Page 269 - Fundamentals of Reservoir Engineering

OILWELL TESTING 206

The MBH curve, fig. 7.12 (IV), shows that for t DA = 4.23 semi-steady state flow
conditions prevail in the reservoir and therefore the method of Dietz can also be
applied to calculate p, i.e.

t +∆ t
log s = log (C t )
ADA
t ∆ s (7.63)
= log (2.07 4.23× ) = 0.942

and entering the buildup plot for this value of the abscissa gives the corresponding
value of p ws(LIN) = p as

p (Dietz) = 2944 psi

To determine the dynamic pressure in the grid block containing the well at the time of
survey, equ. (7.64) can be applied for t ' DA = t DA × 4 since the grid block area is only one
quarter of the total drainage area. Thus

t +∆ t
)
log = log (19.1 16.92 = 2.51
×
t ∆
and from the buildup plot, the corresponding dynamic pressure can be read as

p ws(LIN) = p d = 2820 psi.

2) The theoretical equation of the straight line which matches the observed linear buildup
is

kh t +∆ t 4t
7.08 10 -3 ( i p ) = 1.151log + p () − ½ ln D (7.48)
t
×
p −
qB o ws(LIN) t ∆ D D γ
µ
2
and since t D = t DA × A /r , this may be expressed as
w
t +∆ t
t
0.0144 ( i p ws(LIN) ) = 1.151 log + p D () 9.862
−
p −
D
t ∆
Taking several points on the straight line, p D (t D) can be evaluated as
p D (t D ) = 35.49
and therefore, the correct linear equation is

t +∆ t
0.0144 ( 4800 p ws(LIN) ) = 1.151 log + 25.63 (7.65)
−
t ∆
If the geometry and well position within the bounded area have been estimated
correctly, then it should be possible to match equ. (7.65) by theoretically calculating p D

using equ. (7.42) or, since semi-steady state conditions prevail at the time of the
survey, p can be alternatively expressed as
D