OCC Surface and Interfacial Tension Measurements Lab Report I attached the Experiments manuals as well as some students work. I need the Theory section and

OCC Surface and Interfacial Tension Measurements Lab Report I attached the Experiments manuals as well as some students work. I need the Theory section and procedure section for both experiments. Objectives
The main objectives of the experiments were to determine both the surface and the
interfacial tensions using the du Nouy method (Experiment 10), and to measure the capillary
pressure for both core samples 4C and 4D using capillary pressure curve along with the Leverett
J-function relationship (Experiment 11).
Theory
Experiment 10
Surface tension which measured in dynes per cm occurs when there is interaction between
two immiscible fluids such as liquid and gas, creating a surface energy between the two immiscible
fluids. While, interfacial tension occurs when two immiscible fluids such as liquid and liquid
interface, and it is a measure of the energy in order to minimize the area of contact. Furthermore,
the du Nouy ring method was used to determine both surface and interfacial tensions in order to
overcome the forces thus the fluids in the reservoir can migrate to the surface. Moreover, both
pressure and temperature affect the surface tension, pressure and temperature have and inverse
relationship with surface tension, as the pressure and temperature increase the surface tension
decreases and vice versa.
Wettability is described as the propensity of the fluid to range over the surface and how it
is shaped in respects to the contact angle can be categorized into either wetting phase if the contact
angle is less the 90? or non-wetting phase if the contact angle is greater than 90?. For instance,
water was discharged on a solid surface the water will spread widely on the solid surface creating
a very small contact angle (less than 90?) implying that the water is the wetting phase and air is
the non-wetting phase. On the other hand, mercury was discharged on a solid surface the mercury
will spread narrowly on the solid surface creating a large contact angle (greater than 90?) implying
that the air is the wetting phase and mercury is the non-wetting phase.
Absolute surface tension was calculated using equation 1 shown below along with the
correction factor as equation 2.
?? =??×??
???????????????? 1
Where,
?? = ???????????????? ?????????????? ??????????????,
?? = ???????? ??????????????,
??????????
????
??????????
????
?? = ???????????????????? ????????????
0.01452 ? ??
1.679 ? ?? 0.5
?? = 0.7250 + [ 2
+ 0.04534 ?
]
?? (???? ? ???? )
??
Where,
?? = ?????????????????????????? ???? ????? ????????, 5.92 ????
?? = ???????????? ???? ????? ????????, ????
?? = ???????????? ???? ????????, ????
??
= 53.0322
??
?? = ???????? ?????????????? (???????????????? ?????????????? ??????????????,
???? = ?????????????? ???? ????? ?????????? ?????????, 1.0
????
????
???? = ?????????????? ???? ????? ?????????? ?????????, 0.01237
????
????
??????????
)
????
???????????????? 2
Experiment 11
Capillary pressure is defined as the difference between the non-wetting pressure and the
wetting pressure. Furthermore, capillary pressure depends on many factors such as pore size,
surface tension, water saturation, porosity and permeability. Additionally, pore size, porosity and
permeability have inverse relationship with capillary pressure. On other words, as the porosity or
permeability or pore size decreases the capillary pressure increases and vice versa. However,
surface tension and water saturation have a direct relationship with capillary pressure. On other
words, as the surface tension or water saturation increases the capillary pressure increases and vice
versa. Moreover, it is crucial to overcome the capillary pressure in order to cause the fluids
(hydrocarbons) in the reservoir to migrate to the surface. Additionally, capillary pressure was
measured using both equation 3 and 4 shown below.
???? = ?????? ? ???? = (???????? ? ???????????? )???
???????????????? 3
Where,
???? = ?????????????????? ????????????????, ??????
?????? = ?????? ? ?????????????? ????????????????, ??????
???? = ?????????????? ????????????????, ??????
???? =
Where,
?? = ?????????????? ??????????????,
??????????
????
?? = ?????????????? ??????????, °
?? = ???????????? ???? ????? ????????, ????
2??cos (??)
??
???????????????? 4
The derivation of both equation 3 and 4 are shown below.
????????????????? = ???????????? ???????????
(1)
????????????????? = ???? (2????)
