation equation fulfills the equation (3).
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(3) Dual tubing string injection simultaneously. In this case, as for a random micro-segment in horizontal wellbore, the steam from the short tubing string flows into this random micro-segment in the annulus from point A with the mass flow velocity vsxs, and the steam from the long tubing string flows into this random micro-segment in the annulus from point B with the mass flow velocity vsxl, therefore during a unit time, the mass difference of steams flowing in and out of the random micro-segment is expressed as: x L x 'vsxt ' vsxs vsxl ' ª vss ³ viss dx vsl ³ visl dx º (4) «¬ »¼ 0 0 Put the equation (4) into the equation (3) and acquire the mass conservation equation of steam flow at a random micro-segment in the annulus during simultaneous dual string steam injection as follows: wU 'vsxt 't Aa dx m 't visdx't (5) wt
1.3
Energy conservation equation
The energy conservation equation of steam flow in horizontal wellbore of conventional horizontal wells is expressed as: during a unit time, the incremental formation energy per unit length equals to the energy loss of the steam itself per unit length minus the friction energy loss per unit length and the heat loss per unit length [2], which is expressed as follows: § v v2 · d ¨ vsx hm sx m ¸ 2 § 2 ¹ dQ v v · dW (6) ¨ vis hm is r ¸ © 2 ¹ dx dx dx © 1.3.1
ª v § 1 dT 1 · dp 1 dvsx º vm vsx « sx ¨ ¸ » A T p p x A U U m dx ¼ d d ¹ ¬ m©
SAGD preheating phase
The energy conservation equation for steam flow in horizontal wellbore during SAGD preheating phase is discussed in two cases: (1) No steam flows into the formation from the long tubing string, therefore, vis and vr equal to zero, and the energy conservation equation in the long tubing string is: § v v2 · d ¨ vsxhm sx m ¸ 2 ¹ dQ dW © (7) 0 dx dx dx (2) Steam flows out from the long tubing string at point B into the annulus and enters into the short tubing string at point A, therefore the energy conservation equation for steam flow in the annulus fulfills the equation (6). 1.3.2
(2) Only short tubing string injection. The steam flows into the annulus at point A directly, and then enters into the formation along horizontal section; therefore the energy conservation equation fulfills the equation (6). (3) Dual tubing string injection simultaneously. In this case, as for a random micro-segment in the annulus, the flow velocity of the steam from short tubing string flows into this random micro-segment is vms, and the flow velocity of the steam from long tubing string flows into this random micro-segment is vml, which is in the opposite direction with vms. Therefore the value of the steam flow rate vm in this random micro-segment is the absolute difference between the vml and vms. Since the steam mass flow rate at a random micro-segment in the annulus is expressed as the equation (4), and the steam mass imbibition rate of the formation per unit length equals to the steam from the dual tubing strings , therefore the energy conservation equation in the annulus for steam injection from the dual tubing strings simultaneously is: ª v v v2 º dW « viss visl hm iss isl r » 2 ¬ ¼ dx 2 ª v v v º d «vsxt hm sxt ms ml » 2 ¬« ¼» dQ (8) dx dx According to the steam energy loss equation and PVT phase equation, the equation (6) can be converted into: dh dp dQ dW § vm2 vr2 · dvsx ¨ ® w vsx ¸ dx dx © 2 ¹ dx ¯ dp dx
SAGD production phase
The energy conservation equation for steam flow in horizontal wellbore during SAGD production phase is discussed in three cases: (1) Only long tubing string injection. The energy conservation equation for steam flowing in the long tubing string fulfills the equation (7), while the energy conservation equation for steam flowing into the annulus from the long tubing string at point B and then entering into the formation fulfills the equation (6).
