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- 1. 1 Production Optimization using nodal analysis Introduction 2Production Optimization - Introduction The nodal systems analysis approach is a very flexible method that can be used to improve the performance of many well systems. The nodal systems analysis approach may be used to analyze many producing oil and gas well problems. The procedure can be applied to both flowing and artificial Introduction
- 2. 2 3Production Optimization - Introduction The nodal systems analysis schematic model Introduction 4Production Optimization - Introduction To apply the systems analysis procedure to a well, it is necessary to be able to calculate the pressure drop that will occur in all the system components listed in Fig. 1-l. These pressure drops depend not only on flow rate, but on the size and other characteristics of the components. Unless accurate methods can be found to calculate these pressure drops, the systems analysis can produce erroneous results Introduction
- 3. 3 5Production Optimization - Introduction Kermit Brown, p. 88, Fig. 4.2 Pressure drop that will occur in all the system Introduction 6Production Optimization - Introduction The procedure consists of selecting a division point or node in the well and dividing the system at this point. The locations of the most commonly used nodes are shown in Fig. 1-2. Introduction
- 4. 4 7Production Optimization - Introduction Once the node is selected, the node pressure is calculated from both directions starting at the fixed pressures. Therefore, a plot of node pressure versus flow rate will produce two curves, the intersection of which will give the conditions satisfying requirements Introduction 8Production Optimization - Introduction 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 The procedure can be further illustrated by considering the simple producing system shown in Fig. 1-4 and selecting the wellhead as the node. Introduction
- 5. 5 9Production Optimization - Introduction The effect on the flow capacity of changing the tubing size is illustrated in Fig. 1-5, and the effect of a change in flowline size is shown in Fig. 1-6. Introduction 10Production Optimization - Introduction The effect of a change in tubing size on the total system producing capacity when pwf, is the node pressure is illustrated in Fig. 1-7. Introduction
- 6. 6 11Production Optimization - Introduction 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. This is illustrated in Fig. 1-8 for a system in which the tubing is too small. Introduction 12Production Optimization - Introduction A case in which the well performance is controlled by the inflow is shown in Fig. 1-9. In this case, the exces-sive pressure drop could be caused by formation damage or inadequate perforations. Introduction
- 7. 7 13Production Optimization - Introduction A qualitative example of selecting the optimum tubing size for a well that is producing both gas and liquids is shown in Fig. 1-10 and I-11. Introduction 14Production Optimization - Introduction an example of determining the optimum gas injection rate for a well on gas lift is illustrated in Fig. 1-12 and 1-13. Introduction
- 8. 8 15Production Optimization - Introduction a different inflow curve would exist for each perforating density. This is illustrated qualitatively in Fig. 1-14 and Fig. 1-15 Introduction 16Production Optimization - Introduction Introduction
- 9. 9 17Production Optimization - Introduction A suggested procedure for applying NODAL Analysis is given as follows : • Determine which components in the system can be changed. Changes are limited in some cases by previous decisions. For example, once a certain hole size is drilled, the casing size and, therefore, the tubing size is limited • Select one component to be optimized • Select the node location that will best emphasize the effect of the change in the selected component. This is not critical because the same overall result will be predicted regardless of the node location Introduction 18Production Optimization - Introduction • Develop expressions for the inflow and outflow. • Obtain required data to calculate pressure drop versus rate for all the components. This may require more data than is available, which may necessitate performing the analysis over possible ranges of conditions • Determine the effect of changing the characteristics of the selected component by plotting inflow versus outflow and reading the intersection. • Repeat the procedure for each component that is to be optimized. Introduction
- 10. 10 19Production Optimization - Introduction The nodal systems analysis approach may be used to : 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 re-strictions. 7. Artificial lift design. 8. Well stimulation evaluation. 9. Determining the effect of compression on gas well performance. 10.Analyzing effects of perforating density. 11.Predicting the effect of depletion on producing ca-pacity. 12.Allocating injection gas among gas lift wells. 13.Analyzing a multiwell producing system. 14.Relating field performance to time Introduction 20Production Optimization - Introduction End of slide
- 11. 1 Production Optimization using nodal analysis Predicting Current and Future IPR’s 2Production Optimization – Predicting IPR Reservoir Performance One of the most important components in the total well system is the reservoir. Unless accurate predictions can be made as to what will flow into the borehole from the reservoir, the performance of the system cannot be analyzed. The flow from the reservoir into the well has been called "inflow performance" by Gilbert' and a plot of producing rate versus bottomhole flowing pressure is called an "inflow performance relationship" or IPR.
