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- 1. PRODUCTION SYSTEM OPTIMIZATION FOR SUBMERSIBLE PUMP LIFTED WELLS : A CASE STUDY A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF THE MIDDLE EAST TECHNICAL UNIVERSITY BY NURİ OZAN GÜLER IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN THE DEPARTMENT OF PETROLEUM AND NATURALGAS ENGINEERING APRIL 2004
- 2. Approval of the Graduate School of Natural and Applied Sciences Prof . Dr. Canan ÖZGEN Director I certify that this thesis satisfies all the requirements as a thesis for the degree of Master of Science. Prof. Dr. Birol DEMİRAL Head of Department This is to certify that we have read this thesis and that in our opinion it is fully adequate, in scope and quality, as a thesis for the degree of Master of Science. Prof. Dr. A .Suat Bağcı Supervisor Examining Committee Members Prof. Dr. Birol DEMİRAL (Chair Person) Prof. Dr. A. Suat BAĞCI Prof. Dr. Fevzi GÜMRAH Prof. Dr. Mustafa V. KÖK Prof. Dr. Nurkan KARAHANOĞLU
- 3. iii ABSTRACT PRODUCTION SYSTEM OPTIMIZATION FOR SUBMERSIBLE PUMP LIFTED WELLS : A CASE STUDY GÜLER, Nuri Ozan M.S. Department of Petroleum and Natural Gas Engineering Supervisor: Prof. Dr. A. Suat Bağcı April, 2004, 173 Pages A computer program has been written to perform production optimization in submersible pump lifted wells. Production optimization was achieved by the principles of Nodal Analysis Technique which was applied between the reservoir and the wellhead ignoring the surface choke and separator. Computer program has been written according to two lifting environment, which are: pumping with only liquid and pumping with both liquid and gas. Program played an important role in the study by overcoming difficult iterations existing in the pumping liquid and gas case due to variation of liquid volume between pump intake and discharge pressure. Hagedorn and Brown vertical multiphase flow correlation was utilized in the program to determine the pressure at required depth. However, Griffith Correlation was also used in the program since Hagedorn and Brown Correlation failed to give accurate results at bubble flow.
- 4. iv A case study was done by evaluating the 10 wells located in Diyarbakır-GK field which are all submersible pump lifted. Well, reservoir, fluid and lift-system data was transferred to already written computer program. Output of the computer program for both cases was used to calculate accurately the optimum production rates, required horsepower, number of pump stages and the relation between these parameters with each other. The sensitivity variable selected is the number of pump stages. At the end of the study, by comparing the actual operating data and the computer-based optimized data, it was observed that 3 wells: W-16, W-17, and W-24 were producing completely within their optimum range, 5 wells: W-07, W-08, W-25, W-27 and W-28 were not producing at their optimum range but their production parameters can said to be acceptable , 1 well: W- 22 was producing inefficiently and should be re-designed to reach optimum conditions. It was realized that W-15 has insufficient data to make necessary interpretations. Keywords: Production optimization, nodal system analysis technique, electrical submersible pump, artificial lift, Hagedorn and Brown correlation, Griffith correlation.
- 5. v ÖZET DALGIÇ POMPALARLA ÜRETİMİ YAPILAN KUYULARIN SİSTEM OPTİMİZASYONU: ÖRNEK SAHA ÇALIŞMASI GÜLER, Nuri Ozan M.Sc., Petrol ve Doğal Gaz Mühendisliği Bölümü Danışman: Prof. Dr. A. Suat Bağcı Nisan, 2004, 173 Sayfa Dalgıç pompalarla üretim yapılan kuyuların optimizasyonu için bilgisayar programı yazılmıştır. Üretim optimizasyonu Nodal Analizi Tekniğiyle gerçekleştirilmiş ve rezervuar ile kuyubaşı arasında, kuyubaşı sonrası yüzey donanımı ve separatör dikkate alınmadan uygulanmıştır. Program iki üretim ortamına göre yazılmıştır, bunlar: sadece sıvı ile hem sıvı hem gaz üretim ortamlarıdır. Bu bilgisayar programı, sözü edilen sıvı ile gaz pompalanması sırasındaki pompa emiş ve çıkış basıncı arasında sistemdeki gaz’dan dolayı oluşan sıvı hacmi değişimlerinin hesaplamasında ortaya çıkan iterasyonların çözümü açısından önemli bir rol oynamaktadır. Programda istenilen derinlikteki basınç değerlerini hesaplamak amacıyla Hagedorn ve Brown korelasyonu kullanılmıştır. Hagedorn ve Brown Korelasyonunun yetersiz kaldığı akış rejimlerinde Griffith Korelasyonu kullanılarak sonuca ulaşılmıştır.
- 6. vi Yazılan bu programın pratiğe geçirilmesi açısından Diyarbakır – GK sahasındaki dalgıç pompalarla üretim yapılan 10 kuyu incelemeye alınmıştır. Bu kuyuların rezervuar, akışkan ve üretim verileri hazır olan bilgisayar programına aktarılmıştır. Daha önce belirtilen iki pompalama ortamını kapsayan bu programın çıktısı optimum üretim debisi, gereken beygirgücü ve pompa kademe sayısının belirlenmesi için kullanılmıştır. Bu hesaplamalarda hassas değişken olarak pompa kademe sayısı seçilmiştir. Çalışmanın sonunda GK sahası verileri ile programdan çıkarılan optimize değerler karşılaştırılmış ve dalgıç pompalarla üretim yapılan 10 kuyudan 3’ünün: W-16, W-17, ve W-24’ün optimum değer sınırları içerisinde üretim yaptığı, kuyulardan 5’inin W-07, W-08, W-25, W-27, W-28, optimum değerler içerisinde olmasa bile kabul edilebilir ve geçerli sayılabilir sınırlarda üretim yaptığı, 1 kuyunun, W-22, optimum sınırlar dışında ve verimsiz bir şekilde üretime devam ettirildiği saptanmıştır. W-15’in verileri herhangi bir yorum yapmak için yetersiz kalmıştır. Kelimeler: Üretim optimizasyonu, sistem analiz tekniği, dalgıç pompa, yapay üretim, Hagedorn ve Brown Korelasyonu, Griffith Korelasyonu
- 7. vii To my family, Çiğdem, Yurdahan and Sanem Güler
- 8. viii ACKNOWLEDGEMENTS The author would like to thank his supervising professor, Dr. Suat Bağcı, for his precious assistance throughout this study and also N.V. Turkse Perenco for their cooperation.
- 9. ix TABLE OF CONTENTS ABSTRACT ……………………………………………………………….. iii ÖZET ………………………………………………………………….…… v ACKNOWLEDGEMENTS ……………………………………………….. viii TABLE OF CONTENTS …………………………………………………. ix LIST OF TABLES ………………………………………………………… xiii LIST OF FIGURES ………………………………………………………. xv NOMENCLATURE ……………………………………………………….. xviii CHAPTER 1. INTRODUCTION …………………………………………. 1 2. ELECTRICAL SUBMERSIBLE PUMPS ……………….. 4 2.1 Introduction ………………………………………... 4 2.2 Pump Performance Curves ……………………… 8 2.3 Pump Intake Curves ……………………………... 13
- 10. x 2.3.1 Pumping Liquid Only ……………………… 13 2.3.1.1 Procedure for the Preparation of Tubing Intake Curves for Liquid Only ……………………….. 14 2.3.2 Pumping Liquid and Gas ………..………. 16 2.3.2.1 Determination of the Number of Stages …………………………. 16 2.3.2.2 Determination of Horsepower ….. 19 2.3.2.3 Pump Selection ………………….. 20 2.3.2.4 Procedure for the Preparation of Intake Curves for Wells Pumping Gas …………………… 21 3. NODAL ANALYSIS APPROACH ………………………. 23 3.1 Introduction ……………………………………….. 23 3.2 Application of Nodal Analysis to Electrical Submersible Pumping Wells …………………….. 29 3.3 Description of the Computer Program …………………………………………… 31 3.3.1 Pumping Liquid …………………………… 31 3.3.2 Pumping Liquid and Gas ………………… 32 4. STATEMENT OF THE PROBLEM 34
- 11. xi 5. HAGEDORN AND BROWN VERTICAL MULTIPHASE FLOW CORRELATION SUPPORTED BY GRIFFITH CORRELATION ……….. 36 5.1 Introduction ……………………………………….. 36 5.2 Hagedorn and Brown Method …………………… 38 5.3 Procedure for Calculating a Vertical Pressure Traverse by the Method of Hagedorn and Brown ………………………………………………. 39 5.4 Griffith Correlation (Bubble Flow) ………………. 49 6. DESCRIPTION OF THE GK FIELD ……………………. 51 6.1 Introduction ……………………………………….. 51 6.2 Geology …………………………………………… 52 6.3 Reservoir, Fluid, and Lift System Properties …………………………………………. 53 6.4 Production History ……………………………….. 54 7. RESULTS AND DISCUSSION …………….…………… 57 7.1 Introduction ……………………………………….. 57 7.2 Results and Discussion …………….……………. 58 7.2.1 Construction of Vertical Flowing Pressure Gradient Curves Using Computer Program Output ………………. 58 7.2.2 Sensitivity Analysis by Using the Computer Program Output ……………… 64
- 12. xii 7.2.3 Construction of Possible Production Rate versus Stage and Horsepower Chart for GK Field Wells by Using the Pumping Liquid and Gas Computer Algorithm ……………….…….. 67 7.2.4 Comparison of Theorotical and Actual Production Parameters and Suggestion for Optimum Pump Operating Conditions by Inspecting Possible Production Rate versus Stage and Hordepower Chart …………… 77 8. CONCLUSION AND RECOMMENDATIONS ……….… 81 REFERENCES …………………………………………………………… 83 APPENDIX A Pumping Liquid and Gas Computer Program …….…… 85 B Pumping Only Liquid Computer Program ……………… 101 C Subprograms ……………………………………………… 109 D Sample Calculation of W-08 …………………………….. 128
- 13. xiii LIST OF TABLES TABLE 6.1 Reservoir and Fluid Properties of GK Field ………….... 53 6.2 Submersible Pump Lifted Wells Operated in GK Field and Their Efficiency Ranges ………………. 54 6.3 Gross Production Rate of the Wells in GK Field and Required Pump Stages ……………………….. 56 7.1 Comparison of Computer-Based Vertical Flowing Pressures with Beggs&Brill Correlation at Selected Depths ……..………..………… 63 7.2 Effect of Oil Density on Flowing Bottomhole Pressures at Selected Depths ……………..…………… 64 7.3 Effect of GLR on Flowing Bottomhole Pressures …………………………………………….…… 65 7.4 Effect of WOR on Flowing Bottomhole Pressures at Selected Depths…………………..….…… 65
- 14. xiv 7.5 Results Obtained After The Comparison of Actual and Computer-Based Data for GK Field ……………………………………………..… 79 D1 Well, Fluid, Reservoir and Lift-System Data Used In Calculations for W-08 ……………………. 129 D2 Production History of W-08 ……………………………… 130 D3 Intake Pressures at Assumed Rates for W-08 ………… 161 D4 Horsepower Requirements for Possible Rates from W-08 …………………………………………. 171 D5 Relation of Production Parameters With Each Other …………………..……………………… 173
- 15. xv LIST OF FIGURES FIGURES 2.1 A Typical Submersible Pump Installation ……………… 6 2.2 Submersible Pump Schematic ………………………….. 7 2.3 Pressure Traverses for Pump on Bottom ……………… 7 2.4 A Typical Pump Performance Curve (GN 3200) ……… 9 3.1 Pressure Losses In a Production System ……………… 25 3.2 Tubing Intake Curves for Artificial Lift Systems ………. 26 5.1 Schematic Diagram of Possible Flow Patterns in Two-Phase Pipelines ……………………….. 37 6.1 Generalized IPR Curve ………………………………….. 55 7.1 Pressure Traverse Curve (WC = 0) ……………………. 59 7.2 Pressure Traverse Curve (WC = 0.5) ………………….. 60
- 16. xvi 7.3 Pressure Traverse Curve (WC = 1.0)…………………… 61 7.4 Graphical Analysis of Effect of GLR on Flowing Bottomhole Pressures for W-08 ………………. 66 7.5 Graphical Analysis of Effect of WOR on Flowing Bottomhole Pressures for W-08 ………………. 66 7.6 Possible Production Rate vs Stages and Horsepower for W-07 ……………………………………. 68 7.7 Possible Production Rate vs Stages and Horsepower for W-08 ……………………………………. 69 7.8 Possible Production Rate vs Stages and Horsepower for W-16 ……………………………………. 70 7.9 Possible Production Rate vs Stages and Horsepower for W-17 ……………………………………. 71 7.10 Possible Production Rate vs Stages and Horsepower for W-22 ………………………………….… 72 7.11 Possible Production Rate vs Stages and Horsepower for W-24 ……………………………………. 73 7.12 Possible Production Rate vs Stages and Horsepower for W-25 ……………………………………. 74 7.13 Possible Production Rate vs Stages and Horsepower for W-27 ……………………………………. 75
- 17. xvii 7.14 Possible Production Rate vs Stages and Horsepower for W-28 ……………………………………. 76 D1 IPR Curve for W-08 ……………………………………… 131 D2 Intake Curves for W-08 ………………………………….. 162 D3 Possible Production Rate vs Stages and Horsepower for W-08 ……………………………………. 172
- 18. xviii NOMENCLATURE Symbol Description Unit A area of tubing ft2 B formation volume factor rbbl/stb CNL viscosity number coefficient d tubing inner diameter in Es fraction of free gas f friction factor fo fraction of oil flowing Gf gradient of the pumped fluid psi/ft GLR gas liquid ratio scf/stb GOR gas oil ratio scf/stb h head per stage ft/stage HL liquid hold-up hp horsepower per stage hp/stage HP horsepower hp J productivity index stb/d/psi m mass associated with one bbl of stock tank liquid lbm/stbl Nd pipe diameter number NGV gas velocity number NL liquid viscosity number NLV liquid velocity number (NRE)TP two-phase Reynolds number
- 19. xix Symbol Description Unit P pressure psi q flow rate stb/d Rs solution gas oil ratio scf/stb St pump stage T average flowing temperature °F V capacity stb/d VF volume factor w mass flow rate lbmday W weight of the capacity lb/day WC water cut z gas compressibility ∆ increment µ viscosity cp ν velocity ft/sec ρ density lb/cuft φ hold-up correlating function ψ secondary correction factor σ liquid surface tension dyne/cm γ specific gravity Subscription Description b bubble point dn pump discharge (downstream) f fluid g gas
- 20. xx Subscription Description l liquid m mixture o oil pc pseudo critical pr pseudo reduced R reservoir sc standard condition sg superficial gas sl superficial liquid sep separator up pump intake (upstream) w water wf flowing well wh wellhead 2 discharge 3 intake
