Reservoir Formation Damage Episode 2 Part 1 ppsx

Single-Phase Formation Damage by Fines Migration and Clay Swelling 233pack decreased to zero.. Single-Phase Formation Damage by Fines Migration and Clay Swelling 2350.10 0.20 0.30 INTERS

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232 Reservoir Formation Damage

in which

=G' Unp=U

(10-189)

(10-190)

because all flow goes through the plugging pathways

The fact that the cumulative amounts of deposits reach certain limitingvalues as shown in Figure 10-25 is indicative of attainment of suchequilibrium conditions Note, however, that the amounts shown in Figure10-25 are the cumulative amounts including the amount of deposits inthe plugging pathways Therefore at equilibrium

100 200 PORE VOLUMES

PACK LENGTH CM

Figure 10-27 Constant pressure deposition and entrainment of 5-10 mm

diameter glass beads in a pack of (a) 177-210 mm diameter sand grainssubjected to 900 kPa/m pressure gradient and (b) 250-297 mm diameter sandgrains subjected to 450 kPa/m pressure gradient (after Gruesbeck and Collins,

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Single-Phase Formation Damage by Fines Migration and Clay Swelling 233

pack decreased to zero Because, in the fine sand pack, almost all thepathways are of the plugging type Whereas, in coarse sand packs, thedeposition tended to occur almost uniformly along the sand pack and themean permeability of the sand pack decreased to an equilibrium value.Because, in the coarse sand pack, most of the pathways are of thenonplugging types

Gruesbeck and Collins (1982) state that their computer simulationproduced results similar to measurement reported in Figure 10-27 Civan

et al (1989), and Ohen and Civan (1990, 1993) also simulated theseexperiments successfully

Consolidated Core Tests Gruesbeck and Collins tested Berea and field

cores First, the Berea cores were tested using

1 2% KCl brine in a dry core (single phase system)

2 2% KCl brine and white oil at a 50/50 ratio in a dry core (two phase

system)

3 white oil in a dry core (single phase system)

4 white oil in a core at connate 2% KCl brine saturation (two phase)

Cores were tested at various constant injection rates over a period oftime determined by a prescribed, cumulative pore volume amount of theinjection fluid During each test, the pressure difference was measuredand the permeability was calculated using Darcy's law Typical results

obtained using a 2% KCl brine in a Berea core are presented in Figure

10-28 As can be seen, the permeability remained unchanged at the lowflow rate of 0.0367cm3/-?, while it decreased further at each of theincreased high flow rates of 0.0682, 0.1002, 0.1310, and 0.1702cm3/s.The final permeability values attained after each of the high flow ratesare used to calculate the permeability reductions from the initial state,which are then plotted against these high flow rates as shown in Figure10-29 The results shown in Figure 10-29 are indicative of surfaceparticle removal, similar to Figure 10-24 They stated that the removal

of indigeneous particles in the cores from the pore surface and subsequentredeposition at the pore throats caused the permeability reduction.Second, core samples were taken from an oil field, indicating anabnormal decline of productivity in some wells These cores were tested using

1 white oil in a dry core

2 white oil in a core at connate 2% KCl brine saturation.

The experimental results presented in Figure 10-30 indicate a trendsimilar to Figure 10-29

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Figure 10-28 Effect of fluid velocity on the entrainment and redeposition of

fines in a 3.81 cm diameter and 3.0 cm long Berea core during a 2% KCI

INTERSTITIAL VELOCITY u/</> j; CM/S

.16 18

Figure 10-29 Permeability reduction as a function of the interstitial velocity

The results presented in Figures 10-29 and 10-30 indicate that theindigeneous particles of Berea and field cores are water wet This isapparent by the effect of the two phases on the critical velocity valuesrequired to initiate particle mobilization The implication of this is thatvariation of the fluid system from oil to oil/water can reduce the critical

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0.10 0.20 0.30 INTERSTITAL VELOCITY u/<£j, CM/S

