STUDY OF TAPERED INTERNAL DIAMETER TUBING STRING WELL COMPLETION FOR ENHANCED PRODUCTION. BERTRAND O. AFFANAAMBOMO, B.Sc. A THESIS

Transcription

1 STUDY OF TAPERED INTERNAL DIAMETER TUBING STRING WELL COMPLETION FOR ENHANCED PRODUCTION By BERTRAND O. AFFANAAMBOMO, B.Sc. A THESIS IN PETROLEUM ENGINEERING Submitted to the Graduate Faculty Of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE IN PETROLEUM ENGINEERING Approved M. Rafiqul Awal Chairperson of the Committee Shameem Siddiqui Lloyd R. Heinze Accepted Fred Hartmeister Dean of the Graduate School August, 2008

2 DEDICATION This thesis is dedicated To my late uncle, Ndongo Ebode Louis, whose sacrifice and love eased my accomplishment and made the man that I am today.

3 ACKNOWLEDGEMENTS I would like to start by expressing my heartfelt thanks to Dr. M. Rafiqul Awal who not only introduced this topic to me but also served as my committee chairperson. Dr. M. Rafiqul Awal took me as his protégé soon after his arrival at Texas Tech University, and inspired me into finishing this research and my master s program. I am pleased to have him as my mentor. I also would like to thank Dr. Lloyd R. Heinze and Dr. Shameem Siddiqui, my committee members, for their advice and motivation throughout this research. Thanks to Dr. Ralph Ferguson, Associate Dean, for his help and dedication that made my graduation possible. Special thanks to Simo Stephane, Renee Jones, Waynishet Hebert, Md Rakibul Sarker, Morteza Akbari, and other colleagues and friends for their assistance throughout my research and academic era. I would like to thank my parents, Mr. Affana Ebode Marc and Mrs. Ngondi Edwige for their unconditional love that always keeps me going. Thanks to my brothers, sisters and cousins, Christian, Jojo, Germaine la petite, Camille, Clarisse, Lili, Daniel and Yannick, Marcel, Edwige, Flore, Ebode, Germaine la grande, and Alida, for their encouragement and love. Abega Affana Valentin, to whom I also dedicate this thesis, has always been a blessing and my greatest source of inspiration. Last but not least, I thank God for my Resiliency and His blessings in my life. ii

4 TABLE OF CONTENTS ACKNOWLEDGEMENTS... ii ABSTRACT... vii LIST OF TABLES... viii LIST OF FIGURES... xi LIST OF ABBREVIATIONS... xvi I. INTRODUCTION TYPES OF WELL COMPLETIONS Casing completions Conventional perforated casing completions Permanent well completions Multiple-zone completions Sand-exclusion completions Water- and gas-exclusion completions Open-Hole completions Drainhole completions MOTIVATION FOR THE PRESENT STUDY STATEMENT OF THE PROBLEM APPROACH TO THE PROBLEM II. LITERATURE REVIEW iii

5 2.1 NODAL ANALYSIS FOR NATURAL FLOWS INFLOW PERFORMANCE RELATIONSHIP (IPR) Vogel s Method Wiggins Method Standing s Method Fetkovich s Method The Klins-Clark Method TUBING PERFORMANCE RELATIONSHIP (TPR) ERROR ESTIMATION IN CALCULATION WELL PRODUCTION FORECAST Transient Flow Period Pseudo-Steady State Single Phase Flow Period Pseudo-Steady Two-Phase Flow Period EFFECT OF TUBING SIZE ASSUMPTIONS AND CONSIDERATIONS III. METHODOLOGY ALGORITHM (Step-by-Step Procedure) Different Scenarios Stabilized Flowrate Concept of Equivalent Tubing Diameter Economic Analysis Well Production Forecast Procedure iv

6 3.2 INPUT DATA (Case Studies) IV. RESULTS AND DISCUSSION STABILIZED FLOWRATE RESULTS EQUIVALENT TUBING DIAMETER WELL PRODUCTION FORECAST RESULTS ECONOMIC ANALYSIS RESULTS V. COMPARISON OF RESULTS COST COMPARISONS STABILIZED FLOWRATES COMPARISONS RECOVERY TIME COMPARISONS PAYOUT TIME COMPARISONS NET PRESENT VALUE COMPARISONS RETURN ON INVESTMENT COMPARISONS VI. SUMMARY OF RESULTS VII. CONCLUSIONS AND RECOMMENDATIONS CONCLUSIONS RECOMMENDATIONS REFERENCES APPENDIX v

7 A. WELL PRODUCTION FORECAST INPUT DATA B. ADDITIONAL WELL PRODUCTION FORECAST RESULTS C. COST ASSUMPTIONS D. ADITIONAL ECONOMIC ANALYSIS RESULTS E. VITA vi

8 ABSTRACT Conventional Well Completion involves usually a single, internal diameter (ID) tubing for producing oil from the subsurface reservoir. As the oil flows vertically upward, the flowing pressure decreases as a function of depth. This reduction in flowing pressure causes more and more dissolved gases to come out. Consequently, the flow stream, especially free gas, expands in volume per unit mass flow rate. The motivation of the present study is to investigate the effect of gradually increasing the tubing inside diameter (ID) as the fluid moves up the string. We call this Tapered ID Tubing Well Completion (TTWC), which is expected to give higher flow rates of oil. Apparently the TTWC involves a slight increase in capital expenditure (CAPEX) for the additional cost accrued from using a section of larger ID tubing. Therefore, we performed numerous studies using nodal analysis for various tubing size combinations, and also economic analysis over the entire producing life of the well. The study reveals that the higher flow rates possible through TTWC not only offsets the additional CAPEX, but also gives significant economic benefits compared to the conventional single tubing completion. vii

9 LIST OF TABLES 1. 1 Comparisons of Various Well Completion Types Results Obtained for in. tubing Observations and Results for in. tubing Results Obtained for in. tubing Results Obtained for in. tubing Results Obtained for 2.441&1.995 in. tubing Results Obtained for 3.340&2.441 in. tubing Results Obtained for 3.340, 2.992, & in. tubing Results Obtained for quad tubing ETD for dual tubing ETD for trio tubing ETD for quad tubing Economic Analysis for 1.995" Tubing Economic Analysis for 2.441" Tubing Economic Analysis for dual Tubing (2.441" & 1.995") Economic Analysis for dual Tubing (3.340" & 2.441") Economic Analysis for Trio Tubing viii

10 4.17 Economic Analysis for Quad Tubing Summary of Economic Analysis A1: Input data for well production forecast B1: Oil Production Forecast for N = B2: Gas Production Forecast for N = B3: Production Schedule Forecast for Tubing B4: Production Forecast for 1.995" Tubing B5: Production Schedule Forecast for Tubing B6: Production Forecast for 2.441" Tubing B7: Production Schedule Forecast for Tubing B8: Production Forecast for 2.992" Tubing B9: Production Schedule Forecast for Tubing B10: Production Forecast for 3.340" Tubing B11: Production Schedule Forecast for Dual Tubing (2.441" & 1.995") B12: Production Forecast for Dual Tubing (2.441" & 1.995") B13: Production Schedule Forecast for Dual Tubing (3.340" & 2.441") B14: Production Forecast for Dual Tubing (3.340" & 2.441") B15: Production Schedule Forecast for Trio Tubing ix

11 B16: Production Forecast for Trio Tubing B17: Production Schedule Forecast for Quad Tubing B18: Production Forecast for Quad Tubing C1: costs Assumptions D1: Economic Analysis for 2.992" Tubing D2: Economic Analysis for 3.340" Tubing x

12 LIST OF FIGURES 1. 1 Completed well/ Open-hole completion Two Types of Drainhole completions Conventional Tubing Duplex Tubing Triplex Tubing Quad Tubing Pressure Losses in Producing Well System Most Common Nodal Points Position Inflow Performance Relationship Curve Straight-line IPR Pressure Function Regions flow inside Tubing Nodal Analysis for in. tubing Nodal Analysis for in. tubing Nodal Analysis for in. tubing Nodal Analysis for in. tubing Nodal Analysis for dual tubing (2.441&1.995 in. tubing) xi

13 4. 6 Nodal Analysis for dual tubing (3.340&2.441 in. tubing) Nodal Analysis for trio tubing (3.340, 2.992, & in. tubing) Results Obtained for quad tubing Single Tubing Plot Production Forecast for Tubing Nodal Analysis Plot for Tubing Production Forecast for Tubing Nodal Analysis Plot for 2.441" Tubing Production Forecast for Dual Tubing (2.441" & 1.995") Nodal Analysis Plot for Dual Tubing (2.441" & 1.995") Production Forecast for Dual Tubing (3.340" & 2.441") Nodal Analysis Plot for Dual Tubing (3.340" & 2.441") Production Forecast for Trio Tubing Nodal Analysis Plot for Trio Tubing Production Forecast for Quad Tubing Analysis Plot for Quad Tubing Dual Tubing (2.441" & 1.995") vs. Single Tubing Dual Tubing (3.340 & ) vs. Single Tubing xii

14 5. 3 Trio Tubing vs. Single Tubing Quad Tubing vs. Single Tubing Dual Tubing (2.441" & 1.995") vs. Single Tubing Dual Tubing (3.340" & 2.441") vs. Single Tubing Trio Tubing vs. Single Tubing Quad Tubing vs. Single Tubing Tubing (2.441" & 1.995") vs. Single Tubing (1.995") Dual Tubing (3.340" & 2.441") vs. Single Tubing (2.441 ) Trio Tubing vs. Single Tubing Quad Tubing vs. Single Tubing Dual Tubing (2.441" & 1.995") vs. Single Tubing Dual Tubing (3.340 & ) vs. Single Tubing Trio Tubing vs. Single Tubing Quad Tubing vs. Single Tubing Dual Tubing (2.441" & 1.995") vs. Single Tubing Dual Tubing (3.340" & 2.441") vs. Single Tubing Trio Tubing vs. Single Tubing Quad Tubing vs. Single Tubing xiii

