RS_NOM

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a Prats relative capacity parameter

a Archie constant

a ellipse axis, ft, m

a viscosity degradation coefcient

a intermediate area, ft 2, m 2

ac length scale characteristic

asH,max horizontal axis of the maximum damaged

ellipse, ft, masH,min horizontal axis of the minimum damaged

ellipse, ft, m

asV,max vertical axis of the maximum damagedellipse, ft, m

asV,min vertical axis of the minimum damagedellipse, ft, m

a X chemical activity of species X

A area, ft 2, acre, m 2

A BL representative formation property in theboundary layer

Ac acid capacity number

Ae area at the end of an interval

Aelas elastic area

Aetch acid-etched area

A f fracture face surface area, ft 2, m 2

A fso fracture area at screenout, ft 2, m 2

Aik inuence function

A L leakoff area

APZ representative formation property in the payzone

AT critical transitional pore size

b y-axis intercept for spurt

b channel width

b linear regression constant

b slope of log-log plot of net pressure versus time

b fD dimensionless fracture width

blf linear ow fracture width

b M Mayerhofer et al . (1993) method intercept

b N Nolte method intercept

bs damage extent normal to the fracture plane, ft, m

B formation volume factor, RB/STB, res-ft 3 /scf,res-m 3 /m 3

B Skempton pore pressure coefcient

B ratio of the inner cup radius to bob radius

Bg formation volume factor for gas, res-ft 3 /scf,res-m 3 /m 3

Bo formation volume factor for oil, RB/STB,res-m 3 /m 3

Bw formation volume factor for water

c f fracture compliance

c f pore compressibility, psi 1, bar 1

cg compressibility of gas, psi 1, bar 1

co compressibility of oil, psi 1, bar 1

co borate foam viscosity adjustment factor

ct total compressibility, psi 1, bar 1

ctf fracture compressibility, psi 1, bar 1

cw compressibility of water, psi 1, bar 1

C wellbore storage, bbl/psi, m 3 /bar

C proppant concentration, ft 3 /ft3, m 3 /m 3

C chemical concentration, mol/L

C constrained modulus, psi, bar, Pa

Reservoir Stimulation N-1

Nomenclature

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C discharge coefcient

C rock type and grain size constant

C shape factor accounting for wellbore curvature

C * critical overlap concentration, lbm/1000 gal,dL/g

C A reservoir geometric shape factorC A acid concentration

C c compressibility control leakoff coefcient,ft/min 1/2, m/s 1/2

C ce effective reservoir-controlled uid-leakoff coefcient, ft/min 1/2, m/s 1/2

C CO total interface concentration of carbonatespecies

C cv combined leakoff coefcient, ft/min 1/2, m/s 1/2

C d dimensionless discharge coefcientC D dimensionless wellbore storage coefcient

C div concentration of diverter particles, lbm/gal,kg/m 3

C div net concentration of diverter particles afterdissolution effects, lbm/gal, kg/m 3

C drag drag coefcient

C dyn dynamic constrained modulus, psi, bar, Pa

C eqm equilibrium concentration

C fD dimensionless fracture conductivity

C fDapp apparent dimensionless fracture conductivity

C fD,opt optimal dimensionless fracture conductivity

C fDtrue actual dimensionless fracture conductivity

C gel gel mass concentration in uid

C H shape factor

C HF concentration of hydrouoric acid

C i reactant concentration at the solid/liquid inter-

face, mol/LC L leakoff or uid-loss coefcient, ft/min 1/2,

m/s 1/2

C o rock cohesion, psi, bar, Pa

C o initial reactant concentration

C p product concentration

C p uid heat capacity

C pi product concentration at the solid/liquidinterface, mol/L

C R general reservoir-controlled leakoff coefcient,ft/min 1/2, m/s 1/2

C RD dimensionless reservoir conductivity

C t combined uid-loss coefcient, ft /min 1/2, m/s 1/2

C v viscosity-controlled leakoff coefcient,ft/min 1/2, m/s 1/2

C ve effective ltrate-controlled leakoff coefcient,ft/min 1/2, m/s 1/2

C w wall or lter-cake uid-loss coefcient,ft/min 1/2, m/s 1/2

C W acid concentration at solid/liquid interface

C wall surface acid concentrationC wcv total leakoff coefcient, ft/min 1/2, m/s 1/2

