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C H A P T E R 20

RESERVOIR SANDMIGRATION ANDGRAVEL-PACK

DAMAGE:STRESS-INDUCED

FORMATION DAMAGE,SANDING TENDENCY,AND PREDICTION

Summary

Characteristics of reservoir formations susceptible for sand production arereviewed. The mechanical and hydrodynamic processes causing sand pro-duction, migration, and retention in reservoir formations are described andmodeled. Typical features of effective gravel pack designs are explained.The various parameters affecting the gravel-pack efficiency are discussed.Predictive models for sand filtration and retention in gravel-packs andapplications by means of typical test data are presented.

20.1 INTRODUCTION

As stated by Geilikman and Dusseault (1997), Sand production is afluid-saturated granular flow. It has been observed that fines migrationand well sanding tend to increase by rising water cuts beyond a certain

814



Reservoir Sand Migration and Gravel-Pack Damage 815

threshold as a result of water-coning (or water-cresting) induced byhigh rate production (Hayatdavoudi, 1999c, 2005). Hayatdavoudi (1999c,2005) considers that five important parameters control the sand liquefac-tion process: (1) buoyancy of the fine particles, (2) variation of the effec-tive density of sand, (3) pressure build-up in the near-wellbore region, (4)weak cohesive cement between sand grains, and (5) low internal frictionangle. Hayatdavoudi (1999c) describes that the conditions inducing sandproblems include:

(1) lack of grain to grain cement (25% carbonates, oxides of iron, andoxides of silica cement),

(2) very small sand grain size usually less than 5060 (very fine silt andclay-sized material),

(3) under consolidation/compaction due to the deposition of sediments ina viscous, low energy environment (i.e., turbidities),

(4) rise of the water table, water encroachment, and water coning, and(5) decreased submerged weight of the particle under variable saturation

conditions.

Hayatdavoudi (1999c, 2005) explains that high production rates inducesand production for several reasons. First, the pore pressure (net over-burden stress) increases because of the lowering of the pore fluid pres-sure. Second, water invades the near-wellbore formation as a result ofwater-coning (or cresting), which in turn alters the petrophysical param-eters, including capillary pressure, osmotic pressure, and clay swellingpressure. Consequently, the effective shear resistance of the formationsand against the increasing pore pressure (or effective net overburdenstress) diminishes and conditions favorable for sand liquefaction are cre-ated. Similar reasons were also suggested by Dusseault and Santarelli(1989).

Tremblay et al. (1998) report a communication being establishedbetween injection and production wells 500m apart in a reservoir througha wormhole because of sand production. In fact, Tremblay et al. (1998)point out that even in primary production, such as the cold production pro-cess for recovery of heavy oil from unconsolidated formations, essentiallyfacilitates production for better access to heavy oil by forming worm-holes and/or cavities. Sanding also explains the high sand cuts observedin some oil wells. Therefore, allowing sand production and not usingsand exclusion techniques, such as gravel pack and screen, is essentialfor economic production of oil (Geilikman et al., 1994).



816 Reservoir Sand Migration and Gravel-Pack Damage

20.2 PREDICTION OF SANDING CONDITIONSUSING A SIMPLE MODEL

Hayatdavoudi (1999c, 2005) developed a simplified model by modifyingthe Spangler and Handy (1982) model. The inherent assumptions andequations of this model is presented below.

The induced shear stress, i, in the direction of flow or its equivalentpressure drop and the induced acceleration, ai, of the formation particlescan be related by Newtons second law as (Spangler and Handy, 1982)

i =mai (20-1)

where m is the mass of the sand particle. On the other hand, the max-imum, critical, or threshold shear resistance of the sand, including theadditional factors resulting from water invasion, is expressed as followingby Hayatdavoudi (1999c, 2005):

cr = c+{v

[Pp Ps+Pos+Pc

] }tan cyc (20-2)

where c is the effective cohesive strength of the formation sand lb/ft2

and v is the effective vertical stress lb/ft2. Pp Ps Pos, and Pc denote,

respectively, the pore fluid, clay swelling, osmotic, and capillary pres-sures. cyc denotes the cyclic angle of internal friction. Therefore, sandliquefaction occurs when the prevailing shear stress exceeds the thresholdshear stress, that is,

i cr (20-3)

Neglecting the fluid acceleration effect, Hayatdavoudi (1999c, 2005)expressed the induced acceleration of particles by

ai = 2fswpv (20-4)

where pv is the induced velocity of particles and fsw is the shear wavefrequency. In case of the lack of information for Eq. (20-4), Hayatdavoudi(1999c) recommends estimating ai by

ai 019g (20-5)

where g denotes the gravitational acceleration.