15 5.21 Dual Tubing (2.441" & 1.995") vs. Single Tubing Dual Tubing (3.340" & 2.441") vs. Single Tubing Trio Tubing vs. Single Tubing Quad Tubing vs. Single Tubing Production Forecast for dual Tubing (2.441" & 1.995") & Single Tubing (1.995") Production Forecast for dual Tubing (3.340" & 2.441") & Single Tubing (2.441") Production Forecast for Trio Tubing & Single Tubing (2.441") Production Forecast for Quad Tubing & Single Tubing (2.441") Cost Results for Different Scenarios Recovery Time Results for Different Scenarios Cashflow: Dual Tubing (2.441" & 1.995") & Single Tubing (1.995") Cashflow: Dual Tubing (3.340" & 2.441") & Single Tubing (2.441") Cashflow: Trio Tubing & Single Tubing (2.441") Cashflow: Quad Tubing & Single Tubing (2.441") Payout Time Results for Different Scenarios Net Present Value Results for Different Scenarios Return on Investment Results for Different Scenarios A1 Thermodynamic Properties for Fluid xiv

16 A2 Thermodynamic Properties for Fluid A3 Relative Permeabilities for Fluid B1: Production Forecast for Tubing B2: Production Forecast for Tubing B3: Nodal Analysis Plot for 2.992" Tubing B4: Nodal Analysis Plot for 3.340" Tubing xv

17 LIST OF ABBREVIATIONS Symbol Definition A Cross-sectional Area B o Oil formation volume factor B g Gas formation volume factor C t Total reservoir compressibility D Tubing inner diameter f F Fanning friction factor g Gravitational acceleration g c Unit conversion factor h Reservoir thickness J Productivity index K Permeability kr Relative permeability L Tubing length N p xvi Cumulative produced oil

18 ΔN p Cumulative produced change P Pressure P e Pressure drainage P node Pressure of the chosen nodal point P R Reservoir pressure P R Average reservoir pressure P sep Separator pressure P wf Well flowing pressure ΔP Pressure drop P WFS Pressure through perforations q Production rate rd Reservoir drainage radius re Drainage radius Rs Solution gas-oil ratio rw Well bore radius xvii

19 R Average gas-oil ratio S Skin factor So Oil saturation t Time T Temperature Δt Production time change u Fluid velocity Δz Elevation increase Greek Letter β Formation volume factor ρ Fluid density μ Viscosity Φ Porosity γ Specific gravity Subscript i xviii initial

20 o Oil g Gas sc Standard conditions w Water wf Bottom hole xix

21 Conversion of Units Factors Quantity U.S. Field unit To SI unit To U.S. Field unit SI unit Length (L) feet (ft) meter (m) Area (A) sq. ft (ft 2 ) meter 2 (m 2 ) acre ^ meter 2 (m 2 ) sq. mile (km) 2 Volume (V) gallon (gal) meter 3 (m 3 ) Mass (M) Pressure (P) Temperature (t) Viscosity (m) ounce (oz) gram (g) pound (lb) kilogram (kg) lbm Slug lb/in 2 (psi) kpa (1000 Pa) psi Atm psi/ft kpa/m inch Hg Pa F (F+32) 1.8C+32 Rankine (8R) Kelvin (K) cp ,000 Pa-s lb/ft-sec lbf-s/ft o C kg/(m-sec) or (Pa-s) dyne-s/cm 2 (poise) Density (P) lbm/ft kg/m3 Permeability (k) md md ( =10-15 m 2 ) md ( = 10-3 darcy) m 2 xx

22 CHAPTER I INTRODUCTION Well completion is a set of operations meant to ease production from a well. Based on the definition, this means that well completion is not only one of the most important aspects of a well, but also it constitutes the connection between the borehole and the pay zone, the pay zone treatment (if any), equipment, and etc. of the same well. Completion therefore, can be defined as the interval that goes from well locating to well abandonment. Completion furthermore makes possible well operations using a logical and inexpensive way. As a result, it should not be off the rack, but tailor made 20. Figure 1.1 shows an appropriate illustration of a completed well. To decide on the type of completion, some specific basis of conduct and expectation must be meant 20 : o Completion and maintenance vs. profits; evidently the larger the field with excellence oil production at fast flowrate, the greater the expenses. o Money-saving vs. possible risks; a risk taken should always consider predictable spending and chances of erroneous hazards. o Supposed change in production of the field vs. supposed change in production of the specified well; the selected type of completion must be met from the beginning of production or must allow a trouble-free adjustment for a future workover. 1

23 1.1 TYPES OF WELL COMPLETIONS There are three categories of well completions 18 : Casing completions The casing completion is the most used (90% of the time) of the three types. There are five types of casing completions Conventional perforated casing completions It is a completion technique in which a casing string is run from the surface to the producing zone, followed by its cementing in place. This technique involves the perforation of the casing string. Oil is produced through the casing string Permanent well completions In this completion, the tubing and wellhead are placed permanently. All other activities (completion or corrective operations) are executed with a small diameter tool through the tubing Multiple-zone completions It is a completion used when there is more than one producing zone. The technique permits a synchronized production of two or more producing zones. This technique is complex and pricey due to the downhole equipment and tools used to complete the job. 2

24 Sand-exclusion completions It is a complicated completion used when a well is drilled in unconsolidated sand. Sand-exclusion completion is usually used during completion time or sometimes during the life of a well. The risk is that sand production can wear down the equipment, wellbore and flowlines, thus it can ruin your investment Water- and gas-exclusion completions Water-and gas-exclusion completions are used when free gas conservation and lesser water productions are needed. Thus to achieve it, appropriate zones inside the producing zone are chosen Open-Hole completions Open-hole completions are wells completed with the oil tubing string placed above the productive zone, or in which the productive zone is left open without protection. This technique is merely employed in steady rock formations. It is used since it allows the zone of interest to be tested while drilling, there is no formation damaged from drilling mud or cement, the production is greater than other completions, and it is cheaper. Figure 1.1 shows an illustration of open-hole completion. 3

25 1.1.3 Drainhole completions Drainhole completions are methods used to complete horizontal wells or slant wells. The main advantage of the technique is to elongate the production zone in order to boost the productivity. Figure 1.2 shows two types of drainhole completions. 4

26 Table 1. 1 Comparisons of Various Well Completion Types 18 Well Completion Types Advantages Disadvantages Casing completions Types Conventional perforated casing completions Permanent well completions Multiple-zone completions Sand-exclusion completions Water- and gasexclusion completions Water-bearing rocks from above or below the productive formation are sealed off. Better economy Open-Hole Completions Speed up the rate of flow from the productive interval. More productive than a conventional perforated-casing completion. Less expensive Less cement contamination Required casing swabbing. Tools are tiny and ineffective. More complex and pricey. Less degree of control over the desired productive interval. Drainhole completions Increase in productivity Cost more than other completion types. 5

27 Figure 1.1: Completed well/open-hole completion 24 6

28 Figure 1.2: Two Types of Drainhole completions 18 7

29 1.2 MOTIVATION FOR THE PRESENT STUDY In general, a completion design must be capable to resolve the following problems successfully 20 : o preserve borehole wall stability, if required o guarantee selective fluid production from specific formation, if required o reduce confine in the flow path o guarantee well safety o permit well flow control o permit well operations with minimum workover o facilitate workover, if required Well completion is therefore essential to the performance of a well during its entire life, but it has, for a long time, been expensive to the oil industry. Moreover, with its advanced options of today s technology, it has made an impact in capital expenditure (CAPEX) increase, thus should allow a faster and better investment return. Conventional well completion employs in general a single inside-diameter (ID) tubing string (fig. 1.3). Sometimes a smaller or larger ID tubing string section(s) is used due to workover and borehole constraint necessities. We note that as the oil flows vertically upward, the flowing pressure decreases as a function of depth. This reduction in flowing pressure causes more and more dissolved 8

30 gases to come out. Consequently, the flow stream, especially free gas, expands in volume per unit mass flowrate. If the capacity of the flow string does not increase as the fluid moves up, more and more flow restriction is experienced, causing higher flowing pressure gradient. This will cause an increase in flowing bottomhole pressure (FBHP), which will decrease the reservoir pressure abandonment, and hence the oil production rate. Therefore, the motivation of the present study is to investigate the effect of gradually increasing the tubing ID as the fluid moves up the string. This is conceptualized as Tapered inside diameter Tubing string Well Completion (TTWC). To make TTWC a practical engineering design, from both technical and economical aspects, we envisage two, three, and four ID s in the production string. Comparisons between single and tapered completion string will be made using the following criteria: 1. Effect on production rate, and cumulative production; 2. Effect on capital expenditure (CAPEX); 3. Economic analysis over full life cycle of a well. The TTWC design, used for this study, includes a combination, tapered tubing strings with the smallest size tubing at the bottom and the largest size at the top up. The 9

31 study will be limited to the duplex, triplex and quad strings. An illustration of a duplex tubing, triplex tubing, and quad tubing is shown in Figures 1.4, 1.5, and 1.6, respectively. 10

