The Experimental and Model Study on Variable Mass Flow for Horizontal Wells with Perforated Completion

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1 The Experimental and Model Study on Variable Mass Flow for Horizontal Wells with Perforated Completion Wei Jianguang Lin Xuesong Liu Xuemei Ma Yuanyuan Northeast Petroleum University, Daqing City of Heilongjiang Province, Abstract:The variable mass flow in perforated horizontal wells is very complex. One reason is that the perforation can increase the roughness of the pipe wall which will increase the frictional pressure drop. The other is the fluid boundary layer and velocity profile of axial flow will be changed due to the mixing of the inflow with the axial flow. The influences of the perforation parameters and flux rate on the pressure drawdown in horizontal wellbore are investigated. The perforation parameters include perforation phasing, perforation diameter, perforation density. According to the experiment results, some modes such as friction factor calculation model (the accuracy of the model is 4%), mixing pressure drop calculation model (the accuracy of the model is 3%) and total pressure drop calculation model (the accuracy of the model is 2%) are developed. Key Words: Pressure drop Complex flow Horizontal wellbore Perforated completion 0 Introduction The affecting rules of the pressure drop for complex flow in horizontal wells are important to the prediction of production dynamic, the design of borehole trajectory, the optimization of completion parameters and the inflow control method determination. The variable mass flow in perforated horizontal wellbore is complex compared with the conventional pipe flow which embodies in two aspects. One is that the pipe wall has bigger roughness due to the perforations which increase the frictional pressure losses. The other is that the fluid boundary layer and velocity profile of axial flow changes due to the mixing of the inflow with the axial flow. A considerable number of experimental work on pressure losses of single flow in perforated completed horizontal wells has been published by many scholars, such as Asheim [1] and Su [2-3] of NTNU, Japanese scholar Ihara [4-6],Yuan [7-10] of Tulsa, OuYang [11-13] of Stanford, Zhou Shengtian [14-15] of CUP(East China),Wang Zhiming [16-17] of CUP(Beijing), Abdulwahid,M.A. [18] of Andhra University(India), Quan Zhang [19] of CUP (Beijing), Weipeng Jiang [20] of Tulsa. There are three shortages of the previous work. One is the experiment systems use small size pipes which cannot satisfy geometric similarity, kinematic similarity and dynamic similarity simultaneously which induce the results deviated from the actual production. One is that the pipes are made of organic glass instead of the metal and the fluid is water. The third is that the influences of the perforation phasing, perforation diameter, perforation density on the pressure drop have not been obtained. In this paper, a full size perforated casing pipe JERT , Liu, 1

2 with 5.5 inch external diameter is used to simulate the actual production. Three values of perforation phasing, perforation diameter and perforation density are considered respectively. The Re of axial flow is The flux ratio (the ratio of the radial volume inflow at unit wellbore length to the axial volume flow in production pipe) is 0.01%-10%. The parameters affecting the pressure drop such as perforation phasing, perforation diameter and perforation density, flux ratio are considered in this paper. The influence law obtained in this paper can offer a base for development of the pressure drop model. 1 Experiment Introduction (1) The experiment system include three units:simulation unit, fluid supply and control unit, data collection and analyzing unit which are shown in Fig.1. (2) The simulating unit adopts a casing with mm inner diameter (external diameter is 5.5 inch)and a casing pipe with mm inner diameter(external diameter is 7.5 inch). This unit is 6.5m long and the distance between two pressure monitoring nodes is 6 m. To improve the accuracy of the pressure difference transmitter, the pressure monitoring nodes are connected with difference pressure transmitter by softy sheer plastic pipes. The accuracy of the pressure difference transmitter is the order of magnitude of 1Pa. The outside wall of the inner pipe is covered by compact gauze. At the ends of this unit, there are two liquid inlets to ensure the inflow profile uniform. The simulating unit is shown in Fig.2. (3) The mineral oil of 10 mpa.s is used instead of crude oil. Before every experiment, the indoor temperature and viscosity of the mineral oil is measured to make sure the temperature and viscosity in each experiment is same. (4) Three values of screw perforating phasing in simulation unit are considered: 45,90,180,as shown in Fig.3. The values of perforation density are 8 meter -1, 16 meter -1, 24 meter -1. The values of perforation diameter are 10mm, 20mm, 30mm. (5) The Re of axial flow is The flux ratio is 0.01%-10%. JERT , Liu, 2

