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Perforation inflow reduces frictional pressure loss in horizontal wellbores
Journal of Petroleum Science and Engineering 19 Ž1998. 223–232
Perforation inflow reduces frictional pressure loss in horizontal wellbores Z. Su b
a,1
, J.S. Gudmundsson
b,)
a Imperial Petroleum Consultants AS, P.O. Box 624, 4001 StaÕanger, Norway Department of Petroleum Engineering and Applied Geophysics, Norwegian UniÕersity of Science and Technology, 7034 Trondheim, Norway
Received 24 July 1996; revised 19 August 1997; accepted 19 August 1997
Abstract The total pressure drop in horizontal wellbores has been analyzed in terms of four separate effects: wall friction, flow acceleration, perforation roughness, and fluid mixing. Laboratory experiments have been carried out in test pipes that are geometrically similar to perforated liners used in horizontal wells to investigate different pressure drop effects in a horizontal wellbore. It was demonstrated that the perforation inflow actually reduced the total pressure drop. Results indicated that the pressure drop due to perforation roughness was eliminated by the perforation inflow when the ratio of perforation flow to pipe flow rate reached a certain limit. Beyond this limit, the perforation inflow lubricated the wellbore flow. Such smoothing effect in the perforated section of the wellbore extended into the blank section downstream. It has been shown that different pressure drop effects can be conveniently represented by using a pressure loss coefficient. q 1998 Elsevier Science B.V. Keywords: horizontal well; perforation inflow; pressure drop; friction; mixing effect
1. Introduction Use of horizontal wells is an established practice in the petroleum industry. Horizontal well productivity can be limited by the pressure drop within the wellbore, especially when the pressure drop is comparable with the reservoir drawdown. Because more and longer horizontal wells are being drilled around the world, a better understanding of the factors affecting the total pressure drop within the wellbore is ) Corresponding author. Tel.: q47-73-594952. Fax: q47-73944472. E-mail: [email protected] 1 Tel.: q47-51-414090. E-mail: [email protected]
required. Increased knowledge of different pressure drop effects in horizontal wellbores is crucial in designing successful horizontal wells and optimizing well performance. The great majority of published papers dealing with performance of horizontal wells consider only the wall friction part of the total pressure drop ŽDikken, 1990; Collins et al., 1991; Folefac et al., 1991; Landman and Goldthorpe, 1991; Ihara et al., 1992; Ozkan et al., 1993.. The reality is that flow velocity increases as reservoir fluid continually enters the wellbore through perforations along a perforated wellbore. The increase of flow velocity, and therefore momentum, contributes to the pressure drop
0920-4105r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 9 2 0 - 4 1 0 5 Ž 9 7 . 0 0 0 4 7 - 8
224
Z. Su, J.S. Gudmundssonr Journal of Petroleum Science and Engineering 19 (1998) 223–232
in addition to the frictional pressure drop. This part of the pressure drop has been addressed by several authors in recent years ŽAsheim et al., 1992; Ihara and Shimizu, 1993; Marett and Landman, 1993; Sarica et al., 1994.. Moreover, perforation holes act like roughness elements and increase the friction factor of the wellbore. This part of the pressure drop has been studied by Su and Gudmundsson Ž1993.. The pressure gradient along the perforated wellbore is also affected by the mixing between wellbore flow and perforation flow. How the interaction between the perforation flow and the wellbore flow affects the pressure gradient inside the horizontal wellbore has not been thoroughly investigated in petroleum production engineering. The work presented in this paper concerns pressure drop experiments carried out in uniformly perforated pipes that are geometrically similar to perforated liners used in horizontal wells. The objective is to determine experimentally the various factors that contribute to the total pressure drop in perforated pipes. In addition, pressure profiles along a blank section downstream of a perforated section were also measured, and friction factors calculated using the measured pressure drop. The effect of the perforation flow on a blank section downstream of a perforated section has been analyzed by comparing the friction factors in the blank section with those before the pipe was perforated. More details of this work have been published by Gudmundsson and Su Ž1995. and Su Ž1996..
It is convenient to combine the last two terms in this equation into one term D padd., which is the pressure drop due to the combined effects of fluid mixing and perforation roughness. Eq. Ž1. can then be written as D p s D pwall q D pacc .q D padd ..
Ž 2.
The whole length of a uniformly perforated horizontal well can be divided into perforation units of equal length, with each unit containing one perforation at the upstream end of the unit as shown in Fig. 1. Applying the conservation of linear momentum to the control volume abcd in the axial direction, as shown in Fig. 1, and assuming all the flow is one dimensional, steady, and incompressible, results in the sum of the forces acting on the control volume surfaces toward the downstream direction of the pipe axis
Ý F s m˙ 2 u 2 y m˙ 1 u1 ,
2. Pressure drop in perforated wellbores
Ž 3.
where the mass flow rate is
The total pressure drop in a perforated horizontal wellbore can be divided into a reversible pressure drop and an irreversible pressure drop. The reversible pressure drop is that due to momentum change Žflow acceleration. as more fluid enters the wellbore through perforations. The irreversible pressure drop is that due to pipe wall friction, perforation friction, and mixing effects. The following relationship gives the four pressure drop terms that make up the total pressure drop in a perforated horizontal well D p s D pwall q D pacc .q D pperf .q D pmix .
Fig. 1. Perforation unit Žnot to scale..
Ž 1.
m ˙ s r Au.
Ž 4.
It should be noted here that across any pipe cross section, and especially the cross section at the entrance of the perforation unit, the static pressure is not uniform, and that the velocity profile is not fully developed due to the perforation flow. Therefore, in addition to the force contributed by the pressure difference across the control volume and wall shear force, the sum of the forces acting on the control volume surface includes a force due to the combined effects of the irreversible process of fluid mixing and the presence of the perforation hole, including the
Z. Su, J.S. Gudmundssonr Journal of Petroleum Science and Engineering 19 (1998) 223–232
effect of non-uniformly distribution of static pressure and non-fully developed velocity profile,
Ý F s Ž p1 A y p 2 A . y tw Ž p DD L . y Fadd ..