32 Figure 1.3 Conventional Completion 11

33 Figure 1. 4 Duplex Tubing 12

34 Figure 1. 5 Triplex Tubing 13

35 Figure 1. 6 Quad Tubing 14

36 1.3 STATEMENT OF THE PROBLEM This study is important for the following reasons: o Well inflow-outflow analysis over the full life cycle of an oil well shows that the proposed completion is suitable for a new as well as an old well. o Production Optimization o Accelerated Recovery o Better economy performance The study does not focus on factors affecting the proposed TTWC such as: the mechanical challenge and design of the TTWC. To calculate the well production forecast, we used real field data and the units used are field units. In this study, the terms dual tubing, trio tubing and quad tubing will be used for duplex tubing, triplex tubing and quadruple tubing, respectively. 1.4 APPROACH TO THE PROBLEM To examine the effectiveness of the proposed TTWC well completion, the following objectives are set for this study: o Conduct a focused review of literature on IPR and TPR construction methods, and well performance forecast method. o Collect pertinent reservoir, well, fluid, and production data o Determine stabilized flowrates for the single, dual, triple and quad strings, using nodal analysis software. 15

37 o Run economic analysis (using NPV) for variation strings. o Compare results of a single string vs. dual, triple, and quad strings. 16

38 CHAPTER II LITERATURE REVIEW 2.1 NODAL ANALYSIS FOR NATURAL FLOWS Natural flow is one of the mechanisms that some producing wells exploit to transport produced fluids from the bottom to the surface. Gas wells usually flow naturally. Oil wells, on the other hand, sometimes will flow naturally because of constraint energy gained in their premature phases of their productive life. Typical produced fluids go through many constraints (friction losses) during their transportation from the reservoir to the surface. They must go through reservoir rock matrix, perforations and probable gravel pack, probably a bottomhole standing valve, the tubing, probably a subsurface safety valve, the surface flowline, and flowline choke to the separator. Figure 2.1 shows potential pressure losses in producing well system. 17

39 Figure 2. 1 Pressure Losses in Producing Well System 1 18

40 Where 1. P1 = PR Pwfs = pressure drop in porous medium 2. P2 = Pwfs Pwf = pressure drop across completion 3. P3 = PUR PDR = pressure drop across restriction 4. P4 = PUSV PDSV = pressure drop across safety valve 5. P5 = Pwh PDSC = pressure drop across surface choke 6. P6 = PDSC Psep = pressure drop in flowline 7. P7 = Pwf Pwh = total pressure drop in tubing 8. P8 = Pwf Psep = total pressure drop in flowline First introduced by Gilbert 3 in 1954 then debated by Nind 4 in 1964 and Brown 16 in 1978, nodal analysis has been one of the most used instruments for well analysis. It is based on choosing a point in a producing well system called nodal point or node which separates the producing well system into two sections (inflow/outflow). Inflow section includes upstream components (from the nodal point to the separator). Outflow section includes downstream components (from the nodal point to the reservoir). Figure 2.2 shows the most common nodal points employed: 19

41 Where Figure 2. 2 Most Common Nodal Points Position 1 1. Separator 7. P WFS = pressure through perforations 2. Surface Choke 8. P R = reservoir pressure 3. Wellhead 1A. Gas Sales 4. Safety Valve 1B. Stock Tank 5. Restriction 6. P WF = flowing bottomhole Pressure 20

42 The average reservoir pressure and the separator well are two pressures that stay unchanged, since they are independent of the flowrate, at a specific time of the well life. In order to calculate the flowrate in the system, after the nodal point has been chosen, the subsequent conditions have to be met: o The node inflow must be equivalent to the node outflow. o There must be just one pressure at a particular node. Inflow to the nodal point: P R ΔP (upstream components) = p node (2.1) Outflow from the nodal point: P sep + ΔP (downstream components) = p node (2.2) Where p R= average reservoir pressure, psia Psep = separator pressure, psia ΔP = pressure drop of any component in the system, psia P node = pressure of the chosen nodal point, psia 21

43 2.2 INFLOW PERFORMANCE RELATIONSHIP (IPR) An inflow performance relationship (IPR) is a graphical method used in production engineering to estimate the relationship between the flowrate and the bottomhole flowing pressure. IPR is a most common way in production engineering to estimate reservoir deliverability. It is generally used to estimate various operating conditions such as determining the optimum production scheme and designing production equipment of a particular well. It is a Cartesian plot (IPR plot) of various bottomhole flowing pressure test data versus the flowrate test data of a particular well. The IPR graph (inflow performance relationship) curve or an IPR curve is shown in Figure 2.3. The magnitude of the slope of the IPR is called the productivity index (PI or J), J ( ) = q P e P wf (2.3) Where J = productivity index, STB/D/psi q = flowrate, STB/D pe = pressure at the external boundary of the drainage area, psia p wf = bottomhole pressure, psia 22

44 Figure 2.3 Inflow Performance Relationship Curve 5 Reservoir inflow models used to construct the well IPR curves have either a theoretical basis or an empirical basis. These models are generally verified during test points in the field application. The most common and broadly used IPR equation is a Productivity Index or straight-line IPR. The assumption used is that the flowrate is proportional to the pressure drawdown in the reservoir. Figure 2.4 shows a plot of the straight-line IPR. 23

45 Figure 2.4 Straight-line IPR 6 IPR is used to describe reservoir deliverability. However, it is not enough for a production engineer to comprehend wellbore flow performance to recommend oil well equipment and optimize well production situation Vogel s Method In 1968 Vogel, with the help of a computer model, constructed IPRs for a number of suppositional saturated oil reservoirs which were under a wide range of conditions. This method not only helps to regularize IPR but also generates IPR without any physical units. The following equation is used to generate IPRs curves for different reservoir pressure conditions: 24

46 Q P = P 0.8 o wf wf ( Q ) o max Pr Pr 2 (2.4) Where Q o= oil rate at P wf, bbl/day ( Q o ) max = maximum oil flow rate when wellbore pressure is zero, bbl/day P wf = bottomhole pressure, psig P r = reservoir pressure, psig Other methods used to generate IPR are Wiggins method, Standing s method, Fetkovich s method, and Klins-Clark method Wiggins Method In 1993 Wiggin derived equations to calculate inflow performance using four sets of relative permeability and fluid property input data for a computer model. The assumption used for this method is that the initial reservoir pressure is at its bubble pressure. The followings are the two equations derived: Q P = P 0.48 o wf wf ( Q ) o max Pr Pr 2 (2.5) 25

47 Q P = P 0.28 o wf wf ( Q ) o max Pr Pr 2 (2.6) Where Q o= oil rate at P wf, bbl/day ( Q o ) max = maximum oil flow rate when wellbore pressure is zero, bbl/day P wf = bottomhole pressure, psig P r = reservoir pressure, psig Standing s Method In 1970 Standing rearranged Vogel s equation to calculate future inflow performance relationship of a well as a function of reservoir pressure. The rearranged equation is: Q o ( Qo ) max P wf 1 Pr P P = r wf (2.7) Where Q o= oil rate at P wf, bbl/day ( Q o ) max = maximum oil flow rate when wellbore pressure is zero, bbl/day P wf = bottomhole pressure, psig 26

48 P r = reservoir pressure, psig Fetkovich s Method In 1942, Muskat and Evinger derived a theoretical productivity index equation from the pseudosteady-state flow equation for non-linear flow wells. Qo = kh r e ln S rw P P r wf f ( p)dp (2.8) Where f ( p) k ro = is the pressure function (2.9) µ β o o k ro = oil relative permeability k = absolute permeability, md β o = oil formation volume factor µ o = oil viscosity, cp In 1973 Fetkovich proposed that the pressure function can exist in two regions as shown in figure 3.1: 27

49 Figure 2. 5 Pressure Function Regions For p>pb, the pressure function exists at the right in figure 2.5 above in the undersaturated region, thus: f ( p) 1 = µ oβo p (2.10) 2. For p<pb, the pressure function is at the left in figure 2.5 above in the saturated region, thus: f P ( p) = µ oβo Pb 1 Pb (2.11) 28

50 µo and β o are estimated at the bubble-point pressure. Three cases are to be taken into account in a straight-line function pressure application: For and Pwf > Pb, the production is from an undersaturated reservoir, therefore equation 2.10 will be substituted into equation 2.8, thus: Pr kh 1 Qo f dp r = e Pwf o o S µ β ln rw (2.12) 1 µ o β o = constant therefore equation 2.12 becomes: Qo = kh r e µ oβo ln S rw ( P r P ) wf (2.13) For and Pwf < Pb, the pressure function is a straight line, therefore equation 2.11 will be substituted into equation 2.8, thus: kh Qo = r e ln S rw P P r wf f 1 µ oβo Pb P dp P b (2.14) 1 µ oβo Pb P P b is constant therefore equation 2.14 becomes: Qo = ( µ β ) o o kh 1 r 2P e b ln 0.75 S b + rw P 2 2 ( P P ) r wf (2.15) 29

51 For Pwf < Pb and > Pb, at this condition, equation 2.8 becomes: Qo kh r e ln S rw ( p) dp + f ( p) = f P P b wf P P r b dp (2.16) Combining equation 2.10 and 2.13 with 3.1, we have: Pb Pr kh 1 P 1 Qo = + dp dp r µ P wf oβo P e Pb b µ Pb oβo ln S rw (2.17) µo and βo are estimated at the bubble-point pressure Pb, therefore the integration of equation 2.17 gives: Qo = ( µ β ) o o kh 1 r 2P e b ln S b rw P 2 2 ( P P ) + ( Pr P ) r wf wf (2.18) The Klins-Clark Method In 1993, Klins and Clark introduced an equation comparable to Vogel s equation with an exponent d: Q o ( Qo ) max P P = wf r P P wf r d (2.19) Where 30