(2)
???? = ?????? cos(??)
(3)
(3) ? (2) ????????????????? = ?????? cos(??) (2????)
???????????? ??????????? = ??? ??????????
(4)
(5)
?????????? = ???? 2 (6)
??? = ???????????? ??? ? ???????? ???
(7) (hydrostatics)
(7)&(6) ? (5) ???????????? ??????????? = (???????????? ? ???????? )???(???? 2 )
(8)&(4) ? (1) ?????? cos(??) (2????) = (???????????? ? ???????? )???(???? 2 )
(9) ?????????? ?????? ?, ? =
2?????? cos(??)
(???????????? ? ???????? )????
(10) ? ???????????????? 3 ???? = (???????????? ? ???????? )??
???????????????? (11) ???? =
(9)
(10)
2?????? cos(??)
(???????????? ? ???????? )????
2??cos (??)
??
(8)
(11)
???????????????? 4
Capillary pressure curve which is capillary pressure versus water saturation. There are two
process that could be plotted in capillary pressure curve which are drainage and imbibition process.
In experiment 11, drainage process will be used to replace non-wetting phase to wetting phase.
While, imbibition process replaces wetting phase to non-wetting phase. Moreover, imbibition
curve always lays below the drainage curve, and imbibition curve does not reach 100% water
saturation. When it comes to water saturation there is an important term called irreducible water
saturation which means the water saturation cannot be reduced furthermore even if higher pressure
was applied.
Water saturation was calculated at each capillary pressure level using both equation 5 and
6 shown below.
???????????? (????) =
100% ?????????????????? ???????? ??????????? (????) ? ?????? ???????? ??????????? (????)@??
???????????????? 5
????
?????????????? ???? ?????????? ( ???? )
?????????? ???????????????????? @ ?? (????????????????) =
???????????? @??
?????????? ????????????
???????????????? 6
J-function which is a dimensionless function of saturation was defined by Leverett and it
considered the common affecting parameters. The J-function offered to convert all capillary
pressure data to a universal curve where it differs from formation to another formation.
Additionally, J-function minimize the curve to a common curve and remove inconsistencies in the
capillary pressure versus water saturation curve. Equation 7 was applied to each step, in order to
find J value at each capillary pressure.
????
??
)?
??(???? ) = (
?? cos(??) ??
Where,
??(???? ) = ???????????????? ?? ????????????????, ??????????????????????????
???? = ?????????????????? ????????????????, ??????
?? = ?????????????? ??????????????,
??????????
????
?? = ?????????????? ??????????, °
?? = ????????????????????????, ????
?? = ????????????????, ????????????????
???????????????? 7
Procedure
Equipment used
Figure 1: The du Noury method equipment for experiment 10.
Figure 2: Capillary pressure panel and cell for experiment 11.
Experiment 10
1. Ring was attached to the mechanical arm.
2. Ring was dipped into the water.
3. Force was applied till the ring reached the surface.
4. Mechanical arm stopped when the ring reached the surface.
5. Dial value was recorded as a nominal surface tension in dynes per cm.
Experiment 11
1. Sample and ceramic plate were filled with water.
2. Sample was sealed and pressure was applied.
3. Pressure was released inside the system.
4. Excess water from the sample was collected in a baker outside the system.
5. Sample was left for the next group.
6. Capillary raw data was collected and uploaded by the instructor.
Table 1: Capillary raw data.
Results and Calculations
Experiment 10
Results
All data gathered and calculated throughout conducting experiment 10 were presented in
table 2 and 3.
Table 2: Terms for equation 2.
C
R/r
?water
?veg-oil
?air
5.92
53.0322
1.0
0.93
0.01237
cm
gm/cc
Table 3: Experiment 10 results.
Sample
Water/Air
Oil/Air
Apparent Surface Tension
(P)
dynes/cm
68
49
Correction Factor
(F)
0.93044
0.91422
Absolute Surface Tension
(S)
dynes/cm
63.27
44.80
Calculation
Water/Air:
0.01452 ? ??
1.679 ? ?? 0.5
?? = 0.7250 + [ 2
+ 0.04534 ?
