Reservoir Formation Damage Episode 3 Part 8 docx

1998 correlated their experi-mental data of laminar flow of various liquids over a loose bed of sandparticles linearly on a full logarithmic scale and obtained the followingexpression fo

where v pv is the induced velocity of particles and f sw is the shear wavefrequency In case of the lack of information for Eq 20-4, Hayatdavoudi(1999) recommends estimating a, by:

where g denotes the gravitational acceleration.

Hayatdavoudi (1999) points out the importance of the buoyant unitweight of the in-situ particles when determining the particle mass, andestimates the in-situ particle mass by:

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

ft3) The latter is expressed as:

• avg ri\ I in the I in the

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

and j w and J 0 are the specific weights of the water and oil phases, and

G is the specific gravity of the sand grains.

As a fluid flows over the face of a cohesionless bed of particles, such

as sand or gravel, the particles can be detached and lifted-off when thefluid shear-stress exceeds the minimum, critical shear-stress Yalin and

Karahan (1979) developed a dimensionless correlation to predict thecritical conditions for onset of particle mobilization (or scouring) by fluidshear Following their approach, Tremblay et al (1998) developed:

in which Recr is the critical particle Reynolds number given by

r» cr

where v cr is the critical shear velocity, d is the mean particle diameter,

and p and (I are the density and viscosity of the fluid flowing over theparticle bed

M cr is the critical mobility number given by

pv2

(20-13)

where y s denotes the specific weight of the particles suspended in the fluid.Applying Eq 20-11, Tremblay et al (1998) correlated their experi-mental data of laminar flow of various liquids over a loose bed of sandparticles linearly on a full logarithmic scale and obtained the followingexpression for the critical shear velocity:

v cr = 0.385 (^/p)a0934Y?-453J°-36p^453 (20-14)Then, they predict the critical shear-stress on the scouring face by:

Massive Sand Production Model

Many models with varying degrees of predictive capabilities areavailable for sand production Here, the radial continuum model formassive sand production, coupling fluid, and granular matrix flows byGeilikman and Dusseault (1994, 1997) is presented for instructionalpurposes This is a physics-based approach that includes the essentialingredients of a sand production model However, applications to other

cases, such as horizontal and deviated wells, and different formations mayrequire further developments.

The decline of pressure during production causes flow and induced damage in the near-wellbore region The increase in the deviatoricstress above the yield condition in unconsolidated sandstone formationscause instabilities and plastic flow leading to sand production

stress-As depicted in Figure 20-3, Geilikman and Dusseault (1997) considerstwo regions for modeling purposes: (1) a yielded-zone, initiating from

the wellbore and extending to a propagating front radius, R=R(t), and

(2) an intact-zone, beyond the propagating front of the yielded-zone.They consider a two-phase continuum medium: (1) a viscoplastic solidskeleton, and (2) an incompressible and viscous saturated fluid Themodeling is carried out per unit formation thickness

The yield function, F, for granular matrix is defined as (Jackson, 1983;

Collins, 1990; Pitman, 1990; Drescher, 1991):

(20-16)

where <5r and ae denote the radial and tangential stresses, respectively,

(Pa), c is the cohesive strength (Pa), y is a friction coefficient ensionless), and p is the fluid pressure (Pa).

(dim-intact zone

sand flow flowing, yielded zone

^

of yielding front

intact zone

fry?

