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Reservoir Engineering 2 Course (1st Ed.)

1. Coning Introduction
2. Coning types
3. Coning dependency

1. Conning Vertical Well:
A. Critical Rate Correlations
B. Breakthrough Time
C. Breakthrough Performance

Critical rate definition
Critical rate Qoc is defined as
the maximum allowable oil flow rate that can be
imposed on the well to avoid a cone breakthrough.

The critical rate would correspond to the
development of a stable cone
to an elevation just below the bottom of the perforated
interval in an oil-water system or
to an elevation just above the top of the perforated
interval in a gas-oil system.

Spring14 H. AlamiNia


5

Oil critical rate empirical correlations
There are several empirical correlations that are
commonly used to predict the oil critical rate,
including the correlations of:
Meyer-Garder
Chierici-Ciucci
Hoyland-Papatzacos-Skjaeveland
Chaney et al.
Chaperson
Schols



6

The Meyer-Garder Correlation
Meyer and Garder (1954) suggest that coning
development is a result of the radial flow of the oil
and associated pressure sink around the wellbore.
In their derivations, Meyer and Garder assume a
homogeneous system with a uniform permeability
throughout the reservoir, i.e., kh = kv .
It should be pointed out that the ratio kh/kv is the
most critical term in evaluating and solving the
coning problem.



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The Meyer-Garder Correlation (Cont.)
They developed three separate correlations for
determining the critical oil flow rate:
Gas coning,
Water coning
Combined gas and water coning

Meyer and Garder correlated the critical oil rate
required to achieve a stable gas cone with the following
well penetration and fluid parameters:
Difference in the oil and gas density
Depth Dt from the original gas-oil contact to the top of the
perforations
The oil column thickness h

The well perforated interval hp, in a gas-oil system, is
essentially defined as: hp = h − Dt


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(Gas coning)



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(Gas coning) (Cont.)
Meyer and Garder propose the following
expression for determining the oil critical flow rate
in a gas-oil system:
Qoc = critical oil rate, STB/day
ρg, ρo = density of gas and oil, respectively, lb/ft3
ko = effective oil permeability, md
re, rw = drainage and wellbore radius, respectively, ft
h = oil column thickness, ft
Dt = distance from the gas-oil contact to the top of the
perforations, ft


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(Water coning)



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(Water coning) (Cont.)
Meyer and Garder propose a similar expression for
determining the critical oil rate in the water coning
system. The proposed relationship has the following
form:

ρw = water density, lb/ft3
hp = perforated interval, ft



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The development of gas and water
coning



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(Simultaneous gas and water coning)
If the effective oil-pay thickness h is comprised
between a gas cap and a water zone, the
completion interval hp must be such as

to permit maximum oil-production rate without having
gas and water simultaneously produced by coning,
gas breaking through at the top of the interval and
water at the bottom.

This case is of particular interest in the production
from a thin column underlaid by bottom water and
overlaid by gas.



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(Simultaneous gas and water coning)
For combined gas and water coning, Pirson (1977)
combined previous Equations to produce the
following simplified expression for determining the
maximum oil flow rate without gas and water
coning:



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the optimum placement of the
desired depth of perforation
Pirson (1977) derives a relationship for determining
the optimum placement of the desired hp feet of
perforation in an oil zone with a gas cap above and
a water zone below.
Pirson proposes that the optimum distance Dt from the
GOC to the top of the perforations can be determined
from the following expression:

where the distance Dt is expressed in feet.


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the Meyer-Garder Correlation
assumptions
Slider (1976) points out that the Meyer-Garder
Correlations are not based on realistic assumptions.
One of the biggest difficulties is in the assumption
that the permeability is the same in all directions.
As noted, this assumption is seldom realistic.
Since sedimentary formations were initially laid down in
thin, horizontal sheets, it is natural for the formation
permeability to vary from one sheet to another
vertically.



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the Meyer-Garder Correlation
assumptions (Cont.)
Therefore, there is generally quite a difference
between the permeability measured in a vertical
direction and the permeability measured in a
horizontal direction.
Furthermore, the permeability in the horizontal
direction is normally considerably greater than the
permeability in the vertical direction.
This also seems logical when we recognize that very thin,
even microscopic sheets of impermeable material, such
as shale, may have been periodically deposited.
These permeability barriers have a great effect on the vertical
flow and have very little effect on the horizontal flow, which
would be parallel to the plane of the sheets.


