Productivity Index of Horizontal Oil Wells. Nasser AlMolhem

Transcription

1 Productivity Index of Horizontal Oil Wells Nasser AlMolhem Problem Report Submitted to the College of Engineering and Mineral Resources At West Virginia University In partial fulfillments of the requirements For the degree of Masters of Science In Petroleum and Natural Gas Engineering Kashy Aminian, Ph.D., Chair Sam Ameri, Prof. Mehrdad Zamirian, Ph.D. Department of Petroleum and Natural Gas Engineering Morgantown, West Virginia 2016 Keywords: productivity index, oil horizontal wells Copyright 2016 Nasser AlMolhem

2 Abstract Productivity Index of Horizontal Oil Wells Nasser AlMolhem Productivity index is the practical approach to characterize the performance of oil wells. During the evolution of petroleum industry, many productivity index PI solutions for different well types have been developed. Initially, PI values were calculated for oil vertical wells. As the drilling technology progressed, PI solutions were considered for horizontal wells. There are different methods for predicting the PI of both vertical and horizontal wells. The main objective of this study is to compare the PI values generated from those different approaches. Moreover, this research aims to highlight the most influential reservoir properties to the PI. A range of static data was given to perform this sensitivity analysis.

3 Acknowledgement Firstly, I would like to thank God for giving me the support to be successful in my life. Also, I would like to thank my parents for their encouragement. I want to express my deepest gratitude and appreciation to my advisor Dr. Kashy Aminian, throughout his advising through my research, and for giving me the opportunity to work under his supervision. I want to mention the support of the chairman of the Petroleum and Natural Gas Engineering Department at West Virginia University, Professor Samuel Ameri for his incomparable personality and his fatherhood to every student, which makes our department the best environment for study. Also, I sincerely thank Dr. Zamirian for his guidance, support during my research work and for being on the committee. My special thanks to all the faculty and staff at the Department of petroleum and Natural Gas Engineering. I would like to send my special thanks to all my relatives in Saudi, and all my friends and colleagues that I have met in Morgantown, West Virginia. I also would like to acknowledge Saudi Aramco for their support and consultation throughout the research. iii

4 Table of Content Abstract... Acknowledgement... iii List of Tables... 3 List of Figures... 4 CHAPTER I. INTRODUCTION Overview Background General Definition Geometry of Horizontal Wells Build Rate Azimuth Advantages of Drilling Horizontal Wells Disadvantages of Drilling Horizontal Wells... 4 CHAPTER II. THEORY Transient State Flow Pseudo Steady State Flow Late Transient Flow Steady State Flow... 7 Literature Review... 8 CHAPTER III. METHODOLOGY Steady State Methods Vertical Well PI Borisov s Method Giger-Reiss-Jourdan s Method Joshi s Method Renard-Dupuy s Method Pseudo Steady State Methods Vertical Well PI Babu-Odeh s Method Kuchuk s Method Economides Method CHAPTER IV. DISCUSSION AND RESULTS PI of Steady State Wells Reservoir Radius = 2000 ft Reservoir Radius = 5000 ft PI of Pseudo Steady State Wells Reservoir Radius = 2000 ft Reservoir Radius = 5000 ft CHAPTER V. CONCLUSION AND FUTURE WORK NOMENCLATURE REFERENCES iv

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6 List of Tables Table 1. Classification of Horizontal Wells 2 Table 2. PI of steady state vertical oil well 18 Table 3. PI of Borisov s steady state horizontal oil well 19 Table 4. PI of Giger-Reiss-Jourdan s isotropic steady state horizontal oil well 20 Table 5. PI of Giger-Reiss-Jourdan s anisotropic steady state horizontal oil well 22 Table 6. PI of Jushi s isotropic steady state horizontal oil well 23 Table 7. PI of Jushi s anisotropic steady state horizontal oil well 25 Table 8. PI of Renard-Dupuy s isotropic steady state horizontal oil well 26 Table 9. PI of Renard-Dupuy s anisotropic steady state horizontal oil well 28 Table 10. PI of the vertical steady state oil well Re=5000 ft 30 Table 11. PI of Borisov s steady state horizontal oil well Re = 5000 ft 31 Table 12. PI of Giger-Reiss-Jourdan s isotropic steady state horizontal oil well Re = 5000 ft 33 Table 13. PI of Giger-Reiss-Jourdan s anisotropic steady state horizontal oil well 34 Table 14. PI of Jushi s isotropic steady state horizontal oil well Re= 5000 ft 36 Table 15. PI of Jushi s anisotropic steady state horizontal oil well Re=5000 ft 37 Table 16. PI of Renard-Dupuy s isotropic steady state horizontal oil well Re=5000 ft 39 Table 17. PI of Renard-Dupuy s anisotropic steady state horizontal oil well Re = 5000 ft 40 Table 18. PI of pseudo steady state vertical oil well 43 Table 19. PI of Babu-Odeh s pseudo steady state horizontal oil well 44 Table 20. PI of Kuckuk s pseudo steady state horizontal oil well 46 Table 21. PI of Economides pseudo steady state horizontal oil well 47 Table 22. PI of pseudo steady state vertical oil well 50 Table 23. PI of Babu-Odeh s pseudo steady state horizontal oil well Re = 5000 ft 51 Table 24. PI of Economides pseudo steady state horizontal oil well Re = 5000 ft 52 vi

