This document provides examples and explanations of how to calculate oil and gas flow rates from well test data. It covers three examples of calculating oil rates using different methods: 1) direct shrinkage measurement and meter factor, 2) estimated shrinkage from tables, and 3) combined meter factor. It also provides an example gas rate calculation, explaining the various factors used in the gas flow rate equation such as orifice size, pressure, and temperature corrections. Charts and tables are presented to lookup values for specific gravity, shrinkage, expansion factors and other parameters needed for the calculations. Standard well test report sheets are also demonstrated with the examples.

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SURFACE TESTING
OIL & GAS CALCULATIONS
TE–P1 ELC, Melun

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Objectives
On completion of this presentation you should be able
to:
• Explain the theory behind the calculation of oil and
gas rates using:
– Shrinkage Tester & Meter Factor
– Combined Meter Factor
– Tables
• Be familiar with the standard Well Test Report sheets
for Oil and Gas Calculations

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Oil Information Sheet
• Lists the main variables used
in oil calculations
• Explains various Oil
Calculation equations for:
– Measurement with Tank
– Shrinkage Tester & meter
factor
– Combined Meter Factor
(Shrinkage measured with
Tank)
– Shrinkage from Tables

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Oil Calculations – Basic Theory
V = Volume of liquid recorded by oil meter
BSW = Basic Sediments and Water
F = Meter factor
(physical inaccuracy in meter when checked before the job with water)
SHR = Shrinkage Measurement
(volume reduction in oil taken from separator to tank conditions)
K = Shrinkage Temperature Correction Factor
(correction of shrinkage from tank temperature to 60 degF)
Vo = Corrected Oil Volume
    K
SHR
f
BSW
V
Vo 





 1
1

5. Schlumberger
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Oil Calculations – Basic Theory
3 Cases considered using worked examples:
1. Shrinkage & Meter Factor
2. Shrinkage from Tables
3. Combined Meter Factor
Also, observe how the handwritten reading sheets are
filled in.

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Example #1 – Shrinkage & Meter Factor
In this example:
“SHR” is measured directly using a
shrinkage tester
“f” is measured before the job starts
by flowing water through the meter
and measuring returns at the tank
SHR then has to be corrected from
shrinkage tester conditions to 60
degF using K factor

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Example #1 – Shrinkage & Meter Factor
NOTE THE UNITS
AND NUMBER OF DECIMAL PLACES
2 2 1 2 3 - 3 - 3 3 2 - 2
Values already marked on the sheet come from the
Well Testing Reading Sheets
We have separate
meter factor

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Example #1 – Shrinkage & Meter Factor
Vs = Difference between Meter Readings
d = 33.96 – 13.13 = 20.83 bbls
Interval is time between
each set of readings
V’o* = Corrects Vs for BSW and meter factor
d = Vs.(1-BSW).f
d = 20.83 x (1-1.5/100) x 0.96 = 19.70
Case #1 – Shrinkage Tester used
Shrinkage Factor = 1 – SHR
= 1 – 3.5/100 = 0.965
Temp = Temperature at SHRINKAGE
TESTER
0.965 88

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Example #1 – Shrinkage & Meter Factor
To calculate
specific gravity at
60 degF use
CHART

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Oil SG @ 60 degF
SG = 0.864 @ 90 degF
• SG from Left Axis
• TEMP from Bottom Axis
• Intersection point – draw line
parallel to Red Lines
To find SG@60 degF either:
• Compare position of line to
Red Lines
• Extrapolate to T = 60 degF
and use Left Axis
Measured
SG
Shrinkage
TEMPERATURE
SG @ 60 degF =
60 degF
0.876

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Example #1 – Shrinkage & Meter Factor
CHART
0.876

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Example #1 – Shrinkage & Meter Factor
Next the TEMPERATURE
CORRECTION FACTOR, K must
be calculated.
This corrects the SHRINKAGE @
Observed Shrinkage Temperature to
the SHRINKAGE @ 60 degF
We need to use a CHART…

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SHR K FACTOR
SG/60degF = 0.876
SHRT = 88 degF
• SHRT from Top Axis
• Coincides with SG @60degF
line
• Line to Right Axis to read K
Factor
SHR K factor =
Shrinkage TEMP
= 88 degF
0.988

