Evaluation of Different Modelling Methods Used for Erosion Prediction

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1 Paer No Evaluation o Dierent Modelling Methods Used or Erosion Prediction MYSARA EISSA MOHYALDIN 1, NOAMAN ELKHATIB 2, MOKHTAR CHE ISMAIL 3 1 College o Petroleum Eng. And Tech. Sudan University o Science and Technology, Sudan P O Box 73, Khartoum, Sudan 2 Geoscience and Petroleum Engineering Deartment Universiti Teknologi PETRONAS, Malaysia Bandar Seri Iskandar, Tronoh, Perak, Malaysia mysara12002@yahoo.com 3 Mechanical Engineering Deartment Universiti Teknologi PETRONAS, Malaysia Bandar Seri Iskandar, Tronoh, Perak, Malaysia ABSTRACT In this aer, the three methods o modeling erosion in ie comonents due to sand roduction with oil and gas are investigated by the mean o comarison o results obtained rom Salama model, DIM model, and DPM model, the three models selected to reresent emirical, semi-emirical, and CFD methods, resectively. The DPM model was assumed as a benchmark based on which Salama model and DIM model were investigated. The results obtained rom the DIM model agree airly with those obtained rom the DPM model whereas Salama model highly overestimates the DPM model. Based on the comarison, Salama model was modiied to increase its accuracy, rom one hand, and to extend it to alication to oil, rom the other hand. Keywords: erosion, Salama, direct imingement, discrete hase, model INTRODUCTION The entrainment o sand articles in luids lowing through horizontal or vertical ies is requently encountered during oil and gas roduction and transortation. In conventional oil roduction, sand is roduced with oil and gas rom a sandstone reservoir under certain conditions, such as are unconsolidated ormation, water breakthrough, reservoir ressure deletion, and high lateral tectonics (Carlson et al. October 1992). In unconventional oil or

2 crude bitumen, which is a mixture o sand, bitumen, and water (Tian 2007); sand is roduced with very high volume raction. The entrainment o sand in luids causes wear o ies and ittings through which it lows due to the imingement o sand articles on internal surace o the ies and ittings. The erosion may take lace in dierent subsurace and surace comonents such as in sand control screen (Colwart et al. 2007), choke (Haugen et al. 1995), valve (Mazur et al. 2004), lugged tee, and elbow (Chen et al. 2006) The severity o the wear deends on many actors related to the luid, sand articles, and target material (Finnie 1972) (Deng et al. 2005), (Barton 2003) (Ahlert 1995), (Karelin 2002). N A Barton (Barton 2003) has arranged the comonents, where the erosion takes lace according to erosion vulnerability, in eight ranks ranging rom chokes as the most vulnerable comonent to straight ies as the least vulnerable comonent. The wear (erosion) rate or a material used in any low rocess can be determined either by ield or laboratory tests under simulated conditions or by calculating it using a selected mathematical or comutational model, roviding that all the low arameters are included in the model. Although ield and laboratory tests guarantee more accurate results than modeling, but the later eliminates some disadvantages o the ormer such as: 1. The cost required to set u the exerimental rig. 2. The diiculties o controlling the rocess arameters during the test. 3. Longer time required or a test run 4. In the case o some ield tests, the interrution o the rocess and destruction o the material. Modeling erosion requires roer selection o the model that suitable to the seciied rocess, rom one hand, and rovides acceted accuracy, rom the other hand. The models in oen literature used or rediction o erosion due to sand low with oil or gas can be groued into three categories as shown in Table 1. Table 1: Methods o erosion modeling Category Advantages Disadvantages Examles CFD models The most accurate, rovides erosion rate distribution, solve or the rimary (luid) and secondary (sand articles) hases Costly (Mostly commercial sotware), time consuming, high diiculties Fluent, Ansys Semiemirical models Emirical models Accuracy to be examined, solve or the secondary (sand articles) hase Moderate diiculty Direct imingement model Accuracy to be examined, very easy No articles solution API model, Salama model One model has been selected rom the emirical method and another one rom the semi-emirical method. The two models have been emloyed to develo a comutational code or erosion rate rediction. The results obtained rom the code were comared to those obtained rom the CFD model to evaluate their accuracy, considering the CFD model as a benchmark. 1.1 Emirical method In this method, erosion is redicted or a comonent (most robably elbow or tee) by using the luid velocity (no articles or bubbles tracking). This method is commonly based on simle emirical correlations that redict erosional velocity (the velocity above which erosion occurs) and erosion rate, and it is more alicable to gas low where the disersed hase (articles or bubbles) is almost lowing at the luid mean velocity. The erosional velocity, Ve is widely redicted using the American Petroleum Institute Recommended Practice equation (API RP 14 E) (Institiute 1991). c Ve (1)

