Forecasting Reservoir Y Performance After Breaktrough in

Vertical Well by Kou Desbrisay Method

By:

Keiza Cindy Callista

0801026

STT Migas Balikpapan

Abstract

Coning is the movement of fluids (water, gas) into perforation. Water coning is the

upward movement into perforation. Water coning factors are perforation is close to WOC

and the low well pressure. Water coning impact corotion, oil productivity and recovery

efficency reduce, and also added cost. There are three method to forecasting water coning.

They are critical rate, breaktrough time, and after breaktrough (post breaktrough).

In reservoir Y in the X field has bototm water drive. This well prospect to has water

coning. With some datas, forecasting oil productivity rate and time for adding production

after passed the time to breaktrough when productivity rate is higher than critical rate.

Introduction

To produce oil from reservoir, oil

from reservoir will flow into the

perforation and flow to the surface. And

according to the time when oil is flowing

the other fluids move into the perforation.

The movement called coning. There are

two kinds of coning, gas coning and water

coning. Gas coning is the down movement

of gas into the perforation. And water

coning is the upward movement of water

into the perforation.

Figure 1

Water Coning

Water Coning Factors

When oil is produce there is a

displacement from water that fill the empty

pore. The displacement makes the water

move upward into the perforation. Beside

that there are some factors that makes

water coning, such as :

The well pressure (Pwf) is reduce and

impact drawdown pressure is higher

The perforation is close to water oil

contact (WOC)

Water coning should be controlled because

it impacts some draw backs, such as :

Added cost to handle the water

Oil productivity reduce because of the

relative permeability

Water causing the corotion

Recovery effiency reduce because of

the water cut critical point

Well could be abandon early

Water Coning Control

Based on history there are three

method to control water coning. There are

critical rate, breaktrough time and post

breaktrough.

1. Critical Rate

Critical rate is the first period to

contol water coning. It calculate the

critical rate to prevent water coning.

there are some method to calculate

critical rate, for example Meyer and

Garder Method and Chaney et al

Method.

Basicly all method has the same

principal formula.

Where :

qc

= oil critical rate, STB/day

ko

= effective oil permeability,

md

h = oil thicness, ft

D = interval perforation thicness,

ft

o

= oil viscosity, cp

Bo = formation factor volum,

bbl/STB

qDC

= dimensionless critical rate

= w

o, water oil system

= o -

g oil-gas system

The differences each critical rate

method is formuloa to calculate

dimensionless critical rate.

a. Meyer and Garder Method

Figure 2

Water Coning Vertical Well

Meyer and Garder defined the

dimensionless critical rate.

Combine oil critical rate formula

and dimensionless critical rate

formula.

b. Chaney and et al Method

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).

Curve 1

Critical Production Rate

2. Breaktrough Time

Critical rate show low rates and for

economic reasons, cannot be imposed

on production well. If well produce

above the critical rate, the cone

whould be breaktrough after the time

given. The time is called breaktrough

time. There are several method to

calculate breaktrhough time such as

Sobocinski and Cornelius Method and

Bournazel and Jeanson Method.

a. Sobocinski and Cornelius Method

Sobocinski and Cornelius

defined the dimensionless cone

height and dimensionless time by

simulated into a model.

Figure 3

Water coning model

Where :

Z = Dimensionless cone height

td = Dimensionless time

w = water density, g/cc

o

= oil density, g/cc

kh

= horizontal permeability, md

h = oil thicness, ft

hc

= water cone thicness, ft

o

= oil viscosity, cp

= porosity

= konstanta

M < 1, = 0.5

M 1, = 0.6

M = mobility ratio

Curve 2

Z and td Relation

To calculate breaktrough time,

breaktrough curve is used.

Depature and build up curve is

used to know water coning

performance.

b. Bournazel and Jeanson Method

Bournazel and Jeanson calculate

the breaktrough and always lower

than Sobocinski and Cornelius.