C 0 acid concentration at capillary inlet

C 1 external phase constant

CF concentration factor

d diameter, in., m

d distance, ft, in., m

d prop proppant particle diameter, in., m

d sol

solid particle diameter, in., m

d tbg tubing diameter, in., m

D diameter, in., m

D distance, ft, in., m

D turbulence coefcient

D diffusion constant, cm 2 /s

D A molecular diffusion coefcient, cm 2 /s

De effective acid diffusion coefcient, cm 2 /s

Deff effective acid diffusion coefcient, ft 2 /s, m 2 /s

D H hydraulic diameter, in., m

D p pipe inner diameter, in., m

D p perforation diameter, in., m

D pe effective diffusion coefcient for reactionproducts, cm 2 /s

N-2 Nomenclature

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Dw wire diameter, in., m

Da Damkhler number

Damt mass-transfer-limited Damkhler number

Da rxn reaction-rate-limited Damkhler number

De Deborah number

DR damage ratio

E Youngs modulus, psi, bar, Pa

E plane strain modulus, psi, bar, Pa

E av average Youngs modulus, psi, bar, Pa

E dyn dynamic Youngs modulus, psi, bar, Pa

E f reaction rate constant

E n effect of all previous time steps

E s secant Youngs modulus, psi, bar, Pa

E t tangent Youngs modulus, psi, bar, Pa

E t Youngs modulus of a plastic material, psi, bar,Pa

f friction factor

f elastic inuence function

f aL apparent length fraction

f d drag coefcient

f fL ratio of fracture to loss volume during injection

f LS volume fraction lost to spurt f p pad volume fraction

f pad pad volume fraction

f s slurry volume fraction

f v volume fraction

f w water fractional ow

f spurt fraction

F ll fraction

F formation factorF force, lbf, N

F fracture development function

F b ratio of wellbore width or net pressure

F c critical load

F i surface ux at the ith time step

F L linear ow function

F meas fracture development function for measureddata

F sim fracture development function for simulateddata

F 0 surface ux at time zero

g acceleration of gravity, ft/s 2, m/s 2

g(t D) dimensionless uid-loss volume function

g f fracture gradient, psi/ft, Pa/m

g0 uid-loss volume function

G shear modulus, psi, bar, Pa

G(t D) dimensionless uid-loss time function

G* corrected value of G-function at closure

G elastic storage modulus, psi, bar, Pa

G viscous loss modulus, psi, bar, Pa

Gc uid-loss time function G(t D) at fractureclosure

Gdyn dynamic shear modulus, psi, bar, Pa

Ge strain energy release rate

GR API gamma ray value

h height, ft, m

h formation or reservoir thickness, ft, m

h hardening parameter

h heat transfer coefcient

hcp height at the center of perforations, ft, m

h D dimensionless height

h f fracture height, ft, m

h fD ratio of the leakoff area to the characteristiclength

h fo initial fracture height, ft, m

h L permeable or uid-loss height, ft, mh pay height of the pay zone, ft, m

hs penetration into bounding layer, ft, m

hwD dimensionless completion thickness

H depth, ft, m

i injection rate


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i interest rate

I diffusion ux

I inuence function

I ani index of horizontal-to-vertical permeabilityanisotropy

J acid ux J pseudosteady-state productivity index

J F fractured well productivity index

J H pseudosteady-state productivity index of horizontal well

J ideal ideal productivity index

J o initial productivity index

J real real productivity index

J V

pseudosteady-state productivity index of vertical well

k permeability, md

k c damaged zone permeability, md

k cake lter or diverter cake permeability, md

k d dissociation constant

k f fracture permeability, md

k fD dimensionless fracture permeability

k l relative permeability of the formation to

ltrate, mdk thermal conductivity of a uid

k foam foam permeability, md

k fs fracture permeability in the near-well skineffect zone, md

k g gas effective permeability, md

k h thermal conductivity, BTU/hr ftF,J/s mC

k H horizontal permeability, md

k Hs damaged horizontal permeability, md

k i initial permeability, md

k near wellbore near-wellbore friction proportionalityconstant

k o oil effective permeability, md

k o initial permeability, md

k pf perforation friction proportionality constant

k r relative permeability, md

k r reservoir permeability, md

k r surface reaction rate constant, cm/s

k r,app apparent reservoir permeability, md

k rg gas relative permeability, md

k ro oil relative permeability, md

k rw water relative permeability, md

k s damaged permeability, md

k sph spherical permeability, md

k V vertical permeability, md

k Vs damaged vertical permeability, md

k w water effective permeability, md

k x maximum permeability directed parallel to theprincipal permeability axis, md

k x permeability in the x direction, md

k y minimum permeability directed perpendicularto the principal permeability axis, md

k y permeability in the y direction, md

k z vertical permeability, md

k 0 reaction rate constant at the referencetemperature

K bulk modulus, psi, bar, Pa

K mass-transfer coefcient, cm/s

K equilibrium constant

K coefcient of earth stress, dimensionless

K empirical kinetic constant

K Mark-Houwink coefcient, dL/g

K power law uid rheology consistencycoefcient, lbf-s n /ft2

K power law effective consistency coefcient,lbf-s n /ft2

K a equilibrium constant of acid

K ads equilibrium constant of the exothermic adsorp-tion of molecules at surface reactive sites

K c conditional equilibrium constant

N-4 Nomenclature

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K c G-plot slope correction factor for pressure-dependent leakoff

K d dissociation constant

K dyn dynamic bulk modulus

K eq effective equilibrium constant

K foam consistency coefcient for the foam phaseK g mass-transfer coefcient

K I stress intensity factor, psi/in. 1/2, bar/m 1/2

K Ic critical stress intensity factor, psi/in. 1/2,bar/m 1/2

K Iceff effective fracture toughness, psi/in. 1/2,bar/m 1/2

K Iclag critical stress intensity factor in the uidlag region, psi/in. 1/2, bar/m 1/2

K Ic-apparent apparent fracture toughness, psi/in. 1/2,bar/m 1/2

K Il stress intensity factor at bottom fracturetip, psi/in. 1/2, bar/m 1/2

K Iu stress intensity factor at top fracture tip,psi/in. 1/2, bar/m 1/2

K o coefcient of earth pressure at rest, dimen-sionless

K pipe consistency index for pipe ow, lbf-s n /ft2

K r reaction rateK r temperature-dependent reaction rate con-

stant

K s bulk modulus of the solid constituents, psi,bar, Pa

K s solubility constant

K slot consistency index for slot ow, lbf-s n /ft2

K v consistency index for a concentric cylinderviscometer, lbf-s n /ft2

l length, ft, in., ml diverter cake thickness, ft, m

ld length of damaged zone, ft, m

l p perforation channel length, ft, m

L length, ft, m

L fracture half-length, ft, m

L horizontal well length, ft, m

Lapp apparent of equivalent fracture penetration, ft,m

Le length to tip, ft, m

L p productive length, ft, m

Lt length of the fracture tip region, ft, m Lv length of ltrate-invaded zone, ft, m

m slope on semilogarithmic straight line,psi/cycle (oil), psi 2 /cycle or psi 2 /cp/cycle (gas)

m Archie constant

m linear regression constant

m reaction rate order

m power law turbulence factor

mbf

bilinear ow slope, psi/hr 1/4, bar/hr 1/4

mc early-time slope used to compute the wellborestorage coefcient C

mcf linear ow slope in an elongated reservoir

mepr early pseudoradial ow slope

mG slope of the G-plot, psi, bar, Pa

mGc slope of the G-plot at fracture closure, psi, bar,Pa

mhl linear ow slope of a horizontal well

mlf linear ow slope, psi/hr 1/2, bar/hr 1/2

m M Mayerhofer et al . (1993) method slope

mn straight-line slope

m N Nolte method slope

m p match pressure, psi, bar, Pa

m pp spherical ow slope

mrf radial ow slope, psi, bar, Pa

m3/4 slope of the G-plot at the 3 4 point, psi, bar, Pa

M acid moles of acid per unit rock face area M gel specic density of gel mass in the uid

M v viscosity average molecular weight, g/mol

MW molecular weight, g/mol

n number or order

n index of time step


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n power law uid rheology behavior index,dimensionless