3 Where C is constant, its value as roosed by API RP 14 E is 100 or continuous service and 125 or intermittent service, and is density o the luid. Many researchers and investigators have questioned the accuracy o equation (1) on the ground o neglecting o other imortant actors such as articles size and shaes, comonent geometries and luid density. Thereore many attemts have been made to enhance the accuracy, and to extend the alicability o RP 14 E equation. Salama and Venkatesh roosed a model or rediction o enetration rate in elbows and tees (Salama and Venkatesh 1983). Their model in SI units, assuming a sand density o 2650 kg/m 3, can be written as ollows: 2 WV ER (2) PD Where ER is the erosion rate (mm/year), W is sand roduction rate (Kg/s), V is the luid low velocity (m/s), P is the hardness arameter (Bar), and D is the ie diameter (m). Salama and Venkatesh used equation (2) to calculate the erosional velocity or steel ies using a P value o 1.05X10 4 Bar or allowable erosion rate o mm/year. This resulted in the ollowing equation or erosional velocity D V e (3) W The shortcomings o Salama and Venkatesh model (equation (3)) are its neglect o sand article size and shae, and its inalicability to two-hase (liquid-gas) low. Their model also neglects sand hardness, but since the model only deals with sand articulates where their hardness varies slightly, so we believe that neglecting the hardness is logical. The material hardness is also not considered due to the act that the model only deals with carbon steel materials. Salama (Salama, 2000) incororated the eect o two-hase mixture density and article size into equation 2-15 and roosed the ollowing equation WVm d ER 2 (4) Sm D m Where ER is the erosion rate (mm/year), W is the sand roduction rate kg/s, d is article diameter (micron), D is the ie internal diameter (m), and and are mixture velocity (m/s) and density (kg/m3), resectively. In equation 2-17, S m is a geometry-deendant constant as given in Table 1. Equation (4) was develoed through numerous tests that were carried out using water and nitrogen gas. Since water and gas viscosities are almost constant, thereore the viscosity arameter has not been included in the equation. Salama, however, exected that higher viscosity will result in reduction o erosion rate (Salama, 2000). Table 1: The geometry-deendent constant in Salama equation (Salama, 2000) Geometry Elbow (1.5 and Seamless and Plugged tee Plugged tee (gas 5D cast elbows (1.5 (gas-liquid) low) to 3.25 D) S m In this work, Salama model has been selected as an examle o emirical method or sand erosion rediction. A redictive tool has been develoed by emloying Salama model to Visual Basic rogramming. In the redictive tool, rom the inut data orm o Salama model shown in Figure 1, the user can select the geometry and inut luid and sand roerties, which include low velocity, sand roduction rate, sand size, ie diameter, and luid density. To examine the results o Salama model, the data shown in Figure 1 or velocity, sand roduction rate, sand size, and ie diameter was used. Three values o density were used to redict erosion rate in gas (with density o kg/m3), water (with density o 1000 kg/m3), and oil (with density o 850 kg/m3). The variation o erosion rate with velocity or the three luids is shown in Table 2.

4 Figure 1: Inut data orm o Salama model Table 2: Variation o erosion rate with velocity or gas, water, and oil (Salama model) Velocity m/s Erosion rate mm/year gas water oil

5 By comaring column 3 and column 4 in Table 2, we can notice that the erosion rate or oil is greater than that o water, which is enological result. This error is due to the act that no account is taken or viscosity in the Salama model and erosion rate changes inversely with luid density. This result is shown grahically in Figure 2. Figure 2: Variation o erosion rate with velocity or water and oil (Salama model) 1.2 Semi-emirical method Direct imingement model (DIM) was selected as an examle or this method. In the DIM method, erosion is redicted by using simliied articles trajectory equations (the direct imingement model). This is a mechanistic model develoed by Erosion/Corrosion research center (E/CRC) at University o Tulsa to redict the enetration rate o direct imingement o elbows and tees. The direct imingement model can redict the enetration rate ater determining the direct imact velocity. The data required or the direct imingement model are those relating to the comonent (geometry and size), low (velocity, density and viscosity), and article (density, size, and shae). To account or the article trajectory along the low stream, the concet o equivalent stagnation length has been introduced. The concet o equivalent stagnation length can be exlained by the same way as the equivalent length used to redict local ressure loss in ittings, in which, dierent comonent geometries have dierent equivalent stagnation lengths (McLaury 1996). The DIM model has been emloyed to develo a redictive tool or easy and quick rediction o erosion rate. The tool develoment involves a numerical solution to the simliied equation o article motion roosed by E/CRC (Equation 5). Our numerical solution algorithm is shown in Figure 3 with and Re are the dimensionless article mass ratio and article Reynolds number deined reviously by E/CRC (McLaury 1996). dv 1 0.5( V V ) V V 24 ( V V ) 0.75 (5) dx d V V d The solution o the above equation enables tracking sand articles to calculate their velocity within the stagnation zone and their imingement velocity. The imingement velocity is then introduced to a sand erosion rediction ormula to redict sand erosion rate.

