Page 194 - Petroleum Geology

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will be 20.1 MPa (2915 psi) before the well is put onto production. If the
tubing is now swabbed to oil, the static pressure at the well head will be:

p = (p, - po) gz = 4.7 MPa = 682 psi. (8.11)
This pressure is unbalanced, so the well will flow if the valve is opened. The
rate at which the well will flow depends on the energy losses in the entire sys-
tem - energy lost by flow to the well, and energy lost by flow up the tubing
and through any surface pipes. In the reservoir, the energy losses depend on
the intrinsic permeability, the relative permeability to oil, and the kinematic
viscosity of the oil. In the well, the energy loss depends on the internal dia-
meter and length of the tubing, and also on the kinematic viscosity of the oil.
Within the reservoir, there is now a potential gradient towards the well
from all directions, and the oil flows radially into the well - downdip from
above the well, updip from below the well, and horizontally from along strike.
Intuition is not always reliable in these matters, so we must examine the
flow more carefully.
When a liquid is at rest, the entire body of liquid is at constant potential,
that is:

Cf, = gh = g (- P + z) = constant (8.12)
Pg

so that the change of pressure head to different levels is exactly equal to the
change of elevation. When the well is put onto production, the potential in
the well is made less than that in the reservoir, and a potential gradient is
created down which the oil flows to the well.
The potential is proportional to the total head of the oil in the reservoir:
P
+
h, = - = 2681 - 2050 = 631 m. (8.13)
z
p0g
So the energy of the oil reservoir can be represented by a conceptual surface
known as a potentiometric surface, and while the oil is static, this surface is
horizontal and elevated (in our example) 631 m above the datum surface,
taken here to be the level of the well head. When a well is put onto produc-
tion, a cone of depression is imposed on this surface (Fig. 8-14) and the equi-
potential lines or contours on this surface form circles around the well (Fig.
8-15). Flow in the reservoir is normal to the equipotential surfaces - normal
to the equipotential lines in plan - that is, radial to the well. The better the
effective permeability to oil, the shallower the cone of depression.
The oil flows parallel to the bed surfaces, as it must, and normal to the
equipotential surfaces that form concentric cylinders about the well. Ignoring
compressibility, equal volumes of oil cross any of these concentric surfaces
in unit time, so the oil is accelerating towards the well. Regarding the well as
normal to the reservoir for simplicity, the area of any concentric surface is