n power law effective index, dimensionless

ne index of time step after shut-in

n f power law exponent of the ltrate

n perf number of perforations N DH dimensionless cumulative recovery from a

longitudinally fractured horizontal well

N DV dimensionless cumulative recovery from afractured vertical well

N p oil cumulative production, bbl, m 3

N Re Reynolds number

N Sc Schmidt number

N Sh Sherwood number

N coefcient of passive stress

p pressure, psi, bar, Pa

p reservoir pressure, psi, bar, Pa

pb bubblepoint pressure, psi, bar, Pa

pbh borehole pressure, psi, bar, Pa

pc constant conning pressure, psi, bar, Pa

pc closure pressure, psi, bar, Pa

pc capillary pressure, psi, bar, Pa

pcf casing friction pressure, psi, bar, Pa

pcorr pressure corrected for non-plane-strain contri-bution, psi, bar, Pa

pcp pressure at center of the perforations, psi, bar,Pa

p D dimensionless pressure

p D dimensionless pressure derivative

p DLs dimensionless pressure difference for pressure-dependent leakoff

pdr downstream restriction pressure, psi, bar, Pa

pdsc pressure downstream of the surface choke, psi,bar, Pa

pdsv pressure downstream of the safety valve, psi,bar, Pa

p D,up dimensionless pressure for a uniform-pressure, xed-length fracture

pe constant outer reservoir pressure, psi, bar,Pa

p f ssure or fracture pressure, psi, bar, Pa

p f fracturing uid pressure, psi, bar, Pa

p f far-eld pore pressure, psi, bar, Pa

p fc formation capacity

p fo ssure opening pressure, psi, bar, Pa

ph hydrostatic pressure, psi, bar, Pa

phead hydrostatic head of wellbore uid, psi, bar,Pa

pi initial reservoir pressure, psi, bar, Pa

pif breakdown pressure for fracture initiation,psi, bar, Pa

pinj injection pressure, psi, bar, Pa

p ISI instantaneous shut-in pressure, psi, bar, Pa

pit wellhead injection pressure, psi, bar, Pa

piw bottomhole injection pressure, psi, bar, Pa

pm microannulus pressure, psi, bar, Pa

pm mud pressure in the wellbore, psi, bar, Pa

pmeas measured pressure, psi, bar, Pa

pnet net pressure, psi, bar, Pa pnet,crit critical net pressure, psi, bar, Pa

pnet,fo net pressure required for ssure opening,psi, bar, Pa

pnet,max maximum net pressure, psi, bar, Pa

pnet,si net pressure at shut-in, psi, bar, Pa

pnet,so net pressure at screenout, psi, bar, Pa

po wellbore pressure, psi, bar, Pa

p p far-eld reservoir pressure, psi, bar, Pa

p pf perforation friction, psi, bar, Pa

p pipe friction pipe friction pressure, psi, bar, Pa

p pwD dimensionless pseudopressure

pr reservoir pressure, psi, bar, Pa

N-6 Nomenclature

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ps pressure at the outer bound of the damagedzone, psi, bar, Pa

psc standard condition pressure, psi, bar, Pa

psep separator pressure, psi, bar, Pa

psim simulated pressure, psi, bar, Pa

psurf surface pressure, psi, bar, Pa ptf tubing owing pressure, psi, bar, Pa

ptip net pressure at fracture tip for extension, psi,bar, Pa

pur upstream restriction pressure, psi, bar, Pa

pusv pressure upstream of the safety valve, psi,bar, Pa

pvapor uid vapor pressure, psi, bar, Pa

pw wellbore pressure, psi, bar, Pa

pwD dimensionless wellbore pressure

pwf bottomhole owing pressure, psi, bar, Pa

pwf,ideal ideal bottomhole owing pressure, psi, bar, Pa

pwf,real real bottomhole owing pressure, psi, bar, Pa

pwfs wellbore sandface owing pressure, psi, bar,Pa

pwh wellhead owing pressure, psi, bar, Pa

pws bottomhole shut-in pressure, psi, bar, Pa

p1 hr pressure on extension of semilogarithmicstraight line at t = 1 hr, psi, bar, Pa

p3/4 pressure at the G-plot 3 4 point, psi, bar, Pa

Pe Peclet number

PI productivity index, B/D/psi (oil), Mscf/D/psi(gas), m 3 /d/bar

PI s damaged productivity index, B/D/psi (oil),Mscf/D/psi (gas), m 3 /d/bar

PV BT number of pore volumes to breakthrough

PV inj number of pore volumes injectedq ow rate, B/D (oil), Mscf/D (gas), m 3 /d

qapp apparent ow rate, B/D, bbl/min, m 3 /d, m 3 /s

qave average ow rate, B/D, bbl/min, m 3 /d, m 3 /s

qc ow rate in capillary pores

qc injection rate into core face

q D dimensionless ow rate

q DND dimensionless non-Darcy ow rate

qe ow at tip

q f volume rate of storage in a fracture

qg gas production rate, Mscf/D, m 3 /d

qi injection rate, B/D, bbl/min, m 3 /d, m 3 /s

qi,max maximum injection rate, B/D, bbl/min, m 3 /d,m3 /s

q L rate of uid loss, B/D, bbl/min, m 3 /d, m 3 /s

qlast last ow rate, B/D, bbl/min, m 3 /d, m 3 /s

q L,C rate of uid loss for reservoir-controlledleakoff, B/D, bbl/min, m 3 /d, m 3 /s

qn leakoff rate from one wing through two faces,B/D, m 3 /s

qo initial ow rate, B/D, m 3 /s

qo oil production rate, B/D, m 3 /s

qo,max maximum oil production rate at two-phaseow, B/D, m 3 /s

q perf ow entering a perforation

q RT total reservoir production rate, B/D, m 3 /d

qs damaged ow rate

qT total injection rate

qtot constant total injection rateqw water production rate, B/D, m 3 /d

Q p cumulative production, B/D, m 3 /d

r radial distance, ft, m

r reaction rate

r A rate of reactant consumption, mol/cm 2 /s

r ac stimulation radius, ft, m

r b acid bank radius, ft, m

r bob bob radiusr cup cup radius

r D rate of surface reaction, mol/cm 2 /s

r e reservoir radius, ft, m

r eH radius of horizontal drainage ellipse formedaround a horizontal well, ft, m


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r f radial extent of foam bank, ft, m