Ž 5.
The wall shear force results in wall frictional pressure drop
tw Ž p DD L . s D pwall A,
Ž 6.
and the additional force Fadd. results in an additional pressure drop
It is clear that smaller pressure drop due to momentum change can be achieved, for the same production rate, by using a larger diameter wellbore. The inflow profile along the wellbore has no influence on this part of the pressure drop. The pressure drop due to pipe wall friction in a perforation unit, D pwall , is based on the average velocity u 2 downstream of the perforation, and can be calculated from the Darcy–Weisbach equation ŽWhite, 1986. D pwall s
Fadd .s D padd . A.
Ž 7.
Combining Eqs. Ž3., Ž5. – Ž7. yields m ˙ 2 u 2 y m˙ 1 u1 s Ž p1 y p 2 . A y D pwall A y D padd . A Ž 8. Substituting Eq. Ž4. into Eq. Ž8. yields p 1 y p 2 s r Ž u 22 y u12 . q D pwall q D padd ..
Ž 9.
The pressure drop due to momentum change, D pacc., can be represented as D pacc .s r Ž u 22 y u12 . ,
Ž 10 .
by comparing Eq. Ž9. with Eq. Ž2.. For a horizontal well containing N perforations, the pressure drop due to momentum increase is the sum of pressure drop in each perforation unit N
D pacc .s
Ý r Ž u 2nq1 y u 2n . s r Ž u 2Nq1 y u12 . . Ž 11. ns1
The total reversible pressure drop due to momentum change in a horizontal well is, therefore, an exclusive factor of the fluid density and mean flow velocities at the toe- and heel-ends of the well. When no fluid enters the wellbore at the toe-end, u1 equals zero, and the pressure drop due to momentum change is related only to the average flow velocity at the heel-end of the well, which can be calculated from the well production rate as D pacc .s r u 2Nq1 s r
Q
ž / A
2
.
Ž 12 .
225
f DL 2 D
r u 22 .
Ž 13 .
This equation applies to both laminar and turbulent flow. The pressure drop due to perforation roughness, D pperf., is the extra pressure drop due to the presence of the perforations. It represents the extra friction caused by the perforations acting as roughness elements in the pipe wall. The pressure drop due to perforation roughness is most important when there is no flow through the perforations. It has been shown that the magnitude of the pressure drop due to perforation roughness depends on the pipe-perforation geometry and the perforation density ŽSu and Gudmundsson, 1993.. The pressure drop due to mixing effects, D pmix , is an irreversible pressure drop that cannot be further classified. This pressure effect arises from the complex interaction between perforation flow and wellbore flow, which causes disturbances in the boundary layer and hence affects the pressure drop. The irreversible pressure drop due to mixing needs to be determined by experiments.
3. Experiments Experiments were carried out to determine the additional pressure drop, D padd., due to the combined effect of flow mixing and perforation roughness. A special test section was built into a horizontal flow loop. A schematic diagram of the flow loop is shown in Fig. 2 and a diagram of the test section is illustrated in Fig. 3. The experimental apparatus contained two water circulation loops with one loop that supplied water to
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Z. Su, J.S. Gudmundssonr Journal of Petroleum Science and Engineering 19 (1998) 223–232
Fig. 2. Schematic diagram of experimental apparatus.
the main pipe and the other to the jacket of the test section. The jacket was used outside the test pipe to supply water entering the test pipe through perforations. The pressure in the jacket remained almost constant due to the large cross sectional area Žjacket ID s 190 mm, test pipe OD s 30 mm., so that a uniform inflow through the perforations of the test pipe was provided.
The inlet flow rate through the upstream end of the test pipe and the total flow rate through the perforations were measured by two electromagnetic flowmeters. Total pressure drop and pressure drops for each section of test pipe were measured using differential pressure transmitters. An acrylic pipe, 2 m in length and 30 mm in outer diameter, was used as test pipe. The thickness of the
Fig. 3. Schematic diagram of test section Žnot to scale..
Z. Su, J.S. Gudmundssonr Journal of Petroleum Science and Engineering 19 (1998) 223–232
227
along the pipe with a perforated section upstream. Detailed description of the experimental facilities and test procedures were presented by Su Ž1996.. Fig. 4. Configuration of test pipe Žnot to scale..
4. Pressure drop in perforated section pipe wall was about 4 mm. The test pipe was perforated by drilling perforation holes through the pipe wall that were geometrically similar to a 7-inch perforated casing with 0.83 inch perforation diameter, 12 SPF perforation density, and 608 phasing. The pipe was cleaned after perforating, and both perforation holes and holes for pressure measurement were examined to eliminate burrs. The perforations were covered with a 25 m m pore size filter on top of a water-resistant glue pad. The filter provided a large resistance to the water flowing through the perforations, so that a large pressure difference between the jacket and inside test pipe existed to secure a uniform inflow profile along the pipe. The average value of this pressure difference was about 10 times the pressure drop along the perforated section in the test pipe. The configuration of the test pipe is shown in Fig. 4. Pipe and perforation geometry are listed in Table 1. The pipe was divided into two sections with equal length. One section was perforated all the way through. The other section was divided into four equal sections to investigate the pressure profile
Experiments were carried out before the test pipe was perforated to analyze the effect of natural roughness on the pressure drop. Because the test pipe was separated into several sections, the natural friction factor–Reynolds number relationship of each section was obtained from such experiments. Three tests with different pipe flow rates were carried out after the pipe was perforated. The experimental results were examined in terms of the total pressure drop, as shown in Fig. 5. The individual tests had an average outlet flow Reynolds number in the range of 37,000 to 95,000. The experimental apparatus was operated such that each data point in the figure represents one outlet flow Reynolds number. The total flow rate ratio is the total perforation flow rate divided by the total flow rate at pipe outlet. The measured total pressure drop is higher for higher Reynolds numbers. This effect is caused by the larger wall frictional pressure drop under higher flow velocity. As the rate of flow through the perforations increases, the flow rate ratio increases and the total pressure drop increases. The main reason is that a higher flow rate through the perforations gives a larger acceleration pressure drop. In addition, there is greater wall friction due to larger average flow ve-
Table 1 Geometry of test pipe Outer diameter Inner diameter Perforation diameter Total perforation number Perforation phasing Simulate perforation density Section length Žmm. section 1 section 2 section 3 section 4 section 5 Status section 1 section 2 section 3 section 4 section 5
30.0 mm 21.94 mm 3.0 mm 158 608 12 SPF 150.0 150.0 150.0 150.0 600.0 blank blank blank blank perforated Fig. 5. Total pressure drop across perforated section.