52 Pr d = ( P b ) (2.20) Pb We selected Vogel s method to construct IPR because it was better than the other ones for this particular well. 2.3 TUBING PERFORMANCE RELATIONSHIP (TPR) Tubing performance relationship (TPR) is the relationship between bottomhole pressure and the flowrate. TPR is used to observe the connection between the total tubing pressure drop and a surface flowing pressure value as a function of flowrate, GOR (GLR), tubing ID, density, surface pressure, and average temperature. A well deliverability is mostly dependent of the pressure drop required to raise a fluid through the production tubing at a certain flowrate. The tubing pressure drop is the sum of the surface pressure, the hydrostatic pressure of the fluid, and the frictional pressure loss due to the flow. A fluid inside the tubing string of length L and height Δz goes from position 1 to position 2 (see figure 2.5). Using the first law of thermodynamics, the pressure drop is: 31

53 32 Figure 2.6 flow inside Tubing 22 D g L u f u g z g g p p P c F c c ρ ρ ρ + + = = (2.21)

54 Where ΔP = pressure drop, lbf/ft 2 P 1 = pressure at position 1, lbf/ft 2 P 2 = pressure at position 2, lbf/ft 2 g = gravitational acceleration, ft/s 2 g c = unit conversion factor, lbm-ft/ibf-s 2 ρ = fluid density lbm/ft 3 Δz = elevation increase, ft u = fluid velocity, ft/s f F = Fanning friction factor L = tubing length, ft D = tubing inner diameter, ft As stated in section 2.2, IPR is not enough for a production engineer to comprehend wellbore flow performance and to recommend oil well equipment and optimize well production situation. TPR and IPR intersection is used to find the stabilized flowrate and the corresponding bottomhole pressure which consequently allows a full understanding of the wellbore flow performance to recommend oil well equipment and optimize well production situation. 33

55 2.4 ERROR ESTIMATION IN CALCULATION Hagedorn & Brown correlation used to construct TPR in this study, was made using data from a 1500-ft vertical well, tubing sizes ID ranging from 1-2 in, and 5 different fluid types (water and four types of oil and viscosity ranging between 10 and 110 cp at 80oF), were used to develop the correlation. This correlation is independent of flow patterns. Tubing Size: The correlation has an accurate prediction on the pressure losses for tubing sizes ranging from 1-2 in. For tubing sizes over the above range will result on an over prediction. Oil Gravity: Heavier oils (13-25 o API) result to an over calculation the pressure losses. On the other hand, lighter oils (40-56 o API) result to an under calculation of the pressure losses. Gas-Liquid Ratio (GLR): GLR greater than 5000 result to an over calculation of the pressure drop. Water-Cut: The correlation has an accurate calculation for a large range of watercut

56 2.5 WELL PRODUCTION FORECAST Well production forecasting is a method used in production engineering, based on the basis of principle of material balance, flow regimes, and drive mechanisms, to find future production rate and cumulative production of oil and gas using nodal analysis. It is mostly used in field economics analyses by combining production forecast results with oil and gas prices. IPR and TPR are used to find future production rates. The flow periods for a volumetric oil reservoir are: Transient Flow Period With the use of Nodal analysis in transient IPR and steady flow TPR, the production rate during transient flow period can be calculated by the following equation: kh( pi pwf ) q = k 162.6B0µ o (log t + log S) 2 φµ c r o t w (2.22) Where k = effective horizontal permeability, percentage h = pay zone thickness, feet p i is the reservoir pressure in psia p wf = bottomhole pressure, psia B o = oil formation volume factor, bbl/stb 35

57 μ o = oil viscosity, cp t = time, day Ф = reservoir porosity, percentage c t = total reservoir compressibility, psi-1 r w = wellbore radius, feet S = skin factor Pseudo-Steady State Single Phase Flow Period During pseudo-steady state single phase flow period, the IPR varies with time due to the reservoir pressure decline and the TPR remains stable due to the stability of the fluid properties above the bubble-point pressure. The production rate during pseudosteady one phase flow period is calculated using the following equation: kh( p pwf ) q = 1 4A 141.2Boµ o ( ln 2 γc r ) + S 2 A w (2.23) Where k = effective horizontal permeability, percentage h = pay zone thickness, feet p wf = bottomhole pressure, psia B o = oil formation volume factor, bbl/stb 36

58 μ o = oil viscosity, cp P R = average reservoir pressure, psia A = drainage area, feet scare γ = Euler s constant = 1.78 C A = drainage area shape factor, 31.6 for a circular boundary r w = wellbore radius, feet S = skin factor S = skin factor Pseudo-Steady Two-Phase Flow Period During pseudo-steady two-phase flow period, IPR and TPR both vary with time due to the unsteadiness of fluid properties such as relative permeability and gas-liquid ratio (GLR). The production rate during pseudo-steady two-phase flow period is calculated using the following equation: q = * J p pwf p p p wf 2 (2.24) p = p Where e 141.2qBoµ o 4kh (2.25) P R= average reservoir pressure, psia 37

59 p wf = bottomhole pressure, psia J = productivity index, STB/D/psi B o = oil formation volume factor, bbl/stb μ o = oil viscosity, cp k = effective horizontal permeability, percentage h = pay zone thickness, feet P e = reservoir pressure, psia 2.6 EFFECT OF TUBING SIZE Tubing size generally has an essential function in well production. Wells with larger tubing sizes have less pressure drops due to friction and lesser gas velocities than wells with smaller tubing sizes which have high pressure drops due to friction, but have higher gas velocities. Nodal analyses for oil and gas wells usually reveal that certain large size tubing (ID), well flowrate decreases. The indispensable notion of tubing design will be to install an adequate tubing diameter to allow less friction and have a high velocity. The concepts used to size tubing are nodal analysis and critical velocity. An extensive search in public literature domain revealed any tapered ID string concepts for optimizing production. However, there are reported cases of two sizes (ID) of tubing because of well construction problems; 38

60 Trenchard & Whisenant 27 (1935) reported probably the earliest case of tapered tubing string completion. The purpose was putting wells back on production after shutting them in. Three methods were generally used: pumping, flowing with the aid of valves, and tapered tubing. The tapered tubing string method was found to be quite satisfactory. It usually consisted of a string of pipe, half of which is 3/4-inch, and the other half, i-inch. The use of the tapered tubing afforded a more continuous flow and probably a smaller amount of injected gas at the start. Frederick & DeWeese (1967) reported a tapered tubing string used in a well, "Kaplan Caper," in South Louisiana. In order to flow the well after initial completion, a tapered macaroni string was installed inside the production tubing (ID). The macaroni string consisted of (top to bottom): 1-1/2-in, 2.9-lb N-80 tubing to 7,000-ft, and 1-1/4-in, 2.4-lb/ft N-80 tubing from 7,000-ft to 9,000-ft. The production tubing itself was tapered (top to bottom) as follows: 3-1/2-in, lb/ft N /8-in, 8.7-lb/ft N /8-in, 7.7-lb/ft N /8-in, 7.7-lb/ft P ft -- 7,100-ft; 7,000-ft to 9,000-ft; 9,000-ft -- 15,500-ft 15,500-FT -- 21,230-ft Golan and Whitson 6 (1986) reported using smaller size (ID) of tubing in the liner section of well. Schlumberger 28 (2001) reported using a tapered tubing string of 5.5 to 7 in. in a condensate well with a high GOR. The well was producing 5500 BOPD with a gas/oil 39

61 ratio of 9600 scf/stb through a monobore completion consisting of a 7-in.liner and a tapered tubing string of 5.5 to 7 in. Velocities exceeded 8 m/s, and the flowing wellhead pressure was 1430 psi. Tibbles, R., Ezzat, A., Mahmoud, K.H., Ali, A.H.A., and Hosein, P. (2004). "Hydraulic fracturing the best producer: A myth?" presented at New Zealand Petroleum Conference, Auckland from 7-10 March. Slide #9-10. Tibbles et al. (2004) reported the use of a tapered tubing string as follows: 4-1/2-in 0-ft to 5,000-ft 3-1/2-in 5,000-ft to 5,892-ft The well produced at 2,147 stbo/d before hydraulic fracturing was considered. Prefracturing nodal analysis indicated a high AOFP. The tapered tubing string indicated a production rise to 3,145 stbo/d. After fracturing, the measured flow rate was 3,101 stbo/d. Other instances of tapered tubing are usually for increase outer diameter (OD) necessitated by mechanical performance. 2.7 ASSUMPTIONS AND CONSIDERATIONS The present study is conducted with the following assumptions and considerations. 1. Well is vertical. 2. Reservoir drive is depletion type, i.e. oil and gas are produced by expansion in volume caused by reservoir pressure depletion. 3. Initial average reservoir pressure is at or below bubble point pressure (Pb) of 4350 psia. 40

62 4. A single well is considered in a 640 acre spacing. 5. The well is produced till an assumed abandonment pressure (Pa) of 3350 psia. 6. Wellbore skin is considered via the IPR equation, but is put equal to zero in this study. 7. We consider only naturally flowing oil well. However, the methodology can be extended to wells on artificial lift methods. 8. The design calculations for various sizes of tubing considered in this study do not include mechanical performance (e.g. tensile collapse, burst, and torsion failure). It is implicitly assumed that the selected tubing sizes satisfy the various mechanical performance requirements. 9. Average reservoir pressure declines from 4350psia to 3350 psia in 100 psia steps. 10. Reservoir is solution gas drive at the bubble point with no initial gas cap and rapidly goes below the bubble point pressure after production starts. 41