- 21. 1 CHAPTER I INTRODUCTION The electrical submersible pumping system can said to be an attractive artificial lift technique in reservoirs having high water-cut and low gas-oil ratio. Currently, it is considered as an effective and economical means of lifting large volumes of fluid from great depths under a variety of well conditions. Pumping equipment is capable of producing as high as 60,000 b/d and as low as 200 b/d. The oil cut may also vary within very wide limits, from negligible amounts to 100 %. The pump performs at highest efficiency when pumping liquid only; it can handle free gas with the liquid but high volumes of free gas causes inefficient operation and gas lock problems. The first submersible pumping unit was installed in an oil well in 1928 and since that time the concept has proven itself throughout the oil- producing world1 . A submersible pumping unit consists of an electric motor, a seal section, an intake section, a multistage centrifugal pump, an electric cable, a surface installed switchboard, a junction box and transformers. Additional miscellaneous components also present in order to secure the cable alongside the tubing and wellhead supports. Pressure sentry for sensing bottom-hole pressure, check and bleeder valves are the optional equipment that can be taken into consideration. Under normal operating conditions, submersible pumping unit can be expected to give from 1 to 3 years of good operating life with some units operating over 10 years. Despite this advantage, many submersible pump lifted oil and gas wells produce at rates different than optimum. This fact makes necessary to apply production optimization techniques to wells having low production rates. Nodal Analysis has been applied to artificial lift method for many years to
- 22. 2 analyze the performance of the systems composed of interacting components. It is a process of determining the effect of each component in the production system on the total system performance. The analysis can improve the completion design, well productivity and producing efficiency, all of which lead to increased profitability from oil and gas investments. The Nodal analysis technique is essentially a simulator of the producing well system. The system includes all flow between the reservoir and the separator. As the entire system is simulated, each of the components is modelled using various correlations or equations to determine the pressure loss through that component as a function of flow rate. The summation of these individual losses make up the total pressure loss through the entire system for a given flow rate. The production rate or deliverability of a well can be severely restricted by the poor performance of just one component in the system. If the effect of each component on the performance of the total system can be isolated, the efficiency of the system can be optimized in the most economical way. When performing a Nodal analysis, we divide the production system into its components, i.e., reservoir, perforations, tubing, surface choke, flowline and separator. Then we pick a problem area in this production system as a node. This node acts as the intersection point between the inflow and outflow performances. Different inflow and outflow performance curves intersect on the same plot and give the design considerations for different arrangements2 . Optimization and design of submersible pump lifted wells pumping only liquid are generally straight- forward however pumping gas with the liquid is complicated because of the high compressibility of gas. In this case, volume of the produced fluid rate shows a significant variation between the pump intake and discharge pressures, consequently considerable amount of iterations should be performed to determine the volume factor at any pressure between the intake and discharge pressures. Thus, computer program should be written to overcome these iterations. Optimization of wells with Nodal Analysis requires pressure gradient correlation in order to reach a solution so it is
- 23. 3 necessary to use a vertical multiphase flow correlation method in the computer program. In this study, Hagedorn and Brown vertical multiphase flow correlation3 has been used to determine the pressure and pressure losses at required depth. However, during the study it was observed that Hagedorn and Brown Correlation failed to give accurate output at bubble flow. Thus, Griffith Correlation4 was constructed at bubble flow to obtain accurate results. The purpose of this study was to write a general computer program that gives simultaneously the possible production rates for submersible pump lifted wells and also the optimum required horsepower and number of pump stages at these possible rates both considering pumping liquid and pumping gas with liquid. In addition to that objective, comparison made by using the production data of wells located in the GK field will assist us in suggesting optimum pump operating conditions.
- 24. 4 CHAPTER II ELECTRICAL SUBMERSIBLE PUMPS 2.1 Introduction Many high volume wells are equipped with electric submersible pumps (ESP) to lift the liquid and decrease the flowing bottom hole pressure. A submersible pump is a multistage centrifugal pump that is driven by an electric motor located in the well below the pump. Electrical power is supplied by means of a cable from the surface. The pump and motor are suspended on the tubing at a certain depth in the well. The annulus is either vented or tied into the well’s flowline, so that as much gas as possible is separated from the liquid before it enters the pump. In some cases, a centrifugal separator will be placed between the pump and motor for obtaining maximum gas-liquid separation. A typical submersible pump installation is given in Figure 2.1. A schematic of a well equipped with a submersible pump is given in Figure 2.2, along with the pressure traverse in the well. From the figure it can be seen that, initially, flowing pressure of submersible pump lifted well is not sufficient to lift the fluid (depleted well). This insufficient pressure (Pup) which we define as intake pressure starts to increase at pump setting depth by required pump stages and finally reaches to discharge pressure (Pdn) generated by the pump which will assist fluid to flow throughout the surface. Figure 2.3 is a typical pressure traverses for pump on bottom. Discharge pressure of the pump will be defined as P2, and also intake pressure will be defined as P3 throughout the study. From figure, the effective lift point is that depth at
- 25. 5 which the flowing bottomhole pressure is capable of supporting the fluids in the tubing string. The pump performs highest efficiency when pumping liquid only. It can and does handle free gas along with the liquid. The manner in which the pump handle gas is not completely understood; however high volumes of free gas are known to cause inefficient operation.
- 26. 6 Figure 2.1 A Typical Submersible Pump Installation
- 27. 7 Figure 2.2 Submersible Pump Schematic Figure 2.3 Pressure Traverses for Pump on Bottom
- 28. 8 2.2 Pump Performance Curves Pumps are divided into groups according to the minimum casing size into which the pump can be run. But even within the same group, each pump performs differently. A typical pump performance curve5 is given in Figure 2.4. The performance curves of a submersible electrical pump represent the variation of head, horsepower, and efficiency with capacity. Capacity refers to the volume of the produced flow rate, which may include free and/or dissolved gas. These curves are for a fixed power cycle – normally 50 or 60 cycle – and can be changed with variable frequency controllers6 . k j k j k j k j k j
- 29. 9 k j k j k j k j k j Figure2.3ATypicalPumpPerformanceCurve(GN3200)Figure2.4ATypicalPumpPerformanceCurve(GN3200)5
- 30. 10 The head (in feet per stage) developed by a centrifugal pump is the same regardless of the type or specific gravity of the fluid pumped. But when converting this head to pressure, it must be multiplied by the gradient of the fluid in question. Therefore, the following can be stated: Pressure developed by pump = head per stage × gradient of fluid × number of stages When pumping gas with the liquid, the capacity and, consequently, the head per stage as well as the gradient vary as the pressure of the liquid elevated from the intake value P3 to the discharge value P2. Thus, the above equation can be written as follows6 : )()()( StdVGVhdP f ××= (1) where: dP = the differential pressure developed by the pump, psi h = the head per stage, ft/stage Gf = the gradient of the pumped fluid, psi/ft d(St) = the differential number of stages Note that parentheses are included to indicate that h and Gf are functions of the capacity V, which is: VFqV sc= (2) The gradient of fluid at any pressure and temperature is given by: )(433.0)( VVG ff γ= (3) but:
- 31. 11 V W Vf 350 )( =γ (4) where W is the weight of the capacity V at any pressure and temperature, which is equal to the weight at standard conditions. Hence: V q V fscsc f 350 )( ρ γ = (5) Substituting equation 5 into 3 gives: V q VG fscsc f ρ ) 350 433.0 ()( = (6) ρfsc is the weight of 1 bbl of liquid plus pumped gas (per 1bbl of liquid) at standard conditions, or: gscoscwscfsc GLRGIPwcwc ργγρ ))(()1(350350 +−+= (7) where ρgsc is the density of gas (in lb/scf) at standard conditions. Substituting Equation 6 into Equation 1 gives: dP Vh V q Std fscsc )( ) 433.0 350 ()( ρ = (8) The total number of stages is obtained by integrating the above equation between the intake and discharge pressures: ∫∫ = 2 3 )( ) 433.0 350 ()( 0 P Pfscsc St dP Vh V q Std ρ (9) or:
- 32. 12 ∫= 2 3 )( ) 3141.808 ( P Pfscsc dP Vh V q St ρ (10) The pump performance curves give the horsepower per stage based on a fluid specific gravity equal to 1.0. This horsepower must be multiplied by the specific gravity of the fluid under consideration. Thus the following can be stated: (horsepower requirements) = (horsepower per stage) × (specific gravity of fluid) × (number of stages) Since the horsepower per stage, the specific gravity of fluid, and the number of stages depend on the capacity V, which varies between the intake and the discharge pressures, the above equation can be written as follows: )()()()( StdVVhHPd fp ××= γ (11) Substituting Equations 5 and 8 into the above equation gives: =)(HPd ( dP Vh Vhp )( )( ) 433.0 1 (12) The total horsepower requirement is obtained by integrating the above equation between the intake and the discharge pressures: ∫∫ = 2 )( )( ) 433.0 1 ()( 0 P P p HP dP Vh Vh HPd (13) or:
- 33. 13 ∫= 2 3 )( )( ) 433.0 1 ( P P p dP Vh Vh HP (14) For each pump, there is a capacity range within which the pump performs at or near its peak efficency. The volume range of the selected rate between the intake and the discharge pressures should, therefore, remain within the efficiency range of the pump. This range, of course, can be changed by using a variable frequency controller. 2.3 Pump Intake Curves Predicting intake curves for submersible pumps is considered for two cases: (1) pumping only liquid, and (2) pumping liquid and gas. For both cases, it is assumed that the pump is set at the bottom of well and the wellhead pressure and tubing size are fixed. For case 2, it is assumed that all associated gas is pumped with the liquid. The sensitivity variable selected is the number of stages6 . 2.3.1Pumping Liquid Only Since the liquids are only slightly compressible, the volume of the production rate can be considered constant and equal to the surface rate qsc. Hence, the head per stage will also be constant, and Equation 10 can be integrated to give6 : ))( 3141.808 ( 32 PP h St fsc −= ρ (15) Solving Equation 15 for 3P gives:
- 34. 14 St h PP fsc ) 3141.808 (23 ρ −= (16) Equation 14 also can be integrated to give: )() 433.0 1 ( 32 PP h h HP p −= (17) Substituting Equation 15 into the above equation yields: SthHP fscpγ= (18) Pump selection is limited by the casing size. Another constraint is the desired production rate. If the objective is to maximize the production rate, the proper procedure is to select a pump whose efficiency range includes rates that are close to the maximum rate of the well. 2.3.1.1 Procedure For The Preparation of Tubing Intake Curves for Liquid Only A step-wise procedure for predicting intake curves for the case when only liquid is pumped follows6 : (1) Select a suitable pump as dictated by the casing size and the flow capacity of the well (2) Calculate fscρ from Equation 7 (GLR=0) and fscγ from Equation 5. (3) Assume various production rates and, for each of these rates, do the following: (a) Read the head per stage from the pump performance curves and calculate the quantity (ρfsch/808.3141).