r feldspar reaction rate of feldspar, mol feldspar/cm 2 /s

r HF radial penetration of hydrouoric acid, ft, m

r hyd hydraulic radius

r i specic reaction rate of mineral i

r i inner radius

r o outer radius

r p ratio of permeable area to fracture area

r p probe radius

r pD dimensionless ratio of permeable area tofracture area

r perf perforation radius, in., m

r quartz reaction rate of quartz, mol quartz/cm 2 /s

r s radius of damaged or displaced section, ft, mr v fraction of well drainage volume occupied by

the crest at water breakthrough

r w wellbore radius, ft, m

r w effective or apparent wellbore radius, ft, m

r wD dimensionless effective wellbore radius

r wh wormhole radius

R pore radius

R reaction rate

R universal gas constant, psi ft 3 /mol R,bar m 3 /mol K

R fracture radius, ft, m

R A rate of appearance of reactant

R At rate of reactant consumption at the tip

R B rate of mineral dissolution

Rcake diverter cake resistance, m 1

Reff effective radius, ft, m

R f radial fracture radius, ft, m

Ri overall reaction rate of mineral i

Rmf resistivity of the mud ltrate, ohm-m

Ro resistivity of 100% water-saturated formation,ohm-m

R p pressure-difference curve, dimensionless

Rso solution-gas/oil ratio

Rsw solution-gas/water ratio

Rt true formation resistivity, ohm-m

Rw resistivity of formation water, ohm-m

R xo resistivity of the ushed zone, ohm-m

R0 lter-cake resistance, s m1

R0,app apparent lter-cake resistance, s m1

s skin effect, dimensionless

s reactive surface area

sc skin effect from partial penetration,dimensionless

sc + skin effect due to partial penetration and slant,dimensionless

scake

temporary skin effect due to diverter cake,dimensionless

sd skin effect due to damage, dimensionless

(sd )o perforation skin effect in openhole,dimensionless

(sd ) p perforation skin effect due to perforationsterminating outside the damaged zone,dimensionless

se vertical eccentricity skin effect, dimensionless

s f skin effect while owing at pseudoradialconditions, dimensionless

s f fracture stiffness, ft/psi/m

s f skin effect due to a fracture, dimensionless

s foam foam skin effect, dimensionless

s fs fracture face damage skin effect, dimensionless

s H plane-ow skin effect, dimensionless

so initial skin effect, dimensionless

so constant skin effect, dimensionless

s p skin effect due to perforations, dimensionlessst total skin effect, dimensionless

sV vertical skin effect, dimensionless

swb wellbore skin effect, dimensionless

s x vertical effects skin effect, dimensionless

s skin effect due to slant, dimensionless

N-8 Nomenclature

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S surface area

S F surface area per unit volume of solids for fast-reacting minerals

S g gas-phase uid saturation, fraction

S i reactive surface area of mineral i

S o oil-phase uid saturation, fractionS oi initial oil saturation, fraction

S or residual oil saturation, fraction

S p spurt-loss coefcient, gal/ft 2, m 3 /m 2

S RE rock embedment strength

S S surface area per unit volume of solids forslow-reacting minerals

S w water saturation, fraction

S wc

connate water saturation, fraction

S wi irreducible water saturation, fraction

t time, day, hr, min, s

t * reduced time

t a pseudotime

t aD dimensionless pseudotime

t BT time of water breakthrough, hr

t c closure time, min

t cD dimensionless closure time

t D dimensionless time

t DA dimensionless time referenced to reservoirdrainage area

t Dblf dimensionless time at start of formation linearow regime

t Debf dimensionless time at end of bilinear owregime

t De dimensionless time at which fracture linearow behavior ends

t Delf dimensionless time at which formation linearow behavior ends

t dep time of departure from ow regime trend

t D,knee dimensionless knee time for the pressurederivatives

t Dr w dimensionless time referenced to the effectivewellbore radius r w

t Dx f dimensionless fracture time

t e time at end of pumping or injection, min, s

t end time of the end of dual-porosity behavior

t exp time of fracture opening and initial uidexposure

t i injection time

t i time at the end of the ith step

t knee knee time for the crossing of pressure derivatives

t min minimum time

t n time at the end of step n, s

t on time of onset of dual-porosity behavior

t p

producing time, hr

t p pumping or injection time, hr

t P compressional wave arrival time

t pss time to pseudosteady state, hr

t r time at reference point r

t S time of tip screenout or injection withoutscreenout

t S shear wave arrival time

t so time at screenout

t sp spurt time

t 0 reference time

t D dimensionless ratio of time to pumping time

T temperature, F, C, K

T absolute temperature, R, K

T dimensionless time for after-closure analysis

T constant for tectonic effects on stress

T wire tension, lbf/ft

T d dead weight, lbf

T D dimensionless temperature

T f owing temperature, F, C

T uid temperature, F, C

T i uid temperature at the fracture mouth, F, C


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T inlet temperature at inlet, F, C

