Petr 450
Class 3
Diffusivity Equation
2 1
+
=
2
0.000264
Four Solutions
Bounded Cylindrical Reservoir
Well produces at constant rate qB
Well is centered with a radius of rw
Uniform pressure in the reservoir pi
Solve for pwf
= 141.2
2
3
+
2
4
+2

Decline Curves
Type Curves
Fetkovich
Fetkovich combined the solutions of the diffusivity and Arps equation
to form a generalized method of analyzing decline curves.
Dimensionless values
= 2
=
Analytic solution of the diffusivity equation for the bounda

Decline Curves
Decline Curves that plot flow rate vs. time are the most common tools for
forecasting production and monitoring well performance in the field. These curves
quickly show by graphic means which wells or fields are producing as expected or
und

Petr 450
Class 8
Duration of Afterflow
The first part of the pressure curve is caused by the afterflow into the
wellbore from the reservoir after the well is shut in on the surface. This
can cover the effects of skin and in extreme cases the MTR. It cause

Petr 450
Class 15
Horizontal well tests
A horizontal well is one that the wellbore is parallel to the plane of the
formation that is produced.
Dimensionless variables used for horizontal wells
=
=
141.2
0.0002637
2
=
2
2
=
, =
=
.25
2
+
,
.2

Petr 450
Class 7
Effects and Duration of Afterflow (Wellbore Storage)
Problems caused by afterflow
1) Delays the beginning of the MTR
2) Total lack of MTR in some cases
3) False straight line mistaken for MTR
A lazy S shape of the ETR is typical of afterf

Petro 450
Class 4
Principle of Superposition
The Ei function the most useful of the approximations assumes a single
well with a constant flow rate starting at time zero. The application of
the principle of superposition can remove some of these restrictio

Petr 450
Class 12
Type Curves
The type curve developed by Bourdet, et al is a plot of dimensionless
time PD vs the dimensionless time group tD/CD for wells with wellbore
storage and skin in a infinite acting reservoir with homogeneous
behavior.
=
= /

Petr 450
Class 6
Actual Buildups
Do not follow the idealized tests that have instantaneous shut in with a
zero flow rate. Also idealized models a very thin skin. The radius of
investigation helps explain the more complex shape of the buildup plot.
As the

Petr 450
Class 13
Inifinite Conductivity Fracture Type Curve
Use this curve on wells that have been fraced. Good method to calculate the frac
length.
To find the well properties it is the same as the other type curves, plot dp & dp vs
dt. Find a match on

Decline Curves
Part 2
Hyperbolic Equations
Calculate the time interval spanning the initial and final rate for the
hyperbolic case.
[
]
Rearrange the rate-decline relationship
[ ]
For cumulative production
(
)
[
(
(
)
)
]
Sub in the flow equation for
(
)

Petr 450
Gas Wells
The given equations are for liquids, for compressible fluids some
changes are needed. In many cases just converting the B to gas rb/mscf
and q in mscfpd will work. Square the pressures is needed is some
cases, below 2000 psi. Also the u

Petr 450
Type curve example
Data
Bo = 1.21 rb/stb
Pwf = 2989 psi
h = 23
= .21
= .92 cp
ct = 8.72x10-6
Match points
pD
p
M
1
200
t
tD
1
40
CD
cdes = 1010
Calculations
kh 141.2 2500 1.21 .92
1
200
1965mdft
k 1965 / 23 85.4md
C
C
qB p D
24 p
t
M
tD
CD
2500 1

Nomenclature
a
=
A =
AI =
AR =
Awb =
b
=
1,422j.tPZpgT[ln(~)-0.75+sJ
kh
r;
drainage area of well, sq ft (m 2)
fracture area, sq ft (m ")
reservoir area, acres (m 2)
wellbore area, sq ft (m ")
1 422
,
j.t-zp
TD
pg
kh
b' = intercept of (Pi -Pwl)/qn plot, ps

gm f
n‘ﬁ.
Wk
ma
ﬂ
I
I
.
II“.
E
ﬁﬁﬁ’eﬁﬂiﬂlﬂﬂﬂk‘
“mum: ' 1
£I§I§ﬂlliﬁiii§§§mm1m1£ﬂm5\
mammme
Eﬂﬁ
m
“ﬁﬂﬁﬁ
\
ﬁﬁﬂ
gfﬁﬁﬁﬂﬂﬂ
= Ema
. uh . m
a _ I”. I. I
.I. I u . .

WELLTEST-95
|.2: Derivative Algorithms
2 Derivative Algorithms
Three algorithms are provided to compute the derivative “dAp/d(lnAt).” These are (with increasing
complexity): (i) two—points, (ii) three-consecutive—points, and (iii) three-smoothed—points me

Petro 450
Naturally fractured Reservoirs
Models
Single-Fracture
Double-Porosity This is the one that is mostly used
Dual-Permeability
Diffusivity equation accounting for matrix-fracture interaction, q*
1
=
+
Three Flow Periods
1) Fracture-stor

Take home test.
Plot the type curve and horner plot for this data. Then find the k, s, P * for this well.
Use either the software or by hand. Give the parameters used if by hand, use the report in the software.
There will be in class questions on Wednesda

Petr 450
Class 9
Pressure level
Ideal model suggests a method to find the original pressure of the
reservoir by extending the straight line of the MTR to horner time equal
to 1 on the horner plot. For wells that have had some pressure
depletion this metho

Harmonic Declines
Harmonic equations b = 1
This is a restricted version of the hyperbolic case, the change in the
decline rate is constant.
2
=
2
The producing rate for harmonic
2 =
1+
To solve for the time difference between the initial rate and q2.
=

Petr 450
Class 10
Multiphase flow
Flow equation modified for multiphase flow
The buildup equation
The total flow rate in RB
Total mobility
This imply that the total mobility can be found using m of the buildup
The permeability of each phase can be calcula

Petro 450
Class 5
Buildup Test
Horner Plotting Method
Ideal Test
A test in an infinite, homogeneous isotropic reservoir with a slightly
compressible single phase fluid.
Assumptions
1) Infinite reservoir, no boundary effects
2) Formation and fluid properti

Lonkar Well Testing
Ltd.
Procedures
Review Date:
April 30, 2004
Reviewed By:
Glenn Berry
Section: 9.12
Subject: Lighting Line Heater
Purpose:
Periodically Lonkar Well Testing is required to have a indirect fired line heater on location to warm well
efflue

Lonkar Well Testing
Ltd.
Procedures
Review Date:
01-May-04
Reviewed By:
Glenn Berry
Section: 8.00
Subject: Rig Up Procedures
Purpose:
To properly rig in test equipment according to Industry Recommended Practice.
Potential Hazards:
Weather, eg; snow, rain,

Review Date:
April 30, 2004
Reviewed By:
Lonkar Well Testing
Ltd.
Procedures
Glenn Berry
Section:
Subject: Start up Procedure
Purpose:
On every location there will come a time the well will have to be started up. Start up includes pressure
testing and ini

Lonkar Well Testing
Ltd.
Procedures
Review Date:
19-October-2004
Reviewed By:
Prepared By:
Glenn Berry
Section:
Subject:
Portable Flare Stack Procedures
With Outriggers
Purpose:
To stand flare stack after being spotted.
Potential Hazards:
Pinch Points
Ter