- 35. 15 (b) Determine the required discharge pressure from a pressure gradient correlation. (c) Assume various numbers of stages and, for each of these numbers, calculate the intake pressure from Equation 16. (4) Plot the intake pressures vs rate for each assumed number of stages on the same graph as the IPR curve and to the same scale. (5) Read the rates at the intersection of the pump intake curves with the IPR curve. (6) For each rate, read the horsepower per stage from the pump performance curves; then calculate the total horsepower requirement from Equation 18. (7) Plot the rates vs the number of stages and horsepower requirements. Impose the efficiency range of the pump on the same graph. (8) Select a suitable rate. Whether pumping only liquid or pumping gas with the liquid, the selected rate must satisfy the following criteria: (a) Its volume range between the intake and the discharge pressures must remain within the efficiency range of the pump. (b) It must be economically feasible. As the number of stages and, consequently, the production rate increase, the effect of friction in the tubing string becomes significant, causing the discharge pressure to increase. As a result, the gain in the production rate per one stage continues to diminish until it becomes insignificant.
- 36. 16 2.3.2Pumping Liquid and Gas Because of the high compressibility of gas, the volume of the produced flow rate V may undergo a significant variation as the pressure of the fluid changes from the intake value to the discharge value. At any pressure point between the intake and discharge, if all gas is pumped with the liquid, the volume factor is determined from6 : [ ] gso BRwcGLRBwcwcVF )1()1( −−+−+= (19) if a certain percentage of the gas is vented: [ ] gso BRwcGLRGIPBwcwcVF )1()1( −−+−+= (20) In either case, the volume of the flow rate is given by: VFqV sc= (21) 2.3.2.1 Determination Of The Number of Stages Because V and, consequently, h vary as the fluid passes through the pump, direct integration of Equation 10 is possible only if the integrand V/h(V) can be reduced to a simple function of pressure. But this is difficult because VF is a very complicated function of pressure. For this reason, numerical integration methods are recommended. The existence of gas at the intake section of the pump implies that the intake pressure is below the bubble point of the crude (saturated crude). If that is the case and if the required discharge pressure is above the bubble point, Equation 10 should be broken down into two integrals as follows6 :
- 37. 17 ∫∫ += 2 3 )()( P Psc P Psc b b dP Vh V q A dP Vh V q A St (22) where A = 808.3141/ρfsc = constant (23) For performing numerical integration, Equation 22 can be written in a more convenient form as follows: ∑ ∑= = ∆+∆= m i n mj j j j sc i i i sc P h V q A P h V q A St 1 ,3,3 (24) where: P3,i = any intake pressure above the bubble point P3,j = any intake pressure below the bubble point P3,o = discharge pressure (P2) P3,m = bubble point pressure (Pb) ∆P3,i = P3,i=P3,i-1-P3,i ∆P3,j = P3,j=P3,j-1-P3,j ii hV / and jj hV / = average quantities evaluated at the average pressures iP ,3 and jP ,3 , respectively. where: 2/)( ,31,3,3 iii PPP += − and 2/)( ,31,3,3 jjj PPP += − The main reason for breaking down the number of stages into two summations is the fact that V and, consequently, h undergo only slight change above the bubble point; hence, ∆P3,i can be taken much larger than
- 38. 18 ∆P3,j. In fact, satisfactory results are obtained even if ∆P3 is taken as the difference between Pb and P2 and the quantity hV / is evaluated at the midpoint. When using a computer solution, it is easier to divide the interval between the intake and the discharge pressure into equal increments by taking ∆P3 constant. For this case, Equation 24 can be written as: ∑= ∆ = n i i i sc i h V q PA St 1 3 )( (25) where: P3,0 = discharge pressure (P2) P3,n = intake pressure (P3) n = (P2-P3)/∆P3 P3,i = P3,i-1 - ∆P3 The quantity ii hV / is evaluated at the average pressure given by: 2/)( ,31,3,3 iii PPP += − (26) In reality, any pressure P3,I can be considered an intake pressure. To illustrate this point, Equation 25 can be written in the following form: ∑= ∆= n i ii StSt 1 )( (27) where: i i sc i h V q PA St )()( 3∆ =∆ (28)
- 39. 19 Therefore, inorder to obtain an intake pressure P3,i , we have: i i sc h V q PA StSt )()( 3 11 ∆ =∆= (29) In order to obtain P3,2, we have: )()()( 2 2 1 13 212 h V h V q PA StStSt sc + ∆ =∆+∆= (30) And in order to obtain P3,n, we have: =nSt nStStSt )(...)()( 21 ∆++∆+∆ (31) = )(( 3 scq PA∆ )... 2 2 1 1 n n h V h V h V +++ (32) 2.3.2.2 Determination of Horsepower The horsepower requirement is obtained by integrating Equation 14 between the intake and the discharge pressures. Since the integrand hp(V)/h(V) can not be reduced to a simple function of pressure, direct integration is not possible, and numerical methods must be used. If the interval between the intake and the discharge pressure is divided into equal increments by taking ∆P3 constant, Equation 14 can be written as follows6 : ∑= ∆ = n i i i i h hpP HP 1 3 ) 433.0 ( (33)
- 40. 20 If ∆(HP)I is defined as: ∑= ∆ =∆ n i i i i h hpP HP 1 3 ) 433.0 ()( (34) then Equation 33 can be written as: ∑= ∆= n i ii HPHP 1 )( (35) 2.3.2.3 Pump Selection As mentioned previously, pump selection is limited by the casing size and flow capacity of the well. Another constraint that must be taken into account when pumping gas with the liquid is the volume range of the flow rate. Because of the high compressibility of the gas, the difference between the intake and discharge volumes may be too great to be contained within the efficiency range of one pump. For this reason, the following procedure for pump selection is suggested6 : (1) Prepare IPR curves in stbl/d and b/d to the same scale on the same graph. (2) Enter the b/d IPR curve at the upper limit of the efficiency range of several pumps that are suitable from a casing-size standpoint. Move horizontally to the stbl/d IPR curve and read the intake rate in stbl/d. (3) For each intake rate determined in step 2, do the following: (a) Determine the required discharge pressure from a two-phase flow correlation. (b) Calculate VF at the discharge pressure, then calculate the discharge volume.
- 41. 21 (4) Select the pump for which the discharge volume is greater than or equal to the lower limit of its efficency range. If more than one pump is found to be suitable, choose the one with the highest capacity. 2.3.2.4 Procedure for the Preparation of Intake Curves for Wells Pumping Gas A step-wise procedure for predicting tubing intake curves for the case in which gas is with the liquid is given as follows6 : (1) Select a suitable pump as outlined previously. (2) Calculate ρfsc from Equation 7 and calculate the constant A from Equation 23. (3) Assume several production rates in stbl/d and, for each of these rates, do the following: (a) Determine the required discharge pressure (P3,0) from a two-phase flow correlation. (b) Choose ∆P3 and calculate the quantity (A∆P3/qsc) (c) Calculate 1,3P and 1,3P . (d) Determine 1VF at 1,3P , then calculate 1V . (e) Read 1h at 1V from the pump performance curves. (f) Calculate the required number of stages to obtain the intake pressure P3,1 from Equation 25. (g) Repeat steps c-f for P3,2, P3,3 through P3,i until a convenient intake pressure is reached. Tabulate the intake pressure versus the number of stages. (4) By interpolating or plotting, obtain intake pressure for assumes rates for an identical number of stages.
- 42. 22 (5) Plot the intake pressure (obtained in step 4) versus the assumed production rates for the various number of stages. Plot the stbl/d IPR curve to the same scale on the same graph. (6) Read the rates at the intersection of the pump intake curves with the IPR curve. (7) For each rate, calculate the horsepower requirement from Equation 33. Calculation of horsepower requirements is similar to the calculation of the number of stages. (8) Plot the rate versus the number of stages and horsepower requirements. Impose the efficiency range of the pump on the same graph. (9) Select a suitable rate.
- 43. 23 CHAPTER III NODAL ANALYSIS APPROACH 3.1 Introduction The systems analysis approach, often called NODALTM Analysis, has been applied for many years to analyze the performance of systems composed of interacting components. Electrical circuits, complex pipeline networks and centrifugal pumping systems are all analyzed using this method. Its application to well producing systems was first proposed by Gilbert7 in 1954 and discussed by Nind8 in 1964 and Brown9 in 1978. The production system can be relatively simple or can include many components in which energy or pressure losses occur. Figure 3.1 illustrates a number of the components in which pressure losses occur. The procedure consists of selecting a division point or node in the well and dividing the system at this point. All of the components upstream of the node comprise the inflow section, while the outflow section consists of all of the components downstream of the node. A relationship between flow rate and pressure drop must be available for each component in the system. The flow rate through the system can be determined once the following requirements are satisfied2 : 1 Flow into the node equals flow out of the node 2 Only one pressure can exist at a node. At a particular time in the life of the well, there are always two pressures that remain fixed and are not functions of flow rate. One of these pressures
- 44. 24 is the average reservoir pressure, Rp , and the other is the system outlet pressure. The outlet pressure is usually the seperator pressure, psep, but if the well is controlled by a surface choke the fixed outlet pressure may be the wellhead pressure pwh. Once the node is selected, the node pressure is calculated from both directions starting at the fixed pressures. Inflow to the node: ppR ∆− (upstream components) = nodep (36) Outflow from the node: ppsep ∆+ (downstream component) = nodep (37) The pressure drop, p∆ , in any component varies with flow rate, q . Therefore, a plot of node pressure versus flow rate will produce two curves, the intersection of which will give the conditions satisfying requirements 1 and 2, given previously. The effect of a change in any of the components can be analyzed by recalculating the node pressure versus flow rate using the new characteristics of the component that was changed. If a change was made in an upstream component, the outflow curve will remain unchanged. However, if either curve is changed, the intersection will be shifted, and a new flow capacity and node pressure will exist. The curves will also be shifted if either of the fixed pressures is changed, which may occur with depletion or a change in separation conditions. Figure 3.2 illustrates the comparison of intake curves for artificial lift methods. It can be observed from the figure that electrical submersible
- 45. 25 pump keeps the bottomhole pressure low, thus, creates large amount of pressure drawdown to reach high production rates. Figure 3.1 Pressure Losses In a Production System2
- 46. 26 Figure 3.2 Tubing Intake Curves for Artificial Lift Systems6 Inflow to node: whtubingresR pppp =∆−∆− (38) Outflow from node: whflowlinesep ppp =∆+ (39) The effect of increasing the tubing size, as long as the tubing is not too large, is to give a higher node or wellhead pressure for a given flow rate, because the pressure drop in the tubing will be decreased. This shifts the inflow curve upward and the intersection to the right. A larger flowline will reduce the pressure drop in the flowline, shifting the outflow down and the intersection to the right. The effect of a change in any
- 47. 27 component in the system can be isolated in this manner. Also, the effect of declining reservoir pressure or changing separator can be determined. A more frequently used analysis procedure is to select the node between the reservoir and piping system. The inflow and outflow expressions for the simple system will then be: Inflow to node: wfresR ppp =∆− (40) Outflow from node: wftubingflowlinesep pppp =∆+∆+ (41) A producing system may be optimized by selecting the combination of component characteristics that will give the maximum production rate for the lower cost. Although the overall pressure drop available for a system, sepR pp − , might be fixed at a particular time, the producing capacity of the system depends on where the pressure drop occurs. If too much pressure drop occurs in one component or module, there may be insufficient pressure drop remaining for efficient performance of the other modules. Even though the reservoir may be capable of producing a large amount of fluid, if too much pressure drop occurs in the tubing, the well performance suffers. For this type of well completion, it is obvious that increasing reservoir performance by stimulation would be a waste of effort unless larger tubing were installed. If tubing is too large, the velocity of the fluid moving up the tubing may be too low to effectively lift the liquids to the surface. This could be caused by either large tubing or low production rates.The fluid velocity is the production rate divided by the area of the tubing.
