Reservoir Formation Damage Episode 2 Part 4 doc

308 Reservoir Formation DamageParameter Table 12-2 continued Symbol Data I DataSlurry small particles mass per carrier fluid volume, g small parti-cles/cm3 carrier fluid Slurry small pa

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Cake Filtration: Mechanism, Parameters and Modeling 307

Table 12-2 Model Input Parameters*

Parameter Symbol

Cake porosity without 10 _ ,_ 0

compaction and small *

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/M3 slurry

Slurry total particle (w /• ) P

mass per carrier fluid (c I — ••••*• • "?—

volume, g particle/cm3 * rry 1 — \W ^ J

carrier fluid

1

~p

'|>-)-Data 1 '|>-)-Data II0.39* 0.73C

0.61C 0.21d

1.18* 1.18*0.97* 0.97"0.101* —

>, 0.109C 0.295Crv

i

ny

Slurry carrier fluid vol- / \ - t + fc ) /P f1 0-915e 0.8C

ume fraction, cm3 carrier ^ ''shiny L V PI 'shiny /"P\

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308 Reservoir Formation Damage

Parameter

Table 12-2 (continued)

Symbol Data I DataSlurry small particles

mass per carrier fluid

volume, g small

parti-cles/cm3 carrier fluid

Slurry small particles

volume per carrier fluid

volume, cm 3 small

parti-cles/cm3 carrier fluid

0.415C

Filtrate small particle

mass per carrier fluid

volume, g small

parti-cle/on3 carrier fluid

"-Rate constant for small

particle entrainment

within the cake, s l

5.0 xl(T7"'

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,

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

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Cake permeability

with-out compaction and

small particle

Datal1."

1.0°

1.0"

0,0.01"

Data II1.0*0.07°0.47"3.5xl.0~w

l.Oxl.O-4"1.0"1.0'1/270.0118*1.0"1.0"0,0.01"

p : Data for the constant pressure case

r : Data for the constant rate case

s : Static filtration

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(text continued from page 306)

particle invasion into an inefficient filter is demonstrated by assuming a

value of (C p2i) filer =0.005g/cm3 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 thesimplifying 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 theprogressing cake surface Also, the average porosity of the filter cake canvary 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 tovary 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 forthe linear and radial cases are compared The results presented in Figures12-12 through 12-21 indicate that fine particle invasion into the filterplays an important role The differences between the radial and linear

(text continued on page 315)

Filtration Time, min.

50

Figure 12-12 Comparison of the cake thickness for linear and radial constant

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Filtration Time, min

Figure 12-15 Comparison of the cake porosity for linear and radial constant

Filtration Time, min

50

Figure 12-16 Comparison of the filtrate volume for linear and radial constant

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20 30 40 Filtration Time, min.

Figure 12-21 Comparison of the filtrate volume for linear and radial constant

pressure filtration (Civan, R, 1998b; reprinted by permission of the AlChE,

filtration results are more pronounced and the cake thickness and filtratevolume are less for the constant pressure filtration

Tien et al (1997) have solved their partial differential model numericallyusing a ready-made Fortran subroutine for linear filtration at staticcondition and reported numerical solutions along the filter cake only

at the 100- and 1000-seconds times Their model generates numericalsolutions over the thickness of the filter cake, whereas, Civan's (1998b,1999b) models calculate the thickness-averaged values Therefore, Civanaveraged the profiles predicted by Tien et al (1997) over the cake thick-ness and used for comparison with the solutions obtained with thethickness-averaged filter cake model Because Tien et al (1997) reportednumerical solutions at only two time instances, this resulted in only twodiscrete values Civan generated the numerical solutions with the linearfiltration model using the data identified as Data II in Table 12-2 forconstant rate and constant pressure filtrations As can be seen by Civan's(1998b) results presented in Figures 12-22 through 12-25, his ordinarydifferential model can closely reproduce the results of the Tien et al

(text continued on page 318)

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200 400 600

Filtration Time, sec.

800 1000

Figure 12-22 Comparison of the cake thickness for constant rate filtration

Figure 12-23 Comparison of the cake porosity for constant rate filtration

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Figure 12-24 Comparison of the cake thickness for constant pressure

Figure 12-25 Comparison of the cake porosity for constant pressure filtration

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(1997) partial differential model Note that, as indicated in Table 12-2,the values of the parameters at the present cake thickness-averaged levelshould be different than those for the formulation at the local levelconsidering the spatial variations, such as by Tien et al (1997)

Conclusions

Because of the improved phenomenological description and convenientcake thickness-averaged formulation, the ordinary differential models canprovide faster numerical solutions with reduced computational effort and,therefore, offer certain practical advantages over the partial differen-tial models for the analysis, design, and optimization of the cake filtra-tion processes

The applicability of the models by Corapcioglu and Abboud (1990) andAbboud (1993) is limited to static and low pressure filtration of dilutesuspensions and their assumption of the same rates for the deposition ofthe small and large particles over the progressing cake surface is notreasonable The Tien et al (1997) model can alleviate these problems but

it is computationally intensive and also limited to static filtration Thesemodels are for linear filtration and may sufficiently approximate radialfiltration only when the cake and the filter are much thinner compared

to the radius of the filter surface exposed to the slurry However, the radialmodel developed by Civan (1998a,b, 1999a,b) can better describe theradial filtration involving thick filter cake and filter media

The filtration models presented in this section provide insight into themechanism of compressive cake filtration and a convenient means ofsimulation with additional features

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Part IV

Formation Damage

by Inorganic and Organic Processes

Chemical Reactions, Saturation Phenomena, Deposition, and

Dissolution

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Chapter 13

Inorganic Scaling and Gepchemical Formation Damage

Introduction

Inorganic scaling is a process of deposition of scales from aqueoussolutions of minerals, referred to as brines, when they become super-saturated as a result of the alteration of the state of their thermodynamicand chemical equilibria (Amaefule et al., 1988) Inorganic scaling canoccur in the well tubings and near well bore formations of the productionand injection wells

Amaefule et al (1988) explain that conditions leading to supersaturationcan be created by various mechanisms at different stages of reservoirexploitation Scaling is caused essentially by mixing incompatible fluidsduring well development operations, such as drilling, completion, work-over, such as acidizing Scaling is caused by a decrease of pressure and

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