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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Oil column thickness		ft
Perforated interval		ft
Horizontal permeability		mD
Vertical permeability		mD
Oil relative permeability
Water relative permeability
Oil density		lb/ft3
Water density		lb/ft3
Formation volume factor
Oil Viscosity		cp
Water Viscosity		cp
Porosity		%
Oil production rate		STB/day

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OUTPUT   VARIABLES

Water Breakthrough Time	days
♦  Sobocinski-Cornelius Method
♦  Bournazel-Jeanson Method

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 t_BT.

The two commonly-used methods are:

In both methods, the water breathrough time is correlated with two dimensionless paramters: the Cone height Z and Breakthrough time (t_D)_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 (t_D)_BT is given by the expressions:

The Time to breaktrough (t_BT) is the given by the expression:

   where the water-oil mobility ratio M is defined as:

Where:

   Q_o = well oil production rate, STB/day
   h = oil column thickness, ft
   h_p= perforated interval, ft
   k_h= horizontal permeability, md
   k_v= vertical permeability, md
   (k_rw)_sor = oil relative permeability at connate water saturation
   (k_ro)_swc = water relative permeability at residual oil saturation
   φ = porosity, fraction
  B_o = 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

BIBLIOGRAPHY

• Ahmed T.; Reservoir Engineering Handbook; Pennwell Publ Co, Tulsa, Oklahoma, 2000, chap. 9.
• Joshi S.; Horizontal Well Technology; Pennwell Publ Co, Tulsa, Oklahoma, 1991.