Hayatdavoudi (1999c, 2005) points out the importance of the buoyantunit weight of the in situ particles when determining the particle mass,and estimates the in situ particle mass by

m=(aveg

)z (20-6)

where z represents the depth or height measured from a reference datum(ft) and ave is the average specific weight of the formation sand lb/ft

3.The latter is expressed as

ave =12

(in theoil zone

+in thewater zone

)(20-7)

in which the specific weights of the sand grains in the water and oil zonesare given, respectively, by

in thewater zone

= wG1+ e (20-8)

in theoil zone

= oG1+ e (20-9)

where the void ratio, e, in terms of the fractional porosity, , is given bythe pore volume to solid volume ratio as:

e= 1 (20-10)

and w and o are the specific weights of the water and oil phases, andG is the specific gravity of the sand grains, defined as the density of thegrain material divided by the density of water at 4C temperature.

20.3 PREDICTION OF MASSIVE SANDPRODUCTION USING A DIFFERENTIAL MODEL

Many models with varying degrees of predictive capabilities are availablefor sand production. Here, the radial continuum model for massive sandproduction, coupling fluid and granular matrix flows, by Geilikman andDusseault (1997) is reviewed. This is a physics-based approach that




includes the essential ingredients of a sand production model. However,applications to other cases, such as horizontal and deviated wells, anddifferent formations may require further developments.

The decline of pressure during production causes flow and stress-induced damage in the near-wellbore region. The increase in thedeviatoric stress above the yield condition in unconsolidated sandstoneformations causes instabilities and plastic flow leading to sand production.As depicted in Figure 20-1, Geilikman and Dusseault (1997) consider tworegions for modeling purposes: (1) a yielded-zone, denoted by the sub-script y and initiating from the wellbore and extending to a propagatingfront radius, R = Rt, and (2) an intact-zone, denoted by the subscripti and remaining beyond the propagating front of the yielded-zone. Theyconsider a two-phase continuum medium: (1) a viscoplastic solid skele-ton, and (2) an incompressible and viscous saturated fluid. The modelingis carried out per unit formation thickness.

Let p denote the fluid pressure (Pa). is porosity; K is permeability; is viscosity; f and s denote the fluid- and solid-phase velocities,respectively; and r is the radial distance. The Darcy law is applied forthe mobile fluid phase as (see Chapter 7)

dpdr

=K

f s (20-11)

Note that the tortuosity is approximated as 10 considering acoarse-grain formation. Assuming that the fluid and solid phases are

sand flow

flowing, yielded zone

propagation of yielding front

intact zoneintact zone

wellbore R (t)r w

Figure 20-1. Growing yielded zone and the intact zone around a producing well(reprinted from Journal of Petroleum Science and Engineering, Vol. 17, Geilikman, M. B., andDusseault, M. B, Fluid Rate Enhancement from Massive Sand Production in Heavy-OilReservoirs, pp. 518, 1997, with permission from Elsevier Science).




incompressible, the volumetric balance equations (equation of continuity)of the fluid and solid phases are given by

t+ f= 0 (20-12)

t

+ 1s= 0 (20-13)

where t denotes the time. In the intact zone, the porosity, i, is assumedconstant. Thus, Eqs (20-12) and (20-13) simplify as

if= 0 (20-14) 1i s= 0 (20-15)

Thus, the fluid velocities in the yielded and intact zones can be expressed,respectively, by

f =q t

2yr 1y

y

s (20-16)

f =qf t

2ir(20-17)