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Z. Su, J.S. Gudmundssonr Journal of Petroleum Science and Engineering 19 (1998) 223–232
perforation flow on wall friction. Hence the following equation can be written for a uniformly perforated section Ny1
D pwall s
Ý is1
ž
fi
D L i r u 2i D
2
/
.
Ž 14 .
In the present data analysis, the pipe surface area occupied by the perforations was excluded in the above calculation because no frictional resistance is supplied by this area. Thus the value of D L i in Eq. Ž14. for a uniformly perforated pipe is a constant calculated as Fig. 6. Pressure drop due to wall friction, perforation roughness, and flow mixing.
locity in the pipe, which is caused by inflow through the perforations and increased mixing effect. Subtracting the pressure drop due to momentum increase as calculated by using Eq. Ž11., the remaining pressure drop is shown in Fig. 6. Values of the data points slightly decreased as the flow rate ratio increased, because the pipe inlet flow rate decreased about 22% for the test of low Reynolds numbers and about 8% for the test of high Reynolds numbers as the perforation flow rate increased from zero to their largest values. This negative slope is a property of the experimental apparatus and does not have a bearing on the results. The ordinary wall frictional pressure drop of a perforated section was calculated using Eq. Ž13.. Friction factors were calculated using the natural friction factor–Reynolds number relationship obtained from smooth pipe tests on the same pipe, since it was assumed that the friction factor–Reynolds number relationship for perforated pipe flow was the same as that of the pipe before it was perforated. This assumption implies that the friction factor behavior between the perforations is not affected by the perforation flow. It is necessary to make this assumption in order to calculate the ordinary frictional pressure drop. After the ordinary frictional pressure drop and acceleration pressure drop are subtracted from the measured total pressure drop, the remaining pressure drop must be the additional pressure drop caused by the mixing effect and the perforation roughness, which is actually the effect of
D Li s
d2
L y Ny1
4D
.
Ž 15 .
The lines of data points in Fig. 7 represent the additional pressure drop after both the pressure drop due to ordinary wall friction and the pressure drop due to flow acceleration have been subtracted from the measured total pressure drop. The remaining pressure drop is the additional pressure drop due to the combined effects of fluid mixing and perforation roughness. When the flow rate ratio is zero, the additional pressure drop is caused by perforation roughness only. It was assumed that the pressure drop due to perforation roughness depended on flow Reynolds number and the relative geometrical characters of the perforations and the pipe ŽSu and Gudmundsson, 1993.. The additional pressure drop decreases as the flow rate ratio increases. This shows that the perforation
Fig. 7. Additional pressure drop.
Z. Su, J.S. Gudmundssonr Journal of Petroleum Science and Engineering 19 (1998) 223–232
inflow has a smoothing effect on the wellbore flow, and consequently reduces the total pressure drop. Fig. 7 demonstrates that at higher flow Reynolds numbers, higher values of pressure drop due to perforation roughness were obtained, and more reduction in pressure drop was achieved due to perforation flow. The additional pressure drop became zero when the total flow rate ratio was about 0.18 in the present experiments. At this point, the additional pressure drop caused by the perforation roughness was eliminated by the smoothing effect. Beyond this limit of flow rate ratio, the additional pressure drop had a negative value, which indicated that the total pressure drop was reduced by perforation inflow. Because the acceleration pressure drop is an exclusive function of average flow velocity and the average velocity was computed from the direct measurement of flow rates, the ordinary frictional pressure drop was reduced. The magnitude of the maximum reduction in pressure drop was about 3.4% of the ordinary frictional pressure drop and about 1.1% of the total pressure drop for the experiments conducted on this test pipe. Although these values may not be exact for real perforated liners used in horizontal wells, the consistent downward trend of the additional pressure drop shown in Fig. 7 demonstrated that the frictional pressure drop was indeed reduced when the flow rate ratio increased. A perforated pipe with an extremely high perforation density can be treated as a pipe with porous wall. Wall transpiration caused by injection of fluid through the porous wall has a strong effect on skin friction ŽWhite, 1991.. Experimental results of turbulent flow in a porous pipe with uniform fluid injection through the pipe wall ŽOlson and Eckert, 1966. demonstrated that fluid injection reduced the velocity gradient at the wall. Consequently, the wall shear stress, and hence friction factor, was reduced. Although the perforation density of perforated wellbores is not so high in reality, one can still expect that the velocity gradient at the wall, and hence the distribution of wall shear stress, downstream of a perforation will be altered by the inflow through the perforations. It has been demonstrated in Figs. 5–7 that pressure drop in a perforated pipe is a function of flow
229
Fig. 8. Pressure loss coefficient for the additional pressure drop.
rate. In order to compare the pressure drop behavior of different tests, the pressure drop can be represented in terms of a pressure loss coefficient, which was defined as the corresponding pressure drop across the perforated section divided by the kinetic energy at the outlet of the pipe Ks
DP
Ž 1r2. r u 2out
.
Ž 16 .
The pressure loss coefficients of the additional pressure drop are shown in Fig. 8. The data points fall close to each other, and decrease with increasing total flow rate ratio.
