well test analysis objective,way

7/30/2019 Well Test Analysis Objective,Way

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Chapter1

Principles of Well Testing


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Introduction

The aim of well testing is to get information about a

well and as well as reservoir.

To get this information, the well flow rate is variedand the variation disturbs the existing pressure in thereservoir.

Measuring the variations in pressure vs. time and

interpreting them gives data on the reservoir and the well.

The well response is usually monitored during a

relatively short period of time compared to the life of the

reservoir, depending upon the test objectives.


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The pressure can be measured:

- in the well where the flow rate has been changed:this is the method used in most tests;

- or in another well: this is the aim of interference

tests.

- Before opening the well on production, the initial

pressure pi is constant and uniform in the reservoir.

- The resulting pressure change with time is

measured by a pressure gauge in the well near the

depth of reservoir under study.


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- The variations in pressure are interpreted using a

number of laws of fluid mechanics.

During the flowing period, the drawdown pressure

response p is defined as follows:

When the well is shut-in, the build-up pressure

change p is estimated from the last flowing pressure

p(t=0):

( )tp-pp i

=

( ) ( )0tp-tpp ==


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Fig. 1. Drawdown and buildup test sequence.


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Darcys Law

Darcys law is used to describe fluid flow in a porousmedium.

It states that the flow rate of a fluid flowing through

a rock sample is proportional to:

- the pressure gradient applied to the rock sample;

- the samples cross-section, S;

- the mobility of the fluid, k/.


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Darcys law is valid within a time interval when the

flow rate and other parameters are constant.

It does not depend on the porosity of the medium, or

on the compressibility of either the fluids or the rock.

The vectorial expression ofDarcys law is as follows:

A well test studies the variations in the pressure that

occur after a flow rate variation. Since the flow rate has

varied, Darcys law can not be applied macroscopically to

pk

-pgradSk

-q

=

=


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describe the flow around the well.

Darcys law in radial flow is expressed by:

It can be integrated between two values of distance

from the well, rw and re (Fig. 2):

r

prh2

kq

=

e

w

ew

r

rln

p-pkh2q

=


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Fig. 2


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Compressibility

All the information from a well test is obtainedbecause the rock and the fluids are compressible.

The compressibility of any material is defined by

the relative change in the materials volume per unit ofpressure variation at constant temperature:

It can also be expressed in terms of density:

( )T

p/V1/V-c =

Te

p/1/c =


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Total compressibility of an oil reservoir:

In an oil reservoir several components are compressible:

- the oil;

- the water, even at irreducible saturation;

- the pore volume itself.

When the decompression occurs, the fluid is produced:

- by expansion of the fluids:

- oil: pVSc-V pooo =


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water:

- by a decrease in the pore volume Vp

When decompression occurs, the fluid pressure

decreases while the litho-static pressure remains constant.

The pore volume decreases, thereby causing general fluidproduction;

In contrast, the compressibility of the material itself

is negligible in comparison.

pVSc-V pwww =

pVc-V ppp =


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The overall compressibility of a pore volume unit is due to

the sum of all its compressible components:

The storativity capacity of a unit volume of the

porous medium is equal to ct .

Equivalent compressibility

The reservoir is modeled by:

- an incompressible porous rock with a porosity of

S0;

- and a fluid of equivalent compressibility:

(1.11)

pwwoot cScScc ++=

0

pww00

e

S

cScScc

++

=


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The diffusivity equation is written as follows in radial

flow:

(1.15)

where is called the hydraulic diffusivity of the

porous medium.

Compressible zone

The flow at a distance r from the well at time t can becalculated based on Darcys law and by solving the

diffusivity equation which describes the pressure variations

as:

(1.17)

0t

p

K

1-r

p

r

1

r

p2

2

=+

tc

kK

=

)Kt4/r-exp(qB)t,r(q2

=


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where :

q = is the wellhead flow rate;

qB= is the bottom hole flow rate

Fig. 1.2 shows the flow profile at time t vs. the

distance from the well.

Fig. 1.2 Flow profile ( from Bourdarot, G, 1996)


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It can be seen on the graph that between the wellbore

and r1 the flow rate has almost the same value as near the

wellbore.

There is a negligible flow through the areas located

beyond r2. The pressure drop between r2 and an infinite

distance is negligible.

Let us see at the variations in the flow profile

between two times t and t (Fig. 1.3)


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Fig. 1.3 (from Bourdarot, G, 1996)

The area located between the well and r1 there is a

flow close qB. From t to t the pressure drop between the

well and r1 is small.


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The area located beyond r2 is not yet involved in the

flow. The pressure drop between r2 and an infinite

distance remains negligible.

Between t and t the pressure drop between an

infinite distance and the well is therefore mainly due to

what is occurring between r1 and r2.

It is in this area that the reservoirs compressibility,

allowing the flow to go from 0 to qB, comes into play.

This area is compressible zone.

The pressure drop in the well mainly reflects the

reservoir properties in the compressible zone.


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This is what enables a well test to:

- characterize the average properties far way fromthe, permeability for example;

- detect facies heterogeneities;

- identify permeability barriers.


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