0.40

Figure 10-30 Permeability reduction as a function of the interstitial velocity

of Petroleum Engineers)

velocity, induce surface particle mobilization, and increase permeabilitydamage in the near well bore formation

References

Cernansky, A., & Siroky, R "Deep-bed Filtration on Filament Layers on

Particle Polydispersed in Liquids," Int Chem Eng., Vol 25, No 2,

1985, pp 364-375

Cernansky, A., & Siroky, R., "Hlbkova Filtracia Polydisperznych Castic

z Kvapalin na Vrstvach z Vlakien," Chemicky Prumysl, Vol 32 (57),

Civan, F., & Knapp, R M "Effect of Clay Swelling and Fines Migration

on Formation Permeability," SPE Paper No 16235, Proceedings of the

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SPE Production Operations Symposium, Oklahoma City, Oklahoma,

1987, pp 475-483

Civan, F "A Multi-Phase Mud Filtrate Invasion and Well Bore FilterCake Formation Model," SPE Paper No 28709, Proceedings of theSPE International Petroleum Conference & Exhibition of Mexico,October 10-13, 1994, Veracruz, Mexico, pp 399-412

Civan, F., Knapp, R M., & Ohen, H A "Alteration of Permeability by

Fine Particle Processes," J Petroleum Science and Engineering, Vol 3,

Nos 1/2, October 1989, pp 65-79

Civan, F., Predictability of Formation Damage: An Assessment Study andGeneralized Models, Final Report, U.S DOE Contract No DE-AC22-90BC14658, April 1994

Civan, F "Modeling and Simulation of Formation Damage by OrganicDeposition," Proceedings of the First International Symposium onColloid Chemistry in Oil Production: Asphaltenes and Wax Deposition,ISCOP'95, Rio de Janeiro, Brazil, November 26-29, 1995, pp 102-107.Civan, F "A Multi-Purpose Formation Damage Model," SPE 31101,Proceedings of the SPE Formation Damage Symposium, Lafayette,Louisiana, February 14-15, 1996, pp 311-326

Civan, F "Interactions of the Horizontal Wellbore Hydraulics and FormationDamage," SPE 35213, Proceedings of the SPE Permian Basin Oil &Gas Recovery Conf., Midland, Texas, March 27-29, 1996, pp 561-569.Gruesbeck, C, & Collins, R E "Particle Transport Through Perforations,"

SPEJ, December 1982b, pp 857-865.

Gruesbeck, C., & Collins, R E "Entrainment and Deposition of Fine

Particles in Porous Media," SPEJ, December 1982a, pp 847-856.

Khilar, K C., & Fogler, H S "Colloidally Induced Fines Migration in

Porous Media," in Amundson, N R & Luss, D (Eds.), Reviews in Chemical Engineering, Freund Publishing House LTD., London, England,

January-June 1987, Vol 4, Nos 1 and 2, pp 41-108

Khilar, K C., & Fogler, H S "Water Sensitivity of Sandstones," SPEJ,

February 1983, pp 55-64

Liu, X., Civan, F, & Evans, R D "Correlation of the Non-Darcy Flow

Coefficient, J of Canadian Petroleum Technology, Vol 34, No 10,

1995, pp 50-54

Metzner, A B., & Reed, J C "Flow of Non-Newtonian

Fluids—Corre-lation of the Laminar, Transition, and Turbulent Flow Regions," AIChE J., Vol 1, No 4, 1955, pp 434-440.

Nayak, N V, & Christensen, R W "Swelling Characteristics of pacted Expansive Soils," Clay and Clay Mineral, Vol 19, No 4,December 1970, pp 251-261

Com-Ohen, H A., & Civan, F "Predicting Fines Generation, Migration andDeposition Near Injection and Production Wells," Proceedings of the

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First Regional Meeting, American Filtration Society, Houston, Texas,October 30-November 1, 1989, pp 161-164

Ohen, H A., & Civan, F "Simulation of Formation Damage in Petroleum

Reservoirs," SPE Advanced Technology Series, Vol 1, No 1, April

Seed, H B., Woodward, Jr., R J., & Lundgren, R "Prediction of Swelling

Potential for Compacted Clays," / Soil Mech Found Div., Proc Am.

