SPE 52171 A Comparison of Two-Phase Inflow Performance Relationships Frederic Gallice, SPE, and Michael L. Wiggins, SPE, U. of Oklahoma

Copyright 1999, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the 1999 SPE Mid-Continent Operations Symposium held in Oklahoma City, Oklahoma, 28–31 March 1999. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

Abstract Petroleum engineers are routinely required to predict the pressure-production behavior of individual oil wells. These estimates of well performance assist the engineer in evaluating various operating conditions, determining the optimum production scheme, and designing production equipment and artificial lift systems. In this paper, commonly used empirical inflow performance relationships for estimating the pressureproduction behavior during two-phase flow are investigated. Relationships studied include those proposed by Vogel, Fetkovich, Jones, Blount and Glaze, Klins and Majcher, and Sukarno. Each method will be briefly described and methods used to develop the relationship will be discussed. Based on actual vertical well data, the relationships are used to predict performance for twenty-six cases. The predicted performance is then compared to actual measured rate and pressure data. The variation between the predicted and measured data are analyzed. From this analysis, recommendations are made on the use of inflow performance relationships to predict performance, collection of data, and the quality of performance estimates. Introduction When considering the performance of oil wells, it is often assumed that production rates are proportional to pressure drawdown. This straight-line relationship can be derived from Darcy’s law for steady-state flow of a single, incompressible fluid and is called the productivity index (PI). Evinger and Muskat1 were some of the earliest investigators to look at oilwell performance. They pointed out that a straight-line relationship should not be expected when

two phases are flowing in the reservoir. They presented evidence based on the multiphase flow equations that a curved relationship existed between flow rate and pressure. This work led to the development of several empirical inflow performance relationships (IPRs) to predict the pressure-production behavior of oil wells producing under two-phase flow conditions. These estimates assist the engineer in evaluating various operating conditions, determining the optimum production scheme, and designing production equipment and artificial lift systems. This paper reviews and compares five IPRs proposed in the literature for predicting individual well performance in solution-gas drive reservoirs. The IPRs studied includes those of Vogel,2 Fetkovich,3 Jones, Blount and Glaze,4 Klins and Majcher,5 and Sukarno.6 Using data from 26 field cases, each method is used to predict the pressure-production behavior for the individual cases. The predictions are compared to actual well performance and to predictions of the other methods to develop an understanding of their reliability. Deliverability Methods One of the earliest IPRs was developed by Vogel2 based upon simulation data for twenty-one reservoir data sets representing a wide range of reservoir rock and fluid properties. Vogel noticed the shape of the pressure-production curves for these cases were very similar. He made the curves dimensionless by dividing the pressure at each point by the reservoir pressure and the flow rate by the maximum flow rate to obtain the dimensionless inflow performance curve. He observed that all the points fell within a narrow range and developed a relationship to describe the dimensionless behavior. Vogel’s IPR is qo q o ,max

2

p wf p wf = 1 − 0.2 − 0.8 .............................. (1) pr pr

Fetkovich3 proposed the isochronal testing of oil wells to estimate their productivity. This relationship is based upon the empirical gas well deliverability equation proposed by Rawlins and Schellhardt.7 Using data from multirate tests on forty different oil wells in six different fields, Fetkovich showed the

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FREDERIC GALLICE AND MICHAEL L. WIGGINS

approach was suitable for predicting performance. His relationship is

(

2 q o = C pr2 − pwf

)

n

.........................................................(2)

which can be expressed in a form similar to Vogel’s IPR as follows. n

qo q o ,max

p 2 wf = 1 − .................................................(3) pr

Using Forchheimer’s8 model to describe non-Darcy flow, Jones, Blount and Glaze4 proposed the following relationship between pressure and rate. pr − pwf qo

= C + Dq o ......................................................(4)

From this equation it is evident that a cartesian plot of the ratio of the pressure difference to the flow rate versus the flow rate yields a straight line with a slope D and an intercept C. The term C represents the laminar flow coefficient and D is the turbulence coefficient. This method requires a multipoint test in order to determine these coefficients. Once estimated, the flow rate at any flowing pressure can be determined from the following relationship. qo =

− C + C 2 + 4 D( pr − pwf ) 2D

...................................(5)