- 48. 28 As tubing size is increased, the friction losses decrease, which results in a lower wfp and, therefore, a larger inflow. However, as the tubing size is further increased, the well begins loading with liquid and the flow becomes intermittent or unstable. As the liquid level in the well builds the well will eventually die. Once a well that is producing liquids along with the gas reaches the stage in which it will no longer flow naturally, it will usually be placed on artificial lift. The nodal systems analysis approach may used to analyze many producing oil and gas well problems. The procedure can be applied to both flowing and artificial lift wells, if the effect of artificial lift method on the pressure can be expressed as a function of flow rate. The procedure can also be applied to the analysis of injection well performance by appropriate modification of the inflow and outflow expressions. A partial list of possible applications is given as follows2 : 1. Selecting tubing size 2. Selecting flowline size 3. Gravel pack design 4. Surface choke sizing 5. Subsurface safety valve sizing 6. Analyzing an existing system for abnormal flow restrictions 7. Artificial lift design 8. Well stimulation evaluation 9. Determinig the effect of compression on gas well performance 10.Analyzing the effects of perforating density 11.Predicting the effect of depletion on producing capacity 12.Allocating injection gas among gas lift wells 13.Analyzing a multiwell producing system 14.Relating field performance to time
- 49. 29 3.2 Application of Nodal Analysis to Electrical Submersible Pumping Wells To perform a nodal analysis on a submersible pumping well, the node is selected at the pump. The pump can be handled as an independent component in the system in a manner similar to that used in gravel-packed completions. The node pressure is either the pump intake pressure upp or the pump discharge pressure dnp . The pressure gain that the pump must generate for a particular producing rate is updn ppp −=∆ . The pressure traverse below the pump will be calculated based on the formation gas/liquid ratio and the casing size. The traverse in the tubing above the pump will be based on the gas/liquid ratio entering the pump and the tubing size. The inflow and outflow expressions are2 : Inflow: upcsgresR pbelowpumpppp =∆−∆− )( Outflow: (tubflowlinesep ppp ∆+∆+ dnpabovepump =) The following procedure may be used to estimate the pressure gain and power required to achieve a particular producing capacity. Inflow: 1. Select a value for liquid producing rate Lq . 2. Determine the required wfp for this Lq .using the reservoir performance procedures. 3. Determine the pump suction pressure upp using the casing diameter and the total producing GLR to calculate the pressure drop below the pump. 4. Repeat for a range of liquid producing rates and plot upp versus. Lq .
- 50. 30 Outflow: 1. Select a value for Lq . 2. Determine the appropriate GLR for tubing and flowline pressure drop calculations. a. Determine upp and fluid temperature at the pump at this Lq value from inflow calculations. b. Determine dissolved gas sR at this pressure and temperature. c. Estimate fraction of free gas sE , separated at the pump. This will be dependent whether or not a downhole separator is to be used. If not use 5.0=sE . d. Calculate the GLR downstream of the pump from ))(1( sototalsdn RfREGLR −= −= (42) where: =totalR total producing gas/liquid ratio, sR = solution gas/oil ratio at suction conditions, and =of fraction of oil flowing 3. Determine dnp using GLRdn to calculate the pressure drop in the tubing and the flowline if the casing gas is vented. If the casing tied into the flowline, the total GLR will be used to determine the pressure drop in the flowline. 4. Repeat for a range of Lq and plot dnp vs Lq on the same graph. 5. Select various producing rates and determine the pressure gain ∆p required to achieve an intersection of the inflow and outflow curves at these rates. The suction and discharge pressures can also be determined for each rate.
- 51. 31 6. Calculate the power requirement, pump size, number of stages, etc., at each producing rate. The required horsepower can be calculated from: )(1072.1 5 wwoo BqBqpHP +∆×= − (43) where: HP = horsepower required ∆p = pressure gain, psi qo = oil rate, STB/day qw = water rate, STB/day Bo = oil formation volume factor at suction conditions, bbl/STB, and Bw = water formation volume factor at suction conditions The pressure gain can be converted to head gain if necessary for pump selection. This is accomplished by dividing the pressure gain by the density of fluid being pumped. The actual plotting of the data is not required if the pump is to be selected for specific rates, as all the necessary information is calculated before plotting. 3.3 Description of the Computer Program 3.3.1 Pumping Only Liquid A two-stage computer program in Fortran Code has been written and also EXCEL Worksheet was used to support the program. At the first stage, program input consists of well, fluid, reservoir, and lift- system data. Once these conditions were satisfied, program initially gives the pressure at pump setting depth (discharge pressure) by applying Hagedorn and Brown3 vertical multiphase correlation. In addition to
- 52. 32 Hagedorn and Brown Correlation, Griffith4 Correlation was also used at bubble flow to obtain accurate results. Steps followed in the correlation can be observed in details at Chapter 4. During this process, program takes Pwh as initial pressure and calculates depth increment at every 10 psi pressure increase (pressure interval was taken low to reach an accurate solution) and finally stores the pressure (discharge pressure) when depth reaches to total pump setting depth. After recording discharge value program simply calculates intake pressures at assumed flow rates and number of pump stages. Head per stage data was required during these calculations and this was achieved by constructing equation of each pump performance curve and transferring it to program. These intake pressures are necessary to construct intake curves on the same graph as the IPR curve. At the second stage of the program, user should enter possible production rates to programs, which are obtained manually by intersecting intake curve and IPR curve. This procedure cannot be achieved by program since curve trendline equation changes at every different input value and there is no chance of data transfer between EXCEL Worksheet and the program. At the last step, program calculates HP requirement at every possible rate, which will help us to construct Possible Production Rate versus Stages and Horsepower Figure. It should be kept in mind that pump selection is achieved manually by entering to input, in other words program does not comprise an algorithm that automatically selects a suitable pump for that well. 3.3.2 Pumping Liquid and Gas Pumping gas with the liquid causes produced fluid rate V to undergo a significant variation between the intake and discharge pressures. This is due to high compressibility of gas. At any pressure point between the intake and discharge, the volume factor should be determined. This process can only be achieved by making huge amounts of iteration, which leads to necessity of a computer program. A two-stage computer program in Fortran
- 53. 33 Code has been written and also EXCEL Worksheet was used to support the program. Input parameters of the program are same with pumping only liquid program, however, GOR value should be entered since free gas exists. At first stage, program calculates VF at pressure interval between 200 – 5000 psi. Afterwards, by following same steps with pumping only liquid program, discharge pressure is calculated by Hagedorn and Brown3 Vertical Multiphase Flow Correlation (existing as a subprogram in the algorithm) and program starts to make iterations by decreasing pressure 50 psi at every iteration in order to calculate volume (h), h (head per stage) and number of stage (St) values at desired production rate. As explained previously, program computes Griffith4 Correlation when bubble flow conditions were formed. Program then calculates the intake pressure at various numbers of stages to let us construct tubing intake curve on the same graph as the IPR curve. At the second stage of the program, user should again enter possible production rates to programs, which are obtained manually by intersecting intake curve and IPR curve. This procedure cannot be achieved by program as explained before. At this point, program starts to make iterations to calculate horsepower per stage and total horsepower requirement at every 50 psi pressure drop until it reaches to intake pressure. This data will help us to construct Possible Production Rate versus Stages and Horsepower Figure in order us to make necessary evaluation. It should be kept in mind that pump selection is achieved manually by entering to input, in other words program does not include an algorithm that automatically selects a suitable pump for that well.