3 Fig 1 Experiment System for Complex Flow in Horizontal Wellbore Fig 2 Simulation Unit Diagram A B C D E F G H A B C D E F G H A B C D E F G H Fig 3A 45 Screw Perforating Phasing JERT , Liu, 3

4 A B C D A B C D A A B C D Fig 3B 90 Screw Perforating Phasing B A B A B Fig 3C 180 Screw Perforating Phasing 2 Experiment Results It is need to emphasize that the inner diameter of these experimental pipes are all 124 mm, the distance of two pressure measurement nodes is 6m,and the ordinary casing pipe is the casing without perforation. The relationship curves of Re of axial flow with frictional pressure drop gradient under different perforation density, diameter, phasing without inflow are shown in fig.4a, fig.4b, fig.4c respectively. From fig.4a, fig.4b, fig.4c, the effects of perforation density, diameter, phasing on frictional pressure losses are significant. The frictional pressure losses always increase with the increase of perforation density, diameter and phasing. When the perforation diameter is 20mm, the perforation phasing is 90, the Re of axial flow is 20000,the frictional pressure drop gradient is 376 Pa/m,414 Pa/m,459 Pa/m which is bigger than that of the ordinary casing pipe by 11.11%,22.41%,35.71% corresponding to the perforation density of 8 m -1,16 m -1,24 m -1 respectively. When the perforation density is 16 m -1,the perforation phasing is 90,the Re of axial flow is 20000,the frictional pressure drop gradient is 389Pa/m,414Pa/m,441Pa/m which is bigger than that of the ordinary casing pipe by 15.14%,22.41%,30.46% corresponding to the perforation diameter of 10 mm,20 mm,30 mm respectively. When the perforation density is 16 m -1,the perforation diameter is 20 mm, the Re of axial flow is 20000,the frictional pressure drop gradient is 399Pa/m 414Pa/m 430Pa/m which is bigger than that of the ordinary casing pipe by JERT , Liu, 4

5 17.96%,22.41%,27.14% according to the perforation phasing of 45, 90, 180 respectively. The results indicate that the perforation can increase the roughness of the pipe wall which increases the frictional pressure drop. To analyze the influence of flux ratio on total and mixing pressure drop, the relation curves of total pressure drop with the flux ratio under different perforation density, diameter, phasing when the Re at outlet keeps 5000 are obtained in fig.5a, fig.5b and fig.5c, and the relationship curves when the Re of outlet keeps 5000 are obtained in fig.6a, fig.6b and fig.6c. From the fig.5a, fig.5b and fig.5c, we can see that the effect of flux ratio on total pressure drop is significant. The total pressure drop increases with the flux ratio. The pressure drop gradient is 28Pa/m 36 Pa/m,45 Pa/m,82 Pa/m which is bigger than the frictional pressure drop of the ordinary casing pipe(about 29 Pa/m) by -3%,25%,56%,185% when the flux ratio is 0.01%,0.1%,1%,10% respectively, that indicates that when the flux ratio is small, the inflow can reduce the frictional pressure drop compared with the ordinary casing pipe without perforations while the high flux ratio can increase the mixing and acceleration pressure drawdown obviously. The effect of flux ratio is greater than the effect of perforation parameters. From the fig.6a, fig.6b, fig.6c, the mixing pressure drop increases with the flux ratio, but there exists a critical value of flux ratio. When the actual flux ratio less than the critical value, the mixing pressure drop is negative which means that the inflow fluid can reduce the total pressure drop. When the actual flux ratio bigger than the critical value, the mixing pressure drop is positive and could increases the total pressure drop. The critical flux ratio increases with the perforation density and perforation diameter. In this paper, the critical value is 0.05%-0.1%. Fig.7A and fig.7b present the relation curves of the flux ratio with the pressure drop gradient when the Re at outlet is 5000 and respectively. From fig.7a and fig.7b, no matter the value of the Re, if the flux ratio is less than 0.1% the acceleration pressure drop can be neglected. If the flux ratio is greater than 0.1% the acceleration pressure drop increases significantly with the flux ratio. The Re of axial flow can also affect acceleration pressure drop. When the Re of axial flow is 5000, the frictional pressure drop gradient is 36 Pa/m, the acceleration pressure drop is 0.36 Pa/m, 3.6 Pa/m, 34 Pa/m corresponding to the 0.1%, 1%, 10% flux ratio where the acceleration pressure drop of 10% flux ratio is almost same with frictional pressure drop. When the Re of axial flow is and the frictional pressure drop gradient is 242 Pa/m, the acceleration pressure drop is 3.26 Pa/m, 32 Pa/m, 309 Pa/m corresponding to the 0.1%, 1%, 10% flux ratio where the acceleration pressure drop at 10% flux ratio is more than frictional pressure drop. JERT , Liu, 5

