Water Coning In A Vertical Oil Well
For an reservoir with an underlying water-zone, and the perforated interval at the top of the oil-zone, a number of researchers have proposed methods for determining the Critical oil flow rate (Qoc).
The four commonly-used methods are:
- Meyer-Garder’s Method
- Chaperon’s Method
- Schol’s Method
- Hoyland-Papatzacos-Skjaeveland’s Method
All these methods apply to the isotropic reservoir case where horizontal permeability equals vertical permeability, except for Chaperon’s more general anisotropic case.
The equations for each method is given below:
Meyer-Garder’s Method
Chaperon’s Method
Schol’s Method
Hoyland-Papatzacos-Skjaeveland’s Method
Where:
Qoc = critical oil well rate, STB/day
h = oil column thickness, ft
hp= perforated interval, ft
kh= horizontal permeability, md
kv= vertical permeability, md
ko= effective oil permeability, md
(ko= rock permeability x oil relative permeability)
re = drainage radius of well, ft
rw = wellbore radius, ft
Bo = formation volume factor of oil
μ o = oil viscosity, cp
ρ o = oil density, lb/ft3
ρ w = water density, lb/ft3
Note that the critical rate is the oil rate below which water breakthrough will never occur; this rate may be too low for practical and economic reasons.
Combined Gas & Water Coning In A Vertical Oil Well
For an isotropic reservoir with a gas-cap above, a water-zone below, and the perforated interval somewhere in between, Mayer & Garder proposed the following equation for determining the Critical oil flow rate (Qoc):
Where:
Qoc = critical oil well rate, STB/day
h = oil column thickness, ft
hp= perforated interval, ft
ko= effective oil permeability, md
(ko= rock permeability x oil relative permeability)
re = drainage radius of well, ft
rw = wellbore radius, ft
Bo = formation volume factor of oil
μ o = oil viscosity, cp
ρ o = oil density, lb/ft3
ρ g = gas density, lb/ft3
ρ w = water density, lb/ft3
Note that the critical rate is the oil rate below which water or gas breakthrough will never occur; this rate may be too low for practical and economic reasons.
The optimal placement of the perforated interval is given by the following expression:
Where:
Dt = distance from gas-oil contact to top of perforation, ft
Water Breakthrough Time In A Vertical Oil Well
A well producing above its critical rate from a reservoir with an underlying water-zone below, will eventually experience water breakthrough. A number of researchers have proposed methods for estimating the Time to breakthrough tBT.
The two commonly-used methods are:
- Sobocinski-Cornelius Method
- Bournazel-Jeanson Method
In both methods, the water breathrough time is correlated with two dimensionless paramters: the Cone height Z and Breakthrough time (tD)BT. This dimensionless breaktrough time is then used to derive time to breakthrough in days. The main difference between two methods is in the expression for dimensionless breakthrough time.
The dimensionless Cone height Z is given by the expression:
The dimensionless (tD)BT is given by the expressions:
Sobocinski-Cornelius Method
… Z < 3.5
Bournazel-Jeanson Method
… Z < 4.286
The Time to breaktrough (tBT) is the given by the expression:
where the water-oil mobility ratio M is defined as:
Where:
Qo = well oil production rate, STB/day
h = oil column thickness, ft
hp= perforated interval, ft
kh= horizontal permeability, md
kv= vertical permeability, md
(krw)sor = oil relative permeability at connate water saturation
(kro)swc = water relative permeability at residual oil saturation
φ = porosity, fraction
Bo = formation volume factor of oil
μ o = oil viscosity, cp
μ w = water viscosity, cp
ρ o = oil density, lb/ft3
ρ w = water density, lb/ft3
α = 0.5 for M =< 1
α = 0.6 for 1 < M =< 10