7 List of Figures Figure 1. Azimuth of Horizontal Wells. (Directional drilling Web. 26 April. 2016)... 3 Figure 2. Transient and pseudo steady state flow. (Reservoir flow Web. April )... 6 Figure 3. Impact of the crucial parameters on vertical oil well PI Figure 4. Impact of the crucial parameters on Borisov s PI Figure 5. Impact of the crucial parameters on Giger-Reiss-Jourdan s isotropic PI Figure 6. Impact of the crucial parameters on Giger-Reiss-Jourdan s anisotropic PI Figure 7. Impact of the crucial parameters on Jushi s isotropic PI Figure 8. Impact of the crucial parameters on Jushi s anisotropic PI Figure 9. Impact of the crucial parameters on Renard-Dupuy s isotropic PI Figure 10. Impact of the crucial parameters on Renard-Dupuy s anisotropic PI Figure 11. PIs of Base Case Steady State Oil Wells - Re = 2000 ft Figure 12. PIs of Maximum Effect (1-D Case) Steady State Oil Wells - Re = 2000 ft Figure 13. Impact of the crucial parameters on vertical oil PI Figure 14. Impact of the crucial parameters on Borisov s PI at Re = 5000 ft Figure 15. Impact of the crucial parameters on Giger-Reiss-Jourdan s isotropic PI Figure 16. Impact of the crucial parameters on Giger-Reiss-Jourdan s anisotropic PI Figure 17. Impact of the crucial parameters on Jushi s isotropic PI Figure 18. Impact of the crucial parameters on Jushi s anisotropic PI Figure 19. Impact of the crucial parameters on Renard-Dupuy s isotropic PI Figure 20. Impact of the crucial parameters on Renard-Dupuy s anisotropic PI Figure 21. PI s of Base Case Steady State Oil Wells - Re = 5000 ft Figure 22. PI s of Maximum Effect (1-D Case) Steady State Oil Wells - Re = 5000 ft Figure 23. Impact of the crucial parameters on vertical oil well PI Figure 24. Impact of the crucial parameters on Babu-Odeh s PI Figure 25. Impact of the crucial parameters on Kuckuk s PI Figure 26. Impact of the crucial parameters on Economides PI Figure 27. PIs of Base Case Pseudo Steady State Oil Wells - Re = 2000 ft Figure 28. PIs of Case 1-D Pseudo Steady State Oil Wells - Re = 2000 ft Figure 29. Impact of the crucial parameters on vertical oil well PI Figure 30. Impact of the crucial parameters on Babu-Odeh s PI at Re = 5000 ft Figure 31. Impact of the crucial parameters on Economides s PI Figure 32. PIs of Base Case Pseudo Steady State Oil Wells - Re = 5000 ft Figure 33. PIs of Case 1-D Pseudo Steady State Oil Wells - Re = 5000 ft vii

8 CHAPTER I. INTRODUCTION 1.1 Overview Background Fluid deliverability is the main measure of the wells performance in the petroleum industry. Initially, vertical wells were the only type of wells that produce oil reservoirs. Since the 1920s, drilling technology has been improved to drill wells at deviated angles. This improvement allowed drilling engineers to geo-steer their wells horizontally, which will increase the production rates by as much as 20 times more than drilling vertically. This is true since petroleum prospects are more extensive aerially compared to their thickness (usually thickness is less than 150 ft). In addition, directional drilling permits accessing reservoirs that cannot be accessed directly using vertical wells. The first oil well drilled in North America was in Oil Springs, Ontario in Moreover, production in Santa Barbara County, CA began in the 1890s with the development of the Summerland Oil Field, which included the world s first offshore oil well. Historical records suggest that horizontal drilling dates go back to as early as 1920s, and was first utilized in Pennsylvania in Nevertheless, in the 1980s, horizontal drilling became a popular tradition when improved equipment, motor, and other technologies were developed General Definition A horizontal well is a well which is drilled in such a way that the wellbore deviates laterally to an approximate horizontal orientation within the target formation. The horizontal components usually extend to at least 100 ft in the targeted reservoir, measured from the initial point of penetration to the toe of the well. A deviated well can be categorized as a horizontal well when its inclination exceeds 85. 1

9 1.1.3 Geometry of Horizontal Wells Build Rate The build rate is the increase in the inclination of a horizontal well. Generally, it is expressed in /100 ft. It is denoted as a decline rate if the inclination is decreasing (negative). Based on the buildup/decline rate, horizontal wells can be categorized as short, medium, and long radius (Table 1.1). Table 1. Classification of Horizontal Wells Category Long radius Medium radius Short radius Build Rate 2 to 6 /100 ft 6 to 35 /100 ft 1.5 to 3 / 1 ft Azimuth The azimuth of a borehole at a point is the direction of the borehole on the horizontal plane, measures as a clockwise angle (0-360 ) from the North reference. All magnetic tools give readings referenced to magnetic north; however, the final calculated coordinates are reference to either true north or grid north. Figure 1 shows the azimuth direction of a horizontal well. 2

10 Figure 1. Azimuth of Horizontal Wells. (Directional drilling Web. 26 April. 2016) Advantages of Drilling Horizontal Wells The advantages of drilling horizontal wells are: 1. In reservoirs with water and gas coning problems, horizontal wells have been used to minimize coning problems and enhance oil production. 2. In naturally fractured reservoirs, horizontal wells have been used to intersect fractures and produce from them, which will maximize the cumulative production. 3. Enables drilling multiple wells with one surface wellbore (multi-lateral). 4. A long horizontal well provides a large reservoir contact area and therefore enhances the productivity. 5. It provides solution to drilling under inaccessible locations, such as mountains, riverbeds, and populated cities. 3