§ dh dh · dp dq °½ vsx ¨ s w ¸ vsx hs hw ¾ p p x d d d dx ¿° © ¹
(9)
N1 vsx hs hw
(10)
where
§ dh dh · dp vsx ¨ s w ¸ © dp dp ¹ d x 2 dQ dW vm vr2 dvsx dhw dp vsx dx dx 2 dx dp dx N2
N3
ª v § 1 d T 1 · dp 1 dvsx º vm vsx « sx ¨ ¸ » ¬ AUm © T dp p ¹ dx AUm dx ¼
(11)
(12)
The edge conditions of q x 0 q0 and p x 0 p0 are substituted into the equation (9) to solve the first-order ordinary differential linear equations, and the equation of the steam quality along the annulus is formulated in the case of long tubing string injection and short tubing string production during SAGD preheating phase, and only long or short tubing string injection during SAGD production phase: § N ·ª N §N · N º q exp ¨ 2 x ¸ « 3 exp ¨ 2 x ¸ q0 3 » (13) N2 »¼ © N1 ¹ «¬ N2 © N1 ¹ Similarly, the equation of the steam quality along the annulus is deduced by solving the equation (8) in the case of steam
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injection from the dual tubing strings simultaneously during SAGD production phase: § N ' ·ª N ' §N ' · N 'º q exp ¨ 2 x ¸ « 3 exp ¨ 2 x ¸ q0 3 » (14) N2 ' ¼» © N1 ' ¹ ¬« N2 ' © N1 ' ¹ where
N1 ' vsxt hs hw
(15)
§ dh dh · dp N2 ' vsxt ¨ s w ¸ © dp dp ¹ dx
(16)
2 dQ dW vms vml vr dvsxt dhw dp vsxt dx dx 2 dx dp dx 2
N 3c
ª v § 1 dT 1 · dp 1 dvsxt º vms vml vsxt « sxt ¨ ¸ » A T d p p d x A U Um dx ¼ ¹ ¬ m© 1.4
(17)
Momentum conservation equation
The pressure of the wet steam along horizontal section for a conventional horizontal well is [2]: dv W 2vm is c dp 1 d x dx (18) dx A § 1 dT 1 · vm vis 1 ¨ ¸ © T dp p ¹ A 1.4.1 SAGD preheating phase
The momentum conservation equation for steam flow in horizontal wellbore during SAGD preheating phase is discussed in two cases: (1) The vis equals to zero during SAGD preheating phase, therefore the pressure loss of steam along long tubing string is: dp Wc c (19) dx Aldx
dom time point can be obtained by solving the equation (22) . 1.4.2
The momentum conservation equation for steam flow in horizontal wellbore during SAGD production phase is discussed in three cases: (1) Only long tubing string injection. The pressure along the long tubing string fulfills the equation (21), while when the steam flows into the annulus from the long tubing string at point B and enters into the formation along the annulus, the pressure distribution fulfills the equation (22). (2) Only short tubing string injection. The steam flows into the annulus from point A directly and enters into the formation along the annulus; therefore the momentum conservation equation fulfills the equation (18). The pressure distribution along the annulus in this case is obtained by solving the equation (18): 2 v v § dT pc · ʌDcx § vmx vmx 1 · pc p0 ms iss ¨ ln ¸ f cc U m ¨ ¸ (23) Aa © T p0 ¹ 8 Aa © 2 ¹ (3) Steam injection from the long and short tubing strings simultaneously. The pressure distribution in the long tubing string fulfills the equation (21). Since the steam flow velocity at a random micro-segment along the annulus equals to the absolute velocity of steam from the long tubing string minus that from the short tubing string and the steam imbibition in this segment equals to the total imbibition of steam from the long and short tubing strings, therefore the pressure distribution in the annulus is formulated as follows: v v (v v ) § dT pc · pc p0 ms ml iss isl ¨ ln ¸ Aa T p 0 ¹ ©
f ccU m