63 CHAPTER III METHODOLOGY 3.1 ALGORITHM (Step-by-Step Procedure) The objective of this thesis, as stated in section 1.4, is to determine stabilized flowrates for the single, dual, triple and quad strings, run economic analysis (using NPV) for combination strings, and compare results of a single string vs. dual, triple, and quad strings Different Scenarios The innovation about TTWC is its design. It is a combination of tapered tubing strings with the smallest size tubing at the bottom and the largest size at the top. Most production tubings in the oil industry are made considering outside diameter (OD) for strength. TTWC in the other hand is mainly about inside diameter (ID). The different scenarios below will be used while conducting experiments. Scenario 1: Single tubing 1.995, 2.441, 2.992, and in. tubing sizes were used. Scenario 2: Dual tubing 42

64 Two different sub-scenarios with different tubing inside diameter sizes, 1.995, 2.441, and in., were conducted and their design will be as shown in figure 1.4: 1. d 1 = in. and d 2 = in. 2. d 1 = in. and d 2 = in. Scenario 3: Trio tubing One sub-scenario with different tubing sizes, 2.992, 2.441, and in., was conducted and its design will be as shown in figure 1.5: 1. d 1 = in., d 2 = in., and d 3 = in. Scenario 4: Quad tubing One sub-scenario with different tubing sizes, 1.995, 2.441, 2.992, and in., was conducted and its design will be as shown in figure 1.6: 1. d 1 = in., d 2 = in., d 3 = in., and d 4 = in Stabilized Flowrate As mentioned in section 2.3, TPR and IPR intersection is used to find the stabilized flowrate and the corresponding bottomhole pressure. Stabilized flowrate is achieved when there is a continuous flow between the reservoir and the tubing string. 43

65 The empirical method used in this study to generate IPR is the Vogel s method 7, and the empirical method used to generate TPR is Hagedorn & Brown correlation 25. Both methods are incorporated in the following software used: 1. VirtuWellTM by Fekete 30 and 2. Well performance forecast program (in MS Excel TM ) developed by Guo et al Concept of Equivalent Tubing Diameter Based on stabilized flowrates obtained for different scenarios, a graph of different single tubing diameter sizes vs. their correspondent flowrates will be plotted. A streamline equation will then be derived from the plot. This equation obtained will serve as the equivalent tubing diameter equation in which we will substitute each TTWC stabilized flowrates to find their corresponding single tubing diameter. The objective of this study is to investigate what equivalent single tubing diameter corresponds to each one of TTWC tubing diameter, i.e. dual, trio, and quad tubing. Thus each TTWC will be compared with its equivalent single tubing diameter obtained Economic Analysis In order to carry out the economic analysis, well production forecast must first be calculated. Economic analysis, as stated in section 2.4, will then be conducted based on the results obtained from well production forecast and gas and oil prices. 44

66 Well Production Forecast Procedure Well production forecast calculation for a solution-gas drive reservoir requires the use of material balance models to create the cumulative production and time relationship. The most frequently used material balance model is found in Craft & Terry Hawkins (1991) 12 which was from Tarner s earlier work in The following steps are used in order to calculate the production forecast during the twophase period: 1. Assume average-reservoir pressure (between the bubble pressure Pb and the abandonment reservoir pressure pa). 2. Calculate fluid properties at each average reservoir pressure, and compute incremental cumulative production ΔNp and cumulative production Np inside each average reservoir pressure gap. a. Compute Фn and Фg using the two pressure values within the interval pressure, and then find their average in the interval. Φ n = B o R ( B o B oi ) + ( R si R s ) B g s B g (3.1) Where Ф n = coefficient B o = oil formation volume factor, bbl/stb 45

67 B g = gas formation volume factor, bbl/stb R s = solution gas-oil ratio, scf/stb R si = solution gas-oil ratio at initial reservoir pressure, scf/stb B oi = oil formation volume factor at initial reservoir pressure, bbl/stb Φ g = B ( B o B oi ) + ( R si R s ) B g g (3.2) Where Ф g = coefficient B o = oil formation volume factor, bbl/stb B g = gas formation volume factor, bbl/stb R s = solution gas-oil ratio, scf/stb R si = solution gas-oil ratio at initial reservoir pressure, scf/stb b. Estimate incremental oil and gas production per stb of oil in place by presuming an average gas-oil ratio in interval. N 1 1 p = Φ Φ n n N 1 p Φ + RΦ g g G 1 p (3.3) G p = N p R 46 (3.4)

68 Where Φ g= average coefficient Φ n = average coefficient ΔN p 1 = change in cumulative produced oil at the beginning of the interval, stb N p 1 = cumulative produced oil at the beginning of the interval, stb G p 1 = reservoir gas volume at the beginning of the interval, scf R = average gas-oil ratio in interval, scf/stb ΔG p 1 = incremental oil and gas production per stb of oil, place c. Add ΔNp1 and ΔGp1 to Np1 and Gp1, in that order to estimate cumulative oil and gas production of each end of the interval. d. Determine oil saturation S o B = B o oi 1 ( S )( 1 N ) 1 w p (3.5) Where S o = oil saturation, fraction B o = oil formation volume factor, bbl/stb B oi = oil formation volume factor at initial reservoir pressure, bbl/stb 47

69 S w = water saturation, fraction N p 1 is the cumulative produced oil at the beginning of the interval in stb e. Using S o, find the relative permeabilities krg and kro from the relative permeability curves. f. Determine the average gas-oil ratio R = R s + k k rg ro µ B o µ B g o g (3.6) Where R = average gas-oil ratio in interval, scf/stb R s = solution gas-oil ratio, scf/stb k rg = relative permeability to gas phase, fraction k ro = relative permeability to oil phase, fraction B o = oil formation volume factor, bbl/stb B g = gas formation volume factor, bbl/stb μ o = oil viscosity, cp μ g = gas viscosity, cp g. Contrast in 2f with the assume value in 2b. Repeat 2b through 2f until converges. 48

70 3. Calculate production rate q at each average reservoir pressure using Nodal analyses. 4. Determine production time for each average reservoir pressure interval: N P t = (3.7) q t = t (3.8) Where t = cumulative production time, day Δt = production time for each average reservoir pressure interval, day ΔNp = change in cumulative produced oil, stb q = production rate, stb/day 3.2 INPUT DATA (Case Studies) The most important concern for the choice of the typical production test data is to be capable to run a simulation and obtain the producing capacity of the well using different scenarios described in section 3.1. To accomplish this, the following data inputs were used: GLR and gas gravity are equal to 400 Scf/STB and 0.65, respectively. P b will be at 3600 psia. The reservoir pressure is equal 3482 psia; this means the reservoir is saturated. The well head pressure is equal 400 psig; the water cut is 50%, and 35 o API. The well depth is 10,000 feet. The test data is as follow: ql = 320 STB/day and well head 49

71 pressure is 3445 psig. Input data used for well production forecast and all economic analysis assumptions are listed in Appendix B and Appendix C, respectively. 50

72 CHAPTER IV RESULTS AND DISCUSSIONS The first part of the experience involves the nodal analysis of different scenarios for the single, dual, trio, and quad strings. Their experimental observations and results can be seen below from Table 4.1 to Table 4.6. The outflow values are then obtained from the nodal analysis plots from Figure 4.1 to Figure 4.6 for various production scenarios for the single, dual, trio and quad strings. 4.1 STABILIZED FLOWRATE RESULTS Scenario 1 Single Tubing 51

73 Figure 4. 1 Nodal Analysis for in. tubing Table 4. 1 Results Obtained for in. tubing Outflow Reservoir Pressure (psia) Flowrate (Bbl/d) Pressure (Psia)

74 Figure 4. 2 Nodal Analysis for in. tubing Table 4. 2 Observations and Results for in. tubing Outflow Reservoir Pressure (psia) Flowrate (Bbl/d) Pressure (psia)

75 Figure 4.3 Nodal Analysis for in. tubing Table 4.3 Results Obtained for in. tubing Outflow Reservoir Pressure (psia) Flowrate (Bbl/d) Pressure (psia)

76 Figure 4.4 Nodal Analysis for in. tubing Table 4.4 Results Obtained for in. tubing Outflow Reservoir Pressure (psia) Flowrate (Bbl/d) Pressure (psia)

77 Scenario 2 Dual Tubing Figure 4. 5 Nodal Analysis for dual tubing (2.441&1.995 in. tubing) Table 4. 5 Results Obtained for 2.441&1.995 in. tubing Outflow Reservoir Pressure. (psia) Flowrate (Bbl/d) Pressure (psia)

78 Figure 4. 6 Nodal Analysis for dual tubing (3.340&2.441 in. tubing) Table 4. 6 Results Obtained for 3.340&2.441 in. tubing Outflow Reservoir Pressure (psia) Flowrate (Bbl/d) Pressure (psia)

79 Scenario 3 Trio Tubing Figure 4. 7 Nodal Analysis for trio tubing (3.340, 2.992, & in. tubing) Table 4. 7 Results Obtained for 3.340, 2.992, & in. tubing Outflow Reservoir Pressure (psia) Flowrate (Bbl/d) Pressure (psia)

80 Scenario 4 Quad Tubing Figure 4. 8 Nodal Analysis for Quad tubing Table 4. 8 Results Obtained for quad tubing Outflow Reservoir Pressure (psia) Flowrate (Bbl/d) Pressure (psia)

81 4.2 EQUIVALENT TUBING DIAMETER In order to compare results of a single string vs. dual, triple, and quad strings, an Equivalent Tubing Diameter (ETD), deq, was defined for different TTWC. ETD is derived from the streamline equation obtained from the plot of the different single tubing diameter sizes vs. their correspondent flowrates, see figure 4.7. Flowrate, Bbl/d Single Tubing q = 5813.ln(d eq ) R² = Tubing dia (d i ), inches Figure 4.9 Single Tubing Plot Therefore after derivation, ETD equation obtained is: q 5813ln( d ) 2214 (4.1) = eq 60