Based on Vogel’s work, Klins and Majcher5 developed an IPR incorporating the bubble point pressure. The authors simulated twenty-one wells using Vogel’s data and developed 1,344 IPR curves. Using non-linear regression analysis, they presented the following IPR. qo q o ,max

d

p wf p wf = 1 − 0.295 − 0.705 .......................(6) pr pr

where p d = 0.28 + 0.72 r (1.235 + 0.001 pb ) ...........................(7) pb Sukarno6 developed an IPR based on simulation results that attempts to account for the variation of the flow efficiency due to the rate dependent skin as the flowing bottomhole pressure changes. Sukarno developed the following relationship using non-linear regression analysis. 2 3 pwf pwf pwf = FE1 − 01489 . . . − 04418 − 04093 qo,[email protected]=0 pr pr pr

qo,actual

.........................................................................................(8)

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where 2

3

p wf p wf p wf FE = a 0 + a 1 + a2 + a3 ............ (9) pr pr pr and a n = b0 + b1s + b2 s 2 + b3s 3 .......................................... (10) In Eq. 10, s is the skin factor and a and b are fitting coefficients shown in Table 1. IPR Comparison To compare the various IPRs, data from twenty-six cases presented in the literature are analyzed. Each case utilizes actual field data representing different producing conditions. Data from each case is used to select rate and pressure information as test points and these points are used to predict well performance by each IPR method. The predictions are then compared to actual measured production data at drawdowns greater than the test data. Several cases will be used to demonstrate the analysis and provide insight into the behavior of the various predictive models. Complete details of the analysis are presented in Ref. 9 while the cases analyzed are summarized in Table 2. Case 1. Millikan and Sidewell10 presented multirate test data for a well producing from the Hunton Lime in the Carry City Field of Oklahoma. The test was made over a period of about two weeks with the well produced at random rates rather than in an increasing or decreasing rate sequence. The average reservoir pressure was 1600 psi with an estimated bubble point pressure of 2530 psi and an assumed skin value of zero. The field data is summarized in Table 3. Table 4 presents the performance predictions for test information at a flowing bottomhole pressure of 1267 psi, representing a 21% pressure drawdown. As can be seen, the maximum well deliverability varies from 2562 to 3706 STB/D. The largest flow rate was calculated with Vogel’s IPR while the smallest rate was obtained using Fetkovich’s method. Fig. 1 shows the various IPR curves. Visual inspection indicates that the methods of Fetkovich and Jones, Blount and Glaze do a very good job of estimating the actual well performance. The other methods capture the general shape of the data but overestimate actual performance. If the straightline productivity index is used in this case, a maximum flow rate of 6054 STB/D would have been predicted from the test point. This estimate is over 60% greater than the highest predicted rate by the IPR methods. This shows the importance of using a multiphase flow relationship to evaluate well performance under these conditions. Table 5 shows the percent difference between the recorded flow rate data and the computed rate for the five IPR methods. The multirate methods have differences less than 10%. The average absolute difference for Fetkovich’s method is 4% while Jones, Blount and Glaze is 7%. The single point methods have an absolute average difference ranging from

SPE 52171

A COMPARISON OF TWO-PHASE INFLOW PERFORMANCE RELATIONSHIPS

18% to 31% for Klins and Majcher and Vogel, respectively. In general the difference tends to increase with increasing drawdown. This increased difference in predicted performance versus actual performance is expected. Since each IPR is actually used to extrapolate performance behavior at drawdowns greater than the test point, one would expect these estimates to increase in error as one moves further away from the known data point. As the test data covers a wide range of pressure drawdowns, it allows an investigation of the effect of drawdown on performance estimates. Table 6 presents a summary of the average absolute differences for each method based on drawdown percentages (9%, 21%, 38%, 50% and 78%) of the test point. As shown, the average absolute difference in the performance predictions decrease as the test point drawdown percentage increases for all the methods. For example, Vogel’s method predicted a maximum flow rate of 5108 STB/D at a 9% pressure drawdown compared to 2564 STB/D at a drawdown of 78%. This is almost a 100% reduction in the maximum well deliverability. In addition, the average difference in the performance estimates decrease from 72% at a 9% drawdown to 1.7 % at a 78% drawdown. All the methods show a similar decrease in the average absolute differences in the predicted performance. By increasing the pressure drawdown of the test point from 9% to 21%, the average absolute differences were decreased by over 100% for each method. For this particular case, a 20% pressure drawdown appears sufficient to predict the well performance. This is consistent with the observations of Wiggins11 who, based on analysis of simulation results, recommended that a minimum of pressure drawdown of 20% be used for all well testing utilized in predicting oilwell performance. In summary, Fetkovich’s relation provided the best estimates of well performance over the entire range of interest for this case. In general, the average absolute difference in performance predictions increased as the pressure drawdown increased from the test pressure. Also, the difference in the predictions decreased as the test pressure drawdown increased. Cases 2 and 3. The next cases represent one well located in the Keokuk Pool in Seminole County, Oklahoma where test data were collected eight months apart at two different reservoir pressures. The reservoir pressure decreased from 1734 psi to 1609 psi or 7% between tests. These cases were selected to demonstrate the effect of depletion on the IPR methods. Due to limited test data, performance predictions were made from test information at pressure drawdowns of 13% and 12% for reservoir pressures of 1734 psi and 1609 psi, respectively. The various methods provide a range of performance estimates as anticipated for both reservoir pressure. Table 7 summarizes the absolute differences in the IPR estimates. For the first case, there was little in the estimates to distinguish the multipoint methods from the single