And they modify Sobocinski and

Cornelius formula by changing :

Form td as Z function to

change Sobocinski and

Corneliuss Z and td curve.

Reasess =0.7 for M, in

interval 0.14 7.3

In order to that Bournazel and

Jeanson change Sobinski and

Cornelius formula to determine

time to breaktrough.

3. Post Breaktrough

Once the water breakthrough occurs, it is

important to predict water production as

function to the time. In order that water

cut is predicted. Water cut is a condition

when there is no oil produce, completely

water production. In this contion water

cone has reach the perforation. Kuo and

Desbrisay method is a method is used to

use to determine post breaktrough.

Kuo and Desbray calculate time

to breaktrough first. They determine

time breaktrough a half from

Bournazel and Jeanson time to

braktrough. There are two parameters

to determine water cut performance.

Where :

td

= dimensionless time

t = time, day

tBT

=time to breakthrough

(Bournazel and

Jeanson), day

(WC)d

= dimensionless water

cut

WC = water cut

Where :

Ho

= original oil zone thickness

(between WOC to the top oil

zone), ft

Hw

= original water zone thickness,

ft

ho = oil zone thicness, ft

hw

= water zone thicness, ft

Swc

= water connate saturation

Sor

= oil residual saturation

Np

= cumulative oil production,

STB

N = initial oil in place, STB

Relation between dimensionless water cut

and time.

(WC)d

= 0, for td

< 0.5

(WC)d

= 0.94 log td

+ 0.29

for 0.5 td

5.7

(WC)d

= 1.0, for td

> 5.7

Analysis After breaktrough

In X field, reservoir Y has bottom

water drive. And have data :

Ho = 42 ft

Hw

= 60 ft

qt = 100 STB/day

kh

= 90 md

Fk

= kh/k

v = 10

M = w/

o = 3.27

N = 4.2 x 106

STB

Swc

= 0.288

Sor

= 0.331

Time to breaktrough is the 104.5 day.

Forecasting = 61 after breaktrough

well poducing (Np)1

= 5000 STB water

(qo

= 60.6 STB/day). If the next water

production is (Np)2

= 5000 STB by

assuming , = 92,

determine that = 92 square

with

= , = 0.05

Figure 4

Reservoir scematic

= ()

= 104.5 100 = .

By increasing production (Np)1

= 5000

STB with production rate qo

= 60.6

STB/day in 61 days.

= +

= 10.450 + 5000 = .

=

=15.450

4.2106= 3.68103

Forecasting production increasing 5000

STB in 92 days.

+1 = +

+1 = 15.450 + 5000 = .

+1 =+1

=20.450

4.2106= .

= + +1 1

1

= 60 + 42 4.87103

1 0.288

1 0.288 0.331 =

= 1 +1 1

1

= 42 1 4.87103

1 0.288

1 0.288 0.331 = .

=

+

= 3.27 (60.39)

3.27 (60.39) + 31.61= .

+1 = (1 +1 )

+1 = 1 0.5435 100 = .

Oil productivity until time to break

1 = = = /

Oil productivity after breaktrough

= = /

Oil productivity average rate

=+1 +

2

=45.65 + 60.6

2= . /

Time to added productivity 5000 STB by

productivity rate 53.1 STB/day

=

=5000

53.1= .

Comparing assuming time and calculating

time

92 94.16

92= .

The accuracy is < 0.05

Conclusions

1. Water coning is the upward

movement of water into

perforation.

2. Water coning factors are

perforation close to water oil

contact and the low well pressure.

3. Water coning impacts are corotion,

well abandon earlier, added cost,

oil productivity reduce and

recovery efficiency reduce.

4. Water coning forecasting are

critical rate, breaktrough time, after

breaktrough.

References

1. Ahmed, Tarek. Reservoir

Engineering Handbook, Second

Edition,1946.

2. Kurnia Permadi, Asep. Diktat

Teknik Reservoir II, Edisi pertama,

2004.