G11WT Notes (Grade 1 Topics)
Chapter 1
1.2 Well Inflow Performance
During flow of fluids from reservoir to surface, there are two resistances in series. The first
resistance is due to flow in the porous medium Pr (rock) and the pressure drop Pwf. This is the
drawdown.
A linear relation between flow and pressure drops is known as the inflow performance relation
(IPR):
J = qs / (pr - pwf) → qs = J (pr - pwf)
Flow in the tubing is more complicated and the relation between oil flow-rate Qs and overall pressure
difference for vertical lift, Pwf-Ps, is non-linear. This is known as the vertical loft performance (VLP):
pwf - ps = fVLP(qs)
2.0 Darcy’s Law
The basic equation describing the laminar, creeping flow of a single phase fluid in a porous
medium is Darcy’s Law:
4.2 Basic Well Model
In its simplest form an oil reservoir consists of a single,
homogeneous layer of porous rock of uniform thickness, h, and
permeability, k, bounded above and below by horizontal
impermeable barriers.
The pore space is filled with oil viscosity, u, except for connate water
which does not flow under reservoir conditions. The oil is
everywhere above its bubble pressure (undersaturated) and hence
no free gas phase exists.
If the well is open to flow over the whole interval h, and is produced
at a flowrate, q, the symmetry of the system results in radial flow in
the direction of the well, i.e there are no vertical or tangential
velocity components. Initially it is assumed that his region is circular
in shape with an external radius, Re, and that the well of radius, Rw
is central.
4.3.2 Discussion
Pressure drop increases rapidly as the well-bore is approached. This is associated with the
increase in fluid velocity as the area for flow diminishes. The most significant proportion of the
total drawdown occurs in the near well-bore region, hence Re need only be known very
approximately to get a good estimate of drawdown for a given production rate.
4.4 SS Well Productivity Based on External Pressure
The steady-state radial flow equation shows how the permeability-thickness product, kh,
influences the rate at which oil can be produced from a well. This quantity can also be obtained
from well test analysis. The productivity of an oil well is quantified by the productivity index
Jsse:
As productivity is often expressed in oil field units and given the dimensionless drawdown, the
steady-state radial flow productivity index is given by:
Plotting Pw against Qs is a straight line of slow -1/Jsse and intercept Pe. The intersection of
these lines is known as the well operating point.
4.5 SS Flow Equations Based on Average Pressure
Since the pressure of the external boundary is cannot be measured directly, it is therefore more
common to express the pressure drawdown in terms of average pressure. The steady-state
radial flow the difference between the mean pressure and external pressure is given by: