A CALCULATION MODEL FOR STEAM PROPERTY VARIATION ALONG WELLBORE TRAJECTORY IN SAGD PROCESS

Transcription

1 A CALCULATION MODEL FOR STEAM PROPERTY VARIATION ALONG WELLBORE TRAJECTORY IN SAGD PROCESS A Thesis Subitted to The Faculty of Graduate Studies and Research in Partial Fulfillent of the Requireents for the Degree of Master of Applied Science In Petroleu Systes Engineering University of Regina By Ning Ju Regina, Saskatchewan April 016 Copyright 016: N. Ju

2 UNIVERSITY OF REGINA FACULTY OF GRADUATE STUDIES AND RESEARCH SUPERVISORY AND EXAMINING COMMITTEE Ning Ju, candidate for the degree of Master of Applied Science in Petroleu Systes Engineering, has presented a thesis titled, A Calculation Model for Stea Property Variation Along Wellbore Trajectory in SAGD Process, in an oral exaination held on Deceber 17, 015. The following coittee ebers have found the thesis acceptable in for and content, and that the candidate deonstrated satisfactory knowledge of the subject aterial. External Exainer: Supervisor: Coittee Meber: Coittee Meber: Dr. Kelvin Ng, Environental Systes Enginering Dr. Gang Zhao, Petrorleu Systes Engineering Dr. Fanhua Zeng, Petroleu Systes Engineering Dr. Yang Zhao, Departent of Matheatics & Statistics Chair of Defense: Dr. Guoxiang Chi, Departent of Geology

3 ABSTRACT Stea-Assisted Gravity Drainage is an effective approach for recovering heavy oil and bituen and its essence idea is to introduce stea heat into cold reservoir and reduce oil viscosity. In a typical SAGD process, two horizontal wells were drilled inside the target foration, one is put on the top as stea injection well and another is usually put on the botto of target foration as oil production well. During SAGD process, a large aount of high pressure high teperature stea is injected into reservoir which occupies a big part of the whole SAGD project cost. The stea pressure and quality decreases during the stea flow inside vertical wellbore because the stea loses its heat through wellbore syste to foration due to teperature gradient. And in horizontal wellbore, stea even flow into foration through slotted liner which takes away energy directly. For a SAGD project, the stea pressure and stea quality insides stea injection well are quite iportant paraeters. A high enough quality can offer enough energy for stea chaber to develop and stea pressure will influence the oil production rate, stea trap control as well as ultiate oil recovery. In order to control the cost of SAGD production and offer evidence for stea injection, oil production strategy, the knowledge of stea properties (pressure, teperature, quality) along both vertical and horizontal wellbore are needed. I

4 The stea flow inside wellbore is a two phase (dry stea and hot water) flow and the deterination of phase void fraction is critical in predicting the pressure loss and heat transfer. The ajor difference between stea flow inside horizontal wellbore and vertical wellbore is the existence of wall outflow in horizontal wellbore part. This wellbore outflow has a significant effect on wellbore friction as well as flow pattern transition inside wellbore which ake it difficult to describe flow pattern in horizontal wellbore by forer technology. A odel describe stea flow inside wellbore during conventional Stea Assisted Gravity Drainage stage (after the stea chaber has achieved full height and lateral growth becoes the doinant echanis for recovery) was built and solved in this thesis. A flow pattern independent drift flux odel based void fraction correlation was introduced in this thesis in order to overcoe the uncertainty proble in deterining flow pattern and aking is possible to describe stea flow in both vertical wellbore and horizontal wellbore in an unified way. A odified Reis s drainage odel was used in this thesis which cobined stea flow inside wellbore and stea chaber developent inside foration. The stea properties (pressure, quality) distribution along wellbore trajectory were calculated, the effects of basic stea injection paraeters (pressure, quality and ass flow rate) were analysed in this thesis. These stea property profiles along wellbore trajectory actually build correlations between wellbore flow and oil production, and will iprove the understanding in stea injection strategy adjustent as well as oil production dynaic onitoring. II

5 ACKNOWLEDGEMENTS I would like to take this opportunity to express y sincere appreciation and gratitude to y supervisor, Dr. Gang Zhao, for his guidance and support throughout y studies. His encourageent, expertise, advice, and enthusias helped e accoplish this study. I also would like to thank y parents: Yujun Ju and Xiuei Fan for their endless love and understanding during y graduate studies. Acknowledgent is due to the Faculty of Graduate Studies and Research at the University of Regina for financial support in the for of teaching assistantship. Furtherore, I a thankful to the ebers of y exaination coittee and their valuable suggestions in this study. I would also like to thank y colleagues, Mr. Lei Xiao, Mr. Chang Su, Mr. Wanju Yuan, Mr. Shuai Chen, Mr. Kuizheng Yu, Mr. Jiawei Li, Ms. Jianli Li and Ms. Yue Zhu for their care and helpful discussion regarding this work. III

6 DEDICATION To My best friend and copanion, Ms. Shanshan Yao, and y loving parents Mr. Yujun Ju and Ms. Xiuei Fan. IV

7 TABLE OF CONTENTS ABSTRACT... I ACKNOWLEDGEMENTS... III DEDICATION... IV TABLE OF CONTENTS... V LIST OF TABLES... IX LIST OF FIGURES... X LIST OF APPENDICES... XII NOMENCLATURE... XIII CHAPTER INTRODUCTION Stea-assisted Gravity Drainage Scope and Objectives of This Study Organization of the Thesis... 9 CHAPTER LITERATURE REVIEW Multiphase Flow in Wellbore Multiphase Flow in Vertical Wellbore Multiphase Flow in Horizontal Wellbore Multiphase Flow Modeling Void Fraction Correlations Suary... 3 V