3

methods. However, the second case shows a definite difference between the multipoint methods and the single point methods. This example tends to indicate that the reliability of the various performance methods may change during the life of a well. In addition, the multipoint methods appear to provide better estimates of well performance. Summary. The additional cases and their analysis are presented in detail in Ref. 9. Table 8 presents a summary of the average absolute difference for each method for all the cases examined. As indicated in this table, not one method always provided the most reliable estimates of the actual well data analyzed. However, some general comments can be made based on this table and all the cases analyzed in this study. The multipoint methods of Fetkovich and Jones, Blount and Glaze tend to do a better job of predicting well performance than the single point methods. As a matter of fact, the total average absolute difference is almost twice as great for the single point methods in comparison to Fetkovich’s multipoint method, 15% compared to 8%. The method of Jones, Blount and Glaze had an average difference of 12%. Overall, the single point methods of Vogel, Klins and Majacher, and Sukarno provided similar average differences in the cases examined, 14 to 15%. Case 5 demonstrates the variation in the predicted performance. In this case, Fetkovich’s method did the poorest of estimating actual performance while Vogel’s IPR did the best. This case clearly shows that one cannot rely on one IPR method to make reliable performance predictions in all reservoirs. Case 9 provides another anomaly in this analysis. Each of the methods provide very similar estimates except for Jones, Blount and Glaze. In this case, Vogel’s method provides a somewhat better estimate than Fetkovich. However, the multipoint method of Jones, Blount and Glaze predicted rates that are significantly different than actual performance. For this case, this method estimated performance with an average absolute difference of 58% compared to 16 to 18% for the other methods. As a final note, the available data or costs of obtaining data will influence the selection of an IPR method to predict performance. Overall, multipoint methods will provide more information but will cost more in obtaining the data. Single point methods are simply to apply if a single production test point is available. In the end, the benefit of the data must be carefully considered related to the expense of obtaining the information. Conclusions In this study, five different methods to predict the pressureproduction performance of oil wells producing from solutiongas drive reservoirs have been presented. These are the methods of Vogel, Fetkovich, Jones, Blount and Glaze, Klins and Majcher, and Sukarno. Each method requires parameters that are normally available from a production test. The

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FREDERIC GALLICE AND MICHAEL L. WIGGINS