Here, qt denotes the volumetric production rate of the fluid plus sandsystem. qft denotes the volumetric production rate of the fluid carryingthe sand. Similarly, the solid velocity in the yielded zone is given by

s =qs t

2(1y

)r

(20-18)

qst denotes the volumetric sand production rate. Therefore, substitutingEqs (20-15)(20-18) into Eq. (20-11) and integrating yields the followingfluid pressure profiles in the yielded and intact zones, respectively:

py cr= pw+

2yKy

(q qs

1y

)ln

(r

rw

) rw < r < R (20-19)

and

pi r= peqf

2iKiln

(rer

) R < r < re (20-20)




The porositypermeability relationship is described by the KozenyCarman equation as:

Ky

Ki=(

y

i

)3 [ 1i1y

]2(20-21)

Let V denote the yielded zone front velocity, given by:

V dRdt

(20-22)

in which R=Rt denotes the radial distance to the front. The consistencyand compatibility conditions for the fluid flow at the moving yieldedzone front (interface boundary) are given, respectively, by

i iV= y(

yV

) r = Rt (20-23)

py = pi r = Rt (20-24)Here rw and re denote the wellbore and reservoir radii, respectively, andpw and pe are the fluid pressures at these locations. The consistency andcompatibility conditions for the solid flow at the moving front betweenthe yielded and intact zones are given, respectively, by

1i V =(1y

)V s (20-25)

Substituting Eqs (20-18) and (20-22) into Eq. (20-25), and solving theresulting expression for the cumulative volume of solids production, Qs,yields

Qs t= (

yi

) (R2 r2w

)(20-26)

The volumetric rate of solid production is given by

qs =dQsdt

(20-27)

The yield function, F , for granular matrix is defined as (Jackson, 1983;Collins, 1990; Pitman, 1990; Drescher, 1991)

F = r2

c(r +

2p

)= 0 (20-28)




where r and denote the radial and tangential stresses, respectively,Pa c is the cohesive strength Pa is a friction coefficient (dimen-sionless).

The stress equilibrium condition for the solid skeleton is given by

drdr

+ rr

eKf s= 0 (20-29)

in which e is the coefficient of the body force, approximated by, referredto as the void ratio

e= i1i

(20-30)

In the yielded zone, eliminating the tangential stress, , betweenEqs (20-28) and (20-29) leads to:

drdr

(

21

)1r rp+c

e

Kyf s= 0 (20-31)

subject to the conditions at the wellbore

r = pw r = rw (20-32)

and at the moving front

r = py r = R t (20-33)

Thus, substituting Eqs (20-17) and (20-18) into Eq. (20-31) and solvingleads to the following expression for the radial stress in the yielded zone:

[r rpy r

]r r

w r

[2c1

1+ e 2yKy

(q qs

1y

)]= 0

(20-34)

where = 2/1.Incorporating some simplifying approximations into the preceding

equations, Geilikman and Dusseault (1997) obtain the following expres-sion for sand production rate qs:




1+ e2iKi

(1y

) qs PcPw t1+ e

ln rDe/rDR

+

{1 1+ e PcPw t 2c r

DR

11

} [Kyy

Kii+ ln rDRln rDe/rDR

]

rDR1

1 ln rDR(20-35)

where rDR =Rt/rw and rDe = re/rw. Equation (20-35) can be numericallyevaluated assuming a wellbore fluid pressure history, represented by thefollowing decay function:

pw t= p+ pcp exp(t/tp

)(20-36)

where tp is a characteristic time scale, pc is some critical fluid pressure atwhich the yield criterion is met, and p is the limit value of the wellborepressure for t >> tp.