8 . Heat Transfer around Wellbore Heat Transfer at Chaber Interface SAGD Drainage Model Analytical Drainage Models Nuerical Models... 3 CHAPTER MATHEMATICAL MODEL Definitions Vertical Wellbore Model Heat Loss fro Tubing to Foration Stea Flow inside Tubing Mass Conservation Moentu Conservation Energy Conservation Horizontal Wellbore Model Stea Flow into Foration Stea Flow in Horizontal Wellbore Mass Conservation Moentu Conservation Energy Conservation Solution Process Vertical Wellbore Model Solution Horizontal Wellbore Model Solution VI

9 CHAPTER MODEL VALIDATION Vertical Wellbore Model Validation Field Case Field Case Horizontal Wellbore Model Validation CHAPTER RESULTS AND DISCUSSION Perforance Analysis on Vertical Wellbore Effect of Stea Injection Pressure Effect of Stea Injection Quality Effect of Stea Injection Rate Perforance Analysis on Horizontal Wellbore Effect of Stea Pressure at Heel Effect of Stea Quality at Heel Effect of Stea Rate at Heel Effect of Reservoir Pereability Effect of Oil Viscosity CHAPTER CONCLUSIONS AND RECOMMENDATIONS Conclusions Recoendations LIST OF REFERENCES VII

10 APPENDIX A DERIVATION OF dx/dz APPENDIX B DERIVATION OF HEAT STORED AROUND SAGD STEAM CHAMBER APPENDIX C DERIVATION OF dp/dl AND dx/dl VIII

11 LIST OF TABLES Table.1-Transition criteria for ultiphase flow in vertical pipes (Hasan and Kabir, 1988). 13 Table 4.1-Well paraeters in Field Test 1 (Bleakley, 1964) 60 Table 4.-Well paraeters and injection conditions in Field Test (Herrera et al. 1978) 64 Table 4.3 Basis paraeters for wellbore and stea injection. 67 Table 4.4 Coparison between this odel and Chen et al.'s odel. 68 IX

12 LIST OF FIGURES Figure 1.1-Scheatic of SAGD process (Courtesy of IFPEN, 015). Figure 1.-SAGD production stages (Lackey and Kane, 013). 4 Figure.1-Flow patterns in vertical co-current gas-liquid flow (Bar-Meir, 013).11 Figure.-Flow patterns in horizontal flow (Taitel et al, 1978). 15 Figure.3-Flow pattern ap for gas-liquid flow in horizontal pipes (Mandhane, et al., 1974). 16 Figure 3.1-(a) Scheatic of vertical wellbore syste in SAGD. (b) Stea flow inside tubing. 39 Figure 3. - (a) Stea flow in injection horizontal wellbore. (b) The heated area around stea chaber. 46 Figure 3. 3-Scheatic representation of stea flow in the slotted liner. 49 Figure 3.4-Calculation flow chart for the vertical wellbore odel. 56 Figure 3.5-Calculation flow chart for the horizontal wellbore odel. 57 Figure 4.1-Stea pressure coparison between odel results and field data 61 Figure 4.-Stea quality coparison between different odels. 6 Figure 4.3-Stea teperature coparison between odel results and field data. 65 Figure 5.1-Effect of stea injection pressure on stea quality distribution in vertical wellbore. 71 Figure 5.-Effect of stea injection quality on stea pressure distribution in vertical wellbore. 7 X

13 Figure 5. 3-Effect of stea injection rate on (a) stea quality distribution and (b) pressure distribution in vertical wellbore. 75 Figure 5.4-Effect of stea pressure at the heel on stea quality distribution along horizontal wellbore. 79 Figure 5.5-Effect of stea quality at the heel on stea pressure distribution along horizontal wellbore. 80 Figure 5.6-Effect of stea flow rate at the heel on (a) stea quality distribution and (b) on stea pressure distribution along the horizontal wellbore. 8 Figure 5.7-Effect of reservoir pereability on (a) stea pressure distribution and (b) on stea quality distribution along the horizontal wellbore. 85 Figure 5.8-Effect of oil viscosity on (a) stea pressure distribution and (b) on stea quality distribution along the horizontal wellbore. 87 XI

14 LIST OF APPENDICES APPENDIX A DERIVATION OF DX/DZ 98 APPENDIX B DERIVATION OF HEAT STORED AROUND STEAM CHAMBER 100 APPENDIX C DERIVATION OF DP/DL AND DX/DL 10 XII

15 NOMENCLATURE A cross section area of wellbore, A slot area of each slot, A h cross section area of horizontal wellbore, a C o teperature coefficient, diensionless distribution coefficient, diensionless G r Grashof nuber, diensionless C initial reservoir voluetric heat capacity, J / K vr 3 3 C overburden voluetric heat capacity, J / K vo D hydraulic pipe/wellbore diaeter, dq heat loss to surround, J / dw work done by wall friction force, J f (t) transient heat conduction function, diensionless f o f g friction factor calculated by Colebrook equation, diensionless in-situ gas phase void fraction, diensionless h g enthalpy of dry stea, KJ / Kg h l enthalpy of liquid phase, KJ / Kg h c convective heat transfer coefficient of fluid inside annulus, J / S K h r radiative heat transfer coefficient of fluid inside annulus, J / S K XIII

16 h convective heat transfer coefficient of fluid, J / S K f h height of reservoir above producer, H c heat stored inside stea chaber, J / H out heat accuulation ahead of stea chaber, J / H o heat loss to the overburden foration, J / H inj cuulative heat loss, J / h enthalpy of stea, KJ / Kg k theral conductivity of foration, J / s K e k theral conductivity of tubing, J / s K t k theral conductivity of ceent, J / s K ce k theral conductivity of casing, J / s K cas k o effective oil pereability, M g gas phase ass flow rate, Kg / s M l liquid phase ass flow rate, Kg / s M stea ass flow rate, Kg / s viscosity coefficient, diensionless N slot density, 1 / P P an stea saturatation pressure, kpa annulus liquid pressure, kpa P r Prandtl nuber, diensionless Q instantaneous heat loss to foration and stea chaber, J / s inj XIV