6 0 1, 0.01, , 1 1 1, 1, 0.5,0, X VA VA X VA 24 0,, 1 & 100 Yes No Yes No Figure 3: The numerical solution o the equation o articles motion. The DIM model inut data orm is shown in Figure 4. The user can inut data related to the luid, sand, and target material to this orm; and select the geometry.

7 Figure 4: Inut data orm o the DIM model The change o the article s velocity deends on many actors that are related to the carrier luid, geometry o the target material and the roerties o the disersed articles. Three luids have been considered to analyze the eect o luid roerties on article s velocity in elbow. These luids are air, water, and crude oil with roerties shown in Table 3. Similar roerties and geometry o sand are assumed or all luids. Table 3: Inut data or erosion simulation Proerty Unit Gas Water Oil Density Kg/m Viscosity Pa.s Velocity m/s 20 Sand size Micron 300 Sand density Kg/m Elbow ID m 0.05 The results o sand trajectories or the three luids are shown in Figure 5. The imingement velocities are or air, 1.28 or water, and 0.39 or oil. In air, sand velocity changes very slightly to the extent that the imingement velocity can be assumed as equal to the air velocity. For liquids, sand decelerates raidly to hit the target wall with very low velocity.

8 Figure 5: Sand trajectory along the stagnation zone or air, water, and oil The raid deceleration o liquids is mainly due to eect o viscosity, which is exressed mathematically by rewriting o the equation o article motion (Equation 5) in the ollowing orm: dv b a dx Re (6) With ( V V ) V V a d V 16 b V d d Re ( V V ) dv It means that, or liquids with high viscosity (i.e. low Reynolds number) are high, in contrast to gases. dx For more investigation o the eect o viscosity and density on erosion rate, the variation o erosion rate with low velocity or oil with density o 850 kg/m 3 at dierent viscosity is shown in Figure 6 and the variation o erosion rate with low velocity or oil with viscosity o Pa.s at dierent density is shown in Figure 7 (other arameters are same to those used in Table 3). It is clear that erosion rate decreases with increase o both density and viscosity. The eect o viscosity, however, is more signiicant.

9 Figure 6: Variation o erosion rate with low velocity or oil with dierent viscosity Figure 7: Variation o erosion rate with low velocity or oil with dierent viscosity 1.3 Comutational Fluid Dynamics (CFD) method The CFD is the simulation o luids in dynamic (motion) state using numerical methods. The solution is attained using many models and techniques that suit several alications. CFD simulation o sand erosion is generally erormed in our stes. In the irst ste, the model is built and divided into sub domains using a grid generation technique. In the second ste, the luid velocity values are redicted along the low direction by solving a low model and a turbulence model. In the third ste, sand articles velocity and angle o imingement are redicted using a article equation o motion (Eulerian or Lagrangian). And inally, the data o article velocity and angle o imingement are introduced to a selected erosion rediction model to redict the erosion rate. Figure 8 shows the simulation rocedure using the CFD Fluent sotware.

10 Grid Generation Flow Solution (Navier-Stokes equation and turbulence model) Sand Trajectory Sand Erosion Calculation Figure 8: Sand Erosion Simulation Using Fluent Sotware In this aer, discrete hase model (DPM) model the CFD Fluent sotware was selected as an examle o the CFD method to redict sand erosion in an elbow. The result o the CFD simulation was considered as a benchmark or investigation o the other two methods to determine the accuracy o each or alication in gas, oil, and water low Model creation and grid generation A 2-D geometry has been created and meshed in Gambit and then transerred to Fluent sotware or CFD solution. The geometry is 50 mm (2 in) internal diameter elbow ended with two straight ies 100 mm each and the elbow outer wall curvature length is 157 mm. Quadratic mesh tye with size 1 mm has been selected to obtain a total o cells. Four boundaries have been selected as shown in Figure 9. The INLET VELOCITY boundary is the boundary rom where low is solved and articles are tracked along the stream until the outlow boundary. The erosion is then simulated in one o the two wall boundaries.