5. Friction factor in blank sections Pressure profiles along four blank sections of the test pipe were measured to study the effect of a perforated section upstream. It was assumed that the effect of velocity profile readjustment was very small and that the pressure drop in the blank section was caused only by the pipe wall friction. Experiments with flow through the perforated section were conducted with increasing flow rate ratio. Pressure drops of pipe sections 1 to 4 were measured for each test and the corresponding friction factors calculated. The friction factors are compared with those obtained from the tests before the pipe was perforated as shown in Figs. 9–12. Friction factors for section 1 are plotted in Fig. 9. The friction factors from the smooth pipe tests be-
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Z. Su, J.S. Gudmundssonr Journal of Petroleum Science and Engineering 19 (1998) 223–232
Fig. 9. Friction factor of section 1. Fig. 11. Friction factor of section 3.
fore the pipe was perforated and a hydraulic smooth line are plotted in this display. The smooth pipe test was conducted with a continually increasing Reynolds number that ranged from 30,000 to 100,000. Three groups of experiments with perforation flow were carried out in different ranges of Reynolds number. The friction factors are smaller than those obtained before the pipe was perforated; however, they follow a power function curve with increasing Reynolds number. This demonstrated that the smoothing effect in the perforated section did not affect the characteristic of friction factor–Reynolds number relationships of section 1. Friction factors for section 2 are plotted in Fig. 10. The friction factors are also in three groups of different Reynolds number ranges and follow a power
Fig. 10. Friction factor of section 2.
function curve. The friction factors of section 2 obtained when there was a perforated section upstream are larger than those obtained before the pipe was perforated, which is inconsistent with the results in the other three sections. This might be caused by the errors in the pressure drop measurement in section 2. However, the fact that three groups of friction factors under different Reynolds numbers follow a common power curve suggests that the smoothing effect in the perforated section did not affect the characteristic of friction factor–Reynolds number relationships of section 2. Friction factors of section 3 from perforated pipe tests are smaller than those obtained from the smooth pipe tests, as shown in Fig. 11. In addition, the friction factors within one group of tests drop dra-
Fig. 12. Friction factor of section 4.
Z. Su, J.S. Gudmundssonr Journal of Petroleum Science and Engineering 19 (1998) 223–232
matically when the Reynolds number increases. The data points of three different tests do not follow a common power function curve. The drop of friction factor is more pronounced for section 4, as shown in Fig. 12. The data points from different tests cannot be represented by a single curve for sections 3 and 4. The drop of friction factor in sections 3 and 4 showed the same character as that of the additional pressure drop in the perforated section after the pressure drops due to ordinary wall friction and flow acceleration were subtracted. This indicated that the smoothing effect in the perforated section extended downstream into the blank sections 3 and 4. The influence of smoothing effect on the friction factor–Reynolds number relationship was strongest in section 4, because section 4 is immediately downstream of the perforated section. Such influences were reduced in section 3, and they virtually vanished in sections 1 and 2. These results demonstrated that the smoothing effect in the perforated section extended into the blank section downstream of a combined length of sections 3 and 4, which is about 14 pipe inner diameters. Beyond this distance, the flow in the blank section established itself into a fully developed pipe flow.
231
tance of about 14 pipe inner diameters, within the experimental range of Reynolds number. Under the same Reynolds number, the friction factor in this part of the blank section downstream of the perforated section is smaller than its ordinary friction factor.
7. Nomenclature A d D F f K L DL m ˙ N p Dp Q u r tw
cross sectional area of the pipe Žm2 . perforation diameter Žm. inner diameter of the pipe Žm. force ŽN. friction factor Ž — . pressure loss coefficient Ž — . total length of the perforated section Žm. effective length of a perforation unit Žm. mass flow rate Žkgrs. total number of perforations Ž — . pressure ŽPa. pressure difference ŽPa. volume flow rate Žm3rs. mean flow velocity Žmrs. fluid density Žkgrm3 . wall shear stress ŽNrm2 .
6. Conclusions Acknowledgements The overall pressure drop in a horizontal wellbore is the sum of the pressure drop due to momentum change Žflow acceleration., wall friction, perforation roughness, and fluid mixing. Experimental results have demonstrated that perforation flow reduces the frictional pressure loss in the test pipe. The additional pressure drop caused by the perforation roughness was eliminated by the smoothing effect once the flow rate ratio reached a certain limit. More reduction in pressure drop can be achieved with higher flow rate ratio. The pressure drop reduction was larger at high Reynolds numbers than at low Reynolds numbers. The magnitude of the maximum reduction in pressure drop was about 3.4% of the ordinary frictional pressure drop, and about 1.1% of the total pressure drop for the presented experiments. The smoothing effect in the perforated section extends into the blank section downstream to a dis-
The authors would like to thank the PROFIT group of companies and Norwegian Petroleum Directorate for their support of this study.