17 q ass flow rate into foration, Kg / s in q stea (gas, liquid ixture) volue flow rate, / s 3 q gas phase volue flow rate, 3 / s g q liquid phase volue flow rate, / s l 3 R etp two-phase Reynolds nuber, diensionless R ew Wall Reynolds nuber, diensionless R z length of vertical segent, r to radius of outside tubing, r ti radius of inside tubing, r ins radius of insulation, r co radius of outside casing, r wb radius of wellbore, T T c stea saturation teperature, K water critical teperature under a specific pressure, K T e foration teperature, K T f fluid teperature inside tubing, K T h ceent-foration interface teperature, K v qin stea flow rate into foration, / s v g actual gas flow rate, / s v l actual liquid flow rate, / s v sg superficial velocity of gas phase, / s XV

18 v sl superficial velocity of liquid phase, / s v d drift velocity of gas phase, / s U over-all heat transfer coefficient, J / S K to x dry stea quality, diensionless wellbore orientation easured fro horizontal direction, rad g gas phase density, 3 Kg / l liquid phase density, 3 Kg / stea density, 3 Kg / to eissivity of outside tubing surface, diensionless ti eissivity of inside casing surface, diensionless l liquid phase viscosity, Pa s kineatic oil viscosity at stea teperature, / s os foration theral diffusivity, / s S o initial oil saturation inus residual oil saturation, diensionless porosity, diensionless friction force between stea and liner, N XVI

19 CHAPTER 1 INTRODUCTION 1.1 Stea-assisted Gravity Drainage Heavy oil and oil sands bituen account for 70% of the world proven oil reserves (World s Oil and Natural Gas Scenario). Especially for Canada, 98% of oil reserves, 175 billion barrels, are reserved in the for of oil sands (Hein, Fran, 008). Moreover, conventional oil (light oil) supply peaks eventually and enters into decline. Therefore the efficient developent of heavy oil and oil sands becoes ore iportant for Canada s and even world s energy security. Heavy oil and oil sands bituen are characterized by high viscosity copared with conventional oil. The gas-free viscosity of heavy oil under reservoir condition lies between 100cp and 10,000cp while the bituen s viscosity can reach 10,000,000cp. Such high viscosity akes it difficult for the oil to flow underground (Working Docuent of the NPC Global Oil & Gas Study).As a theral based oil production ethod, the Stea-assisted Gravity Drainage (SAGD) technique appears and attracts enorous attention for its efficiency in reducing viscosity and producing oil. The concept of Stea-Assisted Gravity Drainage (SAGD) becoes practical in the 1970s after the horizontal well was successfully introduced into petroleu industry. In 1978, a first odern horizontal producing well paired with a vertical stea-injection well was drilled at Cold Lake, Alberta, Canada. This is the initial attept of the SAGD concept. In the 1980s, the first-ever twin SAGD 1

20 (Original in color) Figure 1.1-Scheatic of SAGD process (Courtesy of IFPEN, 015).

21 wells were drilled at Dover Underground Test Facility, Canada. The production success of this field test boosts coercial ipleentation of SAGD projects. In 010 approxiately 40,000 barrels of oil per day cae fro SAGD wells in Canada (M Medina, 010). Figure 1.1 shows the scheatic of SAGD process. With the SAGD technique, a pair of horizontal wells, situated 4 to 6 eters above the other, is drilled in a central well pad. Water is heated into stea in a plant nearby and then travels through above-ground pipelines to wells, enters the reservoir via the top well (injection well) and fors a stea chaber. The injected stea flows towards the edge of the chaber where the stea releases its latent heat to the cold oil and condenses. Oil viscosity reduces draatically after receiving the energy. And the ixture of obile oil and stea condensate flows down into the botto well (production well) under gravity drive. As the oil flows away, the stea will fill the place originally occupied by cold oil and expands vertically and/or horizontally. In SAGD, stea injection and oil production happen continuously and siultaneously. Coercial SAGD process usually involves five phases of operations: startup, rap-up, conventional SAGD, stea rapdown and blowdown operations (Figure 1.). In start-up and rap-up, SAGD well-pair are counicated and the stea chaber grows up vertically to reservoir top. Then the conventional 3

22 Top of Pay Duration 3 onths ~ years Base of Pay Stages Start-up Rap-up Top of Pay Duration ~3-6 years 0.5- years Base of Pay Stages Conventional SAGD Conventional SAGD with Wedge Well Technology Top of Pay Duration years 5-10 years Base of Pay Stages Stea Rapdown Blowdown (Original in color) Figure 1.-SAGD production stages (Lackey and Kane, 013). 4

23 SAGD phase begins. The conventional SAGD operation can last for 6 years, which is uch longer than other operations. In conventional SAGD phase, the stea chaber achieves full height and spreads laterally in the reservoir. Usually higher stea injection rates are necessary to guarantee steady oil production in this phase. Stea injection rate gradually reduces to zero during rapdown and blowdown. And SAGD wells are abandoned when oil production declines to an uneconoic rate (Lackey and Kane, 013). Generally, in reservoirs the stea which contacts with in-situ oil coes directly fro the injection well. The injection wellbore conditions are closed related to the chaber developent and oil production. Hence onitoring wellbore conditions becoes necessary for optiizing stea injection and iniizing cost. Measuring devices can stay in the wellbore and collect realtie teperature and pressure data. The easuring devices include therocouples, fiber optic, pressure gauges, etc. But such easuring devices are unstable in high teperature and also very expensive. Moreover, downhole stea quality is an iportant factor in SAGD production surveillance, which cannot be tested by easuring devices. Now wellbore odeling provides another option for onitoring wellbore conditions. Wellbore odeling by analytical and/or nuerical ethods can accurately predict teperature, pressure and stea quality profile along the wellbore. 5

