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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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