6 Fig 4A Frictional Pressure Drop Gradient versus Re with Different Perforation Density without Inflow Fig 4B Frictional Pressure Drop Gradient versus Re with Different Perforation Diameter without Inflow JERT , Liu, 6

7 Fig 4C Frictional Pressure Drop Gradient versus Re with Different Perforation Phasing without Inflow Fig 5A Total Pressure Drop Gradient versus Flux Ratio with different perforation density with Inflow Fig 5B Total Pressure Drop Gradient versus Flux ratio with different perforation diameter with Inflow JERT , Liu, 7

8 Fig 5C Total Pressure Drop Gradient versus Flux Ratio with different perforation phasing with Inflow Fig 6A mixing Pressure Drop Gradient versus Flux ratio with different perforation density with Inflow JERT , Liu, 8

9 Fig 6B mixing Pressure Drop Gradient versus Flux Ratio with different perforation diameter with Inflow Fig 6C mixing Pressure Drop Gradient versus Flux ratio with different perforation phasing with Inflow Fig 7A The Pressure Drop Gradient versus Flux ratio with Re=5000 of Axial Flow JERT , Liu, 9

10 Fig 7B The Pressure Drop Gradient versus Flux ratio with Re=15000 of Axial Flow 3 Models The total pressure drop(the sum of frictional pressure drop, mixing pressure drop, acceleration pressure drop) in horizontal wellbore includes frictional pressure drop, mixing pressure drop, acceleration pressure drop [21] : p p p p (1) t w a m The frictional pressure drop is Darcy Weisbach [22] equation: 2 L V pw fw (2) D 2 The friction factor [3] of perforated wall is 8 Re 8 u 2.5ln B 3.75 * f w 2 f w u (3) in which B is a function of frictional coefficient f0 of ordinary pipe: 8 Re 8 B 2.5ln 3.75 f 0 2 f 0 (4) and the f 0 can be calculated by the Haaland equation [23] given by D 1.8log f0 Re (5) The roughness function * u/ u ( the function of perforation diameter, perforation density and wellbore JERT , Liu, 10

11 diameter) can be calculated from the empirical correlation [24] : d n u p p A * 1 (6) u D A2 From the experiment results, the values of A1, A2under different perforation parameters are given in table 1. The fig.8 presents the accuracy of the frictional pressure drop model. From the fig.8 we can see that the relative error of the model is less than 3%. Fig.8 Precision Verification of Frictional Pressure Drop Calculation Model According to the relation curves of the flux ratio with the mixing pressure drop(the pressure drop caused by heat loss and disturbance after the wall entering current and shaft main current s mixing), the mixing pressure drop is in a linear relationship with flux ratio,so the function is given by m 1 w 2 p B lg R B (7) in which the B1, B 2 is given in table 1. The fig.9 presents the accuracy of the mixing pressure drop model. From the fig.9 we can see that the relative error of the model is less than 5%. JERT , Liu, 11