- 12. 2 3Production Optimization – Predicting IPR WELL PERFORMANCE EQUATIONS To calculate the pressure drop occurring in a reservoir, an equation that expresses the energy or pressure losses due to viscous shear or friction forces as a function of velocity or flow rate is required. Although the form of the equation can be quite different for various types of fluids, the basic equation on which all of the various forms are based is Darcy's law. In 1856, while performing experiments for the design of sand filter beds for water purification, Henry Darcy proposed an equation relating apparent fluid velocity to pressure drop across the filter bed. Although the experiments were performed with flow only in the downward vertical direction, the expression is also valid for horizontal flow, which is of most interest in the petroleum industry. Darcy's Law Reservoir Performance 4Production Optimization – Predicting IPR Darcy's sand filters were of constant cross-sectional area, so the equation did not account for changes in velocity with location. Written in differential form, Darcy's law is: or in terms of volumetric flow rate q Reservoir Performance
- 13. 3 5Production Optimization – Predicting IPR Reservoir Performance 6Production Optimization – Predicting IPR I. Linear Flow For linear flow, that is for constant area flow, the equation may be integrated to give the pressure drop occurring over some length L: If it is assumed that k, µ and q are independent of pressure, or that they can be evaluated at the average pressure in the system, the equation becomes Reservoir Performance
- 14. 4 7Production Optimization – Predicting IPR Integration gives: where C is a unit conversion factor. The correct value for C is 1.0 for Darcy Units and 1.127 x 10-' for Field Units (See Table 2-1). Reservoir Performance 8Production Optimization – Predicting IPR Reservoir Performance
- 15. 5 9Production Optimization – Predicting IPR Reservoir Performance 10Production Optimization – Predicting IPR Oil flow Reservoir Performance
- 16. 6 11Production Optimization – Predicting IPR Gas flow Reservoir Performance 12Production Optimization – Predicting IPR Darcy's law can be used to calculate the flow into a well where the fluid is converging radially into a relatively small hole. Referring to the flow geometry illustrated in Figure 2-2, the cross-sectional area open to the flow at any radius is A = 2π r h. Radial Flow Reservoir Performance
- 17. 7 13Production Optimization – Predicting IPR Oil flow For field units, became : Reservoir Performance 14Production Optimization – Predicting IPR Gas flow For field units, became : Reservoir Performance
- 18. 8 15Production Optimization – Predicting IPR PREDICTING PRESENT TIME IPR'S FOR OIL WELLS The factors affecting the inflow performance for oil wells were discussed qualitatively in the previous section. If all of the variables in the inflow equations could be calculated, the equations resulting from integration of Darcy's law could be used to quantify the IPR. Unfortunately, sufficient information rarely exists to accomplish this and, therefore, empirical methods must be used to predict the inflow rate for a well Several of the most widely used empirical methods for predicting an IPR for a well are presented in this section. Most of these methods require at least one stabilized test on a well, and some require several tests in which pwf test and qtest were measured. Methods to account for the effects of drawdown only are first presented, that is, pR is assumed constant. Modification of the methods for depletion will then be discussed 16Production Optimization – Predicting IPR Vogel Method Vogel reported the results of a study in which he used a mathematical reservoir model to calculate the IPR for oil wells producing from saturated reservoirs. The study deal with several hypothetical reservoirs including those with widely differing oil characteristics, relative per-meability characteristics, well spacing and skin factors. The final equation for Vogel's method was based on calculations made for 21 reservoir conditions. Although the method was proposed for saturated, dissolved gasdrive reservoirs only, it has been found to apply for any reservoir in which gas saturation increases as pressure is decreased
- 19. 9 17Production Optimization – Predicting IPR Vogel's original method did not account for the effects of a non-zero skin factor, but a later modification by Standing extended the method for application to damaged or stimulated wells. The Vogel method was developed by using the reservoir model proposed by Weller' to generate IPR's for a wide range of conditions. He then replotted the IPR's as reduced or dimensionless pressure versus dimension-less flow rate. It was found that the general shape of the di-mensionless IPR was similar for all of the conditions studied. Examples of these plots from the original paper are illustrated in the next Figures Vogel Method 18Production Optimization – Predicting IPR Vogel’s dimensionless IPR Vogel Method
- 20. 10 19Production Optimization – Predicting IPR Vogel Method 20Production Optimization – Predicting IPR Vogel Method
- 21. 11 21Production Optimization – Predicting IPR Vogel arrived at the following relationship between dimensionless flow rate and dimensionless pressure : Vogel Method 22Production Optimization – Predicting IPR The dimensionless IPR for a well with a constant productivity index can be calculated from Vogel pointed out that in most applications of his method the error in the predicted inflow rate should be less than 10%, but could increase to 20% during the final stages of depletion Vogel Method