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The CUMULATIVE production is calculated from the time of the
last FIXED CHOKE CHANGE. In this example consider 08:00
Cumulative = Rate x Time since choke change
= 1803 x 15/1440
= 18.78 bbls
Example #1 – Shrinkage & Meter Factor
0.988
Calculate the rate, using the interval
Rate = Vo/(INTERVAL) x (# min per day)
= 18.78 / 15 x 1440
= 1803 BOPD
Calculate the corrected volume flowed
Vo = V’o*.(1-SHR).K
= 19.70 x 0.965 x 0.988
= 18.78 bbls
18.78 1803 18.78
CHART
0

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Example #1 – Shrinkage & Meter Factor
Now the rest of the remaining lines can be
completed…

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Example #1 – Shrinkage & Meter Factor
Cumulative = 18.78 + 1714/1440 x 15
= 36.63
Or 18.78 + 17.85 = 36.63
36.63

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Example #1 – Shrinkage & Meter Factor

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Example #1 – Shrinkage & Meter Factor

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Example #2 – Shrinkage Tables
In this example:
Shrinkage Factor “(1-SHR)” is
estimated from tables (based on
KATZ Data)
“f” is measured before the job starts
by flowing water through the meter
and measuring returns at the tank
K factor = 1 as KATZ table gives
Shrinkage Factor already at 60
degF

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Example #2 – Shrinkage Tables
Values already marked on the sheet come from the
Well Testing Reading Sheets
In this case we
use f =1as f is
unknown
Correct for BSW and meter factor as before…
Vs = Difference in meter reading
V’o* = Vs.(1-BSW).f

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Example #2 – Shrinkage Tables
Again, we calculate gravity at 60 degF using
Tables
0.818

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Example #2 – Shrinkage Tables
SHRINKAGE FACTOR is estimated from tables
using…
Separator Pressure (psig) & Oil SG @ 60 degF
CHART

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1-SHR @ 60 degF
Sep P. = 1050 psi
SG@60 degF = 0.818
• Draw SG line on chart
• Separator Pressure from Left
scale
• Intersect with SG line, and
vertically down
• Intersect with lower curve
• Horizontal to left axis to get
shrinkage factor @ 60 degF
Sep P.
1050 psi
(1-SHR) @ 60 degF = 0.856
0.856

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Example #2 – Shrinkage Tables
CHART
K Factor = 1 , because Shrinkage Factor already at
60 degF.

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Example #2 – Shrinkage Tables
Then complete Vo and rates as before…
Vo = V’o*.(1-SHR).K

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Example #2 – Shrinkage Tables
The last line can then be completed in the
same way….
1282

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Example #2 – Shrinkage Tables
1282

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Example #3 – Combined Meter Factor
In this example:
During the well test, a meter factor is taken, but we
must
• Wait 30 minutes before taking final gauge tank
reading to allow any Shrinkage to occur
• Record Tank Temperature for K – factor calculation
This meter factor takes account of meter factor, f and
shrinkage of oil and so is called a COMBINED
METER FACTOR, (1-SHR)*
Reading
Meter
Reading
Tank
CMF 
)
1
.(
f
)*
1
( SHR
SHR
CMF 




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Example #3 – Combined Meter Factor
Values already marked on the sheet come from the
Well Testing Reading Sheets
Correct for BSW as before, in this case there is no
meter factor
Vs = Difference in meter reading
V’o* = Vs.(1-BSW)

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Example #3 – Combined Meter Factor
To Calculate CMF….
Tank Vol.= (Tank Final Reading – Tank Initial Reading) x Tank Conversion Factor
= (84 – 50) x 0.264 = 8.976 bbl
0.898
Combined Meter Factor = (Tank (True) Reading) / (Meter Reading) = 8.976/10 = 0.8976

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Example #3 – Combined Meter Factor
To Calculate CMF….
98
0.898
Shrinkage Temperature = Tank Temperature when final reading is taken

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Example #3 – Combined Meter Factor
Again, we calculate gravity at 60 degF using
Tables
0.890

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Example #3 – Combined Meter Factor
And we calculate the Shrinkage Temperature
Factor, K using the tables as in Example 1
0.984

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Example #3 – Combined Meter Factor
Then complete Vo and rates as before…
Vo = V’o*.(1-SHR).K

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Example #3 – Combined Meter Factor
The last line can then be completed in the
same way….

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Example #3 – Combined Meter Factor

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Gas Calculations
Gas flowrate is calculated from the differential
pressure across the daniel orifice plate and static
pressure, as measured by the Barton Chart
Recorder.
hw = Differential Pressure (in. of H20)
Pf = Separator pressure (psia) – measured
downstream of Plate
f
w P
h
C
Q 


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Fu = Unit Conversion Factor
Fb = Basic Orifice Factor
Fg = Specific Gravity Factor
Y2 = Expansion Factor
Ftf = Flowing Temperature Factor
Fpv = Supercompressibility Factor
Gas Calculations – Numerical Constant
pv
tf
g
b
u F
F
Y
F
F
F
C 




 2

39. Schlumberger
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Gas Information Sheet
• Explains basic theory behind
gas calculation
• Lists main data about
metering devices. e.g.
– Daniel Line Bore
– Specific Gravity
Measurement
• Shows selection of Fu to give
desired output units and
reference conditions

40. Schlumberger
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Gas Calculations - Example
Values already marked on the
sheet come from the Well Testing
Reading Sheets…
With Separator Static &
Differential Pressures being the
most important measurements
250
Air:1.00
0

41. Schlumberger
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Gas Calculations - Example
NOTE THE UNITS
Especially psia for P
Most of the factors have no units
The output units of
the gas rate come
from the choice of
Fu…
250
Air:1.00
0

42. Schlumberger
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Fu – Unit Conversion Factor
• Value depends on
the reference
conditions used
and the units of
gas rate desired
• Normally reference
conditions are:
– 14.73 psi
– 60 degF
In this case we desire scf/day
Fu = 24

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Gas Calculations - Example
Note Number of Decimal Places Required
Also
- - - 2 3 3 2 4 4 4 4 1
Number of decimal places for Gas Rates depends
on how large rate is, and how we report it:
SCFD 0 dp
MSCFD 1 dp
MMSCFD 2dp
250

44. Schlumberger
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Gas Calculations - Example
Start the calculations….
10
.
126
60
265 


 f
w P
h
126.10
250
Air:1.00
0

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Gas Calculations - Example
TABLES
250

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Fb – Basic Orifice Factor
Depends on:
• Daniel Line Bore: ID
of the metering tube
– Plate on side of
Daniel
– Normally 5.761 in.
• Orifice Diameter (in)
Fb = 455.03
D = 5.761
in
d = 1.5 in

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Gas Calculations - Example
TABLES
or EQUATION

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Fg – Specific Gravity Factor
Fg corrects the gas flow equation for
gas factors that have a s.g. not
equal to 1
• Calculated by a simple equation
• Or can be taken from the table.
(Interpolate values)
Fg = (1.1834+1.1818)/2 =
1.1826
s.g. =
0.715
SG
Fg
1

Interpolate

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Gas Calculations - Example
TABLES or
GRAPH

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Y2 – Expansion Factor
Y2 takes into account the change in specific gravity of
the gas as it’s velocity and pressure change through
the orifice
Can be calculated from either:
• Tables
• Chart (very user unfriendly!)

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Into the table we input:
• Don’t try to interpolate the
table, just round to the
nearest 1 dp and use this
value
Y2 – Expansion Factor -
Tables
Y2 = 1.0013
3
.
0
~
260
.
0
761
.
5
5
.
1



D
d

2
.
0
~
226
.
0
265
60


f
w
P
h

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The chart is normally only used if we are outside the range of the
tables. To use:
• Draw a line between Pf and hw using the parabolic axis.
– There is a choice of scales so you must be consistent. i.e. if
reading Pf from the outer scale of the big parabola, you must
read hw from the outer scale of the big parabola.
• Where this line intersects the horizontal axis, draw a line
vertically up.
• From the horizontal axis, take the orifice diameter and go
vertically up until we hit the Line bore line, then horizontally
across.
• From the intersection of the horizontal and vertical lines draw
a line to the reference point A and where this line intersects
the vertical axis we can read off Y2.
Y2 – Expansion Factor - Chart

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Y2 – Expansion Factor - Chart
Example
Pf = 180 psig
Hw = 260 in H20
Line Bore = 4.026 in
Orifice Size = 2.125 in hw = 260in
Pf = 180 psig
d = 2.125 in
Y2 = 1.0083