T knee dimensionless knee time for after-closureanalysis

T o offset temperature, F, C

T o tensile strength, psi, bar, Pa

T p dimensionless time at the end of pumping forafter-closure analysis

T r reservoir temperature, F, C

T ref reference temperature, F, C

T s wire strength, lbf/ft

T sc standard condition temperature, F, C, K

TR tool response

u velocity, ft/s, cm/s

u acid ux

ug volumetric ux of gas

u L leakoff velocity, ft/s, cm/s

uP P-wave velocity, ft/s, m/s

ur rising velocity of spherical particles in a uid,ft/s, cm/s

uS S -wave velocity, ft/s, m/s

usol solid particle velocity, ft/s, cm/s

ut terminal settling velocity, ft/s, m/s

utip fracture tip velocity, ft/s, cm/s

uw volumetric ux of water

u terminal proppant settling velocity, ft/s, m/s

v ow velocity, ft/s, cm/s

v^ specic volume of foam

v A,x Ficks law for the velocity of species A

vc damaged zone velocity, ft/s, cm/s

v fall settling rate, ft/s, cm/s

vl specic volume of the base liquid

v L uid-loss velocity, ft /min

v L specic uid-loss volume

vm matrix velocity, ft/s, cm/s

v x average uid velocity along the fracture length,ft/s, cm/s

V volume, ft 3, m 3

V ac acid volume injected, ft 3, m 3

V f fracture volume, ft 3, m 3

V f uid volume

V F volume of fast-reacting minerals

V fp fracture volume at the end of pumping, ft 3, m3

V fso fracture volume at screenout, ft 3, m 3

V HC volume of hydrocarbons, ft 3, m 3

V HCl volume of hydrochloric acid, ft 3, m 3

V HF volume of hydrouoric acid, ft 3, m 3

V i volume of uid injected, bbl, gal, m 3

V iso uid volume injected at screenout, bbl, gal,ft3, m 3

V L leaked-off uid volume, bbl, gal, m 3

V L,C volume of uid lost due to ltration, bbl, gal,m3

V Lp leaked-off volume during pumping, bbl, m 3

V Lp,C volume of uid lost due to ltration at theend of pumping, bbl, gal, m 3

V Ls volume of uid lost during shut-in, bbl, gal,m3

V L,S fluid-loss component due to spurt, bbl, gal, m 3

V Ls,C volume of uid lost due to ltration duringshut-in, bbl, gal, m 3

V M molar volume

V mineral volumetric fraction of a mineral

V p pore volume, ft 3, m 3

V prop bulk proppant volume injected

V rp relative proppant volume, lbm/md-ft 3

V S volume of slow-reacting minerals

V S volume of uid lost to spurt, gal/100 ft

2

V wall volume of uid leaked off at the fracture wall

w width, ft, m

w fracture width, ft, in., m

we average fracture width at end of pumping, ft,m

N-10 Nomenclature

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wetch acid-etched width, ft, m