The edge condition is: p x 0 p0 and the IJcƍ can be calculated using the equation as follows:
W cc
fc Um
ʌDdx § vm x vmx 1 · ¨ ¸ 8 © 2 ¹
2
(20)
The edge condition above and the equation (20) are put into the equation (19) to solve the differential linear equation as follows: p
p0 fc Um
ʌDx § vm x vmx1 · ¨ ¸ 8 Al © 2 ¹
2
(21)
The steam pressure along long tubing string during SAGD preheating phase can be obtained by solving the equation (21). As for the exit point of the long tubing string (point B), since the vmx=vmx+1=vmB, therefore the pressure at point B is : pB=p0 fcȡmʌDLvmB2/8Al. (2) Transforming the coordination system taking the point B as the origin of coordinates to calculate the coupling pressure along the annulus, therefore the p x 0 pB . The pB is put into the equation (18) to solve the first-order ordinary differential equation to obtain the steam pressure pƍ along the annulus: pc
pB
vmlvisl § dT pc · ʌDcx § vmx vmx 1 · ln ¸ fccUm ¨ ¨ ¸ Aa © T pB ¹ 8 Aa © 2 ¹
2
(22)
The pƍ from SAGD circulation preheating phase to a ran-
SAGD production phase
1.5
ʌDcx § vmsx vmsx 1 vmlx vmlx 1 · ¨ ¸ 8 Aa © 2 ¹
2
(24)
The calculation of the unknown variables
(1) The calculation of the wet steam density. The method of Beggs-Brill [3,4] is used to calculate the wet steam density. Firstly, the flow type is determined according to the fluid flow velocity and the flow diameter in the horizontal section, and then, the wet steam density is calculated according to the flow type. (2) The steam imbibition vis in a random micro-segment in horizontal wellbore can be calculated as follows [58]: vis Um Is ps pi Jliq (25) (3) The calculation of the friction coefficient fc between the steam and the inner wall of the long tubing string. The fc is a function of the Reynolds number of steam (Res=Dvmȡm/ȝ) and the relative roughness of the inner wall of the long tubing string (ǻ=İ/D) [913]. When Resİ2 000, fc=54/Res; when Res>2 000, fc=[1.142 lg(ǻ+21.25 Res0.9)]2. Similarly, the friction coefficient fcƍ between the steam and the inner wall of the screener is expressed as: fcƍ=[1.142 lg(ǻƍ+21.25 Resƍ 0.9)]2, in which Resƍ=Dƍvmȡm/ȝ and ǻƍ=İ/Dƍ. (4) The heat transfer calculation between the random mi-
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cro-segment and the formation. The equation of heat loss from the inner wall of the long tubing string to the formation for the steam in a random micro-segment of the long tubing string is: dQ Tl Te (26) dx R While in the annulus, the heat loss of steam from the inner wall of the screener to the formation in a random micro-segment is: dQc Ta Te (27) dx Rc Equations (26) and (27) can be used to calculate the steam heat loss during SAGD preheating phase and SAGD production phase with different combinations of injection and production tubing strings. The total thermal resistance from the inner wall of the long tubing string to the formation is: 1 ª 1 f (t ) ln(rso / rsi ) º R (28) « » 2ʌ ¬ hrlo Oe Os ¼ The total thermal resistance from the inner wall of the screener to the formation is: 1 ª f (t ) ln(rso /rsi ) º Rc (29) « » 2ʌ ¬ Oe Os ¼ where
2.1
Fig. 3 Comparison of the calculated temperature and monitored temperature for Well A-1
culated results agree precisely with the monitored data with only 0.2% of pressure error and 0.19% of temperature error, which validates the reliability of the model.