11 Figure 9: The model generation and meshing Solution o luid and articles trajectory Sand erosion has been simulated using the comutational luid dynamics (CFD) Fluent V commercial sotware. Sand low rate o kg/s was injected rom the INLET VELOCITY boundary shown in the geometry. The sand erosion simulation has been erormed ollowing the low solution and article trajectory stes. In the low solution, the k model was selected or turbulence solution. The luid velocity at the inlet was set to 20 m/s. The solution was initialized, requesting 170 iterations; the solution converged ater 157 iterations. The low is assumed to be two hases (air+ sand) dilute slurry low. The main arameters o the rimary and disersed hases are as shown in Table 4. Table 4: The main arameters o the hases Parameter Unit Value Air (continuous hase) Density Kg/m Viscosity Pa.s Sand (disersed hase) Density Kg/m Size m Mass low rate Kg/s Figure 10 shows the velocity contours o the rimary hase in the elbow. The maximum luid velocity is 26.7 m/s in the vicinity o curvature o the inner wall.

12 Figure 10: Velocity contours o the rimary hase Ater the solution o the rimary hase, sand has been tracked along the axial osition. The article trajectory allowed acquiring o articles velocity (Figure 11 and Figure 12) and articles angles o imingement (Figure 13). The articles angle o imingement as shown in Figure 13) kees constant at zero in the horizontal ie until the start oint o the elbow curvature, where it starts to increase to reach 90o at the end oint o the elbow curvature and the start oint o the vertical ie to remain constant until the end o the vertical ie. Figure 12 shows that no articles iminge the inner wall at this condition, and the imingement velocities at the outer wall are in the range rom to m/s. The variation o the velocity o a single article along the ath length is shown in Figure 14.

13 Figure 11: Particle velocity tracking Figure 12: Particle velocity along the low ath

14 Figure 13: Particle velocity angles Erosion rate calculations The calculated article velocities and angles o imingement are substituted into the ollowing equation to calculate the erosion rate at every node in the assigned wall. N b( v) m C( d ) ( ) v ER (7) 1 A ace Where m and d are article mass low rate and size, resectively, is the angle o imingement, v is the article velocity, and A ace is the area o target subject to erosion. C,, and b are unctions o article size, angle o imingement, and velocity, resectively. In this work, the imact angle unction has been deined to Fluent using a iece-linear roile with values shown in Table 5; and the diameter unction and velocity exonent unction were set to values o 1.8e-09 and 2.6, resectively. Table 5: Values o angle unction deined to the model (degrees) It is assumed that article s velocity changes ater hitting a solid wall. The article velocity u 2 ater the imingement is related to that beore the imingement u 1 as ollows: u 2 eu 11 (8) Where e =the coeicient o restitution, the value o which deends on many actors such as the coeicient o kinetic riction, article velocity, angle o imingement and the materials o articles and substrates (Sommereld

15 1992). Grant and Taako roosed two relationshis between the coeicient o restitution in arallel and erendicular directions, and angle o imingement. The relationshis are exressed as ollows (Chen et al. 2006): 2 3 e arallel (9) 2 3 e er (10) Comaring Table 5 with Figure 13, we can conclude that the maximum angle o imingement unction is, aroximately, at the osition 150 mm o the ath which is emhasized by the maximum erosion rate in Figure 14. The maximum erosion rate is 7.56E-7 kg/m2.s. Erosion rate unit in Fluent is kg/m 2.s. The maximum erosion rate or the outer wall can be obtained in mm/year as ollows: The total erosion rate is 5.512E-05 kg/m2.s which is equivalent to mm/year. Figure 14: Erosion rate variation along the ath (outer wall) To analyze the eect o velocity on the maximum erosion rate and total erosion rate, dierent values o inlet velocity were entered. The variation o maximum erosion rate with velocity is shown in Table 6 and Figure 15; and the variation o total erosion rate with velocity is shown in Table 7.

16 Table 6: Variation o maximum erosion rate with velocity Velocity m/s Max Erosion rate Kg/m 2.s mm/year e e e e e e Table 7: Variation o total erosion rate with velocity Velocity m/s Total Erosion rate Kg/m 2.s mm/year e e e e e Figure 15: Variation o erosion rate with air velocity 1.4 Comarison between the three methods The Salama and DIM models have been comared with the CFD results using the same arameters o the CFD simulation as inut data to the code. Figure 16 shows air agreement between DIM and CFD models, whereas the Salama model redicts much higher erosion rate as comared to the other two models.