w f fracture width, ft, m

w L leakoff width, ft, m

wlost proppant volume lost to the fracture width

wmax maximum width, ft, m

wmax,p maximum fracture width at the end of pumping, ft, m

wmax,si maximum fracture width immediately aftershut-in, ft, m

wn average fracture width at time step n, ft, m

wo wellbore width, ft, m

w p propped width, ft, m

w p-eff effective propped width, ft, m

wso

width at screenout, ft, m

ww width at the wellbore, ft, m

W elas elastic energy stored in a solid

W ext potential energy of exterior forces

W i weighting factors

W kin kinetic energy

W s energy dissipated during propagation ofa crack

x linear distance, ft, m

x e well drainage dimension, ft, m

x e,opt optimal well spacing, ft, m

x f productive fracture half-length, ft, m

x fa apparent fracture half-length, ft, m

x feldspar feldspar volume fraction of a sandstone

x s half-length of the skin effect zone, ft, m

X volumetric dissolving power

X C dissolving power of acid

X HCl bulk rock fraction dissolved by hydrochloricacid

y vertical linear distance, ft, m

z linear distance, ft, m

zTVD true vertical depth, ft, m

zw elevation from reservoir bottom, ft, m

zw standoff from oil-water contact, ft, m

zw elevation of midpoint of perforations from thebottom of the reservoir, ft, m

zwD dimensionless completion elevation

Z gas deviation factor, dimensionless

Symbols Forscheimer equation coefcient

Biot poroelastic constant

proportionality constant

specic diverter cake resistance, m/kg

exponent of fracture area growth, dimensionless

order of reaction

bf bilinear ow constant

c wellbore storage constant

cf elongated reservoir constant

f sealing fault constant

g geometry coefcient

hl linear ow to a horizontal well constant

lf linear ow constant

p dimensionless pressure constant

pp partial penetration constant

t dimensionless time constant

T linear thermal expansion coefcient

0 lower bound of area exponent, dimensionless

1 upper bound of area exponent, dimensionless

perforation-phase-dependent variable

dissolving power coefcient related to acidstrength

stiffness ratio of average to wellbore net pressure or

width

Forscheimer equation coefcient

non-Darcy ow rate coefcient

p net pressure or width ratio during injection


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s net pressure or width ratio during shut-in

shear strain

channel factor

G-plot slope correction factor for pressure-dependent leakoff

specic gravity shear rate, s 1

ab interaction energy per unit surface areabetween liquids a and b

b shear rate at the bob, s 1

F fracture surface energy

uid specic gravity of uid

g specic gravity of gas

I

interfacial tension

prop specic gravity of proppant

v volume-averaged shear rate, s 1

foam quality, fraction

(d ) Euler gamma function

( x ) gamma function

dip of the formation (angle with the hori-zontal), degree

rate of deformation tensor

C change in concentration

E activation energy, kcal/mol

H heat of reaction

MD change in measured depth, ft, m

p pressure difference or gradient, psi, bar, Pa

pc pressure drop between ltrate/reservoirinterface and far-eld reservoir, psi, bar, Pa

pcake pressure drop across the lter cake, psi,bar, Pa

pct total pressure drop, psi, bar, Pa

pdeparture pressure departure, psi, bar, Pa

pentry fracture entry pressure, psi, bar, Pa

p face pressure drop across fracture face domi-nated by lter cake, psi, bar, Pa

p friction friction pressure ratio with and withoutsolids

ph hydrostatic pressure drop, psi, bar, Pa

pint difference in the pressure intercept, psi,bar, Pa

p

misalign perforation misalignment friction, psi,bar, Pa

pnear wellbore near-wellbore pressure loss, psi, bar, Pa

pnf pressure difference due to near-faceleakoff effects, psi, bar, Pa

p pf friction through the perforation, psi, bar,Pa

p piz pressure drop across a polymer-invadedzone, psi, bar, Pa

pr pressure drop in the reservoir, psi, bar,Pa

p R total pressure increase in the reservoirbeyond the ltrate invasion region, psi,bar, Pa

p RC pressure increase in the reservoir beyondthe ltrate region due to Carter-basedleakoff, psi, bar, Pa

p RS pressure increase in the reservoir beyondthe ltrate region due to spurt, psi, bar,Pa

psafe pressure safety margin, psi, bar, Pa pT total pressure difference between the

fracture pressure and initial reservoirpressure, psi, bar, Pa

ptort tortuosity component of pressure, psi,bar, Pa

ptotal difference between fracture pressure andfar-eld reservoir pressure, psi, bar, Pa

