Nomenclaturea = 1,422j.tPZpgT[ln(~)-0.75+sJ

kh r;

A = drainage area of well, sq ft (m 2)AI = fracture area, sq ft (m ")A R = reservoir area, acres (m 2)Awb = wellbore area, sq ft (m ")

j.t-z- TDb = 1 422 p pg

, kh

b' = intercept of (Pi -Pwl)/qn plot, psi/STB-D(kPa/m3/d)

B = formation volume factor,res vol/surface vol

B g = gas formation volume factor, RB/Mscf(m3/m3)

B gi = gas formation volume factor evaluatedat Pi, RB/Mscf (m 3 /m 3)

Bo = oil formation volume factor, RB/STB(m3/m3)

B w = water formation volume factor, RB/STB(m3/m3)

c = compressibility, psi - I (kPa - I)

CI = formation compressibility, psi - I (kPa - I )

Cg = gas compressibility, psi - I (kPa -I )

C gi = gas compressibility evaluated at originalreservoir pressure, psi - I (kPa -I )

C gw = compressibility of gas in wellbore, psi -I

(kPa -I)Co = oil compressibility, psi -I (kPa - I)

cpr = pseudo reduced compressibilityc, = Soco+Swcw+SgCg+cl

=total compressibility, psi -I (kPa -I)

C ti = total compressibility evaluated at Pi,psi - I (kPa - I)

C If = total compressibility evaluated at p , psi - I(kPa -I)

C IV = water compressibility, psi -I (kPa -I)

Cwb = compressibility of liquid in wellbore,psi - I (kPa - I )

C wp = compressibility of pure (gas-free) water,psi - I (kPa - I)

C = performance coefficient in gas-welldeliverability equation

CA = shape constant or factorCs = wellbore storage constant, bbl/psi

(m3/kPa)CsD = 0.894 CsI<t>c,hr~ =dimensionless

well bore storage constantD = non-Darcy flow constant, D/Mscf (d/m 3)E = flow efficiency, dimensionless

00

Ei(-x) = - i (e-Ulu)dux=the exponential integral

P' = fl..tplfl..tc = ratio of pulse length tocycle length

g == acceleration of gravity, ft/sec 2 (m/s 2)

g c = gravitational units conversion factor,32.l7 (lbm/ft)/(lbf-s 2), dimensionless

h = net formation thickness, ft (m)J = productivity index, STBID-psi

(m3/d'kPa)J actual = actual or observed well productivity

index, STBID-psi (m 3 /d· kPa)Jideal = productivity index with permeability

unaltered to sand face, STB/D-psi(m3/d'kPa)

J g = gas-well productivity index, McflD-psi(m3/d'kPa)

J I = Bessel functionk = reservoir rock permeability, mdkl = formation permeability

(McKinley method), mdkg = permeability to gas, mdk H = horizontal permeability, mdkJ = reservoir rock permeability (based on

PI test), mdk; = permeability to oil, mdks = permeability of altered zone

(skin effect), mdk v = vertical permeability, mdkIV = permeability to water, mdkwb = near-well effective permeability

(McKinley method), mdL = distance from well to no-flow

boundary, ft (m)LI = length of one wing of vertical fracture, ft

(m)m = 162.2 qBj.tlkh=absolute value of slope of

middle-time line, psi/cycle (kl'a cycle)m' = 162.6 Bj.tlkh=slope of drawdown curve

with (P i - P wl)/ q as abscissa,psi/STBID-cycle (kPa/m 3 /d· cycle)

m 1/ = slope of P~s or P~I plot for gas well,psia 2 / cycle (kl-a- cycle)

mL = slope of linear flow graph, psi/hr';'(kPa' h Y2)

mmax = maximum slope on buildup curve offractured well, psi/cycle (kf'a: cycle)

muue = true slope on buildup curve uninfluencedby fracture, psi/cycle (kl-a- cycle)

M = molecular weight of gasn = inverse slope of empirical gas-well

deliverability curveP = pressure, psi (kPa)p = volumetric average or static drainage-area

pressure, psi (kPa)p* = MTR pressure trend extrapolated to

infinite shut-in time, psi (kPa)PD = 0.00708 kh(Pi-P)/qBj.t=

dimensionless pressure as defined forconstant-rate problems

152

= 2.303(p*- p)/m, dimensionless= original reservoir pressure, psi (kPa)= pressure on extrapolated MTR, psi (kPa)= arbitrary reference pressure, psia (kPa)= pseudocritical pressure, psia (kPa)= pseudo reduced pressure= pressure at radius r, psi (kPa)

P sc = standard-condition pressure, psia (kPa)(frequently, 14.7 psia)