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Gas Calculations - Example
TABLES or
EQUATION

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Ftf – Flowing Temperature Factor
Ftf corrects the gas rate for
flowing temperatures that are
not 60 degF
• Calculated by an equation
• Or can be taken from the
table
Ftf =0.9768
Tf = 85
degF
 
 
degC
2
.
273
556
.
288
degF
460
520
f
f
tf
T
T
F





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Gas Calculations - Example
TABLES or
CHART

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Fpv – Supercompressibility Factor
Fpv – Corrects the gas flow rate for the fact that real
gases deviate from the ideal behavior as predicted by
Boyle’s law.
To calculate it we need:
• Separator Static Pressure (psig)
• Gas Specific Gravity
• Flowing Temperature
Can be calculated from either:
• Tables
• Chart

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Fpv – Supercompressibility Factor – Table (1)
Second table corrects this
Fpv for the flowing
temperature
Input:
• Fpv
• Tf
• Each heading is
inclusive to next higher
heading. Do not
interpolate
Fpv (uncorrected) =
Pf = 265 psia = 250
psig
sg = 0.715

59. Schlumberger
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Fpv – Supercompressibility Factor – Table (2)
First table calculates Fpv,
then we must correct
for temperature
Input:
• Pf (psig)
• s.g.
• Each heading is
inclusive to next higher
heading. Do not
interpolate
Fpv = 1.027
Fpv = 1.032 psig
Tf = 85 degF

60. Schlumberger
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The chart is normally only used if we are outside the range of the tables.
To use:
1. Left Hand Chart bottom axis - Flowing Temperature go
vertically upwards
2. Intersect with specific gravity line and go horizontally into Right
Hand Chart
3. Intersection of this line with Separator Pressure (psig) from
bottom axis gives Fpv @ 60 degF
Fpv – Supercompressibility Factor – Chart

61. Schlumberger
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Fpv – Supercompressibility Factor – Chart
Example:
Pf = 250 psig
Tf = 85 degF
Sg = 0.715
85 degF 250 psig

62. Schlumberger
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Gas Calculations - Example
C = Fu.Fb.Fg.Y2.Ftf.Fpv
= 24 x 455.03 x 1.1826 x 1.0013 x 0.9768 x 1.0270
= 12972.9
12972.9
250

63. Schlumberger
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Gas Calculations - Example
12972.9
Qgas = C.(hw.Pf)1/2
= 12972.9 x 126.10
= 1635882.7 SCFD
= 1.64 MMSCFD
1.64
250

64. Schlumberger
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Gas Calculations - Example
12972.9 1.64
Cumul.= 1.6359 /1440 x 15
= 0.0170 MMSCF
= 17.0 MSCF
17.0
250

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Gas Calculations - Example
The remaining lines can then be completed in
the same way…. 250

66. Schlumberger
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Gas Calculations - Example
The remaining lines can then be completed in
the same way…. 250

67. Schlumberger
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Gas Calculations - Example
The remaining lines can then be completed in
the same way…. 250

68. Schlumberger
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Gas Calculations - Example
The remaining lines can then be completed in
the same way…. 250

69. Schlumberger
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Gas Calculations - Example
The remaining lines can then be completed in
the same way…. 250

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Gas Calculations - Example
The remaining lines can then be completed in
the same way….
1 . 0020
1 . 0020
250
150
72 Feet - A-Limestone
5190 – 5262 Feet

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Remaining Calculations – Well Testing Data
Sheet
Oil and Gas calculations have been completed. Now we must
calculate:
 
 
BOPD
SCFD
Q
Q
GOR
oil
gas

Gas Oil Ratio
• Units: scf/bbl
• No decimal places
Water Rate:
• Units: BWPD
• Calculation takes account of meter factor and
shrinkage
• WaterCut = BSW - Sediment
  f
SHR
WaterCut
V
V s
water 



 1
Interval
V
Q Water
water /
1440



72. Schlumberger
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Well Testing Data Sheet
Water Rate and GOR are added to the Well Testing Data
sheets.
These also summarize the well test readings and
calculations. Includes:
• BSW, H2S, CO2
• Wellhead and Separator, Temperature and Pressure
• Oil and Gas Rates and Gravities
• Main events always with data from the well test

73. Schlumberger
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Well Testing Data Sheet
Water Rate
& GOR

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THE END