- 54. 34 CHAPTER IV STATEMENT OF THE PROBLEM The objective of this study is to perform a production engineering study at GK oil field in Southeastern Turkey. The main goal of the study is to achieve production optimization of 10 electrical submersible pump lifted wells currently operating in this field. Desired conclusion will be reached after determining the optimum pump stages and horsepower requirement for a possible production rate by a theorotical study and compare it with actual field submersible pump operating data. The study will let us to suggest optimum submersible pump running conditions for each well to continue production in a more economical and cost saving approach. Following steps were considered during the study to reach the aim: • writing computer program that applies vertical multiphase flow correlation and computes the parameters that were required for the optimization • collecting and evaluating the actual reservoir, well, fluid and lifting data that the case study was performed • entering field data to computer program and taking the output for two pumping conditions
- 55. 35 • preparing necessary figures and charts concerning pump stages, production rate and horsepower requirement using the computer output • comparison of actual field values and theorotical values and making necessary suggestions
- 56. 36 CHAPTER V HAGEDORN AND BROWN VERTICAL MULTIPHASE FLOW CORRELATION SUPPORTED BY GRIFFITH CORRELATION 5.1 Introduction The use of multiphase flow pipeline pressure drop correlations is very important in applying nodal analysis. The correlations that are most widely used at the present time for vertical multiphase flow are as follows: 1. Hagedorn and Brown3 2. Duns and Ros10 3. Ros and Gray11 4. Orkiszewski12 5. Beggs and Brill13 6. Aziz14 These are found to calculate pressure drop very well in certain wells and certain fields. However, one may be much better than the other under certain conditions and field pressure surveys are the only way to find out. Without any knowledge in a particular field, it would be recommended beginning initial work with the correlations as listed in the above order. In the literature it is recommended to from a hybrid by using the most dependable parts of the four models. As an example, the commercial vertical multiphase flow model (MTRAN) that was developed by Scientific Software Incorporation uses the following sections:
- 57. 37 1. Duns and Ros10 flow map 2. Use Orkiszewski12 for bubble flow 3. Use Hagedorn and Brown3 for slug flow 4. Use Duns and Ros10 for transitional and mist flow Figure 5.1 illustrates the schematic diagram of possible flow patterns in two-phase pipelines to visualize the flow systems that above correlations used for. Figure 5.1 Schematic Diagram of Possible Flow Patterns in Two-Phase Pipelines6
- 58. 38 5.2 Hagedorn and Brown Method The Hagedorn and Brown3 method was developed by obtaining experimental pressure drop and flow rate data from a 1500 ft deep instrumented well. Pressures were measured for flow in tubing sizes ranging from 1 ¼ to 2 7/8 in O.D. A wide range of liquid rates and gas/liquid ratios was included, and the effects of liquid viscosity were studied by using water and oil as the liquid phase. The oils used had viscosities at stock tank conditions of 10, 35 and 110 cp. Later two adjustments were made to improve this correlation. When bubble flow existed, the Griffith4 Correlation was used and when the no slip holdup was greater than the holdup value, the no slip holdup was used2 . Neither liquid holdup nor flow pattern was measured during the Hagedorn and Brown study, although a correlation for the calculated liquid holdup is presented. The correlations were developed by assuming that the two-phase friction factor could be obtained from the Moody diagram based on a two-phase Reynolds number. This Reynolds Number requires a value for LH in the viscosity term. The Hagedorn and Brown method has been found to give good results over a wide range of well conditions and is one of the most widely used well flow correlations in the industry2 . However, the original Hagedorn and Brown correlation has several weaknesses: At first, it is not very accurate in bubble flow. Moreover, calculated slip holdup is sometimes below no-slip holdup and also the acceleration term is too dominant. Thompson added that, the modified Hagedorn and Brown Correlation tended to overpredict pressure loss in bubble flow (Griffith), while it tended to underpredict slug flow. The Hagedorn and Brown Correlation gives best results for wellbores with low to moderate liquid volume fractions (high gas- liquid ratios) and relatively high mixture velocities (annular-mist or froth flow). The selection of appropriate correlation for a given production system is important to reach to an accurate solution. In this study, Hagedorn and
- 59. 39 Brown correlation was selected to calculate pressure drop for flow in the vertical tubing. However, during the execution of the correlation in this study, Griffith modification was also used when bubble flow conditions were satisfied since Hagedorn and Brown method shows weaknesses at bubble flow. 5.3 PROCEDURE FOR CALCULATING A VERTICAL PRESSURE TRAVERSE BY THE METHOD OF HAGEDORN AND BROWN The general equation of Hagedorn and Brown correlation is15 : 144 h g V d fw h p c m m m m ∆ ∆ + × += ∆ ∆ ) 2 ( 109652.2 2 511 2 ρ ρ ρ (44) Solving for the depth increment, h∆ h∆ = m m c m m d fw g V p ρ ρ ρ ××× + ∆−∆ 511 2 2 109652.2 ) 2 (144 (45) Start with a known pressure p1, assume a value for p2 and calculate the depth increment. 1. Calculate the average pressure between the two pressure points,psia p 7.14 2 21 + + = pp (46) Depending upon the requirements of the problem,i.e., whether or not a flowing bottom-hole pressure is to be determined from surface information, or whether the calculations are to start from total depth and come up the pipe, the starting pressure must be known. Pressure increments or decrements must then be assumed from which the distance between pressure points (1) and (2) will be calculated. As a word of precaution, if starting from the surface with a pressure lower than 100 psi, increments of 25 psi should be taken until reaching 400
- 60. 40 psi. This type of calculation is practically forbidden by long hand but lends itself readily to machine computation. If starting from bottom with pressures in excess of 1,000 psi, the pressure decrements may be as great as 200 psi. 2. Calculate the specific gravity of the oil, γo: γo= API°+5.131 5.141 (47) 3. Find total mass associated with one bbl of stock tank liquid: m = γo (350) ( WOR+1 1 ) + γw (350) ( WOR WOR +1 ) + (0.0764) (GLR) γg (48) 4. Calculate the mass flow rate: w = q m (49) 5. Obtain Rs at P and T by Standing’s16 Correlation : Rs = γg ( )(00091.0 )(0125.0 10 10 18 T API P × )1/0.83 (50) where Rs = scf/bbl Lasater’s17 equation can also be used and it is more accurate than Standing’s correlation especially at higher °API. The equation of Lasater’s correlation is as follows:
- 61. 41 Rs = C Y Y M g g o o ) 1 )( ))(350)(3.379( ( − γ (51) where: Mo = molecular weight T = °R The value of C is 1.0 unless a correction factor is necessary to make the equation check with actual field cases. 6. Obtain Bo according to calculated Rs value: a) If bPP〈 : TRF o g s 25.1)( 5.0 += γ γ (52) 175.1 000147.0972.0 FBob += (53) b) If bPP〉 ))(( PPc obo bo eBB − = (54) 7. Calculate the density of liquid phase: ρL = [ ] [ ]) 1 )(4.62() 1 1 ( 614.5/)0764.0()4.62( WOR WOR WORB R w o gso + + + + γ γγ (55)
- 62. 42 8. Assuming T = constant, find a value of Z for a constant T , p and γg. If T is to be a variable, then a single trial and error solution develops. Although the temperature gradient may be known, the depth at which the pressure increment occurs is not known and, therefore, the temperature at the next pressure point is not known. 4.688852.17292.17 2 +−−= ggpcP γγ (56) 94.17293.3088324.1 2 ++= ggpcT γγ (57) pc pr P P P = (58) pc pr T T T = (59) 101.036.0)92.0(39.1 5.0 −−−= prpr TTA (60) 6 ))1(9( 2 ) 10 32.0 ()037.0 )86.0( 066.0 ()02362.0( prTpr pr prpr PP T PTB pr − +− − +−= (61) )log(32.0132.0 prTC −= (62) )1824.049.03106.0( 2 10 prpr TT D +− = (63) a) If 100〈B
- 63. 43 D prB CP e A Az + − += 1 (64) b) If 100〉B D prCPAz += (65) 9. Calculate the average density of the gas phase gρ = ) 1 )( 520 )( 7.14 )(0764.0( ZT p gγ (66) 10. Calculate the average viscosity of the oil from appropriate correlations. As noted, a knowledge of fluid properties of the oil, p , and / or T is required. a) If bPP ≤ )04658.09824.6(163.1 API eTX −− = (67) 110 −= X oDµ (68) 515.0 )100(715.10 − += sRA (69) 338.0 )150(44.5 − += sRB (70) B oDo Aµµ = (71) b) If bPP ≥ )( 1 43 2 PCCC ePCB + = (72)
- 64. 44 where: C1 = 2.6 C2 = 1.187 C3 = -11.513 C4 = -8.98×10-5 B oDb Aµµ = B b bo P P )(µµ = (73) where: µb = viscosity of the reservoir liquid at the bubble point, cp µoD = dead oil viscosity, cp 11. Determine the average water viscosity from correlation below: )10982.110479.1003.1( 252 TT W e −− ×+×− =µ (74) 12. Calculate the liquid mixture viscosity: µL = µo + + WOR1 1 µw + WOR WOR 1 (75) This can only be an approximation since the viscosity of two immiscible liquids is quite complex. 12. Assuming constant surface tensions at each pressure point, calculate the liquid mixture surface tension.
- 65. 45 σL = σo ( WOR+1 1 ) + σw ( WOR WOR +1 ) (76) Again, this represents only an approximation of the surface tension of the liquid phase. 13. Calculate the liquid viscosity number: NL = 0.15726µL( 3 1 LLσρ )1/4 (77) 14. Determine CNL from the previously formed equation of CNL versus NL graph. 002.002.08612.0069.1022.4804.106222.87 23456 +++−+−= LLLLLLL NNNNNNCN (78) 15. Calculate the area of tubing, Ap. Ap = 4 2 dπ (79) 16. Obtain Bo at Tp, 17. Assuming Bw = 1.0, calculate the superficial liquid velocity sLν , ft/sec: sLν = + + + ) 1 () 1 1 ( 86400 61.5 WOR WOR B WOR B A q wo p L (80) 18. Calculate the liquid velocity number, NLV:
- 66. 46 NLV = 1.938 4/1 )( L L sL σ ρ ν (81) 19. Calculate the superficial gas velocity, sgν : sgν = + − 1520 7.14 86400 1 1 ZT pA WOR RGLRq p sL (82) 20. Determine the gas velocity number, NGV: NGV =1.938 sgν 4/1 L L σ ρ (83) 21. Find the pipe diameter number, Nd: Nd = 120.872d L L σ ρ (84) 22. Calculate the holdup correlating function φ : = d L gV LV N CNp N N 10.0 575.0 7.14 φ (85) 23. Obtain ψ LH from the correlation determined before: ψ LH = 11.02.182310210103104102 2639411513615 ++×−+×−×+×− φφφφφφ (86)
- 67. 47 24. Determine the secondary correction factor correlating parameter, φ: φ = 14.2 380.0 d Lgv N NN (87) 25. Obtain ψ from the previously formed equation of ψ versus φ graph. ψ = 7611.112.15710765300129104103108 23465767 +−+−×+×−× φφφφφφ (88) 26. Calculate a value for HL: HL = [ ]ψ ψ LH (89) For low viscosities there will be no correction and ψ = 1.00. 27. In order to obtain a friction factor, determine a value for the two-phase Reynolds number, (NRe)TP: ))()(( 102.2 )( )1( 2 Re LL H g H L TP d w N − − × = µµ (90) 28. Determine a value for ε/d. If the value of ε is not known, a good value to use is 0.00015 ft which is an average value given for commercial steel. 29. Obtain the friction factor from the Jain18 Equation: ) 25.21 log(214.1 1 9.0 ReNdf +−= ε (91)
- 68. 48 30. Calculate the average two-phase density of the mixtures mρ by two methods. (a) Using the value of HL, calculate mρ as follows: mρ = )1( LgLL HH −+ ρρ (92) (b) Calculate a value of mρ assuming no slippage. 31. Calculate the two-phase mixture velocity at both p1 and p2. νm1=νsL1+νsg1 (93) νm2=νsL2+νsg2 (94) 32. Determine a value for ∆ (νm 2 ) ∆ (νm 2 ) = [ ]2 2 2 1 mm νν − (95) 33. Calculate ∆h corresponding to ∆p = p1 – p2 ∆h = m m c m m d fw g p ρ ρ ν ρ 511 2 2 109652.2 ) 2 (144 × + ∆−∆ (96) 34. Starting with p2 and the known depth at p2, assume another pressure point and repeat the procedures until reaching total depth, or until reaching the surface depending upon whether you are starting from the bottom or top of tube.
- 69. 49 5.4 GRIFFITH CORRELATION (BUBBLE FLOW) The void fraction of gas (Hg) in bubble flow can be expressed as: Hg= −+−+ ps g ps t ps t Av q Av q Av q 4 )1(1 2 1 2 (97) where : vs = slip velocity (bubble rise velocity), ft/sec Griffith suggested that a good approximation of an average vs is 0.8 ft/sec. The average flowing density can be computed as: ρ = gggL HH ρρ +− )1( (98) The friction gradient is: hcLLf dgvf 2/ 2 ρτ = (99) where: [ ])1( gp L L HA q − =ν (100) The Reynolds number is calculated as: L L hL v dN µ ρ1488Re = (101) where:
- 70. 50 dh = hydraulic pipe diameter, ft µL = liquid viscosity, cp Vertical pressure gradient curves (for three different reservoir conditions) obtained from the computer program by following the above steps were given at Chapter 7.
- 71. 51 CHAPTER VI DESCRIPTION OF THE GK FIELD 6.1 Introduction The selected field is located on South East Anatolian. The field was discovered in 1961 and has been on production since then. Currently, there are a total of 29 wells with 12 producers, 13 closed-in, 2 dumpflooders and 2 injection wells. The main drive mechanism of the field is rock and fluid expansion, there also exists a weak aquifer at the system but not sufficient to create a producing force. The field started its production life as a dry and natural flowing field. A steep pressure decline in wells was observed during late 1961 and early 1962. It was decided that the field pressure should be maintained by water injection through peripheral wells –3 and –5 on the Eastern and Western flanks of the field to keep the production wells on natural flow. In 1966, water cut increased and killed natural flow. In 1967, as a result of high field offtake, pressure in producers began to decline rapidly. Thus, in August 1967, water injection was stopped to observe production declines in the field and artificial lift system was installed. After realising that recovery is constrained by pressure decline rather than the watercut development in 1986 dumpflooding started. In June 1997 from two wells re-injection started19 .