82 q = 5813 ln ( ) d eq (4.2) d eq ( q 2214) + = EXP 5813 (4.3) Where d eq is the equivalent tubing diameter in inches q is the stabilized flowrate in bbl/d Calculations of different ETDs were done based on each scenario stabilized flowrate and results can be seen from tables 4.7 to table 4.9: Scenario 2 Table 4. 9 ETD for dual tubing Dual tubing d eq, in & tubing diameters & tubing diameters 2.84 For the first sub-scenario (2.441 & tubing ID), the nearest tubing size available is in. on the upside, and in. on the downside. 61

83 From what it is seen in table 4.3, the Dual (2.441 & tubing ID) completion will be compared with in. tubing Completion, for the following reasons: 1. The Dual completion gives q = STB/d, which is approx. 25% more than flowrate from in single tubing completion. 2. But the Dual completion involves 50% length of higher tubing. Diameter, i.e., in., which will increase capital expenditure (CAPEX) by certain amount. For the second sub-scenario (3.340 & tubing ID), the nearest tubing size available is in. on the upside, and in. on the downside. From the table 4.4, the Dual (3.340 & tubing ID) completion will be compared with in. tubing Completion, for the following reasons: 1. The Dual completion gives q = STB/d, which is approx. 34% more than flowrate from in. single tubing completion. 2. But the Dual completion involves 50% length of higher tubing. Diameter, i.e., in., which will increase capital expenditure (CAPEX) by certain amount. 62

84 Scenario 3 Table ETD for trio tubing Trio tubing d eq, in , 2.992, and tubing diameters 2.90 downside. The nearest tubing size available is in. on the upside, and in. on the From figure 4.5, to make economic comparisons, it makes sense to compare the trio completion with in. tubing Completion, for the following reasons: 1. The trio completion gives q = STB/d, which is approx. 39% more than flowrate from in single tubing completion. 2. But the trio completion involves more than one 50% length of higher tubing. Diameter, i.e., in., which will increase capital expenditure (CAPEX) by certain amount. 63

85 Scenario 4 Quad Tubing Table ETD for quad tubing Quad tubing d eq, in , 2.992, 2.441, &1.995 tubing diameters 2.56 downside. The nearest tubing size available is in. on the upside, and 2.441in. on the From table 4.6, to make economic comparisons, the quad completion will be compared with in. tubing Completion, for the following reasons: 1. The quad completion gives q = STB/d, which is approx. 13.5% more than flowrate from 2.441in single tubing completion. 2. But the quad completion involves more than one 50% length of higher tubing. Diameter, i.e., in., which will increase capital expenditure (CAPEX) by certain amount. 64

86 4.3 WELL PRODUCTION FORECAST RESULTS In the following, the forecast of the well performance is computed with a twophase hydrocarbon reservoir. This is done with the help of Nodal analysis, the principle of material balance, and Tarner s method. The procedure used in doing so is as stated in section The object is to illustrate both recovery and time of the well. Figures 4.8, 4.10, 4.12, 4.14, 4.16, and 4.18 are graphical representation of table C4, C6, C12, C14, C16, and C18 of APENDIX C. IPR results seen in figures 4.9, 4.11, 4.13, 4.15, 4.17, and 4.19 were calculated using Vogel s correlation for two- phase reservoir. Scenario 1 Single Tubing 65

87 1,200 3,000,000 Production Rate, STB/d 1, Production Rate Cumulative Production 2,500,000 2,000,000 1,500,000 1,000, ,000 Cumulative Production, STB Time, month 0 Figure 4.10 Production Forecast for Tubing 66

88 P w f, p s i a Production Rate, STB/d IPR for Pr = 4250 psia IPR for Pr = 4150 psia IPR for Pr = 4050 psia IPR for Pr = 3950 psia IPR for Pr = 3850 psia IPR for Pr = 3750 psia IPR for Pr = 3650 psia IPR for Pr = 3550 psia IPR for Pr = 3450 psia IPR for Pr = 3350 psia TPR for pr = 4250 psia TPR for pr = 4150 psia TPR for pr = 4050 psia TPR for pr = 3950 psia TPR for pr = 3850 psia TPR for pr = 3750 psia TPR for pr = 3650 psia Figure 4.11 Nodal Analysis Plot for Tubing 67

89 1,200 3,000,000 Production Rate, STB/d 1, Production Rate Cumulative Production 2,500,000 2,000,000 1,500,000 1,000, ,000 Cumulative Production, STB Time, month 0 Figure 4.12 Production Forecast for Tubing 68

90 P w f, p s i a Production Rate, STB/d IPR for Pr = 4250 psia IPR for Pr = 4150 psia IPR for Pr = 4050 psia IPR for Pr = 3950 psia IPR for Pr = 3850 psia IPR for Pr = 3750 psia IPR for Pr = 3650 psia IPR for Pr = 3550 psia IPR for Pr = 3450 psia IPR for Pr = 3350 psia TPR for pr = 4250 psia TPR for pr = 4150 psia TPR for pr = 4050 psia TPR for pr = 3950 psia TPR for pr = 3850 psia TPR for pr = 3750 psia TPR for pr = 3650 psia Figure 4.13 Nodal Analysis Plot for 2.441" Tubing 69

91 Scenario 2 Dual Tubing Production Rate, STB/d Production Rate Cumulative Production Time, month Cumulative Production, STB Figure 4.14 Production Forecast for Dual Tubing (2.441" & 1.995") 70

92 Pwf, psia Production Rate, STB/d IPR for pr = 4250 psia IPR for pr = 4150 psia IPR for pr = 4050 psia IPR for pr = 3950 psia IPR for pr = 3850 psia IPR for pr = 3750 psia IPR for pr = 3650 psia IPR for pr = 3550 psia IPR for pr = 3450 psia IPR for pr = 3350 psia TPR for pr = 4250 psia TPR for pr = 4150 psia TPR for pr = 4050 psia TPR for pr = 3950 psia TPR for pr = 3850 psia TPR for pr = 3750 psia TPR for pr = 3650 psia Figure 4.15 Nodal Analysis Plot for Dual Tubing (2.441" & 1.995") 71

93 Production Rate, STB/d Production Rate Cumulative Production Time, month Cumulative Production, STB Figure 4.16 Production Forecast for Dual Tubing (3.340" & 2.441") 72

94 Pwf, psia TPR for pr = 3750 psia TPR for pr = 3650 psia Production Rate, STB/d IPR for pr = 4250 psia IPR for pr = 4150 psia IPR for pr = 4050 psia IPR for pr = 3950 psia IPR for pr = 3850 psia IPR for pr = 3750 psia IPR for pr =3650 psia IPR for pr = 3550 psia IPR for pr = 3450 psia IPR for pr = 3350 psia TPR for pr = 4250 psia TPR for pr = 4150 psia TPR for pr = 4050 psia TPR for pr = 3950 psia TPR for pr = 3850 psia Figure 4.17 Nodal Analysis Plot for Dual Tubing (3.340" & 2.441") 73

95 Scenario 3 Trio Tubing Production Rate, STB/d Production Rate Cumulative Production Time, month Cumulative Production, STB Figure 4.18 Production Forecast for Trio Tubing 74

96 Pwf, psia TPR for pr = 3850 psia TPR for pr = 3750 psia Production Rate, STB/d IPR for pr = 4250 psia IPR for pr = 4150 psia IPR for pr = 4050 psia IPR for pr = 3950 psia IPR for pr = 3850 psia IPR for pr = 3750 psia IPR for pr = 3650 psia IPR for pr = 3550 psia IPR for pr = 3450 psia IPR for pr = 3350 psia TPR for pr = 4250 psia TPR for pr = 4150 psia TPR for pr = 4050 psia TPR for pr = 3950 psia TPR for pr = 3650 psia Figure 4.19 Nodal Analysis Plot for Trio Tubing 75

97 Scenario 4 Quad Tubing Production Rate, STB/d Production Rate Cumulative Production Time, month Cumulative Production, STB Figure 4.20 Production Forecast for Quad Tubing 76

98 Pwf, psia Production Rate, STB/d IPR for pr = 4250 psia IPR for pr = 4150 psia IPR for pr = 4050 psia IPR for pr = 3950 psia IPR for pr = 3850 psia IPR for pr = 3750 psia IPR for pr = 3650 psia IPR for pr = 3550 psia IPR for pr = 3450 psia IPR for pr = 3350 psia TPR for pr = 4250 psia TPR for pr = 4150 psia TPR for pr = 4050 psia TPR for pr = 3950 psia TPR for pr = 3850 psia TPR for pr = 3750 psia TPR for pr = 3650 psia Figure 4.21 Analysis Plot for Quad Tubing 77

99 4.4 ECONOMIC ANALYSIS RESULTS The main motivation of this study is not only to optimize production and lower the recovery time, but it is also to expect a better economic performance of TTWC compare to the conventional tubing completion. Thus the economic analysis of different scenarios was conducted using payout time, net present value (NPV), and return on investment. NPV of cash flows over n (days, months, or years) is the subtraction of the present value and the initial investment, I 17 : NPV n Ct = t r ( =1 ) t I (7.1) Where t = time of the cash flow, days n = total time of the project, days r = discount rate, % C t = net cash flow at time t, $ I = initial investment, $ For NPV > 0, the project may be accepted For NPV < = 0, the project should be rejected 78