§ 2 Dt · f (t ) ln ¨¨ ¸¸ 0.29 © rso ¹
2
Fig. 2 Comparison of the calculated pressure and monitored pressure for Well A-1
Model validation and application
2.2
Model validation
A SAGD injector A-1 in a SAGD pilot test area is used as an example to calculate the pressure and temperature distribution along the long tubing string and the annulus during SAGD preheating phase using the model formulated in this paper. The parameters of the horizontal wellbore are as follows: the horizontal length is 460 m, the well is completed with 177.8 mm (7 in) slotted screener, the inner and outer diameters of the screener are 166.8 mm and 177.8 mm respectively and the heat conductivity is 0.993 W/(m·K), the diameters of the short long tubing strings are 73 mm (2 7/8 in) and 88.9 mm (3 1/2 in)respectively, the inner diameters of the short and long tubings are 62 mm and 77.9 mm respectively, the absolute roughness and the thermal conductivity of the short and long tubing strings are 0.000 05 m and 0.8 W/(m·K) respectively, and 7 thermocouples and piezometers are even distributed along the annulus. Other parameters in the calculation are as follows: the formation temperature is 19 qC, the thermal conductivity of the formation rock is 1.73 W/(m·K), the formation thermal diffusivity is 0.004 m2/hm. During SAGD preheating phase, the steam injection rate is 100 t/d, the downhole steam quality at point A is 60%, the steam injection pressure is 2.5 MPa and the steam temperature is 224 qC. Figs. 2 and 3 are the calculated and monitored results of pressure and temperature along the long tubing string and the annulus of Well A-1. And Figs. 2 and 3 indicate that the cal-
Model applications
The model formulated in this paper is used to calculate the lowest steam injection rate during SAGD preheating phase and the longest horizontal length, and to optimize the wellbore configuration during SAGD production phase according to the reservoir properties and the parameters of the current wellbore configurations of Well A-1. 2.2.1 The calculation of the lowest steam injection rate during SAGD preheating phase
During SAGD preheating phase, the steam is required to have a certain degree of steam quality at Point A when the steam flows from the long tubing string into the annulus at Point B and enters into the short tubing string at Point A so as to ensure the uniform preheating effect in the horizontal section. If the steam quality is zero at Point A, the fluid is water and the liquid holdup at Point A will happen because of in-sufficient power of fluid to flow up from the bottom of the short tubing string to the wellhead. And long-term liquid holdup at Point A will cause preferential heat communication between the injector and the producer in the horizontal section around Point A [14,15], which will cause the steam breakthrough during SAGD production phase. Therefore, the key of determining the lowest steam injection rate is to ensure that the steam quality of the steam flowing back to Point A is above zero. Under the current wellbore configuration of Well A-1, assuming that the steam quality at the entrance of the long
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tubing is 60%, the steam quality along the annulus at the steam injection rates of 0.46 kg/s(40 t/d), 0.69 kg/s(60 t/d), 0.93 kg/s(80 t/d), 1.16 kg/s(100 t/d) is calculated (Fig. 4). The calculation results reveal that when the steam injection rate is 60 t/d, the steam quality of the steam flowing back from the annulus to Point A is 0.2%, while further reducing the steam injection rate to 40 t/d, the fluid flowing back along the annulus to Point A is the hot water with no steam quality, therefore the lowest steam injection rate during SAGD preheating phase is 60 t/d. 2.2.2 The calculation of the longest horizontal length in SAGD process
According to the successful experiences of the foreign SAGD projects, the highest pressure difference along the annulus should not exceed 0.05 MPa during SAGD production phase so as to ensure the uniform steam imbibition along the horizontal section [15,16]. Therefore under conditions of 177.8 mm (7 in) slotted screener completion, 300t/d steam injection rate, and 2.5MPa steam injection pressure at point A, the pressure difference is calculated in the annulus of different horizontal lengths in three cases of wellbore configuration: no long tubing string, 73 mm (2 7/8 in) long tubing string and 88.9 mm (3 1/2 in) long tubing string (Fig. 5). The calculation results reveal that in the case of no long tubing string in horizontal section, the longest horizontal length that fulfills the pressure difference of 0.05 MPa can reach 1500m, when 73 mm (2 7/8 in) long tubing string runs into the horizontal section, the longest horizontal length is 751 m and when 88.9 mm (3 1/2 in) long tubing string runs into the horizontal section, the longest horizontal length is 564 m. therefore under current wellbore configuration and 460m horizontal length, the steam injection rate 300 t/d can fulfill the requirement of highest pressure difference lower than 0.05 MPa. 2.3 Optimization of injector wellbore configuration in SAGD production phase