- 72. 52 6.2 Geology The field is an elongated structure in an approximate East–West direction. Up to date 29 wells have been drilled and two wells are located outside the field (Well-9 and Well-10). The field is a frontal thrust structure consisting of an anticline on the leading edge of the thrust block. The reservoir rock has been divided into Mardin Units, I, II, III and IV. These units are further subdivided based on lithology (limestone and dolomite) and porosity classes. There is a main continues East-West trending normal fault. This main fault separates two blocks as Main Block and Northern Block and there is an another block called Western Block. The unique pressure response of the W-14 with respect to the rest of the field (pressure measured in W-14 showed slight depletion of only a few hundred psi, when the average reservoir pressure in the rest of the field was more than 1000 psi) may show the existence of a barrier between W-14 and W-11 due to either a fault or reservoir rock quality deterioration (a permeability barrier) between those wells. The reservoir deterioration between the wells on the other hand, can not be confirmed due to shallow completion of the W-11 which prevents the correlation of two wells because of the long distance between these two wells, the deterioration of the reservoir quality is still quite possible. The units having the highest porosities are the dolomite in Unit I and the high porosity limestone close to the bottom of the Unit II. The average porosities of this dolomite unit varies between 15% and 20% and the average permeabilities between 6 mD-50mD based on core measurements. Intercrystalline and vuggy porosities, and some solution channels and fractures were also observed on the core samples. Unit II is described as limestone-dolomitic limestone. Cores indicated that it has vuggy porosity and solution channels, and some sub-vertical/sub- horizontal fractures also exist. The average porosity is 10%-15% with air permeabilities between 0.3 mD-1.5 mD based on core measurements.
- 73. 53 All of the producing wells produce from Unit I and II, the dumpflooders W-3, W-5, W-19 inject the water into Unit I and injectors W-11 and W-18 inject to Unit I and II. 6.3 Reservoir,Fluid and Lift-System Properties In the absence of PVT sampling, reservoir fluid properties have been, to large extent, derived from correlations. Estimated values for key parameters are listed in Table 6.1. TABLE 6.1 RESERVOIR AND FLUID PROPERTIES OF GK FIELD ° API 38 GOR, scf/STB 15 γgsc 0.7 γwsc 1.02 γosc 0.83 Pb, psi 160 PR (initial), psi 2400 Tav, °F 170 10 of 12 producer wells were lifted with electrical submersible pumps. These wells and the series of pumps operated are given in Table 6.2.
- 74. 54 TABLE 6.2 SUBMERSIBLE PUMP LIFTED WELLS OPERATED IN GK FIELD AND THEIR EFFICIENCY RANGES WELL PUMP USED EFFICIENCY RANGE (bbl/d) W-07 DN440 83 - 458 W-08 DN675 267 - 692 W-15 GN2000 1300 - 2650 W-16 GN1600 833 - 1792 W-17 GN1600 833 -1792 W-22 DN440 83 - 458 W-24 DN1100 500 - 1125 W-25 GN3200 1834 - 3417 W-27 DN675 267 - 692 W-28 DN675 267 - 692 6.4 Production History Production rates and bottomhole pressures recorded for the producer wells between the years 1961 and 1999 gives the generalized IPR curve showed in Figure 6.1. This figure is the combination of 66 well test data from 12 different producer wells and by inspecting the figure, it can be observed that the (qo)max is 1378 bbl/d or 1385 stb/d and flow rate at bubble point pressure, (qo)b, is 1340 bbl/d or 1347 stb/d.
- 75. 55 0 500 1000 1500 2000 2500 3000 0 200 400 600 800 1000 1200 1400 1600 q (BBL/D or STB/D) Pwf(psi) BBL/D STB/D Figure 6.1 Generalized IPR Curve The gross rate of each submersible pump lifted producer well during the production period and required pump stages used in the field are given in Table 6.3.
- 76. 56 TABLE 6.3 GROSS PRODUCTION RATE OF THE WELLS IN GK FIELD AND REQUIRED PUMP STAGES Well Gross Rate (bbl/d) Pump Stages W-07 180 356 W-08 740 238 W-15 1180 216 W-16 1350 180 W-17 1270 181 W-22 70 320 W-24 1000 332 W-25 1620 239 W-27 400 338 W-28 530 338
- 77. 57 CHAPTER VII RESULTS AND DISCUSSION 7.1 INTRODUCTION Calculations are based on the steps that are summarized in Chapter 2 at sections 2.3.1.1 for pumping liquid and 2.3.2.4 for pumping liquid and gas. These calculations were done for the 10 submersible pump lifted wells indicated in Table 6.2 and by using the pumps that were actually operated in the GK field. Detailed sample calculation for W-08 and the output of computer program can be observed in Appendix B. Results of the study can be categorized into five different parts: a. Construction of vertical flowing pressure gradient (pressure traverse) curves according to computer program output and comparing the results with Beggs&Brill13 Correlation b. Performing Sensitivity Analysis based on effect of of oil density, GLR and WOR on flowing bottomhole pressure by using the computer program output c. Construction of possible production rate versus stage and horsepower chart for each well (GLR = 15 scf / STB) by using the pumping liquid and gas computer algorithm d. Comparison of theoretical and actual production parameters and suggestion for optimum pump operating conditions by inspecting possible production rate versus stage and horsepower chart
- 78. 58 7.2 RESULTS and DISCUSSION 7.2.1 Construction of Vertical Flowing Pressure Gradient Curves Using Computer Program Output Hagedorn and Brown3 subprogram supported with Griffith4 Correlation gives program user a chance to construct the vertical flowing pressure gradient curves at any flow rate and at the desired reservoir, fluid and well conditions. Pressure traverse curves for a flow rate of 100 stb/d and with a water-cut of 0, 0.5 and 1.0 were constructed respectively according to GK field data and by the help of computer program output. These curves can be observed at Figure 7.1, 7.2 and 7.3.
- 79. 59 100400 300 500 0200 GAS-LIQUID RATIO,scf/STB 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 0 400 800 1200 1600 2000 2400 2800 3200 3600 4000 Pressure (psi) Depth(ft) Tubing Size, in : 2.441 Liquid Rate, STBL/D : 100 Water Fraction : 0 Gas Gravity : 0.70 Oil API Gravity : 38 Water Specific Gravity : 1.02 Average Flowing Temp., F : 170 Correlation : Hagedorn&Brown Griffith Correlation (bubble flow) Figure 7.1 Pressure Traverse Curve (WC = 0)
- 80. 60 100200 0 500 300400 GAS-LIQUID RATIO,scf/STB 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 0 400 800 1200 1600 2000 2400 2800 3200 3600 4000 4400 Pressure (psi) Depth(ft) Tubing Size, in : 2.441 Liquid Rate, STBL/D : 100 Water Fraction : 0.5 Gas Gravity : 0.70 Oil API Gravity : 38 Water Specific Gravity : 1.02 Average Flowing Temp., F : 170 Correlation : Hagedorn&Brown Griffith Correlation (bubble flow) Figure 7.2 Pressure Traverse Curve (WC = 0.5)
- 81. 61 500 400 300 200 100 0 GAS-LIQUID RATIO,SCF/STBL 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 0 400 800 1200 1600 2000 2400 2800 3200 3600 4000 4400 4800 Pressure (psi) Depth(ft) Tubing Size, in : 2.441 Liquid Rate, STBL/D : 100 Water Fraction : 1.0 Gas Gravity : 0.70 Oil API Gravity : 38 Water Specific Gravity : 1.02 Average Flowing Temp., F : 170 Correlation : Hagedorn&Brown Griffith Correlation (bubble flow) Figure 7.3 Pressure Traverse Curve (WC = 1.0)
- 82. 62 A comparison was made between pressure traverse curves prepared by Beggs&Brill13 and curves constructed with computer output in order to test the accuracy of correlation used in the program algorithm. Table 7.1 briefly indicates the pressures at selected depths with respect to two conditions. Inspecting Table 7.1, we can understand that computer-based pressures and the Beggs&Brill correlation values are very close to each other. This means that vertical multiphase flow correlation within the program is giving reliable output and encurages us about the accuracy of rest of the study. It should be kept in mind that values determined from Beggs&Brill correlation are recorded at slightly different reservoir and fluid conditions than GK field parameters, that is, gas gravity is 0.65, oil API gravity is 35 and average flowing temperature is 150 °F. Another point that should be taken into account during the comparison is that when GLR increases, difference between pressure values of computer output and Beggs&Brill values are also increases. This behaviour can be interpreted as reliability of Hagedorn and Brown flow correlation supported by Griffith Correlation should be re-tested at high GLR reservoirs.
- 83. 63 TABLE 7.1 COMPARISON of COMPUTER-BASED VERTICAL FLOWING PRESSURES with BEGGS&BRILL CORRELATION AT SELECTED DEPTHS Water Fraction 0 0.5 1.0 GLR (scf/STB) GLR (scf/STB) GLR (scf/STB) 0 100 0 100 0 100 Pressure (psi) Pressure (psi) Pressure (psi) Depth (ft) Output Beggs&Brill Output Beggs&Brill Output Beggs&Brill Output Beggs&Brill Output Beggs&Brill Output Beggs&Brill 4000 1440 1400 1050 1040 1590 1600 1220 1140 1680 1800 1400 1280 6000 2160 2090 1770 1750 2380 2400 2040 1960 2560 2720 2280 2180 8000 2870 2800 2480 2440 3190 3190 2820 2750 3440 3610 3180 3080 10000 3580 3500 3190 3130 3985 4000 3610 3560 4320 4540 4080 3090
- 84. 64 7.2.2 Sensitivity Analysis by Using the Computer Program Output Having a chance of changing all variables related to Hagedorn and Brown vertical multiphase flow correlation within the program, sensitivity analysis was performed by observing the effect of oil density, GLR and WOR on flowing bottomhole pressure. Results were summarized in Table 7.2, 7.3 and 7.4. Reservoir and fluid data of W-08 was used during the study. After making necessary observations for the output, it can be observed that the increase in oil density and GLR creates a slight decrease in bottomhole pressure, and an increase in WOR causes an increase in flowing bottomhole pressure. TABLE 7.2 EFFECT of OIL DENSITY on FLOWING BOTTOMHOLE PRESSURES AT SELECTED DEPTHS Well Depth (ft) API 4000 6000 8000 10000 10 2000 2880 3760 4620 15 2000 2880 3760 4620 20 1990 2870 3760 4610 25 1990 2870 3750 4610 30 1990 2870 3750 4610 35 1990 2870 3750 4600 40 1990 2870 3740 4600
- 85. 65 TABLE 7.3 EFFECT of GLR on FLOWING BOTTOMHOLE PRESSURES Q = 100 STB/D GLR Wellhead Pressure (psi) Flowing Bottomhole Pressure (psi) 0 250 2480 100 250 2190 200 250 1960 300 250 1860 400 250 1800 500 250 1720 TABLE 7.4 EFFECT of WOR on FLOWING BOTTOMHOLE PRESSURES AT SELECTED DEPTHS Flowing Bottomhole Pressure (psi) Well Depth (ft) WOR 0% WOR 50% WOR 100% 4000 1640 1820 2000 6000 2350 2620 2880 8000 3070 3420 3770 Figure 7.4 and 7.5 indicate a graphical analysis for the effect of GLR and WOR on flowing botomhole pressure respectively. It can be observed that flow rates that were selected show no or negligible effect on flowing bottomhole pressures.
