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Well test analysis formulas and calculations Chapter 3 175

m: Slope from Curve (psi/cycle)
m L : Slope from linear Region of Curve (psi/cycle)
p ai : Initial Adjusted Well Pressure (psi)
p ahr : Adjusted Well pressure at t ¼ 1 h (psi)
p D : Dimensionless Pressure (dimensionless)
Ø: Porosity (dimensionless)
c t : Compressibility (1/psi)
r w : Radius of Wellbore (ft)
m: Viscosity (cP)
h: Formation Thickness (ft)
t LfD : Time of end of Linear or Pseudo Radial flow from Plot (dimensionless)
Dt a : Adjusted Delta Time from Derivative Curve (h)

Output(s)
k: Permeability (mD)
L fPR : Length of Fracture for Pseudo Radial Flow (ft)
L fL : Length of Fracture for Linear Flow (ft)
L fMP : Length of Fracture from Match Point Analysis (ft)
s: Skin Factor (dimensionless)
: Adjusted Pressure Difference at Match Point from Plot (psi)
DP a MP
Formula(s)

m
k ¼ 162:6 q B
g g
m h

p p ahr k

ai
L ¼ 1:151 log +3:23
fPR 2
m Ø m c r
t w
L ¼ 2 r 2:71 s
fL w
!
B g 1
L ¼ 4:064 q m *c 2
fMP g 0:5 Ø t
m h k
L

m
s ¼ 141:2 q B h p ð D Þ
g
g
k
1
0:0002637 k Dt a 2

DP ¼ *
Ø m c t t LfD
a MP
Reference: Lee, J., Rollins J.B., and Spivey J.P. 2003, Pressure Transient Testing, Vol. 9, SPE Textbook Series, Vol. 9,
Henry L. Doherty Memorial Fund of AIME, Richardson, Texas, SPE, Chapter: 6, Page: 121.
3.3 Analysis of a post-fracture pressure buildup test with wellbore-storage distortion
Input(s)
q g : Gas flow rate (MSCF/day)
B g : Gas formation Volume Factor (RB/MSCF)
p D : Dimensionless Pressure (dimensionless)
Ø: Porosity (dimensionless)
c t : Compressibility (1/psi)
m: Viscosity (cP)
h: Formation Thickness (ft)