24 1. Scope and Objectives of This Study This study is focused on the stea properties (pressure, quality) distribution along wellbore (both vertical and horizontal) during conventional SAGD production phase since this period last the longest tie and ake a large contribution of the whole oil production in the SAGD well lifetie. The concept of SAGD, initially proposed by Butler and his colleagues (Butler et al. 1981) has been used worldwide for the recovery of heavy oil and bituen. Two horizontal wells are placed close to the botto of a foration, with one above the other at a short vertical distance. Stea is injected continuously into the upper well, and rises in the foration foring a stea chaber. Cold oil surrounding the stea chaber is heated ainly by theral conduction. As its teperature increases, oil becoes obile and flows together with condensate along the chaber boundary toward the lower well that functions as a producer (Butler, 1997). After stea is injected into stea injection, it begins to loss its heat to the wellbore syste and foration around, and this energy loss decreases the ability of stea heating reservoir and also iproves stea-oil ratio (which easures the volue of stea used to produce one unit volue of oil, the lower the ratio, the higher the efficiency of the stea use.) which leading to noneconoic oil production. Many investigators have worked on the odelling and prediction of stea property insider vertical wellbore since the first introduction of theral-based enhanced oil recovery ethod. A series of research work were done step by 6

25 step: Raey gave out approxiate solution to the transient heat-conduction proble in 196. Satter (1965) iproved Raey s analytical odel by considering a depth-dependent overall heat transfer coefficient and phase and teperature-dependent fluid properties; Holst and Flock (1966) added the friction loss and kinetic energy effect to Raey s and Satter s odels; Willhite (1967) proposed the foration of overall heat transfer coefficient, Farouq-Ali (1981) put forward a coprehensive wellbore stea/water flow odel for stea injection and geotheral application. After then, the basic idea and procedure of calculating the heat loss during vertical stea injection was established. The ain difference between horizontal stea injection wellbore and vertical injection wellbore are: (1) horizontal injection wellbore copletion is ore concise, usually with slotted liner and open hole condition, so the heat conduction through wellbore syste is quite sall; () horizontal wellbore copleted with slotted liner leading to a directly ass transfer and heat transfer between wellbore and foration. Because of the two ainly characteristics of SAGD horizontal stea injection wellbore, the stea flow inside horizontal wellbore is draatically changed when copared with that of vertical wellbore, and the technologies used to odel vertical stea flow and technologies used to describe flow behavior in ordinary horizontal pipes are not working well here. Ouyang (1998) conducted a coprehensive research work on pressure drop along wellbore, inflow effect on fluid behavior inside wellbore based on a 5 years experient. However, this research work was ainly focused on the oil 7

26 production well which with a big difference in fluid flow behavior with stea injection well. Considering this situation, this thesis was focused on describing fluid flow behavior inside horizontal stea injection well. The proble was studied fro the basic ass balance, oentu balance, energy balance equation. A flow pattern independent drift flux odel based void fraction correlation was introduced in this thesis in the ai to describe the two-phase flow in a one phase anner, which intended to avoid flow pattern related difficulties. A odified Reis s drainage odel was used within this odel to calculate the ass transfer between wellbore and foration. A new two-phase friction factor was also used to consider the effect of stea outflow on axial wellbore fluid flow. 8

27 1.3 Organization of the Thesis Five chapters coprise this thesis. Chapter 1 introduces the background knowledge of SAGD process and outlines the study objectives. Chapter shows a coprehensive literature review on ultiphase flow, heat transfer around wellbore and stea chaber as well as SAGD drainage odel. Chapter 3 gives the detailed atheatical odel of the injection wellbore in conventional SAGD operation. The atheatical odel is developed by cobing vertical wellbore odel and horizontal wellbore odel. Then Chapter4 validates this odel by using field data and other odels. Chapter 5 analyzes odeling results under different wellbore and reservoir properties. Finally, Chapter 6 draws conclusions and provides recoendations. 9

28 CHAPTER LITERATURE REVIEW In order to predict stea properties variation along wellbore trajectory accurately, several works need to be done, this including the precise description of stea flow behavior inside wellbore, stea chaber developent behavior inside foration, heat transfer behavior between stea and wellbore syste as well as foration. In this chapter, the literature review was conducted towards these four topics..1 Multiphase Flow in Wellbore During the SAGD process, the stea was injected into the target foration through vertical wellbore and then horizontal wellbore, Stea flow along wellbores is gas-liquid two phase flow. And such ultiphase flow effects in wellbores have a strong ipact on the perforance of reservoir and surface facilities. Incorrect consideration of pressure losses resulted by ultiphase flow in wellbore ay lead to a loss of production at the toe and/or overproduction at the heel. In order to optiize the perforance of wells, ultiphase flow odels in wellbore ust be considered. 10

29 (Original in color) Figure.1-Flow patterns in vertical co-current gas-liquid flow (Bar-Meir, 013). 11