11 6. It can be utilized as a remedial operation to sidetrack around an obstruction (fish). 7. This technique is applied to relief wells in case of blow-out Disadvantages of Drilling Horizontal Wells The disadvantages of drilling horizontal wells are: 1. Higher drilling and completion costs. Typically it costs about 1.4 to 3 times more than drilling a vertical well. 2. Needs complex drilling and completion technologies. 3. Generally, it is difficult to produce from multiple zones using a single horizontal well. 4

12 CHAPTER II. THEORY The productivity index is a measure of the ability of a well to produce. It is the ration of the total oil flow rate to the pressure drawdown. In other words, it is the hydrocarbon volume delivered per psi of drawdown at the sand-face (STB/psi/day). It is mathematically expressed as: JJ = qq PP = qq (pppp pppppp) During the production cycle of a reservoir, the producing oil well goes through four main stages based on the pressure drawdown and boundary conditions. These four stages are: Transient state. Pseudo steady state. Steady state. Late transient. 2.1 Transient State Flow Transient state flow takes place when a well is first put into production. It is also known as the infinite acting or unsteady state flow in which the pressure disturbance caused by the production of a well has not reached any reservoir boundary. It is described as the fluid flowing condition at which the rate of change of pressure with respect to time at any position in the reservoir is not zero or constant. This is true since the pressure migrates outward from the well without facing any boundaries. Mathematically, transient flow is described as: dddd = ff(rr, tt), wwheeeeee rr iiii tthee rrrrrrrrrrrr aaaaaa tt iiii tthee tttttttt. dddd Figure 2 illustrations the progression of the transient flow pattern. 5

13 Figure 2. Transient and pseudo steady state flow. (Reservoir flow Web. April ) 2.2 Pseudo Steady State Flow Pseudo steady state flow begins when the pressure disturbance created by the production well is felt at the boundary of the well s drainage area. In other words, when the fluid mass situated at the drainage boundary starts moving towards the producing well, pseudo steady state begins. Mathematically, it is expressed as: dddd = cccccccccccccccc rrrrrrrr dddd Figure 2 shows the behavior of the pseudo steady state flow pattern. 6

14 2.3 Late Transient Flow This flow regime takes place between the unsteady state and the pseudo steady state flow regimes. Moreover, it happens when the pressure disturbance caused by the production of a well has reached some of the reservoir boundaries. 2.4 Steady State Flow Steady state flow occurs when the production of a well does not change the pressure at any point in the reservoir over time. It is usually due to an aquifer support or gas cap expansion. Mathematically, it is expressed as: dddd dddd = 0 7

15 Literature Review There are two well categories in which any well is classified: vertical or horizontal. Generally, un-stimulated horizontal oil well produces two to five times to that of a stimulated vertical well. On the other hand, horizontal wells might produce less in thicker reservoirs (reservoir with thicknesses higher than 500 ft). In addition, they are less efficient in low vertical permeability, and in stratified reservoirs. To overcome these drawbacks, stimulation technology can be utilized. Many calculations have been computed to evaluate the productivity index of a horizontal well and many flow models have been employed for this purpose. Parallelepiped models with no flow/constant pressure boundaries at the top or bottom, and either no flow or infinite acting boundaries at the sides were extensively used to approximate the well drainage area. The first model was presented by Borisov, in which constant pressure drainage ellipse was assumed. After that, Joshi introduced an equation that accounted for the vertical to horizontal permeability anisotropy. Then, Economides developed it to be used in the elliptical coordinates. However, this model did not account for the well and reservoir configurations, as well as early time or late time phenomena. Babu and Odeh presented equations that were complicated to calculate the pressure drawdown at any point by integrating appropriate point source functions in space and time. The assumption of their solutions is based on that the well is parallel to the y-axis of the parallelepiped model (Economides, 1996). Additionally, using a numerical inverter, Goode and Thambynayagam introduced a model for horizontal well pressure transient response in Laplace space. After that, Kuchuk improved Goode and Thambynayagam s equations by including constant pressure at the boundaries. Normally, as the horizontal well length increases, the productivity index associated increases. However, producing high volumes of fluids from long horizontal wells will result in high-pressure losses along the wellbore. As a result, this will decrease the productivity of the well. 8

16 Reservoir and fluid Properties (oil): CHAPTER III. METHODOLOGY Formation thickness (h), ft Horizontal permeability (kh), md Viscosity (u), cp. 0.5 Formation volume factor (Bo), bbl/stb 1.5 Depth (d), ft Drainage radius (Reh), ft Length of horizontal well (L), ft Wellbore radius (rw), ft 0.5 Vertical permeability (kv), md Temperature (T), F Average reservoir radius (re), ft Skin factor (S) 0 Average reservoir pressure (P), psia 3000 Flowing bottom hole pressure (Pwf), psia 500 Drainage area (a*b), ft * * 5000 Location of the center of well in the vertical plane (Zo), ft mid-point Standoff (Zw) Porosity, % 10% To calculate the productivity index of oil wells, there are multiple approaches for each flow regime. 9