The injector wellbore configuration of short tubing string landing at point A and long tubing string landing at point B is
Fig. 4 Steam quality along the long tubing string and the annulus under different steam injection rates
Fig. 5 Relationships between pressure difference in horizontal section and the horizontal length in the case of no long tubing string, 73 mm long tubing string and 88.9 mm long tubing string
extensively used in the current SAGD pilot test area (Fig. 6a). The production performance shows that the steam chamber develops better at point A and point B, even the steam channeling and steam breakthrough occur nearby at point A and point B in some SAGD wells, while no steam chamber or steam chamber develops poorly in the middle of the horizontal section. In order to improve the steam chamber development in horizontal section so as to enhance the tapping efficiency of the formation in the horizontal section, the model formulated in this paper is used to calculate the steam mass rate along the annulus in two cases of wellbore configuration: short tubing string lands at point A and long tubing string lands at point B (Fig. 6a) ( Case 1); short tubing string lands at 150 m behind point A and long tubing string lands at point B (Fig. 7a) (Case 2). According to the field data, the steam rate of the long tubing string is 100t/d while the steam rate of the short tubing string is 150t/d, which means that the proportion of the steam injection rate between the long tubing string and the short tubing string is 2:3. Using the wellbore configuration data and the steam injection data above, the calculation results of steam mass flow rate along the annulus indicate that in Case 1, the steam mass rate from point A and point B into the middle of the horizontal section becomes smaller and smaller gradually because of the steam imbibition in the horizontal section, and the steam mass imbibition rate along the entire horizontal section is distributed as two sections (Fig. 6b). While as for Case 2, the steam from the short tubing string is divided into two portions under the pressure difference between the exit point of the short tubing string and other parts of the horizontal section, one portion of steam flows towards the heel and the other portion of steam flows towards the middle section. Therefore the steam mass imbibition rate along the entire horizontal section is distributed as three sections (Fig. 7b). by using the optimized wellbore configuration (Case 2), the steam from the short tubing string is effectively divided and the steam mass rate is reduced at the exit of the short tubing string, therefore the steam imbibition along the horizontal section is more uniform and the risk of the steam breakthrough at point A can be effectively reduced. And the
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monitored data and verifying the reliability of the model. Meanwhile, the model is used to calculate the minimal steam injection rate during SAGD preheating phase is 60 t/d, the longest horizontal length is 564 m under current configuration. The current configuration has disadvantages of two sections of steam imbibition resulting in risk of section/point steam breakthrough at point A during SAGD production phase, so the combination of long tubing string and short tubing string is optimized: the short tubing string lands at 150 m behind point A and long tubing string lands at point B. Consequently, 3 sections of steam imbibition can be realized, and the risk of section/point steam breakthrough at point A is effectively reduced.
Nomenclature Fig. 6 Wellbore configuration and steam mass flow rate along the annulus before optimization
Fig. 7 Wellbore configuration and steam mass flow rate along the annulus after optimization
wellbore configuration of Case 2 has been recommended as the injector wellbore configuration for the extended SAGD pilot test.