]
?? (???? ? ???? )
??
= 0.7250 + [
0.01452 ? 68
1.679 0.5
+
0.04534
?
] = 0.93044
5.922 (1.0 ? 0.01237)
53.0322
?? = ?? × ?? = 68 × 0.93044 = 63.27
??????????
????
Oil/Air:
0.01452 ? ??
1.679 ? ?? 0.5
?? = 0.7250 + [ 2
+ 0.04534 ?
]
?? (???? ? ???? )
??
0.01452 ? 49
1.679 0.5
= 0.7250 + [
+ 0.04534 ?
] = 0.91422
5.922 (0.93 ? 0.01237)
53.0322
?? = ?? × ?? = 49 × 0.91422 = 44.80
??????????
????
Experiment 11
Results
All data gathered and calculated throughout conducting experiment 11 were presented in
table 4 through 11 along with figures 4 through 7.
Table 4: Capillary pressure and water saturation for all samples along with irreducible water saturation.
Sample
Pc, psi
1
0
1
2
4
8
15
35
Swir, frac
1
1
0.829971182
0.74351585
0.642651297
0.590778098
0.582132565
2
3
4
5
6
7
8
9
10
1
0.684210526
0.403508772
0.28460039
0.214424951
0.18128655
0.173489279
1
0.846754514
0.483162518
0.361151781
0.273304051
0.23670083
0.224499756
1
0.87012987
0.685714286
0.52987013
0.387012987
0.296103896
0.264935065
1
0.888601036
0.541450777
0.430051813
0.321243523
0.269430052
0.259067358
Sw, frac
1
0.927807487
0.580213904
0.390374332
0.286096257
0.229946524
0.213903743
1
0.911167513
0.57106599
0.393401015
0.271573604
0.253807107
0.248730964
1
0.948616601
0.795783926
0.637681159
0.429512516
0.321475626
0.292490119
1
1
0.949636262 0.974504249
0.560716284 0.915014164
0.381645215 0.668555241
0.325685506 0.45325779
0.297705652 0.365439093
0.283715725 0.339943343
0.163489279
Table 5: Capillary pressure and J-function for all samples.
Sample
Pc, psi
1
0
1
2
4
8
15
35
0
0.374120944
0.748241889
1.496483777
2.992967554
5.611814164
13.09423305
2
3
4
5
6
7
8
9
10
0
0.468461822
0.936923645
1.873847289
3.747694579
7.026927335
16.39616378
0
0.472378493
0.944756987
1.889513973
3.779027946
7.085677399
16.53324726
0
0.553805312
1.107610623
2.215221246
4.430442493
8.307079673
19.3831859
0
0.553805312
1.107610623
2.215221246
4.430442493
8.307079673
19.3831859
0
0.505910437
1.011820874
2.023641748
4.047283496
7.588656555
17.7068653
6
7
8
9
10
0.836510721
0.811014971
0.751524886
0.505065962
0.289768512
0.201949815
0.176454064
0.836510721
0.520721248
0.240019493
0.121111111
0.050935673
0.017797271
0.01
0.836510721
0.683265236
0.31967324
0.197662503
0.109814772
0.073211551
0.061010477
0.836510721
0.706640591
0.522225007
0.366380851
0.223523708
0.132614617
0.101445786
0.836510721
0.725111758
0.377961498
0.266562535
0.157754245
0.105940773
0.095578079
J-Function
0
0.549818253
1.099636506
2.199273013
4.398546026
8.247273798
19.24363886
0
0.542000249
1.084000499
2.168000998
4.336001996
8.130003742
18.97000873
0
0.393420203
0.786840406
1.573680812
3.147361624
5.901303044
13.7697071
0
0.524588267
1.049176535
2.098353069
4.196706139
7.86882401
18.36058936
Table 6: Capillary pressure and Sw-Swir for all samples.