References Asheim, H., Kolnes, J., Oudeman, P., 1992. A flow resistance correlation for completed wellbore. J. Petrol. Sci. Eng. 8 Ž2., 97–104. Collins, D.A., Nghiem, L.X., Sharma, R, Agarwal, R.K., Jha, K.N., 1991. Field-Scale Simulation of Horizontal Wells With Hybrid Grids, SPE 21218. Presented at the 11th SPE Symposium on Reservoir Simulation, Anaheim, California, USA, February 17–20. Dikken, B.J., 1990. Pressure Drop in Horizontal Wells and Its Effect on Production Performance. JPT, November, pp. 1426– 1433. Folefac, A.N., Archer, J.S., Issa, R.I., Arshad, A.M., 1991. Effect of Pressure Drop Along Horizontal Wellbores on Well Perfor-
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mance, SPE 23094. Presented at the Offshore Europe Conference, Aberdeen, UK, September 3–6. Gudmundsson, J.S., Su, Z., 1995. Pressure Drop in Perforated Pipes. PROFIT Project Summary Reports, Norwegian Petroleum Directorate, Stavanger, pp. 291–300. Ihara, M., Shimizu, N., 1993. Effect of Accelerational Pressure Drop in a Horizontal Wellbore, SPE 26519. Presented at the 68th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Houston, TX, USA, October 3–6. Ihara, M., Brill, J.P., Shoham, O., 1992. Experimental and Theoretical Investigation of Two-Phase Flow in Horizontal Wells, SPE 24766. Presented at the 67th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Washington, DC, USA, October 4–7. Landman, M.J., Goldthorpe, W.H., 1991. Optimization of Perforation Distribution for Horizontal Wells, SPE 23005. Presented at the SPE Asia Pacific Conference, Perth, Western Australia. Marett, B.P., Landman, M.J., 1993. Optimal Perforation Design for Horizontal Wells in Reservoirs With Boundaries, SPE 25366. Presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition, Singapore, February 8–10. Olson, R.M., Eckert, E.R.G., 1966. Experimental studies of turbu-
lent flow in a porous circular tube with uniform fluid injection through the tube wall. J. Appl. Mech. March, 7–17. Ozkan, E., Sarica, C., Haciislamoglu, M., Raghavan, R., 1993. The Inference of Pressure Drop Along the Wellbore on Horizontal Well Productivity, SPE 25502. Presented at the Production Operations Symposium, Oklahoma City, OK, USA, March 21–23. Sarica, C., Ozkan, E., Haciislamoglu, M., Raghavan, R., Brill, J.P., 1994. Influence of Wellbore Hydraulics on Pressure Behavior and Productivity of Horizontal Gas Wells, SPE 28486. Presented at the SPE 69th Annual Technical Conference and Exhibition, New Orleans, LA, USA, September 25–28. Su, Z., 1996. Pressure Drop in Perforated Pipes for Horizontal Wells, Dr. Ing. Thesis, The Norwegian University of Science and Technology, ISBN 82-7119-929-3, NTH-Trykk. Su, Z., Gudmundsson, J.S., 1993. Friction Factor of Perforation Roughness in Pipes, SPE 26521. Presented at the SPE 68th Annual Technical Conference and Exhibition, Houston, TX, USA, October 3–6. White, F.M., 1986. Fluid Mechanics. McGraw-Hill, Inc. White, F.M., 1991. Viscous Fluid Flow, Second ed. McGraw-Hill, Inc.
Perforation inflow reduces frictional pressure loss in horizontal wellbores Z. Su b
a,1
, J.S. Gudmundsson
b,)
a Imperial Petroleum Consultants AS, P.O. Box 624, 4001 StaÕanger, Norway Department of Petroleum Engineering and Applied Geophysics, Norwegian UniÕersity of Science and Technology, 7034 Trondheim, Norway
Received 24 July 1996; revised 19 August 1997; accepted 19 August 1997
Abstract The total pressure drop in horizontal wellbores has been analyzed in terms of four separate effects: wall friction, flow acceleration, perforation roughness, and fluid mixing. Laboratory experiments have been carried out in test pipes that are geometrically similar to perforated liners used in horizontal wells to investigate different pressure drop effects in a horizontal wellbore. It was demonstrated that the perforation inflow actually reduced the total pressure drop. Results indicated that the pressure drop due to perforation roughness was eliminated by the perforation inflow when the ratio of perforation flow to pipe flow rate reached a certain limit. Beyond this limit, the perforation inflow lubricated the wellbore flow. Such smoothing effect in the perforated section of the wellbore extended into the blank section downstream. It has been shown that different pressure drop effects can be conveniently represented by using a pressure loss coefficient. q 1998 Elsevier Science B.V. Keywords: horizontal well; perforation inflow; pressure drop; friction; mixing effect
1. Introduction Use of horizontal wells is an established practice in the petroleum industry. Horizontal well productivity can be limited by the pressure drop within the wellbore, especially when the pressure drop is comparable with the reservoir drawdown. Because more and longer horizontal wells are being drilled around the world, a better understanding of the factors affecting the total pressure drop within the wellbore is ) Corresponding author. Tel.: q47-73-594952. Fax: q47-73944472. E-mail: [email protected] 1 Tel.: q47-51-414090. E-mail: [email protected]
required. Increased knowledge of different pressure drop effects in horizontal wellbores is crucial in designing successful horizontal wells and optimizing well performance. The great majority of published papers dealing with performance of horizontal wells consider only the wall friction part of the total pressure drop ŽDikken, 1990; Collins et al., 1991; Folefac et al., 1991; Landman and Goldthorpe, 1991; Ihara et al., 1992; Ozkan et al., 1993.. The reality is that flow velocity increases as reservoir fluid continually enters the wellbore through perforations along a perforated wellbore. The increase of flow velocity, and therefore momentum, contributes to the pressure drop
0920-4105r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 9 2 0 - 4 1 0 5 Ž 9 7 . 0 0 0 4 7 - 8
224
Z. Su, J.S. Gudmundssonr Journal of Petroleum Science and Engineering 19 (1998) 223–232
in addition to the frictional pressure drop. This part of the pressure drop has been addressed by several authors in recent years ŽAsheim et al., 1992; Ihara and Shimizu, 1993; Marett and Landman, 1993; Sarica et al., 1994.. Moreover, perforation holes act like roughness elements and increase the friction factor of the wellbore. This part of the pressure drop has been studied by Su and Gudmundsson Ž1993.. The pressure gradient along the perforated wellbore is also affected by the mixing between wellbore flow and perforation flow. How the interaction between the perforation flow and the wellbore flow affects the pressure gradient inside the horizontal wellbore has not been thoroughly investigated in petroleum production engineering. The work presented in this paper concerns pressure drop experiments carried out in uniformly perforated pipes that are geometrically similar to perforated liners used in horizontal wells. The objective is to determine experimentally the various factors that contribute to the total pressure drop in perforated pipes. In addition, pressure profiles along a blank section downstream of a perforated section were also measured, and friction factors calculated using the measured pressure drop. The effect of the perforation flow on a blank section downstream of a perforated section has been analyzed by comparing the friction factors in the blank section with those before the pipe was perforated. More details of this work have been published by Gudmundsson and Su Ž1995. and Su Ž1996..
It is convenient to combine the last two terms in this equation into one term D padd., which is the pressure drop due to the combined effects of fluid mixing and perforation roughness. Eq. Ž1. can then be written as D p s D pwall q D pacc .q D padd ..