30 .1.1 Multiphase Flow in Vertical Wellbore Flow patters describe the various possible phase distributions in ultiphase flow. Hasan and Kabir (00) suarized the four clearly distinguishable flow patterns of ultiphase flow in vertical wellbores: bubbly flow, slug flow, churn flow and annular flow. Figure.1 shows the flow patterns in vertical gas-liquid flow. In vertical bubbly flow, discrete bubbles with low velocity distribute uniforly throughout the continuous liquid phase. In slug flow the gas or vapor bubbles grow to Taylor bubbles which have alost sae diaeter as the pipe. Bubbles are separated fro the pipe wall only by a thin fil of liquid. The Taylor bubbles break down in churn flow. Unlike slug flow, the gas or vapor flows in a chaotic anner when churn flow occurs. For annular flow, the continuous gas phase flows through the core of the pipe while the liquid phase is dragged along the wall. Since the deterination of slow pattern is critical for odeling ultiphase flow, any researchers have tried to find a way to describe different flow patterns. One technology is called the flow pattern ap, is a ethod of represent the various flow patterns, and the individual patterns are areas on a two-diensional (D) graph, where coordinates are the actual superficial phase velocities or generalized paraeters containing these velocities. One exaple of this kind is the flow pattern ap put forward by Hewitt and Roberts (1969). Considering that the flow patter ap are usually in the for of graph, and not easy to be used in atheatical odel, Hasan and Kabir (1988) further 1

31 Table.1-Transition criteria for ultiphase flow in vertical pipes (Hasan and Kabir, 1988). v sg v 1.1 v sl ρ l v sg ρ g Bubbly Flow <(0.49 v sl v ) 4.68d 0.48 ( / ) l 0.6 [ g( ) / ] ( l / ) l g Slug Flow Churn Flow Annular Flow ( 0.49v ls 0.357v ) 3.1[ g( ) / l g g ] 0.5 >50 >50 3.1[ g( ) / ] 0.5 l g g [17.1log10( l v ls ) 3.] 1. 7 < ( v ) 0 ls l [17.1log10( l v ls ) 3.] 1. 7 < ( v ) 0 ls l 13

32 provided transition criteria to deterine different flow patterns. In Hasan s ethod, each flow pattern corresponds to certain range of void fraction values, which are based on atheatical equations. Table.1 suarizes the criteria according to Hasan and Kabir (1988). This ethod becae ore popular since it allows the physical odeling of individual flow patterns to be expressed in the for of equations. Hasan also developed a atheatical odel to calculate void fractions and pressure drop for ultiphase flow in vertical pipes for different flow patterns..1. Multiphase Flow in Horizontal Wellbore Flow patterns during two-phase flow through horizontal pipes are siilar to those observed during vertical flow. However, soe iportant differences exist, arising ainly fro the gravity effect. Unlike liquid phase, the gas phase usually concentrates toward the upper wall in horizontal ultiphase flow. And phase distribution tends to be asyetrical. Hence judgeent in flow patterns for vertical flow causes difficulty in designate flow regies of horizontal ultiphase flow. Taitel et al. (1978) classified flow regies for gas-liquid two-phase flow in horizontal pipes. Figure. shows the flow patterns in horizontal flow. In stratified sooth flow, liquid phase flows at the botto while gas ove at the top. The interface between two phases is sooth. Stratified wavy flow is quite siilar to stratified sooth flow except that the interface is wavy. For plug flow or elongated bubble flow, elongated gas bubbles at the upper part are separated by sections of continuous liquid. In slug flow, liquid slugs separated by gas 14

33 Figure.-Flow patterns in horizontal flow (Taitel et al, 1978). 15

34 Figure.3-Flow pattern ap for gas-liquid flow in horizontal pipes (Mandhane, et al., 1974). 16

35 pockets flow downstrea violently. The liquid slugs ay get aerated by distributed sall bubbles at higher gas flow rates. Usually the degree of agitation and height of liquid fil between slugs ake slug flow different fro plug flow. Annular flow takes place when gas flow rates are high. When the aeration in liquid phase is sufficiently high under large gas flow rates, gas fors a continuous phase and annular flow occurs. In annular flow, gas oves in the pipe center and liquid flows in the annular space. Furtherore liquid fil at the botto is thicker than that at the top. When liquid rates becoe high, sall gas bubbles disperse in the continuous liquid phase and dispersed bubble flow fors. Norally the bubble density at the top is higher than that at the botto. Mandhane et al. (1974) Proposed transition criteria for ultiphase horizontal flow based on 6,000 experient data points. Flow patterns are deterined according to superficial gas velocity v sg and superficial liquid velocity v sl. Figure.3 shows the detailed flow pattern ap in Mandhane et al. s work. Taitel et al. (1978) also gave the transition criteria for ultiphase flow in horizontal wellbore. In stratified to interittent or annular flow, v g 1 h ( l g ) gag (1 )[ ].... (.1) ' D A g l In stratified sooth to stratified wavy flow, v g 1 400ul ( l g ) g [ ]....(.) v g l Here ul is the kineatic viscosity. For interittent to dispersed bubble flow, 1 4Ag g l g vl [ ( )]...(.3) S F i l l 17

36 Here h is liquid level, u is velocity in the x direction, D is pipe diaeter, also hydraulic diaeter, A is flow cross-section area, ' AL is differentiation with respect to h, Fi is the friction factor between well and liquid phase, S i is the gas/liquid interface perieter. 18

37 .1.3 Multiphase Flow Modeling So far three types of odels can describe the ultiphase flow in petroleu industry: the epirical correlations, hoogeneous odels and echanistic odels. The epirical correlations are based on cure fitting of experiental data (Duns and Ros, 1963; Hagedorn and Brown, 1965). These epirical correlations are siple since no coplex physical odel is required. But the correlations can only apply to very liited set of flow conditions under which experients are conducted. Hoogeneous odels treat ultiphase flow as pseudo-single phase flow. The ultiple phases own sae velocity, pressure, teperature and average fluid properties. Hoogeneous odels are siple, continuous and differentiable, which akes the applicable in nuerical reservoir siulators. But Shi et al. (005) pointed out soe siple hoogeneous odels ignore slip between phases and fail to capture the coplex relationship between in-situ volue fraction and the input volue fraction. Mechanistic odels odel each phase separately and reveal the interplay of ultiple phases. Such odels apply local instantaneous conservation equations and develop average relations for variables of interest. The fundaental postulate in these odels is that different flow patterns exist in ultiphase flow. Mechanistic odeling approach is ost rigorous of three odeling techniques. Correspondingly it provides reliable predictions of phase properties. However, several concerns of echanistic odels draw researchers 19