100 The return on investment (ROI) is the percentage of money gained or lost on an investment to the money invested: For ROI = + 100%, the final value is twice the initial value For ROI > 0, the investment is profitable For ROI < 0, the investment is at a loss For ROI = 100%, investment can no longer be recovered NPV will be conducted at 10% interest rate. Prices of oil and gas used are 126.2$/bbl and $/Mmbtu as of May, 2008, respectively 26. Tubing outside diameters in., in., 3.5 in., and 4.0 in. will be 4.02, 5.44, 7.76, and 9.48 $/ft as of May, 2008 respectively. Because the well is presumed to be in natural flow, operation expenditure (OPEX), development cost, and abandonment cost will not be considered. In the economic analysis, we only consider one cost element, tubing cost, and consider all other cost components equal. In reality, however, TTWC will entail additional costs, such as, cost due to increased rig time in handling multiple tubing sizes, additional workover time in pulling out/ running in (if workover is required before reaching the assumed abandonment pressure, Pa), etc. The following are the results obtained for various completion types: 79

101 Scenario 1 Single tubing Table 4.12 Economic Analysis for 1.995" Tubing Time, day Oil Produced, bbl/day Gas Produced, MMbtu/day Gross REVENUE, $/day Cost, $ Cashflow, $ , NPV, $ ROI Payout Time, days 1,654,

102 Table 4.13 Economic Analysis for 2.441" Tubing Time, day Oil Produced, bbl/day Gas Produced, MMbtu/day Gross REVENUE, $/day Cost, $ Cashflow, $ , NPV, $ ROI Payout Time, days 1,763,

103 Scenario 2 Dual Tubing Table 4.14 Economic Analysis for dual Tubing (2.441" & 1.995") Time, day Oil Produced, bbl/day Gas Produced, MMbtu/day Gross REVENUE, $/day Cost, $ Cashflow, $ , NPV, $ ROI Payout Time, days 1,854,

104 Table 4.15 Economic Analysis for dual Tubing (3.340" & 2.441") Time, day Oil Produced, bbl/day Gas Produced, MMbtu/day Gross REVENUE, $/day Cost, $ Cashflow, $ , NPV, $ ROI Payout Time, days 1,840,

105 Scenario 3 Trio Tubing Table 4.16 Economic Analysis for Trio Tubing Time, day Oil Produced, bbl/day Gas Produced, MMbtu/day Gross REVENUE, $/day Cost, $ Cashflow, $ , , NPV, $ ROI Payout Time, days

106 Scenario 4 Quad Tubing Table 4.17 Economic Analysis for Quad Tubing Time, day Oil Produced, bbl/day Gas Produced, MMbtu/day Gross REVENUE, $/day Cost, $ Cashflow, $ , NPV, $ ROI Payout Time, days 1,907,

107 Table 4.18 below is the economic analysis summary. We observe that the quad completion has a better economic performance. Table Summary of Economic Analysis Completion Types Payout Time (d) NPV ($) ROI (%) Conventional Completion 329 1,654, Conventional Completion ,763, Dual Completion ,854, Dual Completion ,840, Trio Completion 279 1,893, Quad Completion 278 1,907,

108 CHAPTER V 5.1 COST COMPARISONS COMPARISON OF RESULTS Figures 5.1, 5.2, and 5.3, and 5.4 show the cost comparisons of dual tubing (3.340 & ) vs. single tubing, trio tubing vs. single tubing, and quad tubing vs. single tubing, respectively. As mentioned in section 4.3, calculations were done with the well that is presumed to be in natural flow. Therefore, OPEX, development cost, and abandonment cost will not be considered. As a result, tubing costs will only be considered. With the assumptions made below, we observe the following cost comparisons: 87

109 300, ,000 Costs, dollars 280, , , , , , ,000 Duplex Tubing (2.441" & 1.995") Single Tubing (1.995") Figure 5.1 Dual Tubing (2.441" & 1.995") vs. Single Tubing 88

110 300,000 Costs, dollars 295, , , , , , , , , ,000 Duplex Tubing (3.340" & 2.441") Single Tubing (2.441") Figure 5. 2 Dual Tubing (3.340 & ) vs. Single Tubing 89

111 300, , , ,230 Costs, dollars 285, , , , , , ,000 Triplex Tubing Single Tubing (2.441") Figure 5. 3 Trio Tubing vs. Single Tubing 90

112 300, , ,000 Costs, dollars 285, , , , , , , ,000 Quad Tubing Single Tubing (2.441") Figure 5. 4 Quad Tubing vs. Single Tubing 91

113 5.2 STABILIZED FLOWRATES COMPARISONS Figures 5.5, 5.6, 5.7, and 5.8 show stabilized flowrates comparison of dual tubing (2.441 & ) vs. single tubing (1.995 ), dual tubing (3.340 & ) vs. single tubing (2.441 ), trio tubing vs. single tubing (2.441 ), and quad tubing vs. single tubing (2.441 ), respectively. As expected, we have a better production rate when using TTWC. This is because TTWC allows the flow stream expansion, in volume per unit mass flowrate, as it moves up Production Rate, Bbl/d , , Duplex Tubing (2.441"&1.995") Sigle Tubing (1.995") Figure 5. 5 Dual Tubing (2.441" & 1.995") vs. Single Tubing 92

114 4500 Production Rate, Bbl/d , , Dual Tubing (3.340" & 2.441") Single Tubing (2.441") Figure 5. 6 Dual Tubing (3.340" & 2.441") vs. Single Tubing 93

115 Production Rate, Bbl/d , , Trio Tubing Single Tubing (2.441") Figure 5. 7 Trio Tubing vs. Single Tubing 94

116 Production Rate, Bbl/d , , Quad Tubing Single Tubing (2.441") Figure 5. 8 Quad Tubing vs. Single Tubing 95

117 5.3 RECOVERY TIME COMPARISONS By calculating well production forecast, we were able to obtain the recovery time in days of different scenarios. Figures 5.9, 5.10, 5.11, and 5.12 show the recovery time comparisons of dual tubing (3.340 & ) vs. single tubing, trio tubing vs. single tubing, and quad tubing vs. single tubing, respectively. As we can see, the recovery time using TTWC is faster than conventional completion. 3,500 3,400 Recovery Time, days 3,300 3,200 3,100 3,000 2,900 2,800 2,700 2,982 3,177 2,600 2,500 Duplex Tubing (2.441" & 1.995") Single Tubing (1.995") Figure 5.9 Tubing (2.441" & 1.995") vs. Single Tubing (1.995") 96

118 Recovery Time, days ,878 3, Duplex Tubing (3.340" & 2.441") Single Tubing (2.441") Figure Dual Tubing (3.340" & 2.441") vs. Single Tubing (2.441 ) 97

119 Recovery Time, days ,838 3, Triplex Tubing Single Tubing (2.441") Figure Trio Tubing vs. Single Tubing 98

120 Recovery Time, days ,864 3, Quad Tubing Single Tubing (2.441") Figure Quad Tubing vs. Single Tubing 99

121 5.4 PAYOUT TIME COMPARISONS Figures 5.13, 5.14, 5.15, and 5.16 show the payout comparison of dual tubing (3.340 & ) vs. single tubing, trio tubing vs. single tubing, and quad tubing vs. single tubing, respectively. We observe a better payout time using TTWC completion than single tubing completion Payout Time, days Duplex Tubing (2.441" & 1.995") Single Tubing (1.995") Figure 5.13 Dual Tubing (2.441" & 1.995") vs. Single Tubing 100

122 Payout Time, days Duplex Tubing (3.340" & 2.441") Single Tubing (2.441") Figure Dual Tubing (3.340 & ) vs. Single Tubing 101

123 Payout Time, days Triplex Tubing Single Tubing (2.441") Figure Trio Tubing vs. Single Tubing 102

124 Payout Time, days Quad Tubing Single Tubing (2.441") Figure Quad Tubing vs. Single Tubing 103

125 5.5 NET PRESENT VALUE COMPARISONS Figures 5.17, 5.18, 5.19, and 5.20 show NPV comparisons of dual tubing (3.340 & ) vs. single tubing, trio tubing vs. single tubing, and quad vs. single tubing, respectively. NPV was calculated at the interest rate of 10%. TTWC completions show better NPV than the conventional tubing completion. 1,950,000 1,900,000 Net Present Value, $ 1,850,000 1,800,000 1,750,000 1,700,000 1,650,000 1,854,242 1,654,170 1,600,000 1,550,000 Duplex Tubing (2.441" & 1.995") Single Tubing (1.995") Figure 5.17 Dual Tubing (2.441" & 1.995") vs. Single Tubing 104

126 1,950,000 1,900,000 Net Present Value, $ 1,850,000 1,800,000 1,750,000 1,700,000 1,650,000 1,840,291 1,763,283 1,600,000 1,550,000 Duplex Tubing (3.340" & 2.441") Single Tubing (2.441") Figure Dual Tubing (3.340" & 2.441") vs. Single Tubing 105

127 1,950,000 1,900,000 1,893,710 Net Present Value, $ 1,850,000 1,800,000 1,750,000 1,700,000 1,650,000 1,600,000 1,763,282 1,550,000 Triplex Tubing Single Tubing (2.441") Figure Trio Tubing vs. Single Tubing 106

128 1,950,000 1,900,000 1,907,249 Net Present Value, $ 1,850,000 1,800,000 1,750,000 1,700,000 1,650,000 1,763,282 1,600,000 1,550,000 Quad Tubing Single Tubing (2.441") Figure Quad Tubing vs. Single Tubing 107

129 5.6 RETURN ON INVESTMENT COMPARISONS Figure 5.21, 5.22, 5.23, and 5.24 show a ROI comparison graphic representative of dual tubing (3.340 & ) vs. single tubing, trio tubing vs. single tubing, quad tubing vs. single tubing. The observation that we can derive these figures is that TTWC has a better rate of return than the conventional completion Return on Investment, % Dual Tubing (2.441" & 1.995") Single Tubing (1.995") Figure 5.21 Dual Tubing (2.441" & 1.995") vs. Single Tubing 108