17 3.1 Steady State Methods There are four major steady state equations to calculate the productivity index of oil horizontal wells. The resulted PI from these equations is compared to the vertical well s PI. These methods are: 1. Vertical well PI. 2. Borisov s method. 3. Giger-Reiss-Jourdan method. 4. Joshi s method. 5. Rendard-Dupuy method Vertical Well PI The following equation is used to predict the PI of oil vertical well: JJ = Borisov s Method kk h BBBB μμ ln rrrr rrrr + ss Borisov proposed the following equation to predict the PI of oil horizontal well in an isotropic reservoir: JJ = h kkh μμoo BBoo ln 4 rreeh LL + LL h ln h 2 ππ rrww Giger-Reiss-Jourdan s Method 10

18 Giger, Reiss, and Jourdan proposed the following equation to predict the PI of oil horizontal well in an isotropic reservoir: JJ = LL KKh μμoo BBoo LL h ln(xx) + ln h 2 rrww For anisotropic reservoir: JJ = KKh μμoo BBoo 1 h ln(xx) + BB2 h LL ln 2 rrww Where: XX = LL 2 2 rreeh LL (2 rreeh) BB = KKh KKKK Joshi s Method 11

19 Joshi proposed the following equation to predict the PI of oil horizontal well in an isotropic reservoir: JJ = h KKh μμoo BBoo ln(rr) + h h LL ln 2 rrww For anisotropic reservoir: JJ = h KKh μμoo BBoo ln(rr) + BB2 h h LL ln 2 rrww Where: BB = KKh KKKK aa = 0.5 LL rreeh 4 LL RR = aa + aa 2 LL 2 2 LL 2 12

20 3.1.5 Renard-Dupuy s Method Renard and Dupuy proposed the following equation to predict the PI of oil horizontal well in an isotropic reservoir: JJ = h KKh μμoo BBoo cosh 1 2aa LL + h h LL ln 2 ππ rrww For anisotropic reservoir: JJ = μμoo BBoo cosh 1 2aa LL h KKh + BBh LL h ln 2 ππ rr ww Where: aa = 0.5 LL rreeh 4 LL BB = KKh KKKK rr ww = (1 + BB)rrrr 2 BB 13

21 3.2 Pseudo Steady State Methods There are three major pseudo steady state equations to calculate the productivity index of oil horizontal wells. The resulted PI from these equations is compared to the vertical well s PI. These methods are: 1. Vertical Well PI. 2. Babu-Odeh method. 3. Kuchuk method. 4. Economides method Vertical Well PI The following equation is used to predict the PI of oil vertical well: JJ = kk h BBBB μμ ln rrrr + ss 0.75 rrrr Babu-Odeh s Method This method is meant to provide an easier model for calculating the PI of a horizontal well. They presented the following equation: JJ = bb kkkk kkkk μμ BB ln CCHH AA 1 2 rrrr SSRR Where: SR is a function that depends strongly on the well length L. SR = 0 when L = b (the fully penetrating case). 14

22 ln(cccc) = 6.28 aa h kkkk kkkk 1 3 xxxx 2 aa + xxxx aa 180 zzzz ln (sin ) h 0.5 ln aa h kkkk kkkk Here: xo and zo are the coordinates measuring the center of the well in the vertical plane, (a) is the dimension of the drainage area Kuchuk s Method Kuchuk suggested an approximate infinite conductivity solution to calculate the productivity index as following: JJ = KKKK h μμ BBBB PPPPPP + SSSS SSSS = h 2LL 1 2 KKKK KKKK SSSS SSSS = 2ππ LL 1 2 KKKK KKKK ΔΔΔΔΔΔ µ qq Since the skin is zero, both Sm and Sm* should be negligible. KKKK = KKKK KKKK 15

23 PPPPPP = h 2LL 1 2 KKKK KKKK 8h ZZZZ ZZZZ h ln ππ rr cccccc ππ + ww 2h LL 1 2 KKKK KKKK Economides Method This approach is general, readily reproduce well-known analytical solutions, and can be used for transient, mixed, and no flow boundary conditions. The PI equation is given by: JJ = KKKKKKKK xxee xxee BB μμ PPDD + 2 ππ LL Σ ss Where: PPPP = xxee CCHH 4 ππ h + xxee 2 ππ LL SSxx h SSSS = ln 2 ππ rrrr h 6 LL + SSSS SSSS = h LL 2ZZZZ h ZZZZ h 1 2 ZZZZ ln ssssss ππ h 16

24 CHAPTER IV. DISCUSSION AND RESULTS Initially, the most influential reservoir properties that greatly impact the productivity index value were distinguished. To achieve this goal, many sensitivity studies were performed by testing the lower and upper limits of each reservoir property. As a result, these crucial properties are reservoir thickness, reservoir permeability, and reservoir radius (dimension). To capture the effect of these properties, two main cases were generated. In the first case, the impact of the reservoir permeability and thickness on the PI value was examined at the lower limit of the reservoir radius (2000 ft for oil wells). That is, the PI value was calculated at various limits of thickness and permeability, independently and collectively. Furthermore, the PI value was computed at the minimum reservoir values (case 1-base). Next, the PI value was calculated at the maximum reservoir thickness without changing the other reservoir parameters (case 1-A). Also, the effect of reservoir permeability on the PI value was estimated by applying its maximum value (case 1- B). In order to distinguish between the effect of permeability and thickness on the PI, case 1-C was created by increasing both parameters at a similar magnitude. That is, both thickness and permeability were increased by a factor of 5. Case 1-D represents the maximum influential reservoir properties. In some models, where the length is a crucial reservoir parameter, additional case (case 1-D-1) was generated to account for length impact on the PI. Similarly, the impact of these properties on the PI was tested at the upper limit of the reservoir radius (5000 ft for oil wells). 4.1 PI of Steady State Wells Reservoir Radius = 2000 ft The PI values of the vertical well are illustrated in Table 2. Clearly, Case 1-A promotes a PI value that is five times greater than the 1-base case. Similarly, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is ten times higher 17