Ž 2.
The whole length of a uniformly perforated horizontal well can be divided into perforation units of equal length, with each unit containing one perforation at the upstream end of the unit as shown in Fig. 1. Applying the conservation of linear momentum to the control volume abcd in the axial direction, as shown in Fig. 1, and assuming all the flow is one dimensional, steady, and incompressible, results in the sum of the forces acting on the control volume surfaces toward the downstream direction of the pipe axis
Ý F s m˙ 2 u 2 y m˙ 1 u1 ,
2. Pressure drop in perforated wellbores
Ž 3.
where the mass flow rate is
The total pressure drop in a perforated horizontal wellbore can be divided into a reversible pressure drop and an irreversible pressure drop. The reversible pressure drop is that due to momentum change Žflow acceleration. as more fluid enters the wellbore through perforations. The irreversible pressure drop is that due to pipe wall friction, perforation friction, and mixing effects. The following relationship gives the four pressure drop terms that make up the total pressure drop in a perforated horizontal well D p s D pwall q D pacc .q D pperf .q D pmix .
Fig. 1. Perforation unit Žnot to scale..
Ž 1.
m ˙ s r Au.
Ž 4.
It should be noted here that across any pipe cross section, and especially the cross section at the entrance of the perforation unit, the static pressure is not uniform, and that the velocity profile is not fully developed due to the perforation flow. Therefore, in addition to the force contributed by the pressure difference across the control volume and wall shear force, the sum of the forces acting on the control volume surface includes a force due to the combined effects of the irreversible process of fluid mixing and the presence of the perforation hole, including the
Z. Su, J.S. Gudmundssonr Journal of Petroleum Science and Engineering 19 (1998) 223–232
effect of non-uniformly distribution of static pressure and non-fully developed velocity profile,
Ý F s Ž p1 A y p 2 A . y tw Ž p DD L . y Fadd ..
Ž 5.
The wall shear force results in wall frictional pressure drop
tw Ž p DD L . s D pwall A,
Ž 6.
and the additional force Fadd. results in an additional pressure drop
It is clear that smaller pressure drop due to momentum change can be achieved, for the same production rate, by using a larger diameter wellbore. The inflow profile along the wellbore has no influence on this part of the pressure drop. The pressure drop due to pipe wall friction in a perforation unit, D pwall , is based on the average velocity u 2 downstream of the perforation, and can be calculated from the Darcy–Weisbach equation ŽWhite, 1986. D pwall s
Fadd .s D padd . A.
Ž 7.
Combining Eqs. Ž3., Ž5. – Ž7. yields m ˙ 2 u 2 y m˙ 1 u1 s Ž p1 y p 2 . A y D pwall A y D padd . A Ž 8. Substituting Eq. Ž4. into Eq. Ž8. yields p 1 y p 2 s r Ž u 22 y u12 . q D pwall q D padd ..
Ž 9.
The pressure drop due to momentum change, D pacc., can be represented as D pacc .s r Ž u 22 y u12 . ,
Ž 10 .
by comparing Eq. Ž9. with Eq. Ž2.. For a horizontal well containing N perforations, the pressure drop due to momentum increase is the sum of pressure drop in each perforation unit N
D pacc .s
Ý r Ž u 2nq1 y u 2n . s r Ž u 2Nq1 y u12 . . Ž 11. ns1
The total reversible pressure drop due to momentum change in a horizontal well is, therefore, an exclusive factor of the fluid density and mean flow velocities at the toe- and heel-ends of the well. When no fluid enters the wellbore at the toe-end, u1 equals zero, and the pressure drop due to momentum change is related only to the average flow velocity at the heel-end of the well, which can be calculated from the well production rate as D pacc .s r u 2Nq1 s r
Q
ž / A
2
.
Ž 12 .
225
f DL 2 D
r u 22 .
Ž 13 .
This equation applies to both laminar and turbulent flow. The pressure drop due to perforation roughness, D pperf., is the extra pressure drop due to the presence of the perforations. It represents the extra friction caused by the perforations acting as roughness elements in the pipe wall. The pressure drop due to perforation roughness is most important when there is no flow through the perforations. It has been shown that the magnitude of the pressure drop due to perforation roughness depends on the pipe-perforation geometry and the perforation density ŽSu and Gudmundsson, 1993.. The pressure drop due to mixing effects, D pmix , is an irreversible pressure drop that cannot be further classified. This pressure effect arises from the complex interaction between perforation flow and wellbore flow, which causes disturbances in the boundary layer and hence affects the pressure drop. The irreversible pressure drop due to mixing needs to be determined by experiments.
3. Experiments Experiments were carried out to determine the additional pressure drop, D padd., due to the combined effect of flow mixing and perforation roughness. A special test section was built into a horizontal flow loop. A schematic diagram of the flow loop is shown in Fig. 2 and a diagram of the test section is illustrated in Fig. 3. The experimental apparatus contained two water circulation loops with one loop that supplied water to
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Fig. 2. Schematic diagram of experimental apparatus.
the main pipe and the other to the jacket of the test section. The jacket was used outside the test pipe to supply water entering the test pipe through perforations. The pressure in the jacket remained almost constant due to the large cross sectional area Žjacket ID s 190 mm, test pipe OD s 30 mm., so that a uniform inflow through the perforations of the test pipe was provided.
The inlet flow rate through the upstream end of the test pipe and the total flow rate through the perforations were measured by two electromagnetic flowmeters. Total pressure drop and pressure drops for each section of test pipe were measured using differential pressure transmitters. An acrylic pipe, 2 m in length and 30 mm in outer diameter, was used as test pipe. The thickness of the
Fig. 3. Schematic diagram of test section Žnot to scale..
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along the pipe with a perforated section upstream. Detailed description of the experimental facilities and test procedures were presented by Su Ž1996.. Fig. 4. Configuration of test pipe Žnot to scale..