Figure 20-3 Growing yielded zone and the intact zone around a producing

well (reprinted from Journal of Petroleum Science and Engineering, Vol 17,

Geilikman, M B., and Dusseault, M B, "Fluid Rate Enhancement fromMassive Sand Production in Heavy-Oil Reservoirs," pp 5-18, ©1997, withpermission from Elsevier Science)

The stress equilibrium condition for the solid skeleton is given by:

(20-17)

in which b is the coefficient of the body force, approximated by:

where <(), is the porosity of the intact zone; K is permeability; \i

is viscosity; v f and v s denote the fluid and solid phase velocities,respectively; and r is the radial distance

The Darcy law is applied for the mobile fluid phase

dp

(2(M9)Assuming that the fluid and solid phases are incompressible, the volumetricbalance equations (equation of continuity) of the fluid and solid phasesare given by:

in which R=R(t) denotes the radial distance to the front

Substitut-ing Eqs 20-26 and 32 into Eq 20-31, and solvSubstitut-ing the resultSubstitut-ing

expres-sion for the cumulative volume of solids production, S c, yields:

subject to the conditions at the wellbore

and at the moving front

ar = py, r = *(r)

(20-35)

(20-36)

(20-37)

Thus, substituting Eqs 20-25 and 26 into Eq 20-35 and solving, leads

to the following expression for the radial stress in the yielded zone:

dSr r_ _ / i \-\-b (1-<>,) dt

where t p is a characteristic time scale, p c is some critical fluid pressure

at which the yield criterion is met, and p^ is the limit value of the wellbore pressure for t~»t p

The volumetric rates of fluid production is given by:

loft ^ln(±\+*M-ln\*®.

<lf(t) =

in which q 0 (t} is the rate of fluid production without any sand

pro-duction, given by:

(20-42)

Geilikman and Dusseault (1997) defined dimensionless sand productionrate, time, characteristic time, and fluid production enhancement ratio,respectively as:

(20-43)

Sand Retention in Gravel-Packs

As stated by Bouhroum et al (1994):

Sand production poses serious problems to tubular material, surfaceequipment and the stability of the well A popular method of

<b

10 20 30 40 30 60 70 I/0.01

Figure 20-4 Dimensionless volumetric sand production rate vs dimensionless

time: Curves 1, 2, and, 3 are for T= 0.1, 0.5, and, 1.0, respectively (reprinted

from Journal of Petroleum Science and Engineering, Vol 17, Geilikman, M.

B., and Dusseault, M B, "Fluid Rate Enhancement from Massive SandProduction in Heavy-Oil Reservoirs," pp 5-18, ©1997, with permission fromElsevier Science)

10 20 30 40 50 60 70 t/0.01

Figure 20-5 Short-term fluid production improvement vs dimensionless time:

Curves 1, 2, and, 3 are for T= 0.1, 0.5, and, 1.0, respectively (reprinted from

Journal of Petroleum Science and Engineering, Vol 17, Geilikman, M B., and

Dusseault, M B, "Fluid Rate Enhancement from Massive Sand Production inHeavy-Oil Reservoirs," pp 5-18, ©1997, with permission from Elsevier Science)

combating sand production is using gravel-packs Gravel-packs have

a protective function to inhibit the flow of sand particulates intothe well

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

of the gravel-pack permeability impairment by sand deposition Theimportant simplifying assumptions of this model are: (a) the sand particlesare generated 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 20-6 and 20-7, their predictions accuratelymatch the experimental values

References

Bouhroum, A., Liu, X., & Civan, F., "Predictive Model and Verificationfor Sand Particulates Migration in Gravel-Packs," SPE 28534 paper,Proceedings of the SPE 69th Annual Technical Conference and Exhibi-tion, September 25-28, 1994, New Orleans, Louisiana, pp 179-191

Figure 20-6 Simulation of experimental data for low and high flow rate

profiles of migrated sand particles in a 7.5 gravel to sand ration gravel-pack (after Bouhroum et al., ©1994 SPE; reprinted by permission of the Society

of Petroleum Engineers).