- 22. 12 23Production Optimization – Predicting IPR In the original paper by Vogel, only cases in which the reservoir was saturated were considered. The method can be applied to undersaturated reservoirs by applying Vogel's equation only for values of Pwf < Pb, Application of Vogel Method-Zero Skin Factor Vogel Method a. Saturated Reservoirs. b. Undersaturated Reservoirs. 24Production Optimization – Predicting IPR Application of Vogel Method- non Zero Skin Factor (Standing Modification) Vogel Method The method for generating an IPR presented by Vogel did not consider an absolute permeability change in the reservoir. Standing6 proposed a procedure to modify Vogel's method to account for either damage or stimulation around the wellbore. The degree of permeability alteration can be expressed in terms of a Productivity Ratio PR or Flow Efficiency FE, where:
- 23. 13 25Production Optimization – Predicting IPR Undersaturated Reservoirs with FE ≠ 1. Standing's modification of Vogel's method to be used when the flow efficiency is not equal to one may also be applied to undersaturated reservoirs. Vogel Method Application of Vogel Method- non Zero Skin Factor (Standing Modification) 26Production Optimization – Predicting IPR Fetkovich proposed a method for calculating the inflow performance for oil wells using the same type of equation that has been used for analyzing gas wells for many years. The procedure was verified by analyzing isochronal and flow-after-flow tests conducted in reservoirs with permeabilities ranging from 6 md to greater than 1000 md. Pressure conditions in the reservoirs ranged from highly undersaturated to saturated at initial pressure and to a partially depleted field with a gas saturation above the critical. In all cases, oil-well back-pressure curves were found to follow the same general form as that used to express the inflow relationship for a gas well. That is: Fetkovich Method
- 24. 14 27Production Optimization – Predicting IPR That is: Fetkovich Method 28Production Optimization – Predicting IPR The value of n ranged from 0.568 to 1.000 for the 40 field tests analyzed by Fetkovich. The applicability of Equation to oil well analysis was justified by writing Darcy's equation as: Fetkovich Method For an undersaturated reservoir, the integral is evaluated over two regions as:
- 25. 15 29Production Optimization – Predicting IPR Three types of tests are commonly used for gas-well testing to determine C and n. These tests can also be used for oil wells and will be described in this section. The type of test to choose depends on the stabilization time of the well, which is a function of the reservoir Fetkovich Method 1. Flow-After-Flow Testing A flow-after-flow test begins with the well shut in so that the pressure in the entire drainage area is equal to pR. The well is placed on production at a constant rate until the flowing wellbore pressure becomes constant. The test may also be conducted using a decreasing rate sequence. 30Production Optimization – Predicting IPR The idealized behavior of production rate and wellbore pressure with time is shown in Figure. Fetkovich Method
- 26. 16 31Production Optimization – Predicting IPR 2. Isochronal Testing If the time required for the well to stabilize on each choke size or producing rate is excessive, an isochronal or equal time test is preferred. The values of PR 2 - Pwf 2 determined at the specific time periods are plotted versus qo and n is obtained from the slope of the line. To determine a value for C, one test must be a stabilized test. The coefficient C is then calculated from the stabilized test. The idealized behavior of producing rate and pressure as a function of time is shown in Figure. Fetkovich Method 32Production Optimization – Predicting IPR Fetkovich Method
- 27. 17 33Production Optimization – Predicting IPR 3. Modified Isochronal Testing If the shut-in time required for the pressure to build back up to PR between flow periods is excessive, the isochronal test may be modified. The modification consists of shutting the well in between each flow period for a period of time equal to the producing time Fetkovich Method 34Production Optimization – Predicting IPR 1. Horizontal Wells IPR Construction for Special Cases The productivity index for a horizontal well in which permeability difference in the vertical and horizontal directions is small was described by Giger, et al as:
- 28. 18 35Production Optimization – Predicting IPR 2. Waterflood Wells It can be assumed that the IPR will be linear for values of pwf > pb. For pwf < pb, Vogel's equation may be used to account for the effect of gas saturation developing around the wellbore when pwf is below pb. IPR Construction for Special Cases 36Production Optimization – Predicting IPR PREDICTING FUTURE IPR's FOR OIL WELLS As the pressure in an oil reservoir declines from depletion, the ability of the reservoir to transport oil will also decline. This is caused from the decrease in the pressure function as relative permeability to oil is decreased due to increasing gas saturation. Standing Method Standing" published a procedure that can be used to predict the decline in the value of qo (max) as gas saturation in the reservoir increases from depletion.
