Reservoir Formation Damage Episode 2 Part 4 doc

Cake Filtration: Mechanism, Parameters and Modeling 307 Table 12-2 Model Input Parameters* Parameter Symbol Cake porosity without 10 _ ,_ 0 compaction and small * particle retention, cm 3 pore volume/cm 3 bulk volume Cake particle volume e ° — 1 — d) ° fraction cm 3 particle/cm 3 J bulk volume Particle density, g/cm 3 p Carrier fluid (water) p density, g/cm 3 Slurry total particle ( w ) mass fraction, V *f'**ry g particles/g slurry Slurry total particle Lj ] volume fraction, cm 3 P sturry particles/c/M 3 slurry Slurry total particle ( w /• ) P mass per carrier fluid (c I — ••••*• • ."?— volume, g particle/cm 3 * rry 1 — \W ^ J carrier fluid 1 ~ p '|>-)- Data 1 Data II 0.39* 0.73 C 0.61 C 0.21 d 1.18* 1.18* 0.97* 0.97" 0.101* — — 0.2' >, 0.109 C 0.295 C rv i ny Slurry carrier fluid vol- / \ -t + fc ) /P f 1 0-915 e 0.8 C ume fraction, cm 3 carrier ^ ''shiny L V P I 'shiny /"P\ fluid/cm 3 slurry = 1 - (a ) V Pf 'shiny Slurry carrier fluid ( u \ volumetric flux, cm 3 s *** carrier fluid/(cm 2 cake surface • s) Slurry injection pres- p e sure, atm Filter outlet pressure, p e atm 2.0 x I O' 3 2.0 xlO' 3 b d 8.9° 8.9* 1.0" 1.0* * Civan, F., 1998b; reprinted by permission of the AIChE, ©1998 AIChE—All rights reserved. 308 Reservoir Formation Damage Parameter Table 12-2 (continued) Symbol Data I Data Slurry small particles mass per carrier fluid volume, g small parti- cles/cm 3 carrier fluid lurry 0.049" 0.059" Slurry small particles volume per carrier fluid volume, cm 3 small parti- cles/cm 3 carrier fluid 0.415 C Filtrate small particle mass per carrier fluid volume, g small parti- cle/on 3 carrier fluid 0, 0.005° 0, 0.005" Filter thickness, cm Lf 0.5° 0.5" Slurry side filter radius, cm 5.08" Filtrate side filter radius, cm 2.54" Rate constant for small particle deposition within the cake, s' 1 l.OxHT 6 "- Rate constant for small particle entrainment within the cake, s l k t 4.35 5.0 xl(T 7 "' Rate constant for total particle deposition over the slurry side cake surface, dimensionless 1.0" Rate constant for total particle erosion over the slurry side cake surface, 0 s 0* Rate constant for small particle deposition over the slurry side cake surface, dimensionless 0.05"'" 0."'" Rate constant for small particle erosion over the slurry side cake surface, 0.' 0.' Parameter dimensionless 30. 30.0 Cake Filtration: Mechanism, Parameters and Modeling 309 Table 12-2 (continued) Parameter Parameter dimensionless Parameter dimensionless Parameter dimensionless Cake permeability with- out compaction and small particle deposi- tion, darcy Filter permeability, darcy Viscosity of carrier fluid (water), cp Parameter dimensionless Parameter dimensionless An empirical constant, atm A constant, dynelcnfls" A constant , dimensionless Tangential velocity of the injected slurry, ants Symbol 0.2 P 8 *; kf n a « Pa k' ri V Datal 1." 0.09° 0.49" 3.5xl.(T 3a l.Oxl.O" 4 " 1.0" 1.0' 1/2' 00* 1.0° 1.0" 0,0.01" Data II 1.0* 0.07° 0.47" 3.5xl.0~ w l.Oxl.O- 4 " 1.0" 1.0' 1/2 7 0.0118* 1.0" 1.0" 0,0.01" a : Data assumed b : Corapcioglu and Abboud ( 1 990) c : Data calculated d : Tien,etal.(1997) f : Adin(1978) p : Data for the constant pressure case r : Data for the constant rate case s : Static filtration 310 Reservoir Formation Damage (text continued from page 306) particle invasion into an inefficient filter is demonstrated by assuming a value of ( C p2i) filer =0.005g/cm 3 in Figures 12-12 through 12-16. Civan's (1998b) results have similar trends, but different values than the results of Corapcioglu and Abboud (1990) and Abboud (1993), because of the simplifying assumptions involved in their calculations, such as incom- pressible cake and constant cake porosity and the use of the same