PRESSURE BUILDUP ANALYSIS - HORNER PLOT

Transient Well Testing (Oil)

INPUT   DATA ♥ EXAMPLE Of Input/Output

Title  

#  Shut-In Time (Δt)  Pressure (pws) 
  (hours)  (psig) 
1 0
2
3
4
5
6
7
8
9
10  
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

Stabilized oil rate STB/d
Effective production time hrs.
Thickness ft
Well radius ft
Porosity  
Viscosity of oil cp
Formation vol. factor  
Total compressibility 10-6psi-1

LINE FITTING CONTROL  
No. of points to Ignore  

     Reset

OUTPUT   VARIABLES   &   GRAPHS

Extrapolated pressure (P*) psig
Slope (m) psi/logcycle
"Press." @ 1-hr shutin (P1hr) psig
Permeability (k) mD
Skin (s)

#  Time (Δt) (tp+Δt)/Δt  Pressure (pws) 
 hours    psig
1
2
3
:
:
29
30
THEORY  &   FORMULAE

Transient Pressure BuildUp Analysis (Oilwell)

Pressure buildup (PBU) survey involves measuring the changes in wellbore pressure with time after a well has been shut in. PBU requires that the well produce at a stabilized rate before shut-in. The PBU equation introduced by Horner is given by:

    

where
     pws = sandface pressure, psig
     pi = initial reservoir pressure, psig
     Qo = stabilized oil rate, STB/day
     μo = oil viscosity, cp
     Bo = formation volume factor, rB/STB
     k = permeability of formation rock, mD
     h = formation thickness, ft
     tp = flowing time before shut-in, hr
     Δt = shut-in time, hr.

A plot of pws versus (tp+Δt)/Δt would ideally produce a straight line with an intercept at pi (or p*) and a slope of ,strong>-m. This plot is known as the Horner plot, a semi-log plot. In practice, there is a deviation from a straight line in the initial section of the plot due to skin and wellbore storage effects. The straightline portion of the plot can be graphically identified by interactively ignoring a number of early plot points and performing a straightline fit on the rest.

When a satisfactory straight line is obtained, the initial reservoir pressure pi is estimated by extrapolation to the pressure corresponding to (tp+Δt)/Δt = 1. That is, the extrapolated pressure (p*) = (pi) for an infinite reservoir or for wells tested early in the life of the reservoir.

Another pressure point of importance on the fitted straightline is the pressure corresponding to Δt = 1 hour. Also computed is the slope (m) of the straight line in units of psi/log cycle.

Finally, the permeability of the formation (k) and the skin factor (s) can be calculated according to the relationships:

    

where
     m = slope of semi-log straight line, psi/log10cycle
     p1hr = pressure at time 1-hour on semi-log straight line, psig
     pwf(Δt=0) = sandface pressure immediately prior to shut-in, psig
     ct = total compressibility coefficient, 1/psi

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point
    ◊ Between 15 to 30 measurements points may be entered
    ◊ Up to 11 points may be ingored in the staright-line fitting process
    ◊ If the required Java plug-in not installed on your computer, an auto-download of this plug-in will be initiated before the plot is displayed.

BIBLIOGRAPHY