Soc Civ Eng., 88(SM3), June 1962, pp 53-87

Wojtanowicz, A K., Krilov, Z., & Langlinais, J P "Study on the Effect

of Pore Blocking Mechanisms on Formation Damage," SPE 16233paper, presented at Society of Petroleum Engineers Production Opera-tions Symposium, Oklahoma City, Oklahoma, March 8-10, 1987, pp.449-463

Wojtanowicz, A K., Krilov, Z., & Langlinais, J P "Experimental mination of Formation Damage Pore Blocking Mechanisms," Trans, of

Deter-the ASME, Journal of Energy Resources Technology, Vol 110, 1988,

pp 34-42

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Chapter 11

Two-Phase Formation Damage by Fines

is presented, as well as applications to typical laboratory core damagetests The formulation can be readily extended for the multi-phase andmulti-dimensional systems and the actual fluid conditions existing inreservoir formations

Introduction

Several investigators including Muecke (1979), Sarkar (1988), andSarkar and Sharma (1990) have determined that fine particles behavedifferently in a multi-phase fluid environment and formation damagefollows a different course than the single-phase systems However, thereported studies on the two-phase formation damage are very limited.Sutton and Roberts (1974) and Sarkar and Sharma (1990) have experi-mentally observed that formation damage in two-phase is less severe than

in single-phase Liu and Civan (1993, 1995, 1996) have shown that two-phase

238

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Two-Phase Formation Damage by Fines Migration 239

formation damage requires the consideration of other factors, such as thewettability affect and partitioning of particles between various phases

In this chapter, mutual interactions and affects between the two-phaseflow systems, fine particles, and porous matrix are described mathe-matically to develop a predictive model for formation damage by finesmigration in two-phase systems flowing through porous formations Theformulation is carried out by extending the Liu and Civan (1993, 1994,

1995, 1996) model for more realistic applications The tests and casestudies used by Liu and Civan (1995, 1996) are presented for demon-stration and verification of the model Although the model presented hereinvolves some simplifications pertaining to the laboratory core damageexperiments, it can be readily modified and generalized for the actualconditions encountered in petroleum reservoirs

Formulation

The equations describing the various aspects for formation damage byfines migration during two-phase fluid flow through porous formationsare formulated here However, the formulation can be extended readily

to multi-phase fluid systems It is safe to assume that the gas phase doesnot carry any solid particles (i.e., it is nonwetting for all particles).For convenience in modeling, the bulk porous media is considered infour phases as schematically depicted in Figure 11-1: (1) the solid matrix,(2) the wetting fluid, (3) the nonwetting fluid, and (4) the interface region

These phases are indicated by S, W, N, and /, respectively The porous

matrix is assumed nondeformable Therefore, it is stationary and itsvolumetric flux is zero The wetting and nonwetting phases flow at the

volumetric fluxes denoted, respectively, by u w and U N The interface

region is located between the wetting and nonwetting phases and isassumed to move at a flux equal to the absolute value of the differencebetween the fluxes of the wetting and nonwetting phases (i.e., its flux is

«/ = U W -U N \).

The various particles involving the formation damage are classified

as (1) the foreign particles introduced externally at the wellbore,(2) the indigeneous particles existing in the porous formation, and (3) theparticles generated inside the pore space by various processes, such asthe wettability alteration considered in this chapter Another classification

of particles is made with reference to the wettability as (1) the wettingparticles, (2) the nonwetting particles, and (3) the intermediately wetting

particles These particles are identified, respectively, by wp, np, and ip.

