Flow Equations
Gas
Assuming puesdo-steady state, the volumetric flow rate at any radius, qr,
qr 
p sc qTz
Tsc p
Darcy’s Law
 k  dp
q r  6.328  10 3   Ac
   dr
where
Ac  2rh
Subing in
p sc qTz 1
dr  6.328  10 3 2  pdp
Tsc h r
Integrating from rw to rd


kh pd2  pw2
q  .703
r 
Tz ln  d 
 rw 
With skin


kh pd2  pw2
q  .703


r
Tz ln  .472 d  s 
rw


kh
C  .703
_
r
T  z ln  d 
 rw 
_

q  C pr2  pw2

qC p  p
2
r


2 n
w
Non-Darcy Flow
Forchhermer equation
_2

kh p  p w2 


q
_ _
 r

1424  z T ln  d   s  Dq 
  rw 

q mscfpd
D in the non darcy coefficent and rd is the effective drainage radius
Rd is time dependant until rd = 0.472re, otherwise
rd
 1.5 t D
rw
tD 
.000264 kt
ct rw2
6  10 5 k s.1 h
D
2
rw h perf
D can be approximated by
(mscf/day)-1
Rearranged in this form
_ 2
p  p w2  aq  bq 2
_ _
1424  z T
a
kh
 .472re

 ln
 s 
rw


_ _
1424  z D
b
kh
a and b can also be found using a multi-point test, plot p2 vs. q on
Cartesian, D can be calculated using this a and b.