25 than the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 25 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote the highest PI value among all the cases (50 times greater than the PI of Case 1-base). Figure 3 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 2. PI of steady state vertical oil well Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Thickness, ft Permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Wellbore radius, ft PI, stb/psi/day Figure 3. Impact of the crucial parameters on vertical oil well PI 18

26 The PI values of the horizontal oil well using Borisov s model are illustrated in Table 3. Clearly, Case 1-A promotes a PI value that is 10.3 times greater than the 1-base case. Similarly, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is ten times higher than the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 51.3 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote the highest PI value among all the cases (102.7 times greater than the PI of Case 1-base). In case 1-D, maximizing the influential parameters will promote the highest PI value among all the cases. Figure 4 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 3. PI of Borisov s steady state horizontal oil well Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Thickness, ft Permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Length, ft Wellbore radius, ft PI, stb/psi/day

27 Figure 4. Impact of the crucial parameters on Borisov s PI The PI values of the horizontal oil well using isotropic Giger-Reiss-Jourdan s model are illustrated in Table 4. Clearly, Case 1-A promotes a PI value that is 4.6 times greater than the 1-base case. Similarly, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is ten times higher than the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 23.1 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote the highest PI value among all the cases (46.2 times greater than the PI of Case 1-base). Figure 5 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 4. PI of Giger-Reiss-Jourdan s isotropic steady state horizontal oil well Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Thickness, ft Horizontal permeability, md Vertical permeability, md Viscosity, cp

28 Formation volume factor, bbl/stb Reservoir radius, ft Length, ft Wellbore radius, ft B, dimensionless factor X, dimensionless factor PI, stb/psi/day Figure 5. Impact of the crucial parameters on Giger-Reiss-Jourdan s isotropic PI The PI values of the horizontal oil well using anisotropic Giger-Reiss-Jourdan s model are illustrated in Table 5. Clearly, Case 1-A promotes a PI value that is 2.9 times greater than the 1-base case. Similarly, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is ten times higher than the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 14.3 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote the highest PI value among all 21

29 the cases (28.7 times greater than the PI of Case 1-base). Figure 6 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 5. PI of Giger-Reiss-Jourdan s anisotropic steady state horizontal oil well Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Thickness, ft Horizontal permeability, md Vertical permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Length, ft Wellbore radius, ft B, dimensionless factor X, dimensionless factor PI, stb/psi/day

30 Figure 6. Impact of the crucial parameters on Giger-Reiss-Jourdan s anisotropic PI The PI values of the horizontal oil well using isotropic Jushi s model are illustrated in Table 6. Clearly, Case 1-A promotes a PI value that is 4.6 times greater than the 1- base case. On the other hand, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is similar to the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 23.1 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote the highest PI value among all the cases (46.2 times greater than the PI of Case 1-base). Figure 7 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 6. PI of Jushi s isotropic steady state horizontal oil well Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Thickness, ft Horizontal permeability, md Vertical permeability, md Viscosity, cp

31 Formation volume factor, bbl/stb Reservoir radius, ft Length, ft Wellbore radius, ft a, dimensionless factor B, dimensionless factor R, dimensionless factor PI, stb/psi/day Figure 7. Impact of the crucial parameters on Jushi s isotropic PI The PI values of the horizontal oil well using anisotropic Jushi s model are illustrated in Table 7. Clearly, Case 1-A promotes a PI value that is 2.9 times greater than the 1- base case. On the other hand, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is similar to the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 14.3 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote the highest PI value among all the cases (28.6 times greater 24

32 than the PI of Case 1-base). Figure 8 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 7. PI of Jushi s anisotropic steady state horizontal oil well Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Thickness, ft Horizontal permeability, md Vertical permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Length, ft Wellbore radius, ft a, dimensionless factor B, dimensionless factor R, dimensionless factor PI, stb/psi/day

33 Figure 8. Impact of the crucial parameters on Jushi s anisotropic PI The PI values of the horizontal oil well using isotropic Renard-Dupuy s model are illustrated in Table 8.. Clearly, Case 1-A promotes a PI value that is 4.7 times greater than the 1-base case. On the other hand, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is similar to the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 23.6 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote the highest PI value among all the cases (47.1 times greater than the PI of Case 1-base). Figure 9 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 8. PI of Renard-Dupuy s isotropic steady state horizontal oil well Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Thickness, ft Horizontal permeability, md Vertical permeability, md Viscosity, cp

34 Formation volume factor, bbl/stb Reservoir radius, ft Length, ft Wellbore radius, ft a, dimensionless factor B, dimensionless factor Effective wellbore radius rw', ft PI, stb/psi/day Figure 9. Impact of the crucial parameters on Renard-Dupuy s isotropic PI The PI values of the horizontal oil well using anisotropic Renard-Dupuy s model are illustrated in Table 9. Clearly, Case 1-A promotes a PI value that is 4.1 times greater than the 1-base case. On the other hand, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is similar to the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 20.6 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote the highest PI value among all the cases (41.2 times greater than the PI of Case 1-base). Figure 10 below indicates the percentage effect of the crucial parameters on the productivity index value. 27