Simulation

• Low Flow Rate

Bouhroum, A., & Civan, F., "A Critical Review of Existing Gravel-Pack

Design Criteria," Journal of Canadian Petroleum Technology, Vol 34,

No 1, 1995, pp 35-40

Burton, R C., "Perforation-Tunnel Permeability Can Assess Cased-Hole

Gravel-Pack Performance," J of Petroleum Technology, March 1998,

Drescher, A., "Analytical Methods in Bin-Load Analysis," Developments

in Civil Engineering Series 36, Elsevier, Amsterdam, 255 p., 1991.Dusseault, M B., & Santarelli, F J., "A Conceptual Model for Massive

Solids Production in Poorly-Consolidated Sandstones," Rock at Great Depth, Maury & Fourmantraux (Eds.), Balkema, Rotterdam, 1989,

pp 789-797

Geilikman, M B., Dusseault, M B., & Dullien, F A L., "Sand duction as a Viscoplastic Granular Flow," SPE 27343 paper, SPEInternational Symposium on Formation Damage Control, February 9-

Pro-10, 1994, Lafayette, Louisiana, pp 41-50

Geilikman, M B., & Dusseault, M B, "Fluid Rate Enhancement from

Massive Sand Production in Heavy-Oil Reservoirs," / of Petroleum Science and Engineering, Vol 17, No 1/2, 1997, pp 5-18.

Hayatdavoudi, A., "Formation Sand Liquefaction: A New Mechanism forExplaining Fines Migration and Well Sanding," SPE 52137 paper, SPEMid-Continent Operations Symposium, March 28-31, 1999, OklahomaCity, Oklahoma, pp 177-180

Jackson, R., "Some Mathematical and Physical Aspects of ContinuumModels for the Motion of Granular Materials," in R.E Meyer (Ed.),

Theory of Dispersed Multiphase Flow, Academic Press, New York,

New York, 1983

JPT, "Specialists Share Knowledge of Sand-Control Methods," J of Petroleum Technology, July 1995, pp 550-609.

Kanj, M., Zaman, M., & Roegiers, J-C., "Highlights from the

Knowledge-Base of a Sanding Advisor Called SITEX," Computer Methods and Water Resources III, Abousleiman, Y, Brebbia, C A., Cheng,

A.H.-D., & Ouazar, D (Eds.), Computational Mechanics Publications,Southampton, Boston, 1996, pp 391-398

Pitman, E B., "Computations of Granular Flow in Hopper," in D D.Joseph & D G Schaeffer (Eds.), Two Phase Flow and Waves, TheIMA Volumes in Mathematics and its Applications Series 26, Springer,New York, 1990, p 30

Saucier, R J., "Successful Sand Control Design for High Rate Oil and

Water Wells," J of Petroleum Technology, Vol 21, 1969, p 1193 Saucier, R J., "Considerations in Gravel-Pack Design," J of Petroleum Technology, Vol 26, 1974, p 205.

Skjaerstein, A., & Tronvoll, J., "Gravel Packing: A Method of WellboreRe-enforcement or Sand Filtering?," SPE 37506 paper, SPE ProductionOperations Symposium, March 9-11, 1997, Oklahoma City, Oklahoma,

pp 871-879

Spangler, M G., & Handy, R L., Soil Engineering, Harper & Row, New

York City, New York, 1982

Tiffin, D L., King, G E., Larese, G E., & Britt, R E., "New Criteriafor Gravel and Screen Selection for Sand Control," SPE 39437 paper,SPE Formation Damage Control Conference, February 18-19, 1998,Lafayette, Louisiana, pp 201-214

Tremblay, B., Sedgwick, G., & Forshner, K., "Modeling of Sand

Pro-duction from Wells on Primary Recovery," Journal of Canadian Petroleum Technology, Vol 37, No 3, March 1998, pp 41-50.