38 attention. The conservation equations in these odels coe fro experiental data atching and therefore ay not be applicable to cases beyond the experient conditions. In addition, for ultiphase flow in a pipe with ass transfer across the pipe wall, no sufficient experiental data are available for echanistic odels. Furtherore, soeties echanistic odels cannot converge during flow pattern transition boundaries. At last, Ouyang (000) argued that echanistic odels ipleented in a full field reservoir siulator could significantly slow down the entire process. Drift flux odel (Zuber and Findlay, 1965), a kind of hoogeneous odel, appears as an interediate technique between rigorous echanistic approach and siple hoogeneous odels. Drift flux odels treat ultiple phases as a ixture but also account for the velocity difference between gas phase and liquid phase. The drift flux odel develops a relationship between the gas phase velocity and ixture velocity as:.1.4 Void Fraction Correlations After understanding the differences between these three ultiphase flow odeling technologies, it is a good choice to use drift-flux odel to describe the stea flow inside wellbore, because it is siple to use and can also get the slip effect between different phases. By using drift flux-odel, the stea flow inside wellbore is described as one hoogeneous odel. In this case, the phase void fractions becoe critical paraeter to our calculation when the ixture paraeters such as density and viscosity need to be deterined. 0

39 Generally, there are four types of void fraction correlations: (1) slip ratio odels; () K εh correlations; (3) drift flux correlations; (4) epirical correlations (Vijayan et al., 000). For annular flow, Zivi (1964) gave out a widely-used correlation of void fraction f g vs. quality.x His work was based on two hypothetical conditions: (1) the principle of iniu entropy production is applicable to a turbulent twophase flow and () the wall shear stress is negligible which is far fro reality in actual two-phase flows. The correlation is: f g 1 x 3 1/[1 ( )( / ) g l ]...(.4) x Where ρ g is the vapor density and ρ l is the liquid density.. Hughark (1965) developed a correlation to estiate the void fraction f g in horizontal slug flow according to the bubble velocity and the liquid slug Reynolds nuber: f g Qg...(.5) Qg Ql Qg Ql R e ( ) A l A where Q g is the voluetric flow rate of gas phase, Q l is the voluetric flow rate of liquid phase, A is the cross-section area and Re l is a function of the liquid Reynolds nuber. Wallis (1970) proposed a siple theory for annular two-phase flow in ters of interfacial and wall shear stress. Wallis showed the correlation of void fraction f g and quality x as 1

40 x (1 F ) [1 75(1 )] g f g 5 f g...(.6) This equation was based on two siplified conditions: (1) there is no liquid entrainent and () the liquid fil velocity is low copared with the velocity of the gas core. Tandon et al. (1985) developed an analytical odel to predict void fraction of two-phase annular flow. Tandon et al. described the annular flow as a vapour core in an axisyetric liquid annulus. The 1D fluid flow is steady and no radial pressure gradient exists. In addition, both liquid and vapour flows are to be turbulent. Moreover, both phases have constant properties corresponding to the saturated state at any locations. The void fraction f g in annular flow is as f f g g 11.98Re Re l l F F X 0.993Re FX,50 Re 115 u l X u Rel FX u,115 Rel u l... (.7a)... (.7b) where F ( X u ) 0.15 X 1 u.85x u,...(.7c) X u 1 x x ( l / g ) ( ) ( g / l ) (.7d) R el is liquid Reynolds nuber, is dynaic viscosity. Jepson and Taylor (1993) conducted an experiental study on slug flow behavior of air and water inside a 30c steel pipe. They copared results with those in sall diaeter pipes (.54c and 5.08c). Their results showed that the slug frequency and pressure gradient along pipe decrease as the pipe

41 diaeter increases. But the slug length increases if the pipe diaeter becoes larger..1.5 Suary The drift flux odel considers the slip effect between phases and it can also be solved easily. So the drift flux odel becoes flexible and useful to odel the gas-liquid two phase flow in the wellbore. However, there is a ajor shortcoe for ost of current drift flux odels: they are developed for a specific flow pattern or need additional inforation related to the flow pattern which is soeties difficult to identify clearly. Thus, judging the correct flow pattern of stea flow when using the drift flux odel becoes a challenging issue and it affects its application. Furtherore, during the stea flow inside the wellbore, the flow patterns are changing along with tie and locations. It s difficult to notice the transition of one flow pattern to another. So it is hard to guarantee correct estiation of stea flow calculation. The flow-pattern-independent drift flux odel based void fraction correlation is able to predict the void fraction of gas and liquid phases over a wide range of syste pressure, pipe diaeters and fluid properties. After introducing this correlation, this study tried to avoid flow pattern related non-continuity and non-convergence proble, and generated acceptable calculation results for the stea-wellbore syste during SAGD process. 3