35 Table 9. PI of Renard-Dupuy s anisotropic steady state horizontal oil well Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Thickness, ft Horizontal permeability, md Vertical permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Length, ft Wellbore radius, ft a, dimensionless factor B, dimensionless factor Effective wellbore radius rw', ft PI, stb/psi/day Figure 10. Impact of the crucial parameters on Renard-Dupuy s anisotropic PI 28

36 Based on Figures 11 and 12 below, Renard-Dupuy model predicts the highest productivity index (12.5 times higher PI than the PI of a vertical well in 1-base and 11.8 times in 1-D) among all the models. On the other hand, Borisov s equation will result in the lowest PI (0.056 of the vertical well s PI value in 1-base and of the PI in 1-D). Figure 11. PIs of Base Case Steady State Oil Wells - Re = 2000 ft Figure 12. PIs of Maximum Effect (1-D Case) Steady State Oil Wells - Re = 2000 ft 29

37 4.1.2 Reservoir Radius = 5000 ft The PI values of the vertical oil well are illustrated in Table 10. Clearly, Case 1-A promotes a PI value that is five times greater than the 1-base case. Similarly, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is ten times higher than the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 25 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote the highest PI value among all the cases (50 times greater than the PI of Case 1-base). Figure 13 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 10. PI of the vertical steady state oil well Re=5000 ft Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Thickness, ft Permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Wellbore radius, ft PI, stb/psi/day

38 Figure 13. Impact of the crucial parameters on vertical oil PI The PI values of the horizontal oil well using Borisov s model are illustrated in Table 11. Clearly, Case 1-A promotes a PI value that is 10.2 times greater than the 1-base case. Similarly, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is ten times higher than the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 50.9 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote the highest PI value among all the cases (101.8 times greater than the PI of Case 1-base). In case 1-D-1, maximizing the influential parameters as well as the horizontal well length will only promote a PI value that is 35.4 greater than the vertical well s PI. Figure 14 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 11. PI of Borisov s steady state horizontal oil well Re = 5000 ft Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Case 1-D-1 Thickness, ft Permeability, md

39 Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Length, ft Wellbore radius, ft PI, stb/psi/day Figure 14. Impact of the crucial parameters on Borisov s PI at Re = 5000 ft The PI values of the horizontal oil well using isotropic Giger-Reiss-Jourdan s model are illustrated in Table 12. Clearly, Case 1-A promotes a PI value that is 4.6 times greater than the 1-base case. Similarly, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is ten times higher than the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 23.6 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote a PI value 47.3 times greater than the PI of Case 1-base. In case 1-D-1, maximizing the influential parameters as well as the horizontal well length will promote the highest PI value among all the cases (

40 times greater than the PI of Case 1-base). Figure 15 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 12. PI of Giger-Reiss-Jourdan s isotropic steady state horizontal oil well Re = 5000 ft Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Case 1-D-1 Thickness, ft Horizontal permeability, md Vertical permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Length, ft Wellbore radius, ft B, dimensionless factor X, dimensionless factor PI, stb/psi/day Figure 15. Impact of the crucial parameters on Giger-Reiss-Jourdan s isotropic PI The PI values of the horizontal oil well using anisotropic Giger-Reiss-Jourdan s model are illustrated in Table 13. Clearly, Case 1-A promotes a PI value that is 3.3 times greater than the 1-base case. Similarly, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is ten times higher than the PI of Case 1-base. By 33

41 increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 16.3 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote a PI value 32.6 times greater than the PI of Case 1-base. In case 1-D-1, maximizing the influential parameters as well as the horizontal well length will promote the highest PI value among all the cases (62.8 times greater than the PI of Case 1-base). Figure 16 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 13. PI of Giger-Reiss-Jourdan s anisotropic steady state horizontal oil well Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Case 1-D-1 Thickness, ft Horizontal permeability, md Vertical permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Length, ft Wellbore radius, ft B, dimensionless factor X, dimensionless factor PI, stb/psi/day

42 Figure 16. Impact of the crucial parameters on Giger-Reiss-Jourdan s anisotropic PI The PI values of the horizontal oil well using isotropic Jushi s model are illustrated in Table 14. Clearly, Case 1-A promotes a PI value that is 4.7 times greater than the 1- base case. Similarly, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is ten times higher than the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 23.6 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote a PI value 47.3 times greater than the PI of Case 1-base. In case 1-D-1, maximizing the influential parameters as well as the horizontal well length will promote the highest PI value among all the cases (76.9 times greater than the PI of Case 1-base). Figure 17 below indicates the percentage effect of the crucial parameters on the productivity index value. 35

43 Table 14. PI of Jushi s isotropic steady state horizontal oil well Re= 5000 ft Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Case 1-D-1 Thickness, ft Horizontal permeability, md Vertical permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Length, ft Wellbore radius, ft a, dimensionless factor 5, , , , , , B, dimensionless factor R, dimensionless factor PI, stb/psi/day Figure 17. Impact of the crucial parameters on Jushi s isotropic PI 36

44 The PI values of the horizontal oil well using anisotropic Jushi s model are illustrated in Table 15. Clearly, Case 1-A promotes a PI value that is 3.3 times greater than the 1-base case. Similarly, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is ten times higher than the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 16.3 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote a PI value 32.6 times greater than the PI of Case 1-base. In case 1-D-1, maximizing the influential parameters as well as the horizontal well length will promote the highest PI value among all the cases (63.3 times greater than the PI of Case 1-base). Figure 18 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 15. PI of Jushi s anisotropic steady state horizontal oil well Re=5000 ft Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Case 1-D-1 Thickness, ft Horizontal permeability, md Vertical permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Length, ft Wellbore radius, ft a, dimensionless factor 5, , , , , , B, dimensionless factor R, dimensionless factor PI, stb/psi/day