The latter classification is more significant from the modeling point ofview Because, as explained by Muecke (1979), the wettability affects thebehavior of these particles in a multi-phase fluid system By means of

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Pore throat

Figure 11-1 Multi-phase system in porous media.

experimental investigations, Muecke (1979) has observed that particlestend to remain in the phases that can wet them Ku and Henry, Jr (1987)have shown that intermediately wet particles accumulate at the interface

of the wetting and nonwetting phases, because they are most stable there.Therefore, in the following formulation, an interface region contain-ing the intermediately wet particles is perceived to exist in betweenthe wetting and nonwetting phases as schematically indicated in Figure11-1 Further, it is reasonable to consider that the wettability of someparticles may be altered by various processes, such as asphaltene, paraffin,and inorganic precipitation or by other mechanisms such as the turbulencecreated by rapid flow in the near-wellbore region Consequently, thesealtered particles should tend to migrate into the phases that wet them asinferred by the experimental studies of Ku and Henry, Jr (1979)

In addition to the particles, the various phases may contain a number

of dissolved species The salt content of the aqueous phase is particularlyimportant, because it can lead to conditions for colloidally induced release

of clay particles when its salt concentration is below a critical saltconcentration (Khilar and Fogler, 1983)

For convenience in formulation, the locations for particles retention can

be classified in three categories: (1) the wetting pore surface, (2) thenonwetting pore surface, and (3) the pore space behind the plugging pore

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Two-Phase Formation Damage by Fines Migration 241

throats These regions are denoted by wS, nS, and tS, respectively, as

indicated schematically in Figure 11-1 The areal fractions of the wettingand nonwetting sites can vary as a result of the various rock, fluid, andparticle interactions during formation damage, such as by asphaltene,

paraffin, and inorganic deposition Therefore, a parameter f ks indicating

the fraction of the pore surface, that is wetting for species k, is introduced

in the formulation

Because the applications to describe and interpret the laboratory coredamage data, conducted at mild temperature and pressure conditions areintended, the formulation is carried out for one-dimensional flow inhomogeneous core plugs, isothermal conditions, and incompressibleparticles and fluids This allows the use of a simplified formulation based

on volumetric balances and a fractional flow concept However, thederivation can be readily extended for compressible systems encountered

at the prevailing elevated pressure conditions of the reservoir formations

Fluid and Species Transport

Assuming incompressible species, the volumetric balance of species j transported via phase J through porous media is given by:

(11-1)

J = W, N, /, wS, nS, tS and j = w,«, wp, np, ip

where ey indicates the volume fraction of phase J in porous media, o;7

is the volume fraction of species j in phase /, u } is the volumetric flux

of phase J through porous media and q jJL represents the volume rate of

transfer of species j from phase J to phase L D- } denotes the coefficient

of dispersion of species j in phase /, and py is the density of phase J,

which varies by its composition even if the individual constituent species

may be considered incompressible, jc and t denote the distance along the flow

direction and time The dispersion term for particles is usually neglected.The volumetric rate of particle lost per unit bulk media by variousprocesses is given by:

in which q ju denotes the volume rate of transformation of species j type

to species / type in phase J expressed per unit bulk volume Summing

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Eq 11-1 over all species j in phase J and considering that the dispersion terms of various species j cancel each other out in a given phase, the volumetric equation of continuity for phase J is obtained as:

where 0 is the angle of inclination of the flow path and PJ and |iy are

the pressure and viscosity of phase J k rj is the relative permeability of

phase / and K is the permeability of porous media N ndJ is the phase J

non-Darcy number given according to the Forchheimer equation as:

(11-9)

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Two-Phase Formation Damage by Fines Migration 243

in which Re } is the phase J Reynolds number given by (Ucan and Civan,

1996):

(11-10)where (3 is the inertial flow coefficient given by a suitable correlation,such as by Liu et al (1995)

Determination of Fluid Saturations and Pressures

Two alternative convenient formulations can be taken for solution ofthe equations of continuity and motion given by Eqs 11-3 and 8 forpressures and saturations of the various phases flowing through porousmedia In the first approach, Eq 11-8 is substituted into Eq 11-3 to obtain:

where (() is porosity and S } is the saturation of phase J.

Thus, substituting Eqs 11-12 and 11-13 into Eq 11-11 yields thefollowing equations for the wetting and nonwetting phases, respectively:

(11-14)

a* \i w i

(11-15)

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