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Master Defense 2011
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Transcript of Master Defense 2011
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COMPARSION OF RELATIVE PERMEABILITY OBTAINED FROM UNSTEADY STATE METHOD WITH THAT OBTAINED FROM A NEW RESISTIVITY MODEL
By AHMED IBRAHIM
M.Eng Defense 14th July, 2011
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OUTLINES
INTRODUCTION
RATIONALE BEHIND ORIGINAL STUDY [KEWEN LI, 2004]
PROJECT OBJECTIVES
THEORETICAL BACKGROUND
EXPERIMENTAL TASK
• MATERIALS USED
• EXPERIMENTAL SET UP
• PROCEDURE
RESULTS
CONCULSIONS
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INTRODUCTION
Relative permeability is considered as a dimensionless term. It can be either expressed as percentage or fraction and is usually expressed as the ratio of effective permeability to absolute permeability. Mathematically,
where,
Kr= Relative Permeability
Ke= Effective Permeability [mD or D]
K = Absolute Permeability [mD or D]
Importance of permeability comes in describing the formation as permeable.
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KK
K er
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RATIONALE BEHIND ORIGINAL STUDY [KEWEN LI, 2004]
Relative permeability is a dynamic property.
It is hard to measure relative permeability in many cases using direct methods.
The most often used method is JBN [Johnson Bosller Naumann].
Resistivity is easy to measure.
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PROJECT OBJECTIVES
The primary objectives of this study were:
1. Measure the relative permeability for an oil/brine system in a sandstone core using the unsteady state method.
2. Measure the resistivity of sandstone cores as a function of saturation.
3. Compare the measured relative permeability with that obtained from a new resistivity model, and
4. Investigate the sensitivity of the new model to brine salinity.
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THEORETICAL BACKGROUND
Relative Permeability is an important parameter of multiphase flow in porous media.
The traditional methods of relative permeability measurement depends on Steady State and Unsteady State Methods.
Relative Permeability, Capillary Pressure and Resistivity are the three main fundamental parameters that govern fluid flow in multi phase flow systems.
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THEORETICAL BACKGROUND CON’
Some models were developed empirically to calculate relative permeability from capillary pressure data.
It is easier to find a relationship between relative permeability and resistivity.
Kewen Li (2004) developed a new method to calculate relative permeability from resistivity data in consolidated porous media.
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THEORETICAL BACKGROUND CON’
His law stated that the wetting phase relative permeability is inversely proportional to the resistivity index of a porous medium. Mathematically,
where,
Krw = Relative Permeability of wetting phase
= Normalized Water Saturation [%]
I =Resistivity Index [Ω/Ω]8
ISK wrw
1"
"
wS
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THEORETICAL BACKGROUND CON’
and,
• The resistivity index can be defined as:
where,
= Resistivity at specific water saturation [Ω/Ω]
= Resistivity at a water saturation of 100% [Ω/Ω]9
wi
wiww
S
SSS
1
"
o
t
R
RI
tR
oR
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EXPERIMENTAL TASK
The new equation for relative permeability was tested using water saturation data derived from capillary pressure test.
The aim of this study was to use unsteady state method to obtain water saturation and based on the relationship between saturation and resistivity, resistivity index was calculated using the following equation:
Where,
n = Saturation Exponent and it is equal to 2
The calculated resistivity index was then used to calculate relative permeability.
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n
w
o
t SR
RI
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EXPERIMENTAL TASK-MATERIALS USED CON’
The test was carried out on three main fontaineblue sandstones GF 14, GV 25, GV 22 and GV 25 where the wetting phases were Tap water, 2% NaCl, 4.5% NaCl and 10% NaCl, respectively and non-wetting phase was kerosene. The solutions were made using distilled water at ambient conditions.
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EXPERIMENTAL TASK-EXPERIMENTAL SET UP CON’
Two instruments were used in this study:
• Electrical Properties System Atmospheric.
• Benchtop Relative Permeameter BRP 350.
• Cydar® Simulator.
