Page 245 - Hydrocarbon Exploration and Production Second Edition

232 Fluid Flow Near the Wellbore

bubble point), and is defined by the productivity index (PI).

Q 3
Productivity index PIðÞ ¼ ðbbl=d=psiÞ or ðm =d=barÞ
DP DD
For an oil reservoir a PI of 1 bbl/d/psi would be low for a vertical well, and a PI
of 50 bbl/d/psi would be high.
The flowrate of oil into the wellbore is also influenced by the reservoir
properties of permeability (k) and reservoir thickness (h), by the oil properties
viscosity (m) and formation volume factor (B o ) and by any change in the resistance
to flow near the wellbore which is represented by the dimensionless term called skin
(S). For semi-steady state flow behaviour (when the effect of the producing well is
seen at all boundaries of the reservoir) the radial inflow for oil into a vertical
wellbore is represented by the equation

DP DD kh
Q ¼ ðstb=dÞ
141:2mB o flnððr e =r w Þ 3=4Þþ Sg
The skin term represents a pressure drop which can arise due to formation
damage around the wellbore. The damage is primarily caused by the invasion of
solids from the drilling mud. The solid particles plug the pore throats and cause
a resistance to flow, giving rise to an undesirable pressure drop near the wellbore.
This so-called damage skin is best prevented by the appropriate choice of mud
and completion technique. The mud and rock compatibility can be tested by core
flood tests. These tests, such as the ‘return permeability test’ use a small core plug
and measure the permeability in the core both before and after mud has been
pumped against or through the core. If damage is not prevented, occasionally the
damage can be removed by backflushing the well at high rates, or by pumping a
limited amount of acid into the well (acidising) to dissolve the solids – assuming that
they are acid soluble. Alternatively the damage will have to be by-passed by
perforations or a small fracture treatment (a ‘skin frac’).
Another common cause of skin is partial perforation of the casing or liner across
the reservoir which causes the fluid to converge as it approaches the wellbore, again
giving rise to increased pressure drop near the wellbore. This component of skin is
called geometric skin, and can be reduced by adding more perforations. However
there is usually a trade-off between increased productivity and the very real risk of
perforating close to unwelcome fluids and coning water or gas into the well.
At very high flowrates, the flow regime may switch from laminar to turbulent flow,
giving rise to an extra pressure drop, due to turbulent skin; this is more common in gas
wells, where the velocities are considerably higher than in oil wells. This pressure drop
is dependent on the rate, hence the term ‘rate dependent skin’ (Figure 10.3).
In gas wells, the inflow equation which determines the production rate of gas
(Q) can be expressed as

2 2
ð ¯ P P Þkh
Q ¼ wf ðMscf =dÞ
141:2mZTflnððr e =r w Þ 3=4Þþ Sg