130 Return on Investment, % Duplex Tubing (3.340" & 2.441") Single Tubing (2.441") Figure Dual Tubing (3.340" & 2.441") vs. Single Tubing 109

131 Return on Investment, % Triplex Tubing Single Tubing (2.441") Figure Trio Tubing vs. Single Tubing 110

132 Return on Investment, % Quad Tubing Single Tubing (2.441") Figure 5.24 Quad Tubing vs. Single Tubing 111

133 CHAPTER VI SUMMARY OF RESULTS Figures 6.1 through 6.13 below show the summary results of both the conventional completion and TTWC: Production Rate, STB/day Dual Tubing (2.441" & 1.995") Single Tubing (1.995") Cum. Prod. For dual Tubing Cumulative Production, STB Time, months 0 Figure 6. 1 Production Forecast for dual Tubing (2.441" & 1.995") & Single Tubing (1.995") 112

134 Production Rate, STB/day Dual Tubing (3.340" & 2.441") Single Tubing (2.441") Cum. Prod. For dual Tubing Cumulative Production, STB 0 Cum. Prod. For Single Tubing Time, months Figure 6. 2 Production Forecast for dual Tubing (3.340" & 2.441") & Single Tubing (2.441") 113

135 Production Rate, STB/day Time, months Triplex Tubing Single Tubing (2.441") Cum. Prod. For Triplex Tubing Cum. Prod. For Single Tubing Cumulative Production, STB Figure 6. 3 Production Forecast for Trio Tubing & Single Tubing (2.441") 114

136 Production Rate, STB/day Quad Tubing Single Tubing (2.441") Cum. Prod. For Quad Tubing Cum. Prod. For Single Tubing Cumulative Production, STB Time, months 0 Figure 6. 4 Production Forecast for Quad Tubing & Single Tubing (2.441") 115

137 295, , ,000 Costs, dollars 280, , , , , , , ,000 Single Tubing (1.995") Dual Tubing (2.441" & 1.995") Single Tubing (2.441") Dual Tubing (3.340" & 2.441") Quad Tubing Trio Tubing Figure 6. 5 Cost Results for Different Scenarios 116

138 3,300 3,200 Recovery Time, days 3,100 3,000 2,900 2,800 2,700 2,600 Trio Tubing Quad Tubing Dual Tubing (3.340" & 2.441") Dual Tubing (2.441" & 1.995") Single Tubing (2.441") Single Tubing (1.995") Figure 6. 6 Recovery Time Results for Different Scenarios 117

139 1,200,000 1,000,000 Cashflow, dollars 800, , , , , , ,321 1,676 2,011 2,312 2,601 2,878 Time, days Dual Tubing (2.441" & 1.995") Single Tubing (1.995") Figure 6. 7 Cashflow: Dual Tubing (2.441" & 1.995") & Single Tubing (1.995") 118

140 1,200,000 1,000, ,000 Cashflow, dollars 600, , , , , ,321 1,676 2,011 2,312 2,601 2,878 Time, days Dual Tubing (3.340" & 2.441") Single Tubing (2.441") Figure 6. 8 Cashflow: Dual Tubing (3.340" & 2.441") & Single Tubing (2.441") 119

141 1,200,000 1,000,000 Cashflow, dollars 800, , , , , , ,301 1,651 1,982 2,279 2,565 2,838 Time, days Trio Tubing Single Tubing (2.441") Figure 6. 9 Cashflow: Trio Tubing & Single Tubing (2.441") 120

142 1,200,000 1,000, ,000 Cashflow, dollars 600, , , , , ,313 1,667 2,000 2,300 2,588 2,864 Time, days Quad Tubing Single Tubing (2.441") Figure Cashflow: Quad Tubing & Single Tubing (2.441") 121

143 Payout Time, days Quad Tubing Trio Tubing Dual Tubing (3.340" & 2.441") Dual Tubing (2.441" & 1.995") Single Tubing (2.441") Single Tubing (1.995") Figure Payout Time Results for Different Scenarios 122

144 1,950,000 1,900,000 Net Present Value, $ 1,850,000 1,800,000 1,750,000 1,700,000 1,650,000 1,600,000 1,550,000 1,500,000 Single Tubing (1.995") Single Tubing (2.441") Dual Tubing (3.340" & 2.441") Dual Tubing (2.441" & 1.995") Trio Tubing Quad Tubing Figure Net Present Value Results for Different Scenarios 123

145 Return on Investment, % Single Tubing (1.995") Single Tubing (2.441") Tri Tubing Dual Tubing (3.340" & 2.441") Quad Tubing Dual Tubing (2.441" & 1.995") Figure Return on Investment Results for Different Scenarios 124

146 CHAPTER VII CONCLUSIONS AND RECOMMENDATIONS 7.1 CONCLUSIONS The following conclusions are drawn from the results obtained: 1. In this study, we have developed a new concept of well completion for enhanced production: Tapered ID Tubing Well Completion (TTWC) 2. Well inflow-outflow analysis over the full life cycle of an oil well shows that TTWC gives high well flowrates and cumulative production. 3. Based on well production forecast results, TTWC showed shorter recovery time. 4. Based on the economy analysis results, TTWC demonstrated a most favorable payout time than the conventional well completion. 5. It also demonstrated a better net present value (NPV) and return on investment (ROI) than the conventional well completion. 125

147 7.2 RECOMMENDATIONS 1. A study should be carried out to compare the natural flow period till liquid loading takes place for each completion described in the present work, and the economic ramifications. 2. Apply the TTWC method using data for various fields in the Permian basin and Gulf of Mexico for old/existing wells, additional economic analysis should be performed to account for workover cost and downtime. 3. Optimize the section lengths in TTWC for maximum flowrate or maximum NPV. A good starting case is the duplex completion. 126

148 REFERENCES 1. Beggs Dale H., Production Optimization Using NODAL TM Analysis, OGCI, OK, Szilas A. P., Production and Transport of Oil and Gas, Second completely revised edition, Elsevier, New York-Tokyo, Gilbert, W. E., Flowing and Gas-Lift Well Performance, API Drill. Prod. Practice, NY, Nind, T. E. W., Principles of Oil Well Production, McGraw-Hill, TX, 1964, James Lea, Nickens Henry V., Well Michael, Gas Well Deliquification Solutions to Gas Well Liquid Loading Problem, Elsevier, Gulf Drilling Guides, MA, Golan, Michael, and Whitson, Curtis H., Well Performance, 2nd ed. Englewood Cliffs, Prentice-Hall, New Jersey, Vogel, J. V., Inflow Performance Relationships for Solution-Gas Drive Wells, JPT, Jan. 1968, pp ; Trans. AIME, p Standing, M. B., Inflow Performance Relationships for Damaged Wells Producing by Solution-Gas Drive, JPT, Nov. 1970, pp Wiggins, M. L., Generalized Inflow Performance Relationships for Three- Phase Flow, SPE Paper 25458, presented at the SPE Production Operations Symposium, Oklahoma, March 21 23,

149 10. Klins, M., and Clark, L., An Improved Method to Predict Future IPR Curves, SPE Reservoir Engineering, November 1993, pp Fetkovich, M. J., The Isochronal Testing of Oil Wells, SPE Paper 4529, presented at the SPE 48th Annual Meeting, Las Vegas, Sept. 30 Oct. 3, Craft B.C., Hawkins M., Applied Petroleum Reservoir Engineering, 2 nd edition, Prentice Hall, New Jersey, Beggs, Dale H., Gas Production Operations, OGCI, Oklahoma, Muskat, M., and Evinger, H. H., Calculations of Theoretical Productivity Factor, Trans. AIME, 1942, pp , Ahmed Terek, McKinney Paul D., Advanced Reservoir Engineering, Elsevier, Jordan Hill, MA, Brown Kermit E., The Technology of Artificial Lift Methods, Vol. 1, PPC, OK, Cholet H., Well Production Practical Handbook, Editions TECHNIP, Gray Forest, Petroleum Production for the Non-technical Person, PennWell Book, OK, Hall Lewis W., Leecraft Jodie, Petroleum Production Operations, PETEX, TX, Perrin, D., Caron Michel, Gaillot, Georges, Well Completion and Servicing, Editions Tecnip, France and Institut francais du petrole, France, Economides Michael J., Hill Daniel A., Ehlig-Economides Christine, Petroleum Production Systems, Prentice Hall PTR, New Jersey,

150 22. Guo Boyun, Lyons William C., Ghalambor Ali, Petroleum Production Engineering a Computer-Assisted Approach, Elsevier Science & Technology Books, MA, Ahmed Tarek, Reservoir Engineering Handbook, 2 nd edition, GPC, TX, Bharath Rao, Multiphase Flow Models Range of Applicability, CTES, L.C, TX, stversion= Trenchard, J. and Whisenant, J. B., "Government Wells Oil Field, Duval County, Texas," Bulletin of the American Association of Petroleum Geologists Vol. 19, No. 8 August, PP Frederick, B. and DeWeese, E., "Kaplan Caper," in Drilling, June, p Schlumberger, GHOST--Gas Holdup Optical Sensor Tool brochure, SMP- 5762,

151 APPENDIX A WELL PRODUCTION FORECAST INPUT DATA Table A1: Input data for well production forecast 21 k H, md 13 µ o, cp 1.7 h, ft 115 γ o o, API 32 p i, psi 4350 γ o g, API 0.71 p b, psi 4350 T, o F 180 C o, psi E-05 T o pc, R 395 C w, psi E-06 P pc, psi 667 C f, psi E-06 S w, fraction 0.3 C t, psi E-05 Φ, fraction 0.21 µ g, cp r w, ft r e, ft

152 Figure A1 Thermodynamic Properties for Fluid

153 Figure A2 Thermodynamic Properties for Fluid