P wf = flowing BHP, psi (kPa)Pws = shut-in BHP, psi (kPa)p, hr = pressure at I-hour shut-in (or flow)

time on middle-time line (or itsextrapolation), psi (kPa)

q = flow rate, STBID (m 3 /d)qD = dimensionless instantaneous flow rate at

constant BHPq g = gas flow rate, Mscf/D (m 3 /d)q gr = total gas flow rate from oil well, Mscf/D

(m 3 /d)Qp = cumulative production at constant BHP,

STB (m3)

BQp

PDMBHPi

PMTPoPpc

Ppr

Pr

QpD1.119 ¢crhr3(pi -Pili)

=dimensionless cumulative productionR = universal gas constantR, = dissolved GOR, scf gas/STB oil (m3/m3)

Rsw = dissolved gas/water ratio,scf gas/STB water (m 3/m 3)

Rswp = solubility of gas in pure (gas-free) water,scf gas/STB water (m 3 /m 3)

r = distance from center of wellbore, ft (m)r dt = transient drainage radius, ft (m)rd = radius of drainage, ft (m)r e = external drainage radius, ft (m)

r-o = re/rwr i = radius of investigation, ft (m)r s = radius of altered zone (skin effect), ft (m)r w = wellbore radius, ft (m)r wa = effective wellbore radius, ft (m)

s = skin factor, dimensionlesss' = s+Dqg =apparent skin factor from

gas-well buildup test, dimensionlesss* = log (k/¢wrr,3)-3.23+0.869s

s = log( k 2) -3.23+0.869s¢jJ.crrw

Sg = gas saturation, fraction of pore volumeSo = oil saturation, fraction of pore volume

Sw = water saturation, fraction of pore volumet = elapsed time, hours

to = 0.000264 kt/¢jJ.crr,~=dimensionless time

tDA = 0.000264 kt/¢jJ.crA=dimensionless time based on drainage

area, A2

toi, = 0.000264 kt/¢WrLf=dimensionless time based on fracture

WELL TESTING

half-lengthtend = end of MTR in drawdown test, hours

tPr = time at which late-time region begins,hours

= lag time in pulse test, hourstp = cumulative production/most recent

production rate = pseudoproducing time,hours

t pss = time required to achieve pseudosteadystate, hours

t s = time for well to stabilize, hourst wbs = wellbore storage duration, hours

T = reservoir temperature, "R (OK)Tpc = pseudocritical temperature, "R (OK)T pr = pseudoreduced temperatureTsc = standard condition temperature, "R (OK)

(usually 5200R)u = flow rate per unit area (volumetric

velocity), RBID-sq ft (m3/d'm2)

Vp = reservoir pore volume, cu ft (m ')VR = reservoir volume, bbl (m 3)Vw = wellbore volume, bbl (m ')x = distance coordinate used in linear flow

analysis, ft (m)Y, = Bessel function

Z = gas-law deviation factor, dimensionlessz, = gas-law deviation factor evaluated at

pressure Pi, dimensionlessZpg = gas-law deviation factor evaluated at p,

dimensionlessan = roots of equation J, (anr eD)Y' (an)

-J, (an)Y, (anr eD) =0'Y g = gas gravity (air= 1.0)'Y 0 = oil gravity (water= 1.0)

MVp = oil production during a time interval, STB(rn ')

t::..p* = P*-Pw, psi (kPa)(t::..P)d = pressure change at departure (Mckinley

method), psi (kPa)(t::..p)s - 141.2 qBjJ.(s)/kh=0.869 ms=additional

pressure drop across altered zone, psi(kPa)

t::..pt,s = Pws -PMT = difference between pressureon buildup curve and extrapolatedMTR, psi (kPa)

t::..t= time elapsed since shut-in, hourst::..tl = time elapsed since rate change in two-rate

flow test, hourst::..tc = cycle length (flow plus shut-in) in pulse

test, hourst::..t d = time at departure (McKinley method),

hourst::..tend = time MTR ends, hours

t::..tp = pulse-period length, hourst::..tx = time at which middle- and late-time

straight lines intersect, hoursTJ = 0.000264 k/¢jJ.c=hydraulic diffusivity,

sq ft/hr (m2/h)

-- -- ~ .-~--- - - _. ~ . - -

NOMENCLATURE 153

At = Cko//ho +kg//hg +kw//hw)=total mobility, md/cp (rnd/Pa- s)

/h = viscosity, cp CPa' s)/hg = gas viscosity, cp (Pa-s)/hi = gas viscosity evaluated at Pi, cp CPa' s)/ho = oil viscosity, cp CPa' s)/hp = gas viscosity evaluated at p, cp CPa' s)p: w = water viscosity, cp CPa' s)

p = density of liquid in wellbore, lbm/cu ft(kg/m ')

¢ = porosity of reservoir rock, dimensionless

if;(P) = 2r ~dp/hZ

Po

= gas pseudopressure, psia 2 /cpCkPa2 /Pa- s)