17 Figure 16: Comarison o results o Salama, DIM, and CFD models The CFD model can be considered as a benchmark or evaluating the Salama and DIM models as it emloys more sohisticated solutions or the rimary and secondary hases beore redicting erosion rate. As the DIM model agreed airly with the CFD results, the Salama model can then be imroved urther by comaring it with the DIM model. Comaring the salama model with DIM model resulted in unexected outcome. It was attained that the erosion rates rom Salama model are higher than those rom the DIM model or gas low, whereas they are lower than the DIM model or liquids (water and oil); and the underestimation is more in water than it is in oil. Figures show comarison between Salama model and DIM model or gas, water, and oil low, resectively. Figure 17: Comarison between Salama model and DIM model (gas)

18 Figure 18: Comarison between Salama model and DIM model (water) Figure 19: Comarison between Salama model and DIM model (oil) From Figure 17 to Figure 19, Salama model can be imroved based on the comarison with the DIM model. Three models are roosed or erosion rediction o gas, water, and oil as ollows: 0.474ERs Gas ERm 3.492ERs Water ERs 0.268ERs Oil Where ER is the erosion rate calculated by Salama model and s ER m is the modiied erosion rate. (11)

19 Conclusion Salama model and DIM model have been emloyed to develo a comutational code or rediction o articles (sand) erosion in ies comonents. The two models have been investigated against results obtained rom the CFD Fluent commercial sotware. The investigation results in air agreement o the DIM model with the CFD, whereas Salama model highly overestimates the CFD. Based on comarison o Salama model with DIM model, an imrovement to Salama model has been roosed to account or viscosity which is not considered in the original model. This imrovement increases its accuracy and extends the model alicability to oil low. The develoed code allows rediction o erosion rate with the same accuracy o CFD while eliminating its limitations o high cost, diiculty, and time-consuming. Reerences [1] Ahlert, K. (1995). The eects o article imingement angle and surace wetting on solid article erosion on AISI 1018 steel, U o Tulsa. M Sc. [2] Barton, N. A. (2003). Erosion in Elbows in hydrocarbon roduction systems: Review document. [3] Carlson, J., Curley, D., King, G., Price-Smith, C. and Waters, F. (October 1992). Sand control: why and how? [4] Chen, X., Mclaury, B. S. and Shirazi, S. A. (2006). "Numerical and exerimental investigation o the relative erosion severity between lugged tees and elbows in dilute gas/solid two-hase low." Wear 261: [5] Colwart, G., Burton, R. C., Eaton, L. F. and Hodge, R. M. (2007). Lessons Learned on Sand-Control Failure and Subsequent Workover at Magnolia Deewater Develoment. SPE/IADC Drilling Conerence, Amsterdam. [6] Deng, T., Chaudhry, A. R., Patel, M., Hutchings, I. and Bradley, M. S. A. (2005). "Eect o article concentration on erosion rate o mild steel bends in a neumatic conveyor." Wear 258: [7] Finnie, I. (1972). "Some observations on the erosion o ductile materials." Wear 19. [8] Haugen, K., Kvernvold, O., Ronold, A. and Sandberg, R. (1995). "Sand erosion o wear-resistant meterials: erosion in choke valves." Wear Cambridge, UK: [9] Institiute, A. P. (1991). API RP 14 E Recommended Practice or Design and Installation o Oshore Production Platorm Piing Systems. Washington DC, American Petroleum Institiute:. 22. [10] Karelin, C. G. D. A. V. Y. (2002). Abrasive erosion and corrosion or hydraulic machinary Vol 2, Imrial college ress. [11] Mazur, Z., Camos-Amezcua, R. and G. Urquiza-Beltr an, A. G.-G. (2004). "Numerical 3D simulation o the erosion due to solid article imact in the main sto valve o a steam turbine." Alied Thermal Engineering 24: [12] Mclaury, B. S. (1996). Predicting Solid Particle Erosion Resulting rom Turbulent Fluctuations in Oilield Geometries, University o Tulsa. PhD Thesis. [13] Salama, M. M. and Venkatesh, E. S. (1983). Evaluation o Erosional Velocity Limitations in Oshore Gas Wells OTC 15th Annual OTC. Houston, Texas. [14] Sommereld, M. (1992). " Modelling o article-wall collisions in conined gas-article lows " Int. J. Multihase Flow 18, 6: [15] Tian, B. (2007). mechanistic understanding and eective revention o erosion-corrosion o hydrotransort ies in oil sand slurries, U o Calgary. M Sc..