Yalin, M S., & Karahan, E., "Inception of Sediment Transport," Journal

of the Hydraulics Division, Vol 105 (HY11), American Society of Civil

Engineers, November 1979, pp 1433-1443

Scale deposition in porous media occurs when the fluid becomessupersaturated by changes of the in-situ pressure and/or temperatureconditions (see Chapters 9, 13 and 14) Mathematical models are requiredfor prediction of the effects of scale deposition on well flow performanceand for development of strategies to mitigate the processes causing scaledeposition In this chapter, Roberts' (1997) simplified radial flow model

is briefly described Then, its applications and results for sulfur deposition

by Roberts (1997) and for calcite deposition by Satman et al (1999) arepresented These applications demonstrate the capabilities of Roberts'(1997) model Leontaritis (1998) developed a radial flow model fororganic deposition, which shares some common ground with Roberts'(1997) model (see Chapter 14)

Sulfur Deposition Model

The affect of sulfur deposition on the loss of well performance in somesour-gas reservoirs has been reported by Roberts (1997) As pointed out

by Roberts (1997), sour-gas contains large quantities of elemental sulfur.Therefore, decrease of pressure and temperature during production ofsour-gas can lead to the elemental sulfur dissolved in sour-gas to separateand deposit as solids and cause a decline of the well performance Sulfur

669

deposition can occur both in the well and reservoir formation (Hyne,

1968, 1980, 1983; Kuo, 1972; Roberts, 1997) In this section, a briefdiscussion of the simplified analytical modeling effort by Roberts (1997)for prediction of the formation damage by sulfur deposition is presented.Hyne (1968, 1980, 1983) has considered the possibility of formation ofhydrogen polysulfides at high pressure and temperature conditions by reaction

of the hydrogen sulfide and sulfur according to the following equation:

Roberts (1997) points out that two mechanisms may be considered forthe solubility of sulfur in the sour-gas: (1) physical and (2) chemical.Hyne (1980, 1983) considered that sulfur may dissolve at high tempera-ture and pressure conditions because of the production of hydrogenpolysulfides by a reaction of the hydrogen sulfide with sulfur according

to the following equation:

Thus, when the pressure and temperature are lowered, this reaction shouldreverse itself to form solid elemental sulfur However, Roberts (1997) arguesthat its affect can be neglected because the reverse reaction is slow compared

to the high flow rate conditions prevailing in the near-wellbore formation.Therefore, for all practical purposes, Roberts (1997) assumes and verifies thatsulfur is physically dissolved in the sour-gas and separates instantaneously

as solids when the pressure declines to below the saturation conditions.Roberts (1997) draws attention to the field experience (Chernik andWilliams, 1993) that sulfur deposition in liquid form does not create manyproblems, whereas sulfur deposition in solid form may cause severeformation damage problems

Solubility of Sulfur in Natural Gas

Roberts (1997) states that elemental sulfur freezes at 119°C at

atmos-pheric pressure, but the freezing point decreases by increasing H 2 S

concentration in the sour-gas Because experimental measurement ofthe sulfur solubility is expensive and tedious, Roberts (1997) uses thesimplified thermodynamic equation given by Chrastil (1982) based on theideal solution theory for estimation of the sulfur solubility as:

(21-3)

In Eq 21-3, c r represents the concentration of the solid sulfur solved in the gas expressed as mass per unit reservoir gas volume

dis-[g/reservoir ra3), p is the density of the gas (&g/m3), T is the reservoir gas temperature, and k, A, and B are some empirically determined para-

meters As shown by Roberts (1997), using the data by Brunner and Woll(1980, 1988), the plots of Eq 21-3 at given temperatures are fairly linear

on the log c r vs log p Also, the plot of logcrv5.(l/7') given by Roberts(1997) shows a linear trend Therefore, Roberts (1997) concludes that

Eq 21-3 can be used for prediction of the sulfur solubility in gas andpresents the following correlation:

Modeling Near-Wellbore Sulfur Deposition

Consider the radial flow model of an areal drainage region around awell Roberts (1997) considered a sour-gas reservoir operating underisothermal and semi-steady state radial flow conditions and expressed thepressure gradient as:

dp _ q\}iB

where q is the constant gas production rate (m 3 /sj, |l is the gas viscosity (Pa.s), B is an empirical constant, the formation volume factor, h is the thickness of the net pay zone of the formation (m), r is the radial distance from the center of the well (m), k is the permeability of the formation

at the initial water saturation (m2), and k r is the relative permeability