12 +5% -5% Fig.9A Precision Verification of mixing Pressure Drop Calculation Model with Re=5000 in Axial Flow Fig.9B Precision Verification of mixing Pressure Drop Calculation Model with Re=15000 of Axial Flow Based on the principle of momentum conservation, the acceleration pressure drop is calculated by Eqs a 2 1 p V V (8) The fig.10 presents the accuracy of the total pressure drop model. From the fig.10 we can see that the relative error of the model is less than 4%. JERT , Liu, 12

13 +4% -4% Fig.10A Precision Verification of Total Pressure Drop Calculation Model with Re=5000 of Axial Flow +4% -4% Fig.10B Precision Verification of Total Pressure Drop Calculation Model with Re=15000 of Axial Flow Tab.1 The Coefficient of Models Perforation Perforation Perforation Density Diameter Phasing A1 A2 B1 B2 (shot/m) (mm) ( ) JERT , Liu, 13

14 4 Conclusions (1) Perforations can increase the roughness of the pipe wall obviously which lead to the additional frictional pressure drop. The frictional pressure drop increases with the perforation density, diameter, phasing. In this paper, the perforation density varies 8-24 shots per meter, the perforation diameter is mm, the perforation phasing is degree, and the frictional pressure drop is greater than that of ordinary pipe by 11%-35%. (2) The effect of flux ratio on total pressure drop is significant.the total pressure drop increases with the flux ratio. The pressure drop gradient is bigger than the frictional pressure drop of the ordinary casing pipe(about 29 Pa/m) by -3%,25%,56%,185% when the flux ratio is 0.01%,0.1%,1%,10% respectively. (3) There is a critical value of flux ratio(in this paper, it is 0.05%-0.1%)for the mixing pressure drop. When the actual flux ratio is less than the critical value, the mixing pressure drop is negative. When the actual flux ratio is bigger than the critical value, the mixing pressure drop will increase to a positive value. The scale of the flux ratio increases with the perforation density and perforation diameter. (4) When the flux ratio is less than 0.1%, the proportion of acceleration pressure drop can be neglected. When the flux ratio greater than 0.1%, the frictional pressure drop increases with the flux ratio obviously. When the Re of axial flow is 5000, the acceleration pressure drop is same with the frictional pressure drop under the 10% flux ratio. When the Re of axial flow is 15000, the acceleration pressure drop is bigger than the frictional pressure drop by 10% under the 10% flux ratio. (5) With the increase of flux ratio, the proportion of frictional pressure drop reduces. When the flux ratio is less than 0.1%, the proportion of frictional pressure drop is 97%.When the flux ratio increases to 1%, the proportion of frictional pressure drop reduces to 75%.When the flux ration is 10%, the proportion of frictional pressure drop is as low as 40%. (6) With the increase of flux ratio, the proportion of acceleration pressure drop increases. When the flux ratio is less than 0.1%, the proportion of acceleration pressure drop can be neglected. When the flux ratio increases to 1%, the proportion of acceleration pressure drop is about 10%. When the flux ration is 10%, the proportion of acceleration pressure drop can increase to 45%. (7) When the flux ratio is less than 1%, the mixing pressure drop increases with the flux ratio. When the flux ratio is bigger than 1%, the proportion of mixing pressure drop is always nearly 15%. (8) The relative error of the results of frictional pressure drop model, mixing pressure drop model and the total JERT , Liu, 14