- 29. 19 37Production Optimization – Predicting IPR PREDICTING FUTURE IPR's FOR OIL WELLS Once the value of qo (max) or J has been adjusted, future IPR's can be generated from 38Production Optimization – Predicting IPR PREDICTING FUTURE IPR's FOR OIL WELLS Fetkovich Method The method proposed by Fetkovich to construct future IPR's consists of adjusting the flow coefficient C in his Equation for changes in ƒ(PR). He assumed that f( PR) was a linear function of PR, and, therefore, the value of C can be adjusted as Future IPR's can thus be generated from
- 30. 20 39Production Optimization – Predicting IPR PREDICTING FUTURE IPR's FOR OIL WELLS Combining Vogel and Fetkovich The method proposed by Fetkovich for adjusting C can also be used to adjust qo(max) if a value for the exponent n is assumed. The expressions for qo(max)P and qo(max)F can be expressed using the Fetkovich equation as: If a value of n equal to one is assumed, then: 40Production Optimization – Predicting IPR PREDICTING PRESENT TIME IPR's FOR GAS WELLS Darcy's equation for radial gas flow including permeability alteration and turbulence may be expressed as follows:
- 31. 21 41Production Optimization – Predicting IPR PREDICTING PRESENT TIME IPR's FOR GAS WELLS This definition of B includes the assumption that re is much greater than rw. The effects of turbulence can also be accounted for by including an exponent in the pressure term of previous Equation. This results in the familiar back-pressure form of the equation. Use of the Back Pressure Equation 42Production Optimization – Predicting IPR Jones, Blount and Glaze Method The method of plotting test data, which was proposed by Jones, et al., can be applied to gas-well testing to determine real or present time inflow performance relationships. The analysis procedure allows determination of turbulence or non-Darcy effects on completion efficiency irrespective of skin effect and laminar flow. PREDICTING PRESENT TIME IPR's FOR GAS WELLS
- 32. 22 43Production Optimization – Predicting IPR PREDICTING PRESENT TIME IPR's FOR GAS WELLS 44Production Optimization – Predicting IPR Predicting Future IPR's for Gas Wells As reservoir pressure declines from depletion in a gas reservoir, the change in the IPR is not as significant as it is for an oil reservoir. If no changes are made in re S or h, the values of C, or A and B can be adjusted for reservoir pressure changes as follows: where the subscript P refers to present or real time and the subscript F refers to some future time.
- 33. 23 45Production Optimization – Predicting IPR END OF SLIDE
- 34. 1 Production Optimization using nodal analysis Inflow and Outflow Performance Curve 2Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Tujuan: Menggabungkan kinerja dari berbagai komponen sumur minyak dan gas dalam sistem produksi untuk menentukan laju produksi dan menentukan suatu sistem produksi yang optimal. Sistem Produksi: Dalam pendekatan analisa nodal ini, sistem produksi meliputi reservoir (aliran dari reservoir ke sandface), perforasi, gravel pack, screen, tubing, downhole safety valves, choke, pipa permukaan dan separator.