- 86. 66 GLR=0 scf/stbl GLR=100 GLR=200 GLR=300 GLR=400 GLR=500 IPR 0 500 1000 1500 2000 2500 3000 0 200 400 600 800 1000 1200 q (BBL/D or STB/D) Pwf(psi) BBL/D STB/D Figure 7.4 Graphical Analysis of Effect of GLR on Flowing Bottomhole Pressure for W-08 WOR=0.5 IPR WOR =0 WOR=1.0 0 500 1000 1500 2000 2500 3000 0 200 400 600 800 1000 1200 q (BBL/D or STB/D) Pwf(psi) BBL/D STB/D Figure 7.5 Graphical Analysis of Effect of WOR on Flowing Bottomhole Pressure for W-08
- 87. 67 7.2.3 Construction of Possible Production Rate versus Stage and Horsepower Chart for GK Field Wells by Using the Pumping Liquid and Gas Computer Algorithm Possible production rate versus stage and horsepower chart was prepared for each electrical submersible pump lifted wells in GK field by considering the intake pressures obtained from computer program at selected flow rates. These charts can said to be the final step of the study and helped us to make necessary suggestions for optimum pump operating conditions. In below figures, actual value point is the real production rate of the well in GK field and the number of pump stages used for that well. It should be noted that actual horsepower requirement data for these wells are not available. On Figures 7.6 to 7.14, the efficiency range of the pumps used and also suggested flow rate and corresponding horsepower requirement and number of pump stages can be observed.
- 88. 68 HP Stages Efficiency Range Actual Value (St) Suggested HP Suggested Stage 0 50 100 150 200 250 300 350 400 450 500 550 600 0 50 100 150 200 250 300 350 400 450 Stages or Horsepower PossibleRate(STB/D) FIGURE 7.6 Possible Production Rate vs Stages and Horsepower for W-07
- 89. 69 HP Efficiency Range Stages Actual Value (St)Suggested HP Suggested Stage 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 0 50 100 150 200 250 300 350 400 450 Stages or Horsepower PossibleRate(STB/D) FIGURE 7.7 Possible Production Rate vs Stages and Horsepower for W-08
- 90. 70 HP Efficiency Range Stages Actual Value(St) Suggested Stage Suggested HP 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 0 100 200 300 400 500 600 700 800 Stages or Horsepower PossibleRate(STB/D) FIGURE 7.8 Possible Production Rate vs Stages and Horsepower for W-16
- 91. 71 HP Stages Efficiency RangeActual Value (St) Suggested HP Suggested Stage 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 100 200 300 400 500 600 Stages or Horsepower PossibleRate(STB/D) FIGURE 7.9 Possible Production Rate vs Stages and Horsepower for W-17
- 92. 72 HP Efficiency Range Stages Actual Value (St) Suggested HP Suggested Stage 0 200 400 600 800 1000 1200 1400 1600 1800 0 100 200 300 400 500 600 Stages or Horsepower PossibleRate(STB/D) FIGURE 7.10 Possible Production Rate vs Stages and Horsepower for W-22
- 93. 73 HP Efficiency Range Stages Actual Value (St)Suggested HP Suggested Stage 0 200 400 600 800 1000 1200 1400 1600 1800 0 50 100 150 200 250 300 350 400 450 Stages or Horsepower PossibleRate(STB/D) FIGURE 7.11 Possible Production Rate vs Stages and Horsepower for W-24
- 94. 74 HP Stages Efficiency Range Actual Value(St) Suggested HP Suggested Stage 0 500 1000 1500 2000 2500 3000 3500 0 100 200 300 400 500 600 700 Stages or Horsepower PossibleRate(STB/D) FIGURE 7.12 Possible Production Rate vs Stages and Horsepower for W-25
- 95. 75 HP Efficiency Range Stages Actual Value (St) Suggested Stage Suggested HP 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 0 50 100 150 200 250 300 350 400 450 Stages or Horsepower PossibleRate(STB/D) FIGURE 7.13 Possible Production Rate vs Stages and Horsepower for W-27
- 96. 76 HP Stages Efficiency Range Actual Value (St)Suggested HP Suggested Stage 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 0 50 100 150 200 250 300 350 400 450 Stages or Horsepower PossibleRate(STB/D) FIGURE 7.14 Possible Production Rate vs Stages and Horsepower for W-28
- 97. 77 7.2.4 Comparison of Theoretical and Actual Production Parameters and Suggestion for Optimum Pump Operating Conditions by Inspecting Possible Production Rate versus Stage and Horsepower Chart Inspection of Possible Production Rate versus Stage and Horsepower charts for GK field wells let us to make following interpretations: Actual operating rate of W-07 is 180 stb/d with 356 stages. This operating rate is within the efficiency range (83-458 bpd) of the pump used (DN 440), however from the Figure 7.6 it can be observed that beyond 100 stb/d, the horsepower requirement and the number of pump stages increase very fast without a significant gain in the production rate. A production rate of 90 stb/d with a horsepower requirement of 40 HP, and a pump stages of 450 can said to be ideal considering the chart. W-08 is operated with 740 stb/d with 238 stages. This production rate is higher than the upper limit of pump efficiency range (267-692 bpd). On the other hand, by examining Figure 7.7, 740 stb/d rate at 238 stages seem to be a good choice, since HP and pump stage curve slope increases significantly with an increase in production rate. A production rate of 680 stb/d and a corresponding horsepower requirement of 35 HP and 230 pump stages can be suggested which are close to actual operating values. 680 stb/d production rate is useful since it is within the upper limit of efficiency range and providing maximum production rate from W-08. W-15 cannot be interpreted due to lack of required data. W-16 is operated with 1350 stb/d with a pump stage of 180. The rate is within the efficiency range of the pump (833-1792 bpd) and the corresponding pump stages and HP requirement can said to be economical by observing Figure 7.8. A production rate of 1200 stb/d with a 70 HP and 160 pump stages can be a perfect design and it should be noted that the actual production rate and pump stage values are nearly equal to theoretical values.
- 98. 78 W-17 is operated with 1270 stb/d with 181 stages. This rate indicates that the pump is used efficiently (833-1792 bpd). Besides, observing Figure 7.9, operating production rate and pump stage values are said to be at optimum range, and the actual and theoretical values are close to each other. Thus, a production rate of 1400 stb/d and a corresponding HP requirement of 100 HP and 220 pump stages can be offered in theorotical circumstances. W-22 produces with a low rate, 70 stb/d, with 320 stages. Figure 7.10 shows that the rate is below pump efficiency range (83-458 bpd) and also 320 stages is useless since HP requirement increases significantly, however production rate increases slightly. This well can said to be operated inefficiently. 390 stb/d production rate can be selected with a 18 HP requirement and a pump stages of 212. W-24 produces 1000 stb/d within upper limit of pump efficiency range (500-1125 bpd). Pump stage value is 332, and entire actual operating data, is acceptable. Suggested values can be given as 1050 stb/d production rate with a 32 HP and 270 pump stages. W-25 is operated with 1620 stb/d with 239 stages. Figure 7.12 shows that the actual operating production rate can be selected higher, especially within efficiency range (1834-3417 bpd) of the pump. 1900 stb/d production rate with a 310 HP and a pump stage of 400 can be suggested for this well but it should be noted that horsepower requirement is too high to be operated in field conditions. W-27 has a production rate of 400 stb/d and a pump stage of 338. Examining Figure 7.13, it can be concluded that the pump is operating at its optimum range (267-692 bpd). Operating with 650 stb/d with a 25 HP and 170 pump stages can be economical. W-28 operates with 530 stb/d within its pump efficiency range (267- 692 bpd) with 338 stages 680 stb/d production rate with a 28 HP and 192 pump stages can be a good selection.
- 99. 79 TABLE 7.5. RESULTS OBTAINED AFTER the COMPARISON of ACTUAL and COMPUTER-BASED DATA for GK FIELD WELL Actual Flow Rate (stb/d) Actual Pump Stages Actual HP Suggested Flow Rate (stb/d) Suggested Pump Stages Suggested HP RESULT W-07 180 356 N/A 90 450 40 not completely optimum but can be acceptable W-08 740 238 N/A 680 230 35 not completely optimum but can be acceptable W-15 1180 216 N/A N/A N/A N/A N/A W-16 1350 180 N/A 1200 160 70 completely optimum W-17 1270 181 N/A 1400 220 100 completely optimum W-22 70 320 N/A 390 212 18 inefficient production W-24 1000 332 N/A 1050 270 32 completely optimum W-25 1620 239 N/A 1900 400 310 not completely optimum but can be acceptable W-27 400 338 N/A 650 170 25 not completely optimum but can be acceptable W-28 530 338 N/A 680 192 28 not completely optimum but can be acceptable
- 100. 80 where: NA = not applicable due to lack of required data
- 101. 81 CHAPTER VIII CONCLUSIONS AND RECOMMENDATIONS System Nodal Analysis is an useful method in designing and optimizing a production system having interacting components. Application of Nodal Analysis technique to electrical submersible pumps lets production engineers to run the pump more efficiently by selecting optimum flow rate and corresponding number of pump stages and horsepower requirement. System optimization is especially important when dealing with gas with liquid rather than producing and pumping only liquid. In these cases, system analysis should be supported by a computer program to overcome large iterations due to production volume change between pump discharge and intake pressures. It should be noted that GK field has a low GOR (15 scf/STB) which allows straight-forward pump designs without a need of detailed optimization procedures. This study is useful especially for high GOR submersible pump lifted wells. A computer program is also necessary to predict pressure at required depth simultaneously by using vertical multiphase flow correlation. It can be observed from the results that Hagedorn and Brown correlation generally gave acceptable program output when compared with Beggs&Brill Correlation, however failed to give accurate values at bubble flow. During the study, Griffith Correlation was used when bubble flow conditions were met. Results indicated that when dealing with high GLR wells by the help of the computer program, Hagedorn and Brown Correlation showed tendency to give less accurate output. In this study, sensitivity analysis was also performed based on the effect of oil gravity, WOR and GLR on flowing bottomhole pressure which was evaluated with graphical analysis. Evaluation of possible production rate versus stage and horsepower chart showed that within 10 submersible pump lifted wells, 3 wells, W-16,
- 102. 82 W-17, and W-24 were operated at their optimum range. 5 wells, W-07, W- 08, W-25, W-27, and W-28, were not operated completely at optimum operating conditions but can said to be acceptable. 1 well, W-22, was operated inefficiently which should be re-designed to reach optimum parameters. W–15 could not be interpreted due to lack of required production data. The study gave the writer a chance to suggest optimum operating parameters for each well. Finally, it should be kept in mind that actual production rates for the wells in GK field can be different from the optimized values because of the commercial production needs of the oil companies.