15 pressure drop model with the experiment results are less than 3%, 5%, 4% respectively. Nomenclature p t total pressure drop in perforated horizontal wellbore, Pa p w frictional pressure drop in perforated horizontal wellbore, Pa p a acceleration pressure drop in perforated horizontal wellbore, Pa p m mixing pressure drop in perforated horizontal wellbore, Pa f w L D friction coefficient of the wall in perforation well, dimensionless wellbore length, m wellbore diameter of the perforation well, m density of the fluid, kg/m 3 V V 1 V 2 Re d p n p f o R w velocity of axial flow in wellbore, m/s velocity at inlet of wellbore, m/s velocity at outlet of wellbore, m/s Reynolds number of axial flow, dimensionless perforation diameter, m perforation density, shot per meter frictional factor of ordinary pipe, dimensionless absolute roughness of pipe wall, m the average-velocity ratio between the wall inflow and wellbore section current, dimensionless References [1] Asheim H,Kolnes J,Oudeman P.A Flow Resistance Correlation for Completed Wellbore[J].Journal of Petroleum Science and Engineering,1992,8(2):97~104. [2] Su Z,Gudmundsson J S. Perforation inflow reduces frictional pressure loss in horizontal wellbores[j]. Journal of Petroleum Science and Engineering [3] Su Z,Gudmundsson J S.Pressure Drop in Perforated Pipes: Experiments and Analysis[C].SPE28800,1994:563~574. [4] Ihara M,Brill J P,Shoham O.Experimental and Theoretical Investigation of Two-Phase Flow in Horizontal Wells[C].SPE24766,1992:57~67. [5] Ihara M,Shimizu N.Effect of Accelerational Pressure Drop in a Horizontal Wellbore[C].SPE26519,1993:125~138. [6] Ihara M,Yanai K,Yakao S.Two-Phase Flow in Horizontal Wells[J].SPE Production & Facilities,1995,10(4):249~256. JERT , Liu, 15

16 [7] Yuan H,Sarica C,Brill J P.Effect of Perforation Density on Single Phase Liquid Flow Behavior in Horizontal Wells[C].SPE37109,1996:603~612. [8] Yuan H.Investigation of Single Phase Liquid Flow Behavior in Horizontal wells[d].tulsa:the University of Tulsa,1997. [9] Yuan H,Sarica C,Brill J P.Effect of Completion Geometry and Phasing on Single-Phase Liquid Flow Behavior in Horizontal Wells[C].SPE48937,1998:93~104. [10]Yuan H,Sarica C,Brill J P. An Experimental and Analytical Study of Single-Phase Liquid Flow in a Horizontal Well[J]. Journal of Energy Resources Technology,1997,119(1),20~25. [11] Ouyang L B.Single Phase and Multiphase Fluid Flow in Horizontal Wells[D].Stanford:Stanford University,1998. [12] Ouyang L B,Arbabi S,Aziz K.A Single-Phase Wellbore-Flow Model for Horizontal, Vertical, and Slanted Wells[J].SPE Journal,1998,3(2):124~133. [13] Ouyang L B,Petalas N,Arbabi S,et al.an Experimental Study of Single-Phase and Two-Phase Fluid Flow in Horizontal Wells[C].SPE46221,1998:1~10. [14] Zhou S T,Zhang Q,Li M Z,et al.experimental Study on Variable Mass Fluid Flow in Horizontal Wells[J].Journal of The University of Petroleum,1998,22(5): 53~55. [15] Zhou S T,Zhang Q,Li M Z,et al.the Advances on The Variable Mass Flow in Horizontal Wells[J].Advances In Mechanics, 2002,32(1): 119~127. [16] Wang Z M, Zhang S J, Xue L et al.pressure Drop of Variable Mass Flow in Perforation Completion of Horizontal Wellbore[J]. Drilling & Production Technology,2007,29(3):4~7. [17] Wang Z M, Xiao J N, Wang X Q et al. Experimental Study for Pressure Drop of Variable Mass Flow in Horizontal Well[J]. Journal of Experiments in Fluid Mechanics,2011,25(5):26~29. [18] Abdulwahid, M. A., Niranjan Kumar, I. N. ;Dakhil, S. F. Influence of Radial Flux Inflow Profile on Pressure Drop of Perforated Horizontal Wellbore[J]. Journal of Energy Resources Technology,2014,136(4):1~7. [19] Quan Zhang, Zhiming Wang, Xiaoqiu Wang, Jiankang Yang. A New Comprehensive Model for Predicting the Pressure Drop of Flow in the Horizontal Wellbore[J]. Journal of Energy Resources Technology,2014,136(4):1~9. [20] Weipeng Jiang, Cem Sarica, Erdal Ozkan, Mohan Kelkar. Investigation of the Effects of Completion Geometry on Single-Phase Liquid Flow Behavior in Horizontal Wells[J]. Journal of Energy Resources Technology,2000,123(2):119~126. JERT , Liu, 16