42 . Heat Transfer around Wellbore Stea pressure, teperature and density change once the stea is injected into the wellbore. Reasons of such changes ainly include the heat transfer between the stea and cold foration around wellbore, the friction between the stea and inner tubing surface and the change of the hydrostatic pressure with respect to depth. In 196, Raey developed an analytical solution of the transient heatconduction proble when hot fluids flow down the tubing. In Raey s work, the single-phase hot fluid is in steady state flow. Also the overall heat transfer coefficient in the odel is independent of depth. The friction loss and kinetic energy were further neglected. Satter (1965) iproved Raey s analytical odel by considering a depth-dependent overall heat transfer coefficient and phase- and teperature-dependent fluid properties in heat conduction equations. In 1966, Holst and Flock added the friction loss and kinetic energy effect to Raey s (196) and Satter s (1965) odels. The friction losses lead to an extra pressure drop in the stea along wellbore. In 1967, Wilhite proposed a widely-used ethod to estiate the overall heat transfer coefficient as. where rto rco rh rto ln rto ln rto ln rto rti 1 rci rco U to,...(.8) r ( ) tih f ktub hc h f kcas kce U to is over-all heat transfer coefficient, 1 4

43 rto is outside radiu of tubing, rti is inside radiu of tubing, rci is inside radiu of casing, rco is outside radiu of casing, k tub is theral conductivity of the tubing aterial at the average tubing teperature, kcas is theral conductivity of the casing aterial at average casing teperature, kce is ceent conductivity of the casing aterial at average ceent teperature, h f is fil coefficient for heat transfer based p the inside tubing or casing surface and the teperature difference between the flowing fluid and either of these surfaces, hc is heat transfer coefficient for natural convection based on the outside tubing surface and the teperature difference between the outside tubing and inside casing surfaces. The overall heat transfer coefficient represents the net resistance of the flowing fluid, tubing, casing annulus, casing wall and ceent sheath to the flow of heat. When heat is transferred fro the flowing fluid inside wellbore to the foration outside wellbore, the fluid properties and heat transfer around wellbore are interrelated. Ali (1981) and Fontanilla and Aziz (198) solved partial 5

44 differential equations (PDEs) nuerically to estiate stea quality when stea flows along wellbore. In 1994, Hasan and Kabir developed an analytical wellbore odel to calculate the hot fluid teperature inside wellbore. They applied the Joule- Thopson coefficient to siplify PDEs into ordinary differential equations (ODEs) and solved the equations analytically under appropriate boundary conditions. Livescu et al. (008) proposed a coprehensive nuerical non-isotheral ultiphase wellbore odel. They confired that decoupling the wellbore energy balance equations fro ass balance equations is reasonable when densities of each phase fluid have saller change with teperature than that with pressure. In 010, Bahonar et al. developed a sei-unsteady-state two-phase flow wellbore nuerical odel to calculate heat transfer between stea and foration around wellbore. This odel coupled ass, oentu and energy balance equations and provides all necessary wellbore data with respect to depth and tie for a predeterined surface condition. 6

45 .3 Heat Transfer at Chaber Interface The center idea of SAGD is to transfer heat fro stea to cold bituen. So it s critical to understand the heat transfer aount and heat transfer echanis at the stea chaber interface. Based on siulation study, Ito and Suzuki (1996) concluded that heat conduction and convection coexist at the chaber interface. They showed that the heat conduction happens at the whole chaber in an even agnitude while heat convection happens at the upper part of chaber interface. Ali (1997) and Ito and Suzuki (1999) further indicated that ain heat transfer echanis in the SAGD process is by heat convection. However, Edunds (1999) argued that the heat transferred by convention only account for 5% of the heat transferred by conduction. Edunds showed that in the chaber edge, water travels alost along the theral isothers and convention ay reduce to zero. Then Shara and Gates (011) re-exained heat transfer at the edge of stea chaber, and took account of convection of war condensate into the oil sand at the edge of stea chaber. Their results showed that heat conduction doinates at the chaber edge approxiately below 5 C. Even if the heat convection is iportant at above 5 C, it cannot enhance the oil recovery since oil obility decreases. Although higher teperature reduces the oil viscosity, the convective flow of water into the oil sands also reduces the oil relative pereability. In ters of oil obility, the effect of convective flow outweighs the teperature. 7

46 Irani and Ghannadi (013) checked the relative roles of conductive and convective heat transfer at the edge of SAGD chabers based on their atheatical odel and field data. They suarized that in oil-rich portion of the chaber edge, the contribution of heat conduction is less than 1% and can be neglected under coon Athabasca reservoir conditions. The calculation of total heat consuption in SAGD process is coplex. Reis (199) divided the energy stored around stea chaber into three parts: (1) energy associated with expanding the stea zone; () energy required to preheat the tar; (3) energy lost to overburden. Edunds and Peterson (007) presented an analytical odel to estiate the cuulative stea/oil ratio of SAGD and other stea based recovery processes based on the research of Reis odel. In this odel the author ade a siplification of Reis s odel by introducing a constant account for heat stored below the stea chaber as a factor of the overburden transient losses which bring convenience in energy calculation. However, the author assue the value of effective sweep efficiency to be one-half and heat stored below oving front plus transient losses below vicinity of production well to be one-third of heat loss to overburden which is subjective and lack of evidence..4 SAGD Drainage Model Since the essence idea of SAGD is to transfer stea latent heat to cold reservoir and decrease oil viscosity, the stea consuption is directly correlated with stea chaber developent inside foration and oil production. So a 8

47 concise and accurate SAGD drainage odel is need to calculate the aount of stea flow into the foration..4.1 Analytical Drainage Models In 1979, Butler et al. originally proposed an analytical odel to describe the SAGD drainage process when the stea chaber has reached the reservoir top. The odel is based on Darcy s law, aterial balance equations and heat conduction principles. Two ain assuptions were given out for this odel: (1) The interface oved at a fixed velocity noral to the interface; () Heat transfer ahead of interface is by conduction only. The total drainage rate is calculated as Q KgS o....(.9) v s h where Q is oil drainage rate in volue per unit length of well per unit tie for each side of the chaber, K is effective pereability to oil flow, is the theral diffusivity of the reservoir aterial, is porosity, So is the difference between the initial oil saturation and the residual saturation, h is the distance fro the botto of the reservoir to the top, is diensionless constant, s is viscosity of the oil at stea teperature. 9

