Page 214 - Intelligent Digital Oil And Gas Fields

168 Intelligent Digital Oil and Gas Fields

represent energy loss is by using the relationship between kinetic, gravita-
tional, and viscous/frictional forces as given in Eq. (5.2):
dp g ρv dv f ρv 2
¼ ρsinθ + + (5.2)
dL 32:2 32:2dL 2g c d
where dp/dL is the total pressure losses from a node at a perforation to a node
2
at the surface in psi/ft.; g the gravitational acceleration in ft./s ; ρ the density
3
of the mixed fluid in lbm/ft ; θ the wellbore angle; v the fluid velocity across
the tubing in ft./s; f the Moody friction factor (dimensionless); d the internal
tubing diameter in inches; and dv/dL is the velocity differential per length.
In absence of down-hole pressure gauges, the most important parameter
determined by VLP is the flowing bottom-hole pressure (BHP). If we
assume a fixed THP, then the BHP is calculated as a function of rate.
Near-wellbore reservoir model. The most common method for modeling
this zone is use of the IPR, which calculates the flow rates at bottom-hole,
assuming a constant reservoir-pressure-boundary condition. The expression
estimates the ability of the reservoir to deliver fluids to the wellbore using
Eq. (5.3):

Q tot
PI ¼ (5.3)
Pe f BHP
where PI is productivity index in STB/psi; Q tot the total fluid rates at surface
conditions in STB/d; Pe the reservoir pressure in psi at the boundary of the
reservoir; and f BHP is the flowing BHP in psi at the middle of the
perforations.
Numerical and analytical models can predict with high accuracy the well
inflow (PI). However, it is time consuming and normally petroleum engi-
neers use well performance software to estimate the PI.

5.3.2 Building Blocks
The IPR and VLPcurves can beintegrated into a single plot showing f BHP as a
function of flow rates (Fig. 5.9). The intersection of the curves indicates the
operating point of the current well production in terms of total liquid rate, gas
rate, and THP. The IPR/VLP models are calibrated using flow tests at sep-
arator conditions approximately every month or quarter; the flow test mea-
sures oil and water at a tank and gas using an orifice. With this known
production value set point and THP, the f BHP is estimated using the VLP
model and extrapolating the down-hole pressure at the perforations. To meet