rates of deposition for small and all (large plus small) particles over the progressing cake surface. Also, the average porosity of the filter cake can vary significantly in actual cases as described by Tien et al. (1997). Next, Civan (1998b) obtained the numerical solution for the constant pres- sure drive filtration. Corapcioglu and Abboud (1990) and Abboud (1993) did not present any results for this case. The flow rate is allowed to vary according to Eqs. 12-129 and 12-119 for the radial and linear cases, respectively. In Figures 12-17 through 12-21, Civan's (1998b) results for the linear and radial cases are compared. The results presented in Figures 12-12 through 12-21 indicate that fine particle invasion into the filter plays an important role. The differences between the radial and linear (text continued on page 315) 10 20 30 40 Filtration Time, min. 50 Figure 12-12. Comparison of the cake thickness for linear and radial constant rate filtration (Civan, R, 1998b; reprinted by permission of the AlChE, ©1998 AlChE. All rights reserved). >o5 a oo 2. • 1! = —• O ca'_ o^ 5T <• c* CD 3 co - co CD T| C P J CO ® -"-"CD B<0 13 Ml 0 . 05 Q. 03 CT 3 1 . •< O. ~O CD CD W 1 O CO ~* CO =: O 3 —J (p Q) 2, ~" ZT 03 3- u CD Q. Suspended Small Particle Volume/Bulk Cake Volume §- o' H <D ©8 2 ill 00 0) a > 2- H- iff — 3 =.0-0 (Q 3 0) o CO D O CD ' •* < 715 CD - CD 00 03 CT = •O B: =. O CT-0 << O • 3 = 8? o = 3 D Deposited Small Particle Volume/Bulk cake volume o o o o -n o n R- 0) o G. 2- 5' cro m 312 Reservoir Formation Damage 10 20 30 40 Filtration Time, min. Figure 12-15. Comparison of the cake porosity for linear and radial constant rate filtration (Civan, R, 1998b; reprinted by permission of the AlChE, ©1998b AlChE. All rights reserved). 10 20 30 40 Filtration Time, min. 50 Figure 12-16. Comparison of the filtrate volume for linear and radial constant rate filtration (Civan, F., 1998b; reprinted by permission of the AlChE, ©1998b AlChE. All rights reserved). >8 3 Ou og 3- co C m JD 3 ?i CD TO <£ co s Deposited Small Particle Volume/Bulk Cake Volume Cake Thickness, cm 2 < -' » g g CO Tl O <D - "" CD CO CD Q. CD I CD CD a. co CO •a . ® 5' q CD 3. 03 co ~« CO jij o >§ Oco o CD 31 I o' s CD O cr »_ en "d P 0> O s o era as a ~* Q-cra IT 55' fi 0 3 >o h- O Suspended Small Particle Volume/Bulk Cake Volume Cake Filtration: Mechanism, Parameters and Modeling 315 20 30 40 Filtration Time, min. 50 60 Figure 12-21. Comparison of the filtrate volume for linear and radial constant pressure filtration (Civan, R, 1998b; reprinted by permission of the AlChE, ©1998 AlChE. All rights reserved). (text continued from page 310) filtration results are more pronounced and the cake thickness and filtrate volume are less for the constant pressure filtration. Tien et al. (1997) have solved their partial differential model numerically using a ready-made Fortran subroutine for linear filtration at static condition and reported numerical solutions along the filter cake only at the 100- and 1000-seconds times. Their model generates numerical solutions over the thickness of the filter cake, whereas, Civan's (1998b, 1999b) models calculate the thickness-averaged values. Therefore, Civan averaged the profiles predicted by Tien et al. (1997) over the cake thick- ness and used for comparison with the solutions obtained with the thickness-averaged filter cake model. Because Tien et al. (1997) reported numerical solutions at only two time instances, this resulted in only two discrete values. Civan generated the numerical solutions with the linear filtration model using the data identified as Data II in Table 12-2 for constant rate and constant pressure filtrations. As can be seen by Civan's (1998b) results presented in Figures 12-22 through 