methods can be separated into multipoint methods and single point methods. The primary concern in this study was to evaluate the reliability of the IPR methods based on actual production test data. Detailed analysis and comparisons for 26 different cases were performed. From this study the following conclusions are presented. 1. There is no one method which is the most suitable for every test. It has been observed that in one case method A will provide the most reliable estimates while providing the worst estimates in the next case. From this observation, consideration should be given to using more than one method in predicting performance in order to provide a range of possible outcomes. 2. Overall, Fetkovich’s multipoint method tended to be the most reliable. It has been shown based on the test data of this study that the overall absolute difference for Fetkovich’s method was less than the other methods. Also, Fetkovich’s method provided steady performance predictions throughout the pressure drawdown range while the single point methods appeared to be more sensitive to the drawdown pressure of the test point. 3. The selection of a drawdown pressure for testing purposes is an important parameter related to the reliability of the IPR methods. It appears that a minimum drawdown pressure of 20% of the average reservoir pressure is required to obtain reliable estimates of well performance for any of the IPR methods. In general, it is recommended that one obtain test information as near to operating conditions as possible. 4. Due to the effects of depletion, one IPR method may be more reliable at one reservoir pressure but not at the second pressure. This may be caused by changes in reservoir parameters with time which can lead to changes in its flow properties. Once again this suggests the use of multiple IPR methods to estimate well performance. Nomenclature a = fitting parameter defined in Eq. 10 b = constant in Eq. 10 C = deliverability coefficient in Eq. 2, STB/D/psi2n C = laminar flow coefficient in Eq. 4, psi/STB/D D = turbulence coefficient in Eq. 4, psi/(STB/D)2 FE = defined in Eq. 9 d = flow exponent defined in Eq. 7 n = flow exponent in Eq. 2 pb = bubble point pressure, psi pr = reservoir pressure, psi pwf = flowing bottomhole pressure, psi qo = oil flow rate, STB/D qo,max = maximum oil flow rate, STB/D s = skin factor References 1. Evinger, H.H. and Muskat, M.: “Calculation of Theoretical Productivity Factors,” Trans.,AIME (1942) 146, 126-139. 2. Vogel, J.V.: “Inflow Performance Relationships for SolutionGas Drive Wells,” JPT (Jan. 1968) 83-92.

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3. Fetkovich, M.J.: “The Isochronal Testing of Oil Wells,” paper SPE 4529 presented at the 1973 SPE Annual Meeting, Las Vegas, NV, Sept. 30-Oct. 3. 4. Jones, L.G., Blount, E.M. and Glaze, O.H.: “Use of Short Term Multiple Rate Flow Tests to Predict Performance of Wells Having Turbulence,” paper SPE 6133 presented at the 1976 SPE Annual Technical Meeting and Exhibition, New Orleans, Oct. 3-6. 5. Klins, M.A. and Majcher, M.W.: “Inflow Performance Relationships for Damaged or Improved Wells Producing Under Solution-Gas Drive,” JPT (Dec. 1992) 1357-1363. 6. Sukarno, P. and Wisnogroho, A.: “Genaralized Two-Phase IPR Curve Equation Under Influence of Non-linear Flow Efficiency,” Proc. of the Soc. of Indonesian Petroleum Engineers Production Optimization International Symposium, Bandung, Indonesia, July 24-26, 1995, 31-43. 7. Rawlins, E.L. and Schellhardt, M.A.: Backpressure Data on Natural Gas Wells and Their Application to Production Practices, USBM (1935) 7. 8. Forchheimer, Ph.D.: Ziets V. deutsch Ing., (1901) 45, 1782. 9. Gallice, F.: “A Comparison of Two-Phase Inflow Performance Relationships,” MS thesis, U. of Oklahoma, Norman, OK (1997). 10. Millikan, C.V. and Sidewell, C.V.: “Bottom-Hole Pressures in Oil Wells”, Trans, AIME (1931), 194-205. 11. Wiggins, M.L.: “Inflow Performance of Oil Wells Producing Water,” PhD dissertation, Texas A&M U., College Station, TX (1991). 12. Haider, M.L.: “Productivity Index,” API Drilling and Production Practice (1936) 181-190. 13. Sukarno, P.: “Application of the New IPR Curve Equations in Sangatta and Tanjung Miring Timur Fields,” Proc., Indonesian Petroleum Association Sixteenth Annual Convention, Oct. 1987. 14. Walls, W.S.: “Practical Methods of Determining Productivity in Reservoirs on Leases by Bottomhole Pressure and Core Analysis, API Drilling and Production Practice (1938) 146-161. 15. Kemler, E. and Poole, G.A.: “A Preliminary Investigation of Flowing Wells,” API Drilling and Production Practice (1936) 140-157.

Table 1 - Constants for Sukarno’s IPR a0 a1 a2 a3

b0 1.03940 0.01668 -0.08580 0.00952

b2 0.12657 -0.00385 0.00201 -0.00391

b2 0.01350 0.00217 -0.00456 0.00190

b3 -0.00062 -0.00010 0.00020 -0.00001

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A COMPARISON OF TWO-PHASE INFLOW PERFORMANCE RELATIONSHIPS

Table 2 - Field Cases Analyzed Test Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Well Identification Carry City Field, OK Well A, Keokuk Field, OK, December Well A, Keokuk Field, OK, August Well B, Keokuk Field, OK, December Well B, Keokuk Field, OK, August Well C, Lucien Field, OK Well D, Lucien Field, OK Well E, Lucien Field, OK Well F, South Burbank Field, OK Well G, South Burbank Field, OK Well H, South Burbank Field, OK Well 6, Field A Well 3, Field A Well 3-c, Field C Well 14, Field A Well 5, Field D Well 6, Field D Well 1, Field E Well TMT-27, Miring Timur Field, Indonesia Well 1, Field F Well 2, Field F Well A Well 8, West Texas Area Well 2-b, Field C Well 4, Field C Well 4, Field D