Sample
Pc, psi
1
0
1
2
4
8
15
35
0.836510721
0.836510721
0.666481903
0.580026571
0.479162018
0.427288819
0.418643286
2
3
4
5
Sw-Swir, frac
0.836510721
0.764318208
0.416724625
0.226885053
0.122606978
0.066457245
0.050414465
0.836510721
0.747678234
0.407576711
0.229911736
0.108084325
0.090317828
0.085241686
0.836510721
0.785127322
0.632294647
0.474191881
0.266023238
0.157986347
0.12900084
0.836510721
0.786146983
0.397227006
0.218155937
0.162196228
0.134216373
0.120226446
Table 7: J and Sw-Swir for all samples @ Pc.
Pc, psi
1
2
4
8
15
35
Table 8: Core sample 4C data.
J-Function Sw-Swir, frac
0.374120944
0.549818253
0.542000249
0.393420203
0.524588267
0.836510721
0.764318208
0.747678234
0.785127322
0.786146983
0.468461822
0.472378493
0.553805312
0.553805312
0.505910437
0.748241889
1.099636506
1.084000499
0.786840406
1.049176535
0.936923645
0.944756987
1.107610623
1.107610623
1.011820874
1.496483777
2.199273013
2.168000998
1.573680812
2.098353069
1.873847289
1.889513973
2.215221246
2.215221246
2.023641748
2.992967554
4.398546026
4.336001996
3.147361624
4.196706139
3.747694579
3.779027946
4.430442493
4.430442493
4.047283496
5.611814164
8.247273798
8.130003742
5.901303044
7.86882401
7.026927335
7.085677399
8.307079673
8.307079673
7.588656555
13.09423305
19.24363886
18.97000873
13.7697071
18.36058936
16.39616378
16.53324726
19.3831859
19.3831859
17.7068653
0.811014971
0.520721248
0.683265236
0.706640591
0.725111758
0.666481903
0.416724625
0.407576711
0.632294647
0.397227006
0.751524886
0.240019493
0.31967324
0.522225007
0.377961498
0.580026571
0.226885053
0.229911736
0.474191881
0.218155937
0.505065962
0.121111111
0.197662503
0.366380851
0.266562535
0.479162018
0.122606978
0.108084325
0.266023238
0.162196228
0.289768512
0.050935673
0.109814772
0.223523708
0.157754245
0.427288819
0.066457245
0.090317828
0.157986347
0.134216373
0.201949815
0.017797271
0.073211551
0.132614617
0.105940773
0.418643286
0.050414465
0.085241686
0.12900084
0.120226446
0.176454064
0.01
0.061010477
0.101445786
0.095578079
Table 9: Core Sample 4D data.
Core Sample 4C
Core Sample 4D
Sw, frac
0.17
0.19
0.21
0.23
J-Function
98.78278118
24.22581548
13.80074394
9.647358577
Pc, psi
292.2587425
76.11062461
43.35801379
30.30925782
Sw, frac
0.17
0.19
0.21
0.23
J-Function
98.78278118
24.22581548
13.80074394
9.647358577
Pc, psi
240.8470482
59.06612548
33.64825734
23.52168879
0.25
0.27
0.29
0.31
0.33
0.35
0.37
0.39
0.41
0.43
0.45
0.47
0.49
0.51
0.53
0.55
0.57
0.59
0.61
0.63
0.65
0.67
0.69
0.71
0.73
0.75
0.77
0.79
0.81
0.83
0.85
0.87
0.89
0.91
0.93
0.95
0.97
0.99
1
7.415080204
6.021463336
5.06866083
4.37610114
3.849984019
3.436750593
3.103594198
2.829297302
2.599529512
2.404262968
2.236270404
2.090211294
1.962053903
1.848697522
1.747718398
1.657194557
1.575582349
1.50162773
1.434301389
1.372750569
1.316262769
1.264238047
1.216167642
1.171617283
1.130214038
1.091635856
1.055603176
1.02187214
0.990229076
0.96048596
0.932476689
0.906053969
0.881086731
0.857457954
0.835062834
0.813807231