48 One ain proble for this odel is that the calculated chaber interface curves ove away fro the production well during production. When the lower part of the interface lies at the sae height as the production well, it is unrealistic for the oil to ove towards the production well without gravity force. Another concern is that the chaber tends to spread to infinity in horizontal direction. In 1981, Butler and Stephens iproved the earlier theory by introducing the TANDRAIN assuption. The chaber interface becoes straight in its lower part. This assuption enables the oil behind the interface to flow horizontally to production well. The drainage rate then becoes Q 1.5KgS o.... (.10) v s h In addition, no-flow boundary was added in the odified odel and the stea interface was only allowed to spread halfway between adjacent well pairs. Reis (199) developed a siplified analytical odel for SAGD process. Reis assued the stea chaber to be an inverted triangle in conventional SAGD process. The up-side chaber oves horizontally and the lower part are fixed at the production well. The oil production per unit length along the horizontal well in this odel is Q o S oko gh t.... (.11) av os where α is diensionless teperature coefficient and equals 0.4. Reis also gave the stea oil ratio by considering the stea enthalpy and heat loss to overburden. 30

49 In 005, Akin put forward a ore coprehensive atheatical odel based on Reis s work. In previous study, oil viscosity was fully deterined by teperature. This work considered the influence of asphaltene content on oil viscosity by using the theory of Werner et al. (1998) when fluid copositions are deterined: where ( P, T) 1 1 D ln[ ] c( ) E ln( ( P, T ) T T D P0 P )..... (.1) c is paraeter that deterines the variation of viscosity as a function of teperature, P is pressure, T is teperature, D and E are paraeters that deterine the variation of viscosity as a function of pressure. If fluid copositions are unknown, a reference viscosity under reference teperature and pressure is necessary for calculating arbitrary oil viscosity. Azad and Chalaturnyk (010) further considered the oil saturation variation and geo-echanical effect in SAGD process. The volue of stea chaber can be divided into up to 90 slices. This is because though the nuber of slices is optional, choosing a high nuber increases coputational tie with no increase in accuracy. For siplicity in that study, the nuber of slices was assued to be 90. The oil saturations change in every slice at the end of each tie step. This allows for choosing different relative pereability in oil rate calculation according 31

50 to oil saturations. Moreover, liit equilibriu approach (Duncan, 1996) was applied to calculate porosity and pereability change with stress field..4. Nuerical Models Nuerical siulation has been used widely by any researchers to help understand the SAGD process. It can be a ethod to validate nuerical odel by history atching physical odel results and it can also be used to investigate the effect of a specific reservoir paraeter when there are inadequate easured physical properties. Chow and Butler (1996) conducted a nuerical siulation of the SAGD process based on the Chung and Butler s (1988) experiental data. A two-diensional, three-phase and two-coponent black oil nuerical odel for the SAGD process was developed and tested. The results showed that STARS nuerical siulator can provide a good atch of SAGD process during the stea chaber spreading sideways and downwards period while didn t odel the rising stea chaber well for lacking of built-in physics to siulate water/oil eulsification and stea fingering. Ito and Suzuki (1999) conducted a siulation study on the Hangingstone SAGD project in order to iprove the understanding of oil production echanis and study subcooling teperature optiization for stea trap control. The geoechanical change of foration during SAGD process was discussed and the author also put forward the conclusion that convective energy carried by stea condensate doinates the heat transfer echanis. Law and Nasr (000) conducted a fiddle-scale nuerical siulation of SAGD process in order to investigate the SAGD perforance in the Athabasca oil sands in the presence of a top water zone. A 3

51 series of field-scale nuerical odeling case were studied to analyse the applicability of SAGD process under different reservoir conditions as well as water zones and gas caps. This research extended the knowledge gained fro lab-scale studies to predict field-scale SAGD perforance. Chen (009) conducted a nuerical study of reservoir heterogeneity effects on SAGD process by using a stochastic odel of shale distribution. The effect of reservoir heterogeneity on SAGD was studied separately in two regions called the near well region (NWR) and the above well region (AWR).The author found that the drainage and flow of hot fluids within the NWR are of short characteristic length and to be very sensitive to the presence and distribution of shale while the AWR affects the expansion of the stea chaber that is of characteristic flow length on the order of half of foration height. It is also shown that SAGD yields low or oderate oil production rate and recovery in the reservoir with poor vertical counication due to the presence of high percentage of shale. 33

52 CHAPTER 3 MATHEMATICAL MODEL In SAGD process, the stea quality in vertical wellbore drops with the depth because of the heat loss fro stea to wellbore syste towards foration. Inside the horizontal wellbore, the stea flows horizontally while soe stea flows into the foration through the slotted liner. The stea into the foration offers the energy for heating the bituen foration and keeping the stea chaber spread. In this study, the stea flow process was divided into two sub-syste. The first sub-syste is the stea flow inside vertical wellbore, and it s a co-current gas-liquid two-phase flow with a constant ixture flow rate. And the second subsyste is the stea flow along the horizontal well with radial outflow into foration. It s a co-current gas-liquid two-phase flow but the ixture flow rate decreases along horizontal wellbore. 3.1 Definitions In this study, the stea is saturated wet stea, the ixture of gas (dry stea) and liquid (hot water). The stea ixture voluetric flow rate is the su of gas phase rate and liquid phase rate: q q q....(3.1) g l For this two-phase flow, neither phase occupies the entire wellbore cross area. The actual flow rates for each phase are 34