Reference 11 12 12 12 12 12 12 12 12 12 12 3 3 3 3 3 3 3 13 3 3 14 15 3 3 3

Table 3 - Well Test Information for Carry City Well pr = 1600 psi pwf, psi 1600 1558 1497 1476 1470 1342 1267 1194 1066 996 867 787 534 351 183 166

pb = 2530 psi (est) Test Data

s = 0 (assumed) qo, STB/D 0 235 565 610 720 1045 1260 1470 1625 1765 1895 1965 2260 2353 2435 2450

5

Table 4 - Performance Predictions for Case 1 at 21% Pressure Drawdown Field Data pwf psi 1194 1066 996 867 787 534 351 183 166 0

Vogel

qo STB/D 1470 1625 1765 1895 1965 2260 2353 2435 2450 -

1502 1896 2096 2434 2624 3129 3401 3583 3597 3706

Fetkovic h

1426 1680 1800 1995 2099 2353 2472 2538 2542 2562

Jones

Klins

Sukarno

qo STB/D 1260 1468 1571 1747 1848 2140 2330 2492 2508 2658

1480 1823 1989 2256 2399 2753 2933 3060 3071 3172

1489 1852 2029 2320 2477 2867 3058 3174 3183 3248

Table 5 - Percent Difference in Predictions for Case 1 at 21% Pressure Drawdown Field Data pwf psi 1194 1066 996 867 787 534 351 183 166

Vogel

qo STB/D 1470 1625 1765 1895 1965 2260 2353 2435 2450

Average Absolute Difference

Fetkovic h

Jones

Klins

Sukarno

Difference, % 2 17 19 28 34 38 45 47 47

-3 3 2 5 7 4 5 4 4

-14 -10 -11 -8 -6 -5 -1 2 2

1 12 13 19 22 22 25 26 25

1 14 15 22 26 27 30 30 30

31%

4%

7%

18%

22%

Table 6 - Comparison of Pressure Drawdown Affects on Performance Predictions for Case 1 Pressure Drawdown

Vogel

9 21 38 50 78

72% 31% 18% 8% 2%

Fetkovic Jones Klins h Average Absolute Difference 58% 64% 52% 4% 7% 18% 3% 32% 9% 3% 3% 2% 1% 8% 1%

Sukarno

58% 22% 11% 3% 1%

Table 7 - Comparison of Depletion Affects on Performance Estimates for Cases 2 and 3 Vogel Time December August

15% 17%

Fetkovic Jones Klins h Average Absolute Difference 6% 6% 7% 6% 10% 13%

Sukarno

11% 15%

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FREDERIC GALLICE AND MICHAEL L. WIGGINS

Table 8 - Summary of Performance Predictions for All Cases Vogel Test Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

31 15 17 9 4 5 18 14 16 17 12 11 17 13 0 38 19 8 3 51 27 20 2 13 17 5

Average

15%

Fetkovic Jones h Average Absolute Difference, % 4 7 6 6 6 10 10 10 21 5 20 5 9 31 2 21 17 58 10 35 11 14 11 21 3 2 2 4 3 0 15 15 6 13 18 22 1 0 4 15 9 13 2 1 5 2 4 7 3 5 11 2 8%

12%

1600 1400 Flowing Bottomhole Pressure, psi

Test Point 1200

Klins

Sukarno

18 7 13 11 9 12 24 18 16 17 12 13 15 7 3 33 16 13 1 40 21 17 4 2 13 2

22 11 15 10 6 8 20 16 18 19 14 13 12 12 3 38 18 9 1 50 26 19 5 11 17 5

14%

15%

Field Vogel Fetkovich n=1 Jones Klins Sukarno Fetkovich

1000 800 600 400 200 0 0

500

1000 1500 2000 2500 3000 3500 4000 Flow Rate, STB/D

Fig. 1 - Predicted inflow performance curves compared to actual field data for Case 1.

SPE 52171

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