Page 177 - Fundamentals of Reservoir Engineering

DARCY'S LAW AND APPLICATIONS 115

q oil rate (stb / d)
PI = =
p − p wf pressure drawdown (psi)
e
3
−
7.08 10 kh (4.29)
×
= r
µ B o ln e + S
r w
where the PI, or Productivity Index of a well, expressed in stb/d/psi, is a direct measure
of the well performance.

One of the aims of production engineering is to make the PI of each well as large as is
practically possible, consistent with the economics of doing so. This is termed well
stimulation. The ways in which a well can be stimulated can be deduced by considering
how to vary the individual parameters in equ. (4.29) so as to increase the PI. The
various methods are summarised below.

a) Removal of Skin (S)

Before making any capital expenditure to remove a positive mechanical skin, it is first
necessary to check that the formation has in fact been damaged during drilling. This
can best be done by performing a pressure buildup test, which is normally carried out
as routine, immediately after completing the well. The manner in which S can be
calculated in the analysis of such a test is detailed in Chapter 7. sec. 7.

If it is determined that S is positive, the formation damage can be reduced by acid
treatment. The type of acid used depends on the nature of the reservoir rock and the
type of plugging materials which must be removed. If the formation is limestone,
treatment with hydrochloric acid will invariably remove the skin because of the solubility
of the rock itself. In sandstone reservoirs, in which the rock matrix is not soluble,
special, so-called, mud acids are used. As a result of a successful acid job, the skin
factor can be reduced to zero or may even become negative.

b) Increasing the effective permeability (k)

As noted al ready, due to the logarithmic increase of pressure with radius, the main
part of the pressure drawdown occurs close to the well. Therefore, if the effective
permeability in this region of high drawdown can be increased, the productivity can be
considerably enhanced. This can be achieved by hydraulic fracturing, in which high
fluid pressures maintained in the wellbore will induce vertical fractures in the formation.
Once the fractures have been initiated, they can be propagated deep into the formation
by increasing the wellbore pressure and injecting a suitable fracturing fluid, carrying
granular propping agents. In carbonate reservoirs the same effect can be achieved by
fracture-acidising.

c) Viscosity reduction (µ)

If the oil viscosity is very high, the flow rate in the reservoir will be correspondingly low,
and the time scale attached to the recovery will be greatly extended. The viscosity can
be siginificantly reduced by raising the temperature of the oil, a typical viscosity-
temperature relation being shown in fig. 4.6(a). The thermal stimulation process