45 Figure 18. Impact of the crucial parameters on Jushi s anisotropic PI The PI values of the horizontal oil well using isotropic Renard-Dupuy s model are illustrated in Table 16. Clearly, Case 1-A promotes a PI value that is 4.8 times greater than the 1-base case. On the other hand, increasing the permeability up to 50 md in Case 1-B will not affect the PI (same PI as Case 1-base s PI). By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 24 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote a PI value 48 times greater than the PI of Case 1- base. In case 1-D-1, maximizing the influential parameters as well as the horizontal well length will promote the highest PI value among all the cases (77.4 times greater than the PI of Case 1-base). Figure 19 below indicates the percentage effect of the crucial parameters on the productivity index value. 38

46 Table 16. PI of Renard-Dupuy s isotropic steady state horizontal oil well Re=5000 ft Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Case 1-D-1 Thickness, ft Horizontal permeability, md Vertical permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Length, ft Wellbore radius, ft a, dimensionless factor 5,012 5,012 5,012 5,012 5,012 5,113 B, dimensionless factor Effective wellbore radius rw', ft PI, stb/psi/day Figure 19. Impact of the crucial parameters on Renard-Dupuy s isotropic PI The PI values of the horizontal oil well using anisotropic Renard-Dupuy s model are illustrated in Table 17. Clearly, Case 1-A promotes a PI value that is 4.4 times greater than the 1-base case. On the other hand, increasing the permeability up to 50 md in 39

47 Case 1-B will not affect the PI (same PI as Case 1-base s PI). By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 21.8 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote a PI value 43.5 times greater than the PI of Case 1-base. In case 1-D-1, maximizing the influential parameters as well as the horizontal well length will promote the highest PI value among all the cases (73.7 times greater than the PI of Case 1-base). Figure 20 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 17. PI of Renard-Dupuy s anisotropic steady state horizontal oil well Re = 5000 ft Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Case 1-D-1 Thickness, ft Horizontal permeability, md Vertical permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Length, ft Wellbore radius, ft a, dimensionless factor 5, , , , , , B, dimensionless factor Effective wellbore radius rw', ft PI, stb/psi/day

48 Figure 20. Impact of the crucial parameters on Renard-Dupuy s anisotropic PI Based on Figures 21 and 22 below, Renard-Dupuy model predicts the highest productivity index (9.8 times higher PI than the PI of a vertical well in 1-base and 15 times in 1-D) among all the models. On the other hand, Borisov s equation will result in the lowest PI (0.082 of the vertical well s PI value in 1-base and of the PI in 1-D). Figure 21. PI s of Base Case Steady State Oil Wells - Re = 5000 ft 41

49 Figure 22. PI s of Maximum Effect (1-D Case) Steady State Oil Wells - Re = 5000 ft 4.2 PI of Pseudo Steady State Wells Reservoir Radius = 2000 ft The PI values of the vertical well are illustrated in Table 18. Clearly, Case 1-A promotes a PI value that is five times greater than the 1-base case. Similarly, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is ten times higher than the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 25 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote the highest PI value among all the cases (50 times greater than the PI of Case 1-base). Figure 23 below indicates the percentage effect of the crucial parameters on the productivity index value. 42

50 Table 18. PI of pseudo steady state vertical oil well Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Thickness, ft Permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Wellbore radius, ft PI, stb/psi/day Figure 23. Impact of the crucial parameters on vertical oil well PI The PI values of the horizontal oil well using Babu-Odeh s model are illustrated in Table 19. Clearly, Case 1-A promotes a PI value that is 3.1 times greater than the 1- base case. On the other hand, increasing the permeability up to 50 md in Case 1-B will not affect the PI value (same PI as 1-basse Case). By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 15.5 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential 43

51 parameters will promote the highest PI value among all the cases (30.9 times greater than the PI of Case 1-base). Figure 24 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 19. PI of Babu-Odeh s pseudo steady state horizontal oil well Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Thickness, ft Horizontal permeability, md Vertical permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Wellbore radius, ft a, dimensionless factor B, dimensionless factor Vertical location, ft Well location in x-direction, ft Shape factor CH 6.33E E E E E+2 Skin effect, SR Area, sq ft 4,000,000 4,000,000 4,000,000 4,000,000 4,000,000 PI, stb/psi/day

52 Figure 24. Impact of the crucial parameters on Babu-Odeh s PI The PI values of the horizontal oil well using Kuckuk s model are illustrated in Table 20. This approach does not depend on the reservoir radius. However, modifying the well length will greatly impact the reservoir productivity index. Clearly, Case 1-A promotes a PI value that is lower than 1-base case (PI of Case 1-A is 0.7 of that in basecase). On the other hand, increasing the permeability up to 50 md in Case 1-B will increase the PI ten times than the base-case s PI. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will only increase to around 3.5 times higher compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote a PI value 7.1 times greater than the PI of Case 1- base. In case 1-D-1, maximizing the influential parameters as well as the horizontal well length will promote the highest PI value among all the cases (21.2 times greater than the PI of Case 1-base). Figure 25 below indicates the percentage effect of the crucial parameters on the productivity index value. 45

