Page 246 - Introduction to Petroleum Engineering

OIL WELL PRESSURE TRANSIENT TESTING 233

qB
.
p p 141 2 p t t p t (12.11)
ws i kh D F D D D
where p is the initial reservoir pressure (psia), q is the stabilized flow rate (STB/D),
i
B is the formation volume factor (RB/STB), μ is the viscosity (cp), k is the
]
permeability (md), and h is the net thickness (ft). The term p ([ t t ) is
D F D
dimensionless pressure evaluated at dimensionless time [t ] t , and the term
F D
p (Δt ) is dimensionless pressure evaluated at dimensionless time Δt . Dimensionless
D D D
pressure in Equation 12.11 is replaced by Equation 12.10 to obtain
p ws p i m log t H (12.12)
where t is the dimensionless Horner time:
H
t t
t H F (12.13)
t
The hour is the unit of both times t , Δt to be consistent with the unit of time used in
F
the dimensionless time calculation. The variable m is given by
qB
m 162 6 (12.14)
.
kh
The unit of m is psia per log cycle when pressure is in psia, q is stabilized flow rate
(STB/D), B is formation volume factor (RB/STB), μ is viscosity (cp), k is perme-
ability (md), and h is net thickness (ft). The concept of log cycle is clarified later.

Example 12.2 Horner Time
A well flows for 8 hr with a stabilized rate before being shut in. Calculate
Horner time at a shut‐in time of 12 hr.
Answer
t t 812
The previous data gives Horner time t H F 1 667.
.
t 12

Equation 12.12 is the equation of a straight line if we plot p versus the logarithm
ws
of Horner time on a semilogarithmic plot. The slope of the straight line is −m.
An example of the semilogarithmic plot for a PBU test is shown in Figure 12.3.
The plot is called a Horner plot.
The early time behavior of a Horner plot is displayed at large Horner times on
the right‐hand side of the plot. Later times correspond to smaller Horner times on
the left‐hand side of the plot. The wellbore storage effect appears as the rapid increase
of shut‐in pressure at early times in Figure 12.3 and does not end until Horner
time ≈ 25. The infinite‐acting period appears as the straight line in the Horner time