17 [21] Wang Z M, The Optimization Theory and Application of Well Completion for Complex Structure Wells[M], Petroleum Industry Press,2010,55~57. [22] White, F.M., Fluid Mechanics, McGraw-Hill, Inc., [23] Ito,H. and Imai, K., Energy Losses at 90 Pipe Junctions, Journal of the Hydraulics Division, Proc. ASCE, September, [24] Gardel, A., Les Pertes de Charge Dans Les Ecoulements au Travers de Branchements En Te, Lausanne Univ. Polytech. Ecole Pub. 44, 1957, 1~13. Author:. Author introduction: Wei Jianguang, male, associate professor. Research area: theory and technique of well completion optimization, theory and technique of EOR, seepage mechanism of unconventional oil and gas. Tel: , weijianguang@163.com. Natural Science Foundation of Heilongjiang Province project research on the change pattern of working viscosity of polymer solution in the reservoir (No.D ) Natural Science Foundation of China project research on seepage mechanism of gas-water two phase in the shale gas reservoir considering the condition of pollution (No ) Figure captions Fig 1 Experiment System for Complex Flow in Horizontal Wellbore Fig 2 Simulation Unit Diagram Fig 3A 45 Screw Perforating Phasing Fig 3B 90 Screw Perforating Phasing Fig 3C 180 Screw Perforating Phasing Fig 4A Frictional Pressure Drop Gradient versus Re with Different Perforation Density without Inflow Fig 4B Frictional Pressure Drop Gradient versus Re with Different Perforation Diameter without Inflow Fig 4C Frictional Pressure Drop Gradient versus Re with Different Perforation Phasing without Inflow Fig 5A Total Pressure Drop Gradient versus Flux Ratio with different perforation density with Inflow Fig 5B Total Pressure Drop Gradient versus Flux ratio with different perforation diameter with Inflow Fig 5C Total Pressure Drop Gradient versus Flux Ratio with different perforation phasing with Inflow Fig 6A mixing Pressure Drop Gradient versus Flux ratio with different perforation density with Inflow Fig 6B mixing Pressure Drop Gradient versus Flux Ratio with different perforation diameter with Inflow Fig 6C mixing Pressure Drop Gradient versus Flux ratio with different perforation phasing with Inflow Fig 7A The Pressure Drop Gradient versus Flux ratio with Re=5000 of Axial Flow JERT , Liu, 17

18 Fig 7B The Pressure Drop Gradient versus Flux ratio with Re=15000 of Axial Flow Fig.8 Precision Verification of Frictional Pressure Drop Calculation Model Fig.9A Precision Verification of mixing Pressure Drop Calculation Model with Re=5000 in Axial Flow Fig.9B Precision Verification of mixing Pressure Drop Calculation Model with Re=15000 of Axial Flow Fig.10A Precision Verification of Total Pressure Drop Calculation Model with Re=5000 of Axial Flow Fig.10B Precision Verification of Total Pressure Drop Calculation Model with Re=15000 of Axial Flow Table captions Tab.1 The Coefficient of Models JERT , Liu, 18

FE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering)

FE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering) Topic: Fluid Properties 1. If 6 m 3 of oil weighs 47 kn, calculate its specific weight, density, and specific gravity. 2. 10.0 L of an incompressible liquid exert a force of 20 N at the earth s surface.