The volumetric rate of fluid production is given by

qf t=qo t

Kyy

Kiiln

(rerw

)+ qst1y ln

[Rt

rw

]

ln[Rt

rw

]+ Kyy

Kiiln

[re

Rt

] (20-37)

in which qot is the rate of fluid production without any sand production,given by

qo t=2Kii

ln re/rwpepw t (20-38)

Geilikman and Dusseault (1997) defined dimensionless sand produc-tion rate qD, time D, characteristic time p, and fluid productionenhancement ratio ED, respectively, as

qD = qs1+ e

2Kii(1y

)pcp

(20-39)

D = t2Kii pcp 1+ e r2w

(20-40)

p = tp2Kii pcp 1+ e r2w

(20-41)




10

8

6 1

2

3

4

2

0 10 20 30 40 50 60 70 /0.01

q D

Figure 20-2. Dimensionless volumetric sand production rate vs. dimensionless time:Curves 1, 2, and 3 are for = 01 05, and 1.0, respectively (reprinted from Journalof Petroleum Science and Engineering, Vol. 17, Geilikman, M. B., and Dusseault, M. B, FluidRate Enhancement from Massive Sand Production in Heavy-Oil Reservoirs, pp. 518,1997, with permission from Elsevier Science).

ED t=qf t

qo t(20-42)

The symbol tp denotes the characteristic time. Figures 20-2 and 20-3 byGeilikman and Dusseault (1997) present typical solutions for the rate ofsand production and enhancement of fluid production.

20.4 MODELING SAND RETENTIONIN GRAVEL-PACKS

As stated by Bouhroum et al. (1994):

Sand production poses serious problems to tubular material, surface equip-ment and the stability of the well . A popular method of combating sandproduction is using gravel-packs. Gravel-packs have a protective functionto inhibit the flow of sand particulates into the well.

Bouhroum et al. (1994) essentially applied the Ohen and Civan (1993)model, given in Chapter 10 with several simplifications for prediction of




2.0

1.5

1.0

0.5

1

23

0 10 20 30 40 50 60 70 /0.01

E

Figure 20-3. Short-term uid production improvement vs. dimensionless time:Curves 1, 2, and 3 are for = 01 05, and 1.0, respectively (reprinted from Journalof Petroleum Science and Engineering, Vol. 17, Geilikman, M. B., and Dusseault, M. B, FluidRate Enhancement from Massive Sand Production in Heavy-Oil Reservoirs, pp. 518,1997, with permission from Elsevier Science).

the gravel-pack permeability impairment by sand deposition. The impor-tant simplifying assumptions of this model are (a) the sand particles aregenerated in the near-wellbore formation and deposited in the gravel-pack, and (b) the clay swelling effects are not considered. As attested bythe results given in Figures 20-4 and 20-5, their predictions accuratelymatch the experimental values.

20.5 RESERVOIR COMPACTIONAND SUBSIDENCE

Production of oil and gas from petroleum reservoirs declines the pore fluidpressure and increases the net overburden stress. In weakly-consolidatedor unconsolidated reservoir formations, this may cause reservoir for-mation compaction and ground surface subsidence. Examples of suchcases have been encountered in many places in the world, including theOffshore North West Java field of Indonesia (Susilo et al., 2003) and




Sand

con

tent

in g

rave

l by

weig

ht (%

)

Distance form sand-gravel interface, cm

Simulation

High flow rate

Low flow rate

25

25

20

20

10

10

15

15

5

50

0

Figure 20-4. Simulation of experimental data for low and high ow rate proles ofmigrated sand particles in a 7.5 gravel to sand ration gravel-pack (after Bouhroumet al., 1994 SPE; reprinted by permission of the Society of Petroleum Engineers).

Sand

con

tent

in g

rave

l by

weig

ht (%

)

Distance form sand-gravel interface, cm

Simulation

High flow rate

Low flow rate

25

30

20

10

15

5

0252010 1550

Figure 20-5. Simulation of experimental data for low and high ow rate proles ofmigrated sand particles in a 6.3 gravel to sand ration gravel-pack (after Bouhroumet al., 1994 SPE; reprinted by permission of the Society of Petroleum Engineers).




the Campos Basin of Brazil (Soares et al., 2003). Susilo et al. (2003)report the occurrence of rapid surface subsidence reaching to the levelsof 1015 ft during a period of eight years in the Offshore North WestJava field.

Compaction reduces the porosity and permeability of the reservoirformation, and therefore has two mutually opposing effects on petroleumproduction. Porosity reduction enhances the production and permeabilityreduction hinders the production. Soares et al. (2003) developed a simplemodel for analysis of the effect of reservoir compaction on production bymeans of a simple analytical steady-state radial flow model. This modelis described below with some modifications.

