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Reservoir Engineering 2 Course (1st Ed.)

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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 Reservoir Engineering 2 Course (1st Ed.) 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


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.


The Meyer-Garder Correlation (Cont.)

They developed three separate correlations for determining the critical oil flow rate:Gas coning, Water coningCombined 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 densityDepth Dt from the original gas-oil contact to the top of the

perforationsThe oil column thickness h

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


The Meyer-Garder Correlation (Gas coning)


The Meyer-Garder Correlation (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

The Meyer-Garder Correlation (Water coning)


The Meyer-Garder Correlation (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


The development of gas and water coning


The Meyer-Garder Correlation (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.


The Meyer-Garder Correlation (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:


the optimum placement of the desired depth of perforationPirson (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.


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.


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.


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.


The Hoyland-Papatzacos-SkjaevelandMethodsHoyland, 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.


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.


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


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)


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


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


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


Water production performance predictionOnce 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)DDimensionless breakthrough time tDBTDimensionless limiting water cut (WC)limit


Procedure of predicting the rise in the OWCStep 1. Calculate the time to breakthrough tBT by using

the SobocinskiCornelius method or the Bournazel-Jeanson 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


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

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