pv pressure drop across the ltrate-invadedzone, psi, bar, Pa

pw difference in wellbore pressure, psi, bar,Pa

p viscous pressure contribution, psi, bar,Pa

t time difference, hr

t sonic transit time in the formation

N-12 Nomenclature

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t shut-in time, hr, min, s

t ae effective pseudotime

t c closure time

t C compressional wave traveltime

t cD dimensionless closure time

t D dimensionless time difference

t D dimensionless shut-in time

t Dso dimensionless time after a screenout

t e effective time

t ma sonic transit time in the rock matrix

t S shear wave traveltime

t so time following screenout

t sup superposition time function

T surf temperature change at the surface, F, C

TBT change in true bed thickness, ft, m

TVD change in true vertical depth, ft, m

V change in volume

density difference, lbm/ft 3, g/cm 3

max difference in maximum porosity

stress difference, psi, bar, Pa

$n incremental revenue

introduced error

ratio of closure time to the time interval

longitudinal strain

a axial strain

e elastic strain

f acid front position divided by the linear owcore length

h minimum tectonic strain

H maximum tectonic strain p plastic strain

r radial strain

S specic volume expansion ratio

V volumetric strain

poroelastic stress coefcient

efciency

diffusivity constant

C efciency including spurt loss

f fracture hydraulic diffusivity

fD dimensionless fracture hydraulic diffusivity

p efciency at end of pumping

so efciency at screenout

angle, degree

uid-loss exponent

dimensionless time

opening-time distribution factor

ratio of fracture-opening stress to minimumstress

spurt effect factor thermal diffusivity

overall dissolution rate constant, cm/s

so spurt correction at screenout

interporosity constant

experimental coefcient for the tortuosity reori-entation of a fracture path

apparent time multiplier

characteristic relaxation time

rt total mobility

t multiphase mobility

length scale corresponding to pore size

viscosity, cp

a apparent viscosity, cp

base viscosity of base fracturing uid, cp

eff effective viscosity, cp

l viscosity of fracturing uid ltrate, cp

uid uid viscosity, cp

g gas viscosity, cp

gi gas viscosity at initial reservoir pressure andtemperature, cp

i intrinsic viscosity, cp


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N-14 Nomenclature

inh inherent viscosity, cp

o oil viscosity, cp

r viscosity ratio

r viscosity of reservoir uid, cp

r relative viscosity, cp

slurry slurry viscosity, cp

sp specic viscosity, cp

w water viscosity, cp

0 zero-shear viscosity, cp

100 viscosity at 100F [40C], cp

high-shear-limiting viscosity, cp

Poissons ratio

stoichiometric ratio of reactants to products

CaCO 3 stoichiometric coefcient of CaCO 3 dyn dynamic Poissons ratio

HCl stoichiometric coefcient of hydrochloric acid

u undrained Poissons ratio

uid-loss term

dimensionless area or position

f forward rate constant

r reverse rate constant

density, lbm/ft 3, g/cm 3

a mass of diverter cake per unit area of avail-able sandface, g/cm 3

A density of reactant, g/cm 3

b bulk density, lbm/ft 3, g/cm 3

brine brine density, lbm/ft 3, g/cm 3

C density of acid solution

CaCO 3 density of calcium carbonate, lbm/ft 3, g/cm 3

div density of diverter particles, kg/m3

f uid density, lbm/ft 3, g/cm 3

l liquid density, lbm/ft 3, g/cm 3

ma density of matrix components, lbm/ft 3, g/cm 3

o oil density, lbm/ft 3, g/cm 3

p proppant or particle density, lbm/ft 3, g/cm 3

r ratio of slurry density to uid density

rock rock density, lbm/ft 3, g/cm 3

s slurry density, lbm/ft 3, g/cm 3

sol solid particle density, lbm/ft 3, g/cm 3

stress, psi, bar, Pa

effective stress, psi, bar, Pa

a axial stress, psi, bar, Pa

BL stress acting on a bounding layer, psi, bar, Pa

c uniaxial compressive strength, psi, bar, Pa

c closure pressure or stress, psi, bar, Pa

c effective conning stress, psi, bar, Pa

f normal stress across a ssure, psi, bar, Pa

failure effective ultimate strength, psi, bar, Pa

h minimum horizontal stress, psi, bar, Pa

h minimum effective horizontal stress, psi, bar,Pa

H maximum horizontal stress, psi, bar, Pa

H,max maximum horizontal stress, psi, bar, Pa

h,min minimum horizontal stress, psi, bar, Pa

m mean stress, psi, bar, Pa

min minimum stress or minimum principal stress,psi, bar, Pa

n normal stress component, psi, bar, Pa

n effective normal stress, psi, bar, Pa

o equal-stress constant, psi, bar, Pa

pay stress of the pay zone, psi, bar, Pa

PZ stress acting on the pay zone, psi, bar, Pa

r radial stress, psi, bar, Pa

ref constant state of stress, psi, bar, Pa

r shear stress, psi, bar, Pa

v vertical stress, psi, bar, Pa

v effective vertical stress, psi, bar, Pa

1 maximum principal stress, psi, bar, Pa

1 maximum principal effective stress, psi, bar,Pa

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2 intermediate principal stress, psi, bar, Pa

2 intermediate principal effective stress, psi, bar,Pa

3 minimum principal stress, psi, bar, Pa

3 minimum principal effective stress, psi, bar, Pa

tangential stress, psi, bar, Pa circumferential stress, psi, bar, Pa

shear stress, psi, bar, Pa

time of fracture opening

dimensionless slurry time

c characteristic time for fracture propagation,dimensionless

o foam yield stress, lbf/ft 2, bar, Pa

oct octahedral shear stress, psi, bar, Paw wall shear stress, lbf/ft 2, bar, Pa

yp yield point, lbf/ft 2, bar, Pa

porosity, fraction

angle of internal friction, degree

cake diverter cake porosity, fraction

D porosity from density, fraction

eff effective porosity, fraction

f fracture porosity, fraction

i initial porosity, fraction

N porosity from neutron, fraction

p proppant pack porosity, fraction

S porosity from sonic, fraction

total total porosity, fraction

angle, degree

channel ow function

change of angle, degree

dimensionless hydrouoric acid concentration

dimensionless rock dissolution rate

angular velocity, rad/s, rpm

storativity ratio

stoichiometric coefcient


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RS_NOM