3
Conclusions
Based on the parameter forecast model of conventional horizontal injector wellbore, combined with coupling calculation of dual-tubing steam mass flow, the mass conservation equation, energy conservation equation and momentum conservation equation of steam flow within injector wellbore under different tubing combinations in preheating and production phases are formulated and the key parameter calculation model along the dual-tubing injector wellbore are established. Take the reservoir properties and injector wellbore configurations of a SAGD pilot test area as an example, the changes of temperature and pressure along the injector wellbore during SAGD preheating phase are calculated, showing that the simulation data has a good match to the downhole
L—Horizontal length between point A and point B, m; vsx—Steam mass flow rate in a random micro-segment in the horizontal section, kg/s; t—Time, s; A—Cross section area in the horizontal section for conventional horizontal wells, m2; x—Location of a random point A along the horizontal wellbore, m; ȡm—Fluid density in the micro-segment, kg/m3; vis—Steam mass imbibition rate in the horizontal section per unit length, kg/s; Al—Cross section area of the long tubing string, m2; Aa—Cross section area of the annulus, m2; vsxt—Steam mass flow rate in the random micro-segment of annulus in the case of the dual string injections, kg/s; vsxs—Steam mass flow rate in a random micro-segment of the annulus in the case of only short tubing string injection, kg/s; vsxl—Steam mass flow rate in a random micro-segment of the annulus in case of only long tubing string injection, kg/s; vss—Steam mass flow rate in the short tubing string, kg/s; viss—Mass imbibition rate of the formation to the steam per unit length from the short tubing, kg/s; vsl—Steam mass flow rate in the long tubing string, kg/s; visl—Mass imbibition rate of the formation to the steam per unit length from the long tubing, kg/s; hm—Heat enthalpy of steam, J/kg; vr—Flow velocity of steam into the formation, m/s; W—Power the friction has done in a unit time, W; vm—Flow velocity of steam in the random micro-segment, m/s; Q—Heat loss of steam in a unit time, W; vms—Flow velocity of steam from the short tubing string into a random micro-segment of the annulus, m/s; vml—Flow velocity of steam from the long tubing string into a random micro-segment of the annulus, m/s; T—Temperature of wet steam in a random micro-segment, qC; hw—Heat enthalpy of the condensed water in the random micro-segment, J/kg; p—Pressure of wet steam in a random micro-segment, Pa; hs—Heat enthalpy of the dry steam in a random micro-segment, J/kg; q—Steam quality in a random micro-segment,%; q0—Steam quality at point A in the wellbore, %;
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p0—Steam pressure at point A in the wellbore, Pa; IJc—Shear friction between the fluid in the wellbore and the inner wall of the screener, N; IJcƍ—Shear friction between the fluid and the inner wall of the long tubing string, N; fc—Friction coefficient between wet steam and the inner wall of the long tubing string, dimensionless; D—Inner diameter of the long tubing, m; vmx—Steam flow velocity at a random micro-segment of dx in the wellbore, m/s; vmx+1—Steam flow velocity at a random micro-segment of dx+1 in the wellbore, m/s m/s; pB—Steam pressure at point B, Pa; vmBüSteam flow velocity at poing B, m/s; pƍ—Steam pressure at point in the wellbore where the distance from point B is x, Pa; fcƍ—Friction coefficient between wet steam and the inner wall of the screener, dimensionless; Dƍ—Inner diameter of the screener, m; vmsx—Flow velocity of steam from the short tubing string at a random micro-segment of dx in the annulus, m/s; vmsx+1—Flow velocity of steam from the short tubing string at a random micro-segment of dx+1 in the annulus, m/s; vmlx—Flow velocity of steam from the long tubing string at a random micro-segment of dx in the annulus, m/s; vmlx+1—Flow velocity of steam from the long tubing string at a random micro-segment of dx+1 in the annulus, m/s; Is—Steam imbibition index of the formation per unit horizontal length, m1; ps—Average steam injection pressure, Pa; pi—Initial reservoir pressure before steam injection, Pa; Jliq—Liquid production index of the formation, m3/(Pa·s); ȝ—Wet steam viscosity in the annulus, Pa·s; İ—Absolute roughness of the inner wall of the screener, m; Tl—Steam temperature at a random micro-segment of the long tubing string, K; Te—Formation temperature outside of the random micro-segment, K; R—Total heat resistance from inner wall of the long tubing string to the formation, (m·K)/W; Qƍ—Heat loss of steam in a random micro-segment of annulus in a unit time, W; Ta—Steam temperature in a random micro-segment of annulus, K; Rƍ—Total heat resistance from inner wall of the annulus to the formation, (m·K)/W; h—Convective heat transfer coefficient of the long tubing, W/(m2·K); rlo—Outer radius of the long tubing, m; Ȝe—Thermal conductivity of the formation, W/(m·K); rso—Outer radius of the screener, m; rsi—Inner radius of the screener, m; Ȝs—Thermal conductivity of the screener, W/(m·K); Į—Thermal diffusivity of the formation, m2/s.
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