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EXPERIMENTAL TASK- PROCEDURE CON’
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RESULTS
SAMPLE SALINITY (NaCl)
ɸ (%) Ka (mD) Ro (Ω.m) ConfiningPressure (psi)
Back Pressure (psi)
GF 14 3.6*10-3 6.77 6.66 39,504,269 759.7 205.8
GV 25 2 7.08 6.51 60 737.7 259.8
GV 22 4.5 6.41 5.44 35.290 691.3 230.7
GV 25 10 6.32 3.86 16.524 738.6 190.9
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RESULTS-MONOPHASIC PERMEABILITY CON’
GV 25 2% NaCl
GV 22 4.5% NaCl
R² = 0.999
0
20
40
60
80
100
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140
160
0 1 2 3 4 5 6
Del
ta P
[p
si]
Flow Rate [cm3/min]
GV 25 Monophasic Permeability
R² = 0.999
020406080
100120140160180200
0 1 2 3 4 5 6
Del
ta P
[p
si]
Flow Rate [cm3/min]
GV 22 Monophasic Permeability
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RESULTS-MONOPHASIC PERMEABILITY CON’
GV 25 10% NaCl R² = 0.998
0
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0 1 2 3 4 5 6
Del
ta P
[p
si]
Flow Rate [cm3/min]
GV 25 Monophasic Permeability
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RESULTS-COMPARSION OF RELATIVE PERMEABILITY CON’
GV 22 2% NaCl
GV 25 4.5% NaCl
0
0.2
0.4
0.6
0.8
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0 0.2 0.4 0.6 0.8 1
Rel
ativ
e P
erm
eab
ilit
y
Water Saturation [%]
Comparsion GV 25
Krw BRP 350
Krw resis
Krw Corey
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0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Rel
ativ
e P
erm
eab
ilit
y
Water Saturation [%]
Comparison GV 22
Krw BRP 350
Krw resis
Krw corey's 17
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RESULTS-COMPARSION OF RELATIVE PERMEABILITY CON’
GV 25 10% NaCl
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0 0.2 0.4 0.6 0.8 1
Rel
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e P
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eab
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Water Saturation [%]
Comparsion GV 25
Krw BRP
Krw resis
Krw Corey
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RESULTS-RELATIVE PERMEABILITY CURVES CON’
GV 25 2% NaCl
GV 22 4.5% NaCl
0
0.2
0.4
0.6
0.8
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0 0.2 0.4 0.6 0.8 1
Rel
ativ
e P
erm
eab
ilit
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Water Saturation [%]
Relative Permeability Curve GV 25
Krw
Kro
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Rel
ativ
e P
erm
eab
ilit
y
Water Saturation [%]
Relative Permeability Curve GV 22
Krw
Kro19
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RESULTS-RELATIVE PERMEABILITY CURVES CON’
GV 25 10% NaCl
0
0.1
0.2
0.3
0.4
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0.6
0.7
0.8
0.9
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0 0.2 0.4 0.6 0.8 1
Rel
ativ
e P
erm
eab
ilit
y
Water Saturation [%]
Relative Permeability Curve GV 25
Krw
Kro
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RESULTS-PRODUCED WATER VOLUME VERSUS TIME CON’
GV 25 2% NaCl GV 22 4.5% NaCl21
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RESULTS-PRODUCED WATER VOLUME VERSUS TIME CON’
GV 25 10% NaCl
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RESULTS-DIFFERENTIAL PRESSURE VERSUS TIME CON’
GV 25 2% NaCl GV 22 4.5% NaCl
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RESULTS-DIFFERENTIAL PRESSURE VERSUS TIME CON’
GV 25 10% NaCl
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RESULTS-SENSITIVITY CON’
0
0.1
0.2
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0.8
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0 0.2 0.4 0.6 0.8 1
Rel
ativ
e P
erm
eab
ilit
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Water Saturation [%]
Sensitivity of brine Salinity
Krw resis 2%
Krw resis 4.5%
Krw resis 10%
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CONCULSIONS
The new model is found to calculate relative permeability in close agreement with that obtained from Benchtop Relative Permeameter BRP 350 at higher and lower water saturations.
The wetting phase relative permeability inferred from the resistivity data are close to those calculated from the Benchtop Relative Permeameter for a concentration of 2% NaCl.
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CONCULSIONS CON’
At higher brine concentrations (4.5% &10% NaCl) close agreement is observe only at lower and higher water saturations and a deviation between these saturations.
The new model has been found not to be sensitive to salinity variation for the range of brine concentration investigated in this study (2% NaCl - 10% NaCl).
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