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The Chierici-Ciucci Approach
Chierici and Ciucci (1964) used a potentiometric model
to predict the coning behavior in vertical oil wells.
The results of their work are presented in dimensionless
graphs that take into account the vertical and horizontal
permeability.

The diagrams can be used for solving the following two
types of problems:
Given the reservoir and fluid properties, as well as
the position of and length of the perforated interval,
determine the maximum oil production rate
without water and/or gas coning.

Given the reservoir and fluids characteristics only,
determine the optimum position of the perforated interval.



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The Hoyland-Papatzacos-Skjaeveland
Methods
Hoyland, Papatzacos, and Skjaeveland (1989)
presented two methods
for predicting critical oil rate
for bottom water coning
in anisotropic,
homogeneous formations
with the well completed
from the top of the formation.
The first method is an analytical solution, and
the second is a numerical solution to the coning
problem.


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Critical Rate Curves by Chaney et al.
Chaney et al. (1956) developed a set of working
curves for determining oil critical flow rate.
The authors proposed a set of working graphs that were
generated by using a potentiometric analyzer study and
applying the water coning mathematical theory as
developed by Muskat Wyckoff (1935).
The graphs are designed to determine the critical flow rate in
oil-water, gas-oil, and gas-water systems with a specific fluid
and rock properties.
The hypothetical rates as determined from the Chaney et al.
curves (designated as Qcurve), are corrected to account for the
actual reservoir rock and fluid properties.



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Chaperson’s Method
Chaperson (1986)
proposed a simple
relationship
to estimate the critical
rate of a vertical well
in an anisotropic
formation (kv ≠ kh).
The relationship accounts
for the distance between
the production well and
boundary.


Qoc = critical oil rate,
STB/day
kh = horizontal
permeability, md
Δρ = ρw − ρo, density
difference, lb/ft3
h = oil column thickness,
ft
hp = perforated interval,
ft

Joshi (1991) correlated
the coefficient q*c with
the parameter α″ as


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Schols’ Method
Schols (1972) developed an empirical equation
based on results obtained from numerical simulator
and laboratory experiments.
His critical rate equation has the following form:

ko = effective oil permeability, md
rw = wellbore radius, ft
hp = perforated interval, ft
ρ = density, lb/ft3

It is only valid for isotropic formation, (kh = kv)


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breakthrough
Critical flow rate calculations frequently show low
rates that, for economic reasons, cannot be
imposed on production wells.
Therefore, if a well produces above its critical rate,
the cone will break through after a given time
period.
This time is called time to breakthrough tBT.
Two of the most widely used correlations are:
The Sobocinski-Cornelius Method
The Bournazel-Jeanson Method



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The Sobocinski-Cornelius Method
Sobocinski and Cornelius (1965) developed a
correlation for predicting water breakthrough time
based on laboratory data and modeling results.
The authors correlated the breakthrough time with
two dimensionless parameters,
the dimensionless cone height (Z) and
the dimensionless breakthrough time (tD)BT



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The Bournazel-Jeanson Method
Based on experimental data, Bournazel and
Jeanson (1971) developed a methodology that uses
the same dimensionless groups proposed in the
Sobocinski-Cornelius method.
Step 1. Calculate the dimensionless core height Z
Step 2. Calculate the dimensionless breakthrough time
by applying the following expression:
Step 3. Solve for the time to breakthrough tBT



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Water production performance
prediction
Once the water breakthrough occurs, it is important
to predict the performance of water production
as a function of time.
Normally,
using numerical radial models solves such a problem.
Currently, no simple analytical solution exists to predict
the performance of the vertical well after breakthrough.

Kuo and Desbrisay (1983) applied the material balance
equation to predict the rise in the oil-water contact in a
homogeneous reservoir and correlated their numerical
results in terms of the following dimensionless
parameters:
Dimensionless water cut (fw)D
Dimensionless breakthrough time tDBT
Dimensionless limiting water cut (WC)limit



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Procedure of
predicting the rise in the OWC
Step 1. Calculate the time to breakthrough tBT by using
the SobocinskiCornelius method or the BournazelJeanson correlation.
Step 2. Assume any time t after breakthrough.
Step 3. Calculate the dimensionless breakthrough time
ratio tDBT
Step 4. Compute the dimensionless limiting water cut
Step 5. Calculate the dimensionless water cut (fw)D
based upon the dimensionless breakthrough time ratio
Step 6. Calculate the actual water cut fw
Step 7. Calculate water and oil flow rate


31

1. Ahmed, T. (2010). Reservoir engineering
handbook (Gulf Professional Publishing).
Chapter 9

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