Assume a constant viscosity fluid, and slightly-compressible reservoirfluid and formation. The oil density and reservoir permeability variationswith pressure are described, respectively, by:

c =[1

ppf

]

T

(20-43)

cK =[1K

K

peff

]

T

=[

1K

K

ppf

]

T

(20-44)

in which, T is the reservoir temperature, c and cK are the empiricalparameters denoting the isothermal compressibility and permeability vari-ation coefficients, and peff denotes the effective overburden stress givenaccording to Nieto et al. (1994) and Bustin (1997) as:

peff = pobppf (20-45)

in which is Biots constant, and pob and ppf are the overburden stressand pore fluid pressure, respectively. Assuming constant average valuesfor the coefficients of the isothermal compressibility, Eqs (20-43) and(20-44) can be readily integrated to obtain the following expressions:

p= o exp[c ppo

](20-46)

K p= Ko exp cK ppo (20-47)

Where p ppf and the subscript o indicates the initial or reference condi-tion. The reference pressure may be selected as being the condition underwhich the effective net stress vanishes.




Consider the radial flow of oil towards a well completed in a homo-geneous formation undergoing compaction as a result of depletion by oilproduction at a constant rate. Consequently, application of Darcys lawyields the following expression for the mass flux m of the produced fluid:

m= q = uA= 2rhK krowc

dpdr

(20-48)

Where , p, u, and krowc denote the density, viscosity, pressure,volumetric flux, and relative permeability at the connate water conditionfor the oil, respectively, K and h represent the absolute permeability andthickness of the reservoir formation, and r denotes the radial distancemeasured from the well center-line. The following expression can bederived by combining the above equations and integrating the resultingdifferential equation analytically for m= constant production rate (Soareset al., 2003):

qw exp[c pwpo

]

2hKo krowcln(rcrw

)=(1cT

)exp cT pcpo

1 exp cT pwpo (20-49)Where the total isothermal compressibility is defined as:

cT = c+cK (20-50)This result can be used to derive the following expression for thereciprocal-productivity ratio index under a constant pressure drawdownpressure p= popwo = pcpw = constant:

qoq

= exp cK popc (20-51)

The slope of the straight-line fit of field data on a semi-log plot yields thevalue of the cK product. Then, the above equation can be used to predictthe future effects of compaction on the production rate (Soares et al., 2003).

Exercises

1. Consider the typical parameter values given by Geilikman andDusseault (1994, 1996) for shallow sand-producing formations of east-ern Alberta. i = 030 y = 040 Pe = 3450kPa Pc = 3000kPa




P = 200kPa re/rw = 200, and c = 00. The heavy oil gravity isaround 1418API. Cohesionless sandstone formation thickness isaround 315m. The oil saturation is 88% with gas dissolved in theoil. The production rate of oil without sand production is less than15m3/day. Tremblay et al. (1998) report 8000 cp heavy-oil viscos-ity and 3.0D permeability sandstone formation. Make reasonableassumptions for missing data. Construct plots similar to those givenin Figures 20-2 and 20-3.

2. Consider the following data given by Hayatdavoudi (1999c, 2005).The vertical depth of a sandstone formation is 7005 ft. The effectivecohesive strength of the sandstone is 35 psi and the porosity is 29%.The specific gravities of the oil and water phases are 0.80 and 1.08,respectively. The actual specific gravity of the sand particles is 2.59.The angle of the internal friction is 26. The minimum sand particleacceleration necessary for sand liquefaction is 019g, where g denotesthe gravitational acceleration. Make reasonable assumptions for miss-ing data. Determine the sand liquefaction potential of this formationunder the following scenarios:a. The oilwater contact surface rises by 10 ft above its initial position

as a result of the water coning effect. Prepare a sketch of the system.b. A properly designed completion technique helps lower the oil

water contact surface by 20 ft below its initial position. Prepare asketch of the system.

3. Derive Eqs (20-49) and (20-51). Describe the proper mathematicalmanipulations and assumptions required for derivation and discusstheir implications.

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