53 Table 20. PI of Kuckuk s pseudo steady state horizontal oil well Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Case 1-D-1 Thickness, ft X-direction permeability, md Y-direction permeability, md Vertical permeability, md Average horizontal permeability, md Formation volume factor, bbl/stb Viscosity, cp Length, ft Wellbore radius, ft Effective wellbore radius, ft Vertical well location, ft Dimensionless pressure PD PI, stb/psi/day Figure 25. Impact of the crucial parameters on Kuckuk s PI 46

54 The PI values of the horizontal oil well using Economides s model are illustrated in Table 21. Clearly, Case 1-A promotes a PI value that is 3.7 times greater than the 1- base case. Similarly, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is ten times higher than the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 18.7 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote the highest PI value among all the cases (37.5 times greater than the PI of Case 1-base). Figure 26 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 21. PI of Economides pseudo steady state horizontal oil well Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Thickness, ft X-direction permeability, md Vertical permeability, md y-direction permeability, md Average permeability, md Viscosity, cp Formation volume factor, bbl/stb Wellbore radius, ft Skin factor Reservoir radius, ft L/Xe Shape factor, CH Stand off, Zw Eccentricity effect, Se Skin effect, Sx Dimensionless pressure PD PI, stb/psi/day

55 Figure 26. Impact of the crucial parameters on Economides PI Based on Figures 27 and 28 below, Kuckuk model predicts the highest productivity index (194 times higher PI than the PI of a vertical well in 1-base and 28 times in 1- D) among all the models. On the other hand, Vertical well equation will result in the lowest PI. Figure 27. PIs of Base Case Pseudo Steady State Oil Wells - Re = 2000 ft 48

56 Figure 28. PIs of Case 1-D Pseudo Steady State Oil Wells - Re = 2000 ft Reservoir Radius = 5000 ft The PI values of the vertical oil well are illustrated in Table 22. Clearly, Case 1-A promotes a PI value that is five times greater than the 1-base case. Similarly, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is ten times higher than the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 25 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote the highest PI value among all the cases (50 times greater than the PI of Case 1-base). Figure 29 below indicates the percentage effect of the crucial parameters on the productivity index value. 49

57 Table 22. PI of pseudo steady state vertical oil well Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Thickness, ft Permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Wellbore radius, ft PI, stb/psi/day Figure 29. Impact of the crucial parameters on vertical oil well PI The PI values of the horizontal oil well using Babu-Odeh s model are illustrated in Table 23. Clearly, Case 1-A promotes a PI value that is 3.1 times greater than the 1- base case. On the other hand, increasing the permeability up to 50 md in Case 1-B will not affect the PI value (same PI as 1-basse Case). By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 15.5 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote the highest PI value among all the cases (30.9 times greater 50

58 than the PI of Case 1-base). Figure 30 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 23. PI of Babu-Odeh s pseudo steady state horizontal oil well Re = 5000 ft Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Thickness, ft Horizontal permeability, md Vertical permeability, md Viscosity, cp Formation volume factor, bbl/stb Reservoir radius, ft Wellbore radius, ft a, dimensionless factor B, dimensionless factor Vertical well location, ft Well location in x-direction, ft ln(ch) Shape factor CH 6.33E E E E E+2 Skin effect, SR Area, sq ft 4,000,000 4,000,000 4,000,000 4,000,000 4,000,000 PI, stb/psi/day

59 Figure 30. Impact of the crucial parameters on Babu-Odeh s PI at Re = 5000 ft The PI values of the horizontal oil well using Economides s model are illustrated in Table 24. Clearly, Case 1-A promotes a PI value that is 4.1 times greater than the 1- base case. Similarly, increasing the permeability up to 50 md in Case 1-B will result in a PI value that is ten times higher than the PI of Case 1-base. By increasing the reservoir thickness and permeability by a factor of 5 (Case 1-C), the PI value will increase 20.5 times compared to the PI of the 1-base Case. In case 1-D, maximizing the influential parameters will promote a PI value 40.9 times greater than the PI of Case 1-base. In case 1-D-1, maximizing the influential parameters as well as the horizontal well length will promote the highest PI value among all the cases (82.9 times greater than the PI of Case 1-base). Figure 31 below indicates the percentage effect of the crucial parameters on the productivity index value. Table 24. PI of Economides pseudo steady state horizontal oil well Re = 5000 ft Properties Case 1-base Case 1-A Case 1-B Case 1-C Case 1-D Case 1-D-1 Thickness, ft X-direction permeability, md Vertical permeability, md y-direction permeability, md

60 Average permeability, md Viscosity, cp Formation volume factor, bbl/stb Well Length, ft Wellbore radius, ft Skin factor Reservoir radius, ft L/Xe Shape factor CH Stand off, Zw Eccentricity effect, Se Skin effect, Sx Dimensionless pressure PD PI, stb/psi/day Figure 31. Impact of the crucial parameters on Economides s PI Based on Figures 32 and 33 below, Babu-Odeh s model predicts the highest productivity index among all the models. On the other hand, Vertical well s equation 53

61 will result in the lowest PI. This is applicable for both the base case and case 1-D. In Economides s model, case 1-D-1 will promote even higher productivity index by increasing the well length to 3000 ft (not shown since it s the only model where it s possible to increase the well length in Re of 5000 ft). Figure 32. PIs of Base Case Pseudo Steady State Oil Wells - Re = 5000 ft Figure 33. PIs of Case 1-D Pseudo Steady State Oil Wells - Re = 5000 ft 54