- 35. 2 3Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Skema Sistem Produksi Kermit Brown, p. 88, Fig. 4.2 4Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Posisi “Node” dalam Analisa Nodal Kermit Brown, p. 88, Fig. 4.3
- 36. 3 5Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Dasar Sumur Posisi “node” di dasar sumur adalah yang paling umum digunakan dalam analysis nodal. Sistem dibagi menjadi dua bagian, reservoir dan sistem pipa (sumur dan permukaan). Kermit Brown, p. 89, Fig. 4.4 6Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Dasar Sumur (Lanjutan) Bagian reservoir dalam hal ini meliputi aliran fluida dari reservoir ke sand-face, aliran melalui perforasi, gravel pack dan screen.
- 37. 4 7Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Dasar Sumur (Lanjutan) Sistem pipa dalam hal ini meliputi aliran fluida dari dasar sumur ke wellhead (melalui tubing string dan downhole valves) atau ke separator (melalui pipa permukaan dan chokes). 8Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Dasar Sumur (Lanjutan) Kinerja dari setiap sistem dievaluasi pada “node” yang sama dalam bentuk hubungan antara tekanan pada “node” dan laju alir. Untuk “node” di dasar sumur, hubungannya adalah antara tekanan alir dasar sumur (pwf) dan laju alir (q). Konsep dari analisa nodal ini adalah pada “node”, yang merupakan titik temu antara dua atau lebih sistem yang berbeda, kinerja dari sistem yang bertemu di “node” itu haruslah sama. Kinerja reservoir dalam bentuk hubungan antara tekanan dan laju alir disebut dengan “Inflow Performance Relationship” (IPR). Sedangkan kinerja sistem pipa disebut “Outflow Pressures”. Satu kurva IPR dibuat pada satu harga tekanan reservoir rata-rata.
- 38. 5 9Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Dasar Sumur (Lanjutan) Kermit Brown, p. 91, Fig. 4.9a 10Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Dasar Sumur (Lanjutan) Pemilihan “node” di dasar sumur digunakan untuk melihat pengaruh dari penurunan tekanan reservoir terhadap laju produksi. Hal ini berguna dalam peramalan produksi.
- 39. 6 11Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Wellhead Sistem dibagi menjadi dua bagian, reservoir+tubing strings dan flowline+separator. 12Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Wellhead (Lanjutan) Flowline dan separator. Kermit Brown, p. 92, Fig. 4.13
- 40. 7 13Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Wellhead (Lanjutan) Reservoir dan tubing strings. 14Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Wellhead (Lanjutan) Untuk berbagai laju produksi, dihitung tekanan wellhead yang diperlukan untuk mengalirkan fluida dari wellhead ke separator. Dari langkah ini kita mendapatkan “node” tekanan outlow. Menggunakan laju produksi yang sama, dengan tekanan reservoir rata- rata yang tertentu hitung tekanan alir dasar sumur, kemudian tentukan tekanan di wellhead dengan mengurangi tekan alir dasar sumur dengan kehilangan tekanan di tubing strings. Prosedur ini menghasilkan “node” tekanan inflow. Laju produksi untuk kombinasi dua sistem tersebut diperoleh dari perpotongan dua kurva tekanan outflow dan inflow.
- 41. 8 15Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Wellhead (Lanjutan) Kermit Brown, p. 93, Fig. 4.15b 16Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Wellhead (Lanjutan) Kermit Brown, p. 94, Fig. 4.16 Pemilihan “node” di wellhead adalah untuk mengetahui pengaruh dari perubahan flowline terhadap produksi.
- 42. 9 17Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Separator Kermit Brown, p. 96, Fig. 4.22 18Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Separator (Lanjutan) Kermit Brown, p. 96, Fig. 4.23
- 43. 10 19Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Separator (Lanjutan) Kermit Brown, p. 96, Fig. 4.24 20Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Separator (Lanjutan) Sumur A memperlihatkan bahwa peningkatan produksi akan terjadi cukup besar apabila tekanan separatornya rendah. Tetapi sumur D menunjukkan tidak ada perubahan produksi yang cukup berarti dengan perubahan tekanan separator.
- 44. 11 21Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Reservoir Kermit Brown, p. 98, Fig. 4.26 22Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve Analisa Nodal di Reservoir (Lanjutan)
- 45. 12 23Production Optimization – Inflow and outflow Performance curve Inflow and Outflow Performance Curve END OF SLIDE

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