4. Pressure drop in perforated section pipe wall was about 4 mm. The test pipe was perforated by drilling perforation holes through the pipe wall that were geometrically similar to a 7-inch perforated casing with 0.83 inch perforation diameter, 12 SPF perforation density, and 608 phasing. The pipe was cleaned after perforating, and both perforation holes and holes for pressure measurement were examined to eliminate burrs. The perforations were covered with a 25 m m pore size filter on top of a water-resistant glue pad. The filter provided a large resistance to the water flowing through the perforations, so that a large pressure difference between the jacket and inside test pipe existed to secure a uniform inflow profile along the pipe. The average value of this pressure difference was about 10 times the pressure drop along the perforated section in the test pipe. The configuration of the test pipe is shown in Fig. 4. Pipe and perforation geometry are listed in Table 1. The pipe was divided into two sections with equal length. One section was perforated all the way through. The other section was divided into four equal sections to investigate the pressure profile
Experiments were carried out before the test pipe was perforated to analyze the effect of natural roughness on the pressure drop. Because the test pipe was separated into several sections, the natural friction factor–Reynolds number relationship of each section was obtained from such experiments. Three tests with different pipe flow rates were carried out after the pipe was perforated. The experimental results were examined in terms of the total pressure drop, as shown in Fig. 5. The individual tests had an average outlet flow Reynolds number in the range of 37,000 to 95,000. The experimental apparatus was operated such that each data point in the figure represents one outlet flow Reynolds number. The total flow rate ratio is the total perforation flow rate divided by the total flow rate at pipe outlet. The measured total pressure drop is higher for higher Reynolds numbers. This effect is caused by the larger wall frictional pressure drop under higher flow velocity. As the rate of flow through the perforations increases, the flow rate ratio increases and the total pressure drop increases. The main reason is that a higher flow rate through the perforations gives a larger acceleration pressure drop. In addition, there is greater wall friction due to larger average flow ve-
Table 1 Geometry of test pipe Outer diameter Inner diameter Perforation diameter Total perforation number Perforation phasing Simulate perforation density Section length Žmm. section 1 section 2 section 3 section 4 section 5 Status section 1 section 2 section 3 section 4 section 5
30.0 mm 21.94 mm 3.0 mm 158 608 12 SPF 150.0 150.0 150.0 150.0 600.0 blank blank blank blank perforated Fig. 5. Total pressure drop across perforated section.
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perforation flow on wall friction. Hence the following equation can be written for a uniformly perforated section Ny1
D pwall s
Ý is1
ž
fi
D L i r u 2i D
2
/
.
Ž 14 .
In the present data analysis, the pipe surface area occupied by the perforations was excluded in the above calculation because no frictional resistance is supplied by this area. Thus the value of D L i in Eq. Ž14. for a uniformly perforated pipe is a constant calculated as Fig. 6. Pressure drop due to wall friction, perforation roughness, and flow mixing.
locity in the pipe, which is caused by inflow through the perforations and increased mixing effect. Subtracting the pressure drop due to momentum increase as calculated by using Eq. Ž11., the remaining pressure drop is shown in Fig. 6. Values of the data points slightly decreased as the flow rate ratio increased, because the pipe inlet flow rate decreased about 22% for the test of low Reynolds numbers and about 8% for the test of high Reynolds numbers as the perforation flow rate increased from zero to their largest values. This negative slope is a property of the experimental apparatus and does not have a bearing on the results. The ordinary wall frictional pressure drop of a perforated section was calculated using Eq. Ž13.. Friction factors were calculated using the natural friction factor–Reynolds number relationship obtained from smooth pipe tests on the same pipe, since it was assumed that the friction factor–Reynolds number relationship for perforated pipe flow was the same as that of the pipe before it was perforated. This assumption implies that the friction factor behavior between the perforations is not affected by the perforation flow. It is necessary to make this assumption in order to calculate the ordinary frictional pressure drop. After the ordinary frictional pressure drop and acceleration pressure drop are subtracted from the measured total pressure drop, the remaining pressure drop must be the additional pressure drop caused by the mixing effect and the perforation roughness, which is actually the effect of
D Li s
d2
L y Ny1
4D
.
Ž 15 .
The lines of data points in Fig. 7 represent the additional pressure drop after both the pressure drop due to ordinary wall friction and the pressure drop due to flow acceleration have been subtracted from the measured total pressure drop. The remaining pressure drop is the additional pressure drop due to the combined effects of fluid mixing and perforation roughness. When the flow rate ratio is zero, the additional pressure drop is caused by perforation roughness only. It was assumed that the pressure drop due to perforation roughness depended on flow Reynolds number and the relative geometrical characters of the perforations and the pipe ŽSu and Gudmundsson, 1993.. The additional pressure drop decreases as the flow rate ratio increases. This shows that the perforation
Fig. 7. Additional pressure drop.
Z. Su, J.S. Gudmundssonr Journal of Petroleum Science and Engineering 19 (1998) 223–232
inflow has a smoothing effect on the wellbore flow, and consequently reduces the total pressure drop. Fig. 7 demonstrates that at higher flow Reynolds numbers, higher values of pressure drop due to perforation roughness were obtained, and more reduction in pressure drop was achieved due to perforation flow. The additional pressure drop became zero when the total flow rate ratio was about 0.18 in the present experiments. At this point, the additional pressure drop caused by the perforation roughness was eliminated by the smoothing effect. Beyond this limit of flow rate ratio, the additional pressure drop had a negative value, which indicated that the total pressure drop was reduced by perforation inflow. Because the acceleration pressure drop is an exclusive function of average flow velocity and the average velocity was computed from the direct measurement of flow rates, the ordinary frictional pressure drop was reduced. The magnitude of the maximum reduction in pressure drop was about 3.4% of the ordinary frictional pressure drop and about 1.1% of the total pressure drop for the experiments conducted on this test pipe. Although these values may not be exact for real perforated liners used in horizontal wells, the consistent downward trend of the additional pressure drop shown in Fig. 7 demonstrated that the frictional pressure drop was indeed reduced when the flow rate ratio increased. A perforated pipe with an extremely high perforation density can be treated as a pipe with porous wall. Wall transpiration caused by injection of fluid through the porous wall has a strong effect on skin friction ŽWhite, 1991.. Experimental results of turbulent flow in a porous pipe with uniform fluid injection through the pipe wall ŽOlson and Eckert, 1966. demonstrated that fluid injection reduced the velocity gradient at the wall. Consequently, the wall shear stress, and hence friction factor, was reduced. Although the perforation density of perforated wellbores is not so high in reality, one can still expect that the velocity gradient at the wall, and hence the distribution of wall shear stress, downstream of a perforation will be altered by the inflow through the perforations. It has been demonstrated in Figs. 5–7 that pressure drop in a perforated pipe is a function of flow
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Fig. 8. Pressure loss coefficient for the additional pressure drop.