- 103. 83 REFERENCES 1. Brown, K.E., “The Technology of Artificial Lift Methods”, Vol. 2b, PennWell Publishing Company, Tulsa, Oklahoma, 1980. 2. Beggs, H.D., “Production Optmization Using Nodal Analysis”, OGCI Publications, Tulsa, Oklahoma, 1991. 3. Hagedorn, Alton R., Brown, K.E., “Experimental Study of Pressure Gradients Occuring During Continuous Two-phase Flow in Small Diameter Vertical Conduits”, Journal of Petroleum Technology, April 1965, p.475 4. Griffith, P., ‘’Two-Phase Flow In Pipes’’, Summer Program, M.I.T., 1962. 5. Reda Pump Company Pte. Ltd., 1992 6. Brown, K.E., “The Technology of Artificial Lift Methods”, Vol. 4, PennWell Publishing Company, Tulsa, Oklahoma, 1984. 7. Gilbert, W.E., ‘’Flowing and Gas-Lift Well Performance’’, API Drill.Prod.Practice,1954. 8. Nind, T.E.W., ‘’Principles of Oil Well Production’’, McGraw-Hill, 1964. 9. Brown, K.E., Beggs, H.D., ‘’ The Technology of Artificial Lift Methods”, Vol. 1, Petroleum Publishing Company, Tulsa, Oklahoma, 1978
- 104. 84 10.Duns, H.Jr., Ros, N.C.J., ‘’Vertical Flow of Gas and Liquid Mixtures in Wells’’, 6th World Petroleum Congress, Frankfurt, Germany. 11.Gray, H.E., ‘’Vertical Flow Correlations in Gas Wells’’, User Manual for API 14B Subsurface Control Safety Valve Sizing Computer Program App.B., June 1974 12.Orkizewski, J. “Predicting Two-Phase Pressure Drops in Vertical Pipe”, Journal of Petroleum Technology, June 1967 13.Beggs, H.D., Brill, J.P. “A Study of Two Phase Flow in Inclined Pipes”, Journal of Petroleum Technology, May 1973 14.Aziz, K., Govier, G.W., and Fogarasi, M., “Pressure Drop in Wells Producing Oil and Gas”, Journal of Canadian Petroleum Technology, July-September 1972 15.Brown, K.E., “The Technology of Artificial Lift Methods”, Vol. 1, Petroleum Publishing Company, Tulsa, 1977 16.Standing, M.B., ‘’Volumetric and Phase Behavior of Oilfield Hydrocarbon Systems’’, NewYork, Reinhold Publishing Corp., 1952 17.Lasater, J.A., ‘’Bubble Point Pressure Correlation’’, Transactions of the AIME, 1958, pg379 18.Jain, A.K., “Accurate Explicit Equation for Friction Factor”, J.Hydl.Div.ASCE, NoHY5, May, 1976 19.Private Communication with N.V. Turkse Perenco, 2003
- 105. 85 APPENDIX A PUMPING LIQUID AND GAS COMPUTER PROGRAM 1. Nomenclature 2. Flow Chart 3. Main Program
- 106. 86 PUMPING LIQUID AND GAS A1 Nomenclature: A1.1 Simple Variables Used In The Program A,B,C,D terms used in z factor calculation API API value of the oil AREA area of the tubing, ft2 AVALUE constant used in determination of the number of pump stages BHT bottomhole temperature, °F BO formation volume factor of oil, rbbl/STB BOB formation volume factor of oil at bubble point pressure, rbbl/STB CNL viscosity number coefficient CO coefficient of isothermal compressibility DELP pressure increment, psi DENAV average density of the gas phase, lb/ft3 DENF weight of 1 bbl liquid plus pumped gas at standard conditions, lb/stbl DENGAS gas density at standard conditions, lb/scf DENLIQ density of the liquid phase, lb/ft3 DENMIX average two phase density of the mixture, lb/ft3 DIA inner diameter of tubing, in. DIANUM pipe diameter number DIST distance used in Hagedorn and Brown correlation, ft DOV dead oil viscosity, cp ED pipe roughness
- 107. 87 F term used in calculating formation volume factor of oil FF friction factor GLR gas liquid ratio, scf/STB GOR gas oil ratio, scf/STB HEADCAP head per stage, ft/stage HOLDCOF holdup correlating function HOLDUP liquid holdup HOLOSEC liquid holdup over secondary correction factor HPLOAD horsepower per stage, HP/stage PAV average pressure between P1 and P2 PBUB bubble point pressure, psi PPC pseudo critical pressure PPR pseudo reduced pressure P1 initial pressure (wellhead pressure in this case), psi P2 final pressure, psi Q flow rate term used in pump head capacity subprogram, STB/D QOIL oil flow rate, STB/D QOPTM flow rate term used in pump horsepower subprogram, STB/D QWATER water flow rate, STB/D RS solution gas oil ratio, scf/STB RS1 solution gas oil ratio at initial condition, scf/STB RS2 solution gas oil ratio at final condition, scf/STB SCF secondary correction factor SECORF secondary correction factor correlating parameter SGGAS specific gravity of gas SGOIL specific gravity of oil SGWATER specific gravity of water T average flowing temperature, °F TD total depth of the well, ft TENLIQ liquid mixture surface tension, dynes/cm
- 108. 88 TPC pseudo critical temperature TPR pseudo reduced temperature VELNGAS gas velocity number VELNLIQ liquid velocity number VISAV average viscosity between initial and final condition, cp VISGAS gas viscosity (assumed constant), cp VISNLIQ liquid viscosity number VISO1 oil viscosity at initial condition, cp VISO2 oil viscosity at final condition, cp VISWAT average water viscosity, cp VSG superficial gas velocity, ft/sec VSL superficial liquid velocity, ft/sec W mass flow rate, lb/day WM mass associated with one barrel of stock tank liquid, lb/STBL WC water cut WOR water oil ratio A1.2. Arrays Used In The Program BE array showing factor ‘B’ used in z factor calculation HP array showing the calculation of required pump horsepower P array showing VF data at various pressures PR array showing the calculation of number of pump stages ST array showing the intake pressures at various pump stages ZE array showing z factor
- 109. 89 A2 Flow Chart MAIN PROGRAM START Input: Well, fluid, reservoir, and lift- system data Calculate: Rs, Bo, Bg and VF at various pressures (200 – 5000 psi) CALL HAGBROWN (pressure gradient correlation) Store discharge pressure at pump depth. Apply Griffith Correlation if bubble flow exists Begin with first iteration. At every iteration decrease the pressure 50 psi (∆P) starting from the discharge pressure A Calculate: Average pressure Pav = 2 finalinitial PP + Output: file name is Table1 volume factor data at various pressures
- 110. 90 Calculate: volume factor at the average pressure by making interpolation and volume of fluid according to volume factor value According to input lift data: CALL DN440H for pump DN440 CALL DN675H for pump DN675 CALL DN1100H for pump DN1100 CALL GN1600H for pump GN1600 CALL GN2000H for pump GN2000 CALL GN3200H for pump GN3200 Store head per stage at volume of fluid Calculate: stage increment and total number of stages If average pressure is less than 200 psi A F Output: file name is Table2 iterations to calculate total number of pump stages at various pressures T
- 111. 91 Input: number of pump stages (7 values) at which intake pressure will be calculated Calculate: intake pressures at selected pump stages by interpolation Output: file name is Table3 intake pressure values at selected pump stages Input: possible (optimized) production rate and corresponding intake pressure determined from EXCEL Worksheet CALL HAGBROWN Store discharge pressure at possible (optimum) flow rate. Apply Griffith Correlation if bubble flow exists Begin with first iteration. At every iteration decrease the pressure 50 psi (∆P) starting from the discharge pressure B
- 112. 92 Calculate: Average pressure Pav = 2 finalinitial PP + Calculate: volume factor at the average pressure by making interpolation and volume of fluid according to volume factor value According to input lift data: CALL DN440HP for pump DN440 CALL DN675HP for pump DN675 CALL DN1100HP for pump DN1100 CALL GN1600HP for pump GN1600 CALL GN2000HP for pump GN2000 CALL GN3200HP for pump GN3200 Store horsepower per stage at volume of fluid According to input lift data: CALL DN440H for pump DN440 CALL DN675H for pump DN675 CALL DN1100H for pump DN1100 CALL GN1600H for pump GN1600 CALL GN2000H for pump GN2000 CALL GN3200H for pump GN3200 Store head per stage at volume of fluid Calculate: horsepower increment and total required horsepower
- 113. 93 If average pressure is less than intake pressure F B Output: file name is Table4 iterations to calculate total horsepower requirement between intake and discharge pressures STOP T
- 114. 94 A3 Main Program C **********LIQUID AND GAS CASE MAIN PROGRAM********** DIMENSION P(25,5),BE(25),ZE(25),PR(100,8),ST(10,10),HP(100,9) REAL HEAD,XY,YX,HPPERST C **********OPEN FILE********** OPEN (15,FILE='TABLE1.FOR') OPEN (35,FILE='TABLE2.FOR') OPEN (41,FILE='TABLE3.FOR') OPEN (31,FILE='TABLE4.FOR') C **********INPUT DATA********** PRINT *,'SELECT YOUR PUMP' PRINT *,'TYPE 1 FOR DN440' PRINT *,'TYPE 2 FOR DN675' PRINT *,'TYPE 3 FOR DN1100' PRINT *,'TYPE 4 FOR GN1600' PRINT *,'TYPE 5 FOR GN2000' PRINT *,'TYPE 6 FOR GN3200' READ *,SELECT IF (SELECT.EQ.1) PRINT *,'YOU CHOOSE DN440' IF (SELECT.EQ.2) PRINT *,'YOU CHOOSE DN675' IF (SELECT.EQ.3) PRINT *,'YOU CHOOSE DN1100' IF (SELECT.EQ.4) PRINT *,'YOU CHOOSE GN1600' IF (SELECT.EQ.5) PRINT *,'YOU CHOOSE GN2000' IF (SELECT.EQ.6) PRINT *,'YOU CHOOSE GN3200' PRINT *,'ENTER WATERCUT' READ *,WC PRINT *,'ENTER SPECIFIC GRAVITY OF WATER' READ *,SGWAT PRINT *,'ENTER SPECIFIC GRAVITY OF OIL' READ *,SGOIL
- 115. 95 PRINT *,'ENTER GOR' READ *,GOR PRINT *,'ENTER SPECIFIC GRAVITY OF GAS' READ *,SGGAS PRINT *,'ENTER VISCOSITY OF GAS' READ *,VISGAS PRINT *,'ENTER WELLHEAD PRESSURE' READ *,P1 PRINT *,'ENTER PRESSURE INTERVAL' READ *,DELP PRINT *,'ENTER BOTTOMHOLE TEMPERATURE' READ *,BHT PRINT *,'ENTER BUBBLE POINT PRESSURE' READ *,PBUB PRINT *,'ASSUME A LIQUID FLOW RATE' READ *,QLIQ PRINT *,'ENTER INNER DIAMETER OF TUBING' READ *,DIA PRINT *,'ENTER TOTAL DEPTH' READ *,TD **********CALCULATION OF VF DATA ATVARIOUS PRESSURES***** T=BHT QWATER=QLIQ*WC QOIL=QLIQ-QWATER GLR=GOR/(1/(1-WC)) DENGAS=SGGAS*0.0763 DENF=350*WC*SGWAT+350*(1-WC)*SGOIL+GLR*DENGAS PRINT *,'FLUID DENSITY IS',DENF AVALUE=808.3141/DENF API=(141.5/SGOIL-131.5) P2=P1+DELP
- 116. 96 PAV=(P1+P2)/2+14.7 PPC=-17.292*SGGAS**2-17.852*SGGAS+688.4 TPC=1.8324*SGGAS**2+308.93*SGGAS+172.94 TPR=(T+460)/TPC PPR=PAV/PPC A=1.39*(TPR-0.92)**0.5-0.36*TPR-0.101 B=(0.62-0.23*TPR)*PPR+(0.066/(TPR-0.86)-0.037)*PPR**2 + +(0.32/10**(9*(TPR-1)))*PPR**6 C=(0.132-0.32*ALOG10(TPR)) D=10**(0.3106-0.49*TPR+0.1824*TPR**2) DO 10 I=2,26 P(I-1,1)=200+200*(I-2) P(I-1,2)=SGGAS*((P(I-1,1)/18)*(10**(0.0125*API)/10**(0.00091*T))) + **(1/0.83) IF (P(I-1,1).GE.PBUB) P(I-1,2)=GOR IF (P(I-1,1).LT.PBUB) THEN P(I-1,3)=0.972+0.000147*(P(I-1,2) + *(SGGAS/SGOIL)**0.5+1.25*T)**1.175 ELSE P(I-1,3)=(0.972+0.000147*(P(I-1,2)*(SGGAS/SGOIL)**0.5+1.25*T) + **1.175)*EXP(((-1433+5*P(I-1,2)+17.2*T-1180*SGGAS+12.61*API) + /(10**5*P(I-1,1))*(PBUB-P(I-1,1)))) END IF BE(I-1)=(0.62-0.23*TPR)*(P(I-1,1)/(-17.292*SGGAS**2-17.852*SGGAS + +688.4))+(0.066/(TPR-0.86)-0.037)*(P(I-1,1)/(-17.292*SGGAS + **2-17.852*SGGAS+688.4))**2+(0.32/10**(9*(TPR-1)))*(P(I-1,1) + /(-17.292*SGGAS**2-17.852*SGGAS+688.4))**6 IF (BE(I-1).LT.100) ZE(I-1)=A+(1-A)/EXP(BE(I-1))+C + *(P(I-1,1)/(-17.292*SGGAS**2-17.852*SGGAS+688.4))**D IF (BE(I-1).GT.100) ZE(I-1)=A+C*(P(I-1,1)/(-17.292*SGGAS + **2-17.852*SGGAS+688.4))**D

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