Nomenclature
a
=
A =
AI =
AR =
Awb =
b
=
1,422j.tPZpgT[ln(~)-0.75+sJ
kh
r;
drainage area of well, sq ft (m 2)
fracture area, sq ft (m ")
reservoir area, acres (m 2)
wellbore area, sq ft (m ")
1 422
,
j.t-zp
TD
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 evaluated
at 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 original
reservoir 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 compressibility
c, = 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)
C wb = 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-well
deliverability equation
C A = shape constant or factor
C s = wellbore storage constant, bbl/psi
(m3/kPa)
CsD = 0.894 CsI<t>c,hr~ =dimensionless
well bore storage constant
D = non-Darcy flow constant, D/Mscf (d/m 3)
E = flow efficiency, dimensionless
Ei(-x)
= -
i
00
(e-Ulu)du
x
=the exponential integral
P' = fl..tplfl..tc = ratio of pulse length to
cycle 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 function
k = reservoir rock permeability, md
kl = formation permeability
(McKinley method), md
kg = permeability to gas, md
k H = horizontal permeability, md
kJ = reservoir rock permeability (based on
PI test), md
k; = permeability to oil, md
ks = permeability of altered zone
(skin effect), md
k v = vertical permeability, md
kIV = permeability to water, md
kwb = near-well effective permeability
(McKinley method), md
L = 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 = 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 of
fractured well, psi/cycle (kf'a: cycle)
muue = true slope on buildup curve uninfluenced
by fracture, psi/cycle (kl-a- cycle)
M = molecular weight of gas
n = inverse slope of empirical gas-well
deliverability curve
P = 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 for
constant-rate problems
1/
WELL TESTING
152
PDMBH
Pi
PMT
Po
Ppc
Ppr
Pr
P sc
=
=
=
=
=
=
=
=
=
Pws =
p, hr =
P
wf
q =
qD =
qg =
q gr =
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)
standard-condition pressure, psia (kPa)
(frequently, 14.7 psia)
flowing BHP, psi (kPa)
shut-in BHP, psi (kPa)
pressure at I-hour shut-in (or flow)
time on middle-time line (or its
extrapolation), psi (kPa)
flow rate, STBID (m 3 /d)
dimensionless instantaneous flow rate at
constant BHP
gas flow rate, Mscf/D (m 3 /d)
total gas flow rate from oil well, Mscf/D
tend =
tPr =
=
tp =
t pss =
ts =
t wbs =
T =
=
=
=
Tpc
T pr
Tsc
u =
Vp =
(m 3 /d)
Qp = cumulative production at constant BHP,
VR =
Vw =
x =
STB (m3)
BQp
QpD
1.119 ¢crhr3(pi
R =
R, =
Rsw =
Rswp
=
r =
r dt =
rd =
re =
r-o
ri
rs
rw
=
=
=
=
r wa =
s =
s' =
s* =
s
-Pili)
=dimensionless cumulative production
universal gas constant
dissolved GOR, scf gas/STB oil (m3/m3)
dissolved gas/water ratio,
scf gas/STB water (m 3 /m 3)
solubility of gas in pure (gas-free) water,
scf gas/STB water (m 3 /m 3)
distance from center of wellbore, ft (m)
transient drainage radius, ft (m)
radius of drainage, ft (m)
external drainage radius, ft (m)
re/rw
radius of investigation, ft (m)
radius of altered zone (skin effect), ft (m)
wellbore radius, ft (m)
effective wellbore radius, ft (m)
skin factor, dimensionless
s+Dqg =apparent skin factor from
gas-well buildup test, dimensionless
log (k/¢wrr,3)-3.23+0.869s
= log(
k
¢jJ.crrw
2) -3.23+0.869s
Sg = gas saturation, fraction of pore volume
So = oil saturation, fraction of pore volume
Sw = water saturation, fraction of pore volume
t = elapsed time, hours
to = 0.000264 kt/¢jJ.crr,~
=dimensionless time
tDA = 0.000264 kt/¢jJ.crA
=dimensionless time based on drainage
area, A
2
t oi, = 0.000264 kt/¢WrLf
=dimensionless time based on fracture
Y, =
Z =
z, =
=
Zpg
an =
'Y g =
'Y 0 =
MVp =
half-length
end of MTR in drawdown test, hours
time at which late-time region begins,
hours
lag time in pulse test, hours
cumulative production/most recent
production rate = pseudoproducing time,
hours
time required to achieve pseudosteady
state, hours
time for well to stabilize, hours
wellbore storage duration, hours
reservoir temperature, "R (OK)
pseudocritical temperature, "R (OK)
pseudoreduced temperature
standard condition temperature, "R (OK)
(usually 5200R)
flow rate per unit area (volumetric
velocity), RBID-sq ft (m3/d'm2)
reservoir pore volume, cu ft (m ')
reservoir volume, bbl (m 3)
wellbore volume, bbl (m ')
distance coordinate used in linear flow
analysis, ft (m)
Bessel function
gas-law deviation factor, dimensionless
gas-law deviation factor evaluated at
pressure Pi, dimensionless
gas-law deviation factor evaluated at p,
dimensionless
roots of equation J, (anr eD)Y' (an)
-J, (an)Y, (anr eD) =0
gas gravity (air= 1.0)
oil gravity (water= 1.0)
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 pressure
on buildup curve and extrapolated
MTR, psi (kPa)
t::..t= time elapsed since shut-in, hours
t::..t = time elapsed since rate change in two-rate
flow test, hours
t::..tc = cycle length (flow plus shut-in) in pulse
test, hours
t::..t d = time at departure (McKinley method),
hours
t::..tend = time MTR ends, hours
t::..t p = pulse-period length, hours
l
t::..tx = time at which middle- and late-time
straight lines intersect, hours
TJ
= 0.000264 k/¢jJ.c=hydraulic
sq ft/hr (m2/h)
diffusivity,
-- ~
--
.-~
---
-
- _. ~
.
-153
NOMENCLATURE
At
=
=
/hg =
/hi =
/ho =
/hp =
p: w =
/h
Cko//ho +kg//hg
+kw//hw)
=total mobility, md/cp (rnd/Pa- s)
viscosity, cp CPa' s)
gas viscosity, cp (Pa-s)
gas viscosity evaluated at Pi, cp CPa' s)
oil viscosity, cp CPa' s)
gas viscosity evaluated at p, cp CPa' s)
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,
CkPa2 /Pa- s)
psia 2 /cp