rate. In order to compare the pressure drop behavior of different tests, the pressure drop can be represented in terms of a pressure loss coefficient, which was defined as the corresponding pressure drop across the perforated section divided by the kinetic energy at the outlet of the pipe Ks
DP
Ž 1r2. r u 2out
.
Ž 16 .
The pressure loss coefficients of the additional pressure drop are shown in Fig. 8. The data points fall close to each other, and decrease with increasing total flow rate ratio.
5. Friction factor in blank sections Pressure profiles along four blank sections of the test pipe were measured to study the effect of a perforated section upstream. It was assumed that the effect of velocity profile readjustment was very small and that the pressure drop in the blank section was caused only by the pipe wall friction. Experiments with flow through the perforated section were conducted with increasing flow rate ratio. Pressure drops of pipe sections 1 to 4 were measured for each test and the corresponding friction factors calculated. The friction factors are compared with those obtained from the tests before the pipe was perforated as shown in Figs. 9–12. Friction factors for section 1 are plotted in Fig. 9. The friction factors from the smooth pipe tests be-
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Fig. 9. Friction factor of section 1. Fig. 11. Friction factor of section 3.
fore the pipe was perforated and a hydraulic smooth line are plotted in this display. The smooth pipe test was conducted with a continually increasing Reynolds number that ranged from 30,000 to 100,000. Three groups of experiments with perforation flow were carried out in different ranges of Reynolds number. The friction factors are smaller than those obtained before the pipe was perforated; however, they follow a power function curve with increasing Reynolds number. This demonstrated that the smoothing effect in the perforated section did not affect the characteristic of friction factor–Reynolds number relationships of section 1. Friction factors for section 2 are plotted in Fig. 10. The friction factors are also in three groups of different Reynolds number ranges and follow a power
Fig. 10. Friction factor of section 2.
function curve. The friction factors of section 2 obtained when there was a perforated section upstream are larger than those obtained before the pipe was perforated, which is inconsistent with the results in the other three sections. This might be caused by the errors in the pressure drop measurement in section 2. However, the fact that three groups of friction factors under different Reynolds numbers follow a common power curve suggests that the smoothing effect in the perforated section did not affect the characteristic of friction factor–Reynolds number relationships of section 2. Friction factors of section 3 from perforated pipe tests are smaller than those obtained from the smooth pipe tests, as shown in Fig. 11. In addition, the friction factors within one group of tests drop dra-
Fig. 12. Friction factor of section 4.
Z. Su, J.S. Gudmundssonr Journal of Petroleum Science and Engineering 19 (1998) 223–232
matically when the Reynolds number increases. The data points of three different tests do not follow a common power function curve. The drop of friction factor is more pronounced for section 4, as shown in Fig. 12. The data points from different tests cannot be represented by a single curve for sections 3 and 4. The drop of friction factor in sections 3 and 4 showed the same character as that of the additional pressure drop in the perforated section after the pressure drops due to ordinary wall friction and flow acceleration were subtracted. This indicated that the smoothing effect in the perforated section extended downstream into the blank sections 3 and 4. The influence of smoothing effect on the friction factor–Reynolds number relationship was strongest in section 4, because section 4 is immediately downstream of the perforated section. Such influences were reduced in section 3, and they virtually vanished in sections 1 and 2. These results demonstrated that the smoothing effect in the perforated section extended into the blank section downstream of a combined length of sections 3 and 4, which is about 14 pipe inner diameters. Beyond this distance, the flow in the blank section established itself into a fully developed pipe flow.
231
tance of about 14 pipe inner diameters, within the experimental range of Reynolds number. Under the same Reynolds number, the friction factor in this part of the blank section downstream of the perforated section is smaller than its ordinary friction factor.
7. Nomenclature A d D F f K L DL m ˙ N p Dp Q u r tw
cross sectional area of the pipe Žm2 . perforation diameter Žm. inner diameter of the pipe Žm. force ŽN. friction factor Ž — . pressure loss coefficient Ž — . total length of the perforated section Žm. effective length of a perforation unit Žm. mass flow rate Žkgrs. total number of perforations Ž — . pressure ŽPa. pressure difference ŽPa. volume flow rate Žm3rs. mean flow velocity Žmrs. fluid density Žkgrm3 . wall shear stress ŽNrm2 .
6. Conclusions Acknowledgements The overall pressure drop in a horizontal wellbore is the sum of the pressure drop due to momentum change Žflow acceleration., wall friction, perforation roughness, and fluid mixing. Experimental results have demonstrated that perforation flow reduces the frictional pressure loss in the test pipe. The additional pressure drop caused by the perforation roughness was eliminated by the smoothing effect once the flow rate ratio reached a certain limit. More reduction in pressure drop can be achieved with higher flow rate ratio. The pressure drop reduction was larger at high Reynolds numbers than at low Reynolds numbers. The magnitude of the maximum reduction in pressure drop was about 3.4% of the ordinary frictional pressure drop, and about 1.1% of the total pressure drop for the presented experiments. The smoothing effect in the perforated section extends into the blank section downstream to a dis-
The authors would like to thank the PROFIT group of companies and Norwegian Petroleum Directorate for their support of this study.
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