12-25, his ordinary differential model can closely reproduce the results of the Tien et al. (text continued on page 318) 316 Reservoir Formation Damage 200 400 600 Filtration Time, sec. 800 1000 Figure 12-22. Comparison of the cake thickness for constant rate filtration (Civan, R, 1998b; reprinted by permission of the AlChE, ©1998 AlChE. All rights reserved). - Present study • Tien etal( 1997) 0.5 200 400 600 Filtration Time, sec. 800 1000 Figure 12-23. Comparison of the cake porosity for constant rate filtration (Civan, F., 1998b; reprinted by permission of the AlChE, ©1998 AlChE. All rights reserved). [...]... Veracruz, Mexico, October 10-13, 19 94, pp 399 -4 12 Civan, F., "A Multi-Purpose Formation Damage Model," SPE 31101 paper, Proceedings of the SPE Formation Damage Control Symposium held in Lafayette, Louisiana, February 14- 15, 1996, pp 311- 326 Civan, F, "Incompressive Cake Filtration: Mechanism, Parameters, and Modeling," AIChE J., Vol 44 , No 11, November 1998a, pp 23 7 923 87 Civan, F., "Practical Model for... Washington, DC, October 4- 7, 19 92, pp 21 9 -23 4 Sherman, N E., & Sherwood, J D., "Cross-Flow Filtration: Cakes With Variable Resistance and Capture Efficiency," Chemical Engineering Science, Vol 48 , No 16, 1993, pp 29 13 -29 18 Smiles, D E., & Kirby, J M., "Compressive Cake Filtration—A Comment," Chem Engng ScL, Vol 48 , No 19, 1993, pp 343 1- 343 4 Cake Filtration: Mechanism, Parameters and Modeling 321 Tien, C., Bai,... Petroleum Technology, Vol 34, No 10, December 1995, pp 50- 54 Metzner, A B., & Reed, J C., "Flow of Non-Newtonian Fluids—Correlation of the Laminar, Transition, and Turbulent Flow Regions," AIChE J., Vol 1, No 4, 1955, pp 43 4 -44 0 Peng, S J., & Peden, J M., "Prediction of Filtration Under Dynamic Conditions," SPE 23 8 24 paper, presented at the SPE Intl Symposium on Formation Damage Control held in Lafayette,... Engineering, Vol 17, No 1 /2, February 1997, pp 29 -40 Part IV Formation Damage by Inorganic and Organic Processes Chemical Reactions, Saturation Phenomena, Deposition, and Dissolution Chapter 13 Inorganic Scaling and Gepchemical Formation Damage Summary Various processes leading to inorganic scaling and formation damage are discussed Special attention is given to formation damage caused by the adverse... precipitate, CO2 partial and total pressures, and temperature, based on the equilibrium relationship for the calcium carbonate scale formation by the reaction Ca +2 CaCO3(s) + CO2(g} + H2O (13-1) The chart given in Figure 13-1 by Shaughnessy and Kline (19 82) shows the calcium carbonate precipitation regions located above the equilibrium curves of the 2. 8 MPa (40 0 psi) and 3 .4 MPa (500 psi) CO2 partial pressures... (Nordstrom and Munoz, 19 94) However, alteration of the composition and saturation of the aqueous phase and the fluid shear can induce the entrainment, 326 Reservoir Formation Damage migration, and redeposition of fine mineral particles and therefore cause formation damage (Chang and Civan, 1991, 19 92, 1997) Formation damage resulting from the injection of incompatible waters into reservoirs can be avoided... this phenomenon by the Le Chatelier principle Because H2O 20 0«F C) 46 44 42 ~ 40 Q 01 3 38 O V) . Chatelier principle. Because H 2 O 46 44 42 ~ 40 Q 01 3 38 O V) < ;2 s 20 0«F C) DISSOLVED CALCIUM, MMOLE/B Figure 13-1. Natural and induced scale damage mechanisms (Shaughnessy and . pp. 43 4 -44 0. Peng, S. J., & Peden, J. M., "Prediction of Filtration Under Dynamic Conditions," SPE 23 8 24 paper, presented at the SPE Intl. Symposium on Formation Damage. D Deposited Small Particle Volume/Bulk cake volume o o o o -n o n R- 0) o G. 2- 5' cro m 3 12 Reservoir Formation Damage 10 20 30 40 Filtration Time, min. Figure 12- 15. Comparison