0.793606342
0.774383578
0.765117061
23.29607383
18.91772584
15.92429126
13.74846562
12.0955552
10.79729326
9.750610589
8.888847728
8.166982655
7.553510691
7.025725818
6.566849619
6.164215534
5.808082014
5.490834314
5.206434142
4.950031788
4.7176874
4.506167179
4.312792002
4.135323393
3.971876509
3.820852964
3.680888401
3.550811177
3.429609499
3.316405062
3.210431738
3.111018225
3.017573813
2.929576646
2.846563972
2.768124007
2.693889108
2.62353001
2.556750946
2.493285498
2.432893037
2.403780276
Pd
0.25
0.27
0.29
0.31
0.33
0.35
0.37
0.39
0.41
0.43
0.45
0.47
0.49
0.51
0.53
0.55
0.57
0.59
0.61
0.63
0.65
0.67
0.69
0.71
0.73
0.75
0.77
0.79
0.81
0.83
0.85
0.87
0.89
0.91
0.93
0.95
0.97
0.99
1
7.415080204
6.021463336
5.06866083
4.37610114
3.849984019
3.436750593
3.103594198
2.829297302
2.599529512
2.404262968
2.236270404
2.090211294
1.962053903
1.848697522
1.747718398
1.657194557
1.575582349
1.50162773
1.434301389
1.372750569
1.316262769
1.264238047
1.216167642
1.171617283
1.130214038
1.091635856
1.055603176
1.02187214
0.990229076
0.96048596
0.932476689
0.906053969
0.881086731
0.857457954
0.835062834
0.813807231
0.793606342
0.774383578
0.765117061
18.07906356
14.68121927
12.35814567
10.66958259
9.386831142
8.379306859
7.567022233
6.898245784
6.338037886
5.861949138
5.452358392
5.096244652
4.783777956
4.507398314
4.261196256
4.040485726
3.841503078
3.661190765
3.497039177
3.346969163
3.209243541
3.082399567
2.965196801
2.856576428
2.755629186
2.661569867
2.573716856
2.491475597
2.414325119
2.341807
2.273516249
2.209093745
2.148219921
2.090609464
2.036006846
1.984182537
1.934929779
1.888061833
1.865468693
Pd
Table 10: ‘a’ and ‘b’ values from Leverett plot.
Leverett Plot Values
0.6402
-0.999
a
b
Table 11: Core Samples 4C and 4D data.
Core Sample
4C
0.309
125.32
? (Exp. 3), frac
KL (Exp. 4), md
4D
0.1989
133.94
Capillary Pressure Curves
40
Sample 1
Pc, psi
35
30
Sample 2
25
Sample 3
20
Sample 4
15
Sample 5
10
Sample 6
5
Sample 7
0
0
0.2
0.4
0.6
0.8
1
Sample 8
1.2
Sample 9
Sw, frac
Figure 4: Capillary pressure curves for all samples.
Leverett J-Function
70
J-Function
60
y = 0.6402x-0.999
50
40
b
a
30
20
10
0
0
0.1
0.2
0.3
0.4
0.5
Sw-Swir, frac
Figure 5: Leverett J-Function.
0.6
0.7
0.8
0.9
Capillary Pressure Curve (4C)
350
300
Pc, psi
250
200
150
100
50
0
0
0.2
0.4
0.6
0.8
1
1.2
1
1.2
Sw, frac
Figure 6: Capillary pressure curve for core sample 4C.
Capillary Pressure Curve (4D)
300
250
Pc, psi
200
150
100
50
0
0
0.2
0.4
0.6
Sw, frac
Figure 7: Capillary pressure curve for core sample 4D.
0.8
Sample Calculation
STWater/Air=63.27 dynes/cm, Sample 1 @ Pc= 8 psi:
???? =
??@ 8 ?????? ? ????????
43.76 ? 41.53
=
? 0.6427 = 64.27%
??@ 0 ??????=%100 ??????. ? ????????
45 ? 41.53
???????? = ??????(???? ) ? 0.01 = 0.1735 ? 0.01 = 0.1635
??=
????
??
8
105
?
? =
? 2.99
?????????? ? 63.27 ? 1 0.1874
???? ? ???????? = 0.6427 ? 0.1635 ? 0.4792
STWater/Air=63.27 dynes/cm, Core Sample 4C @ Sw=0.17:
1
1
???? ? ???????? ??
0.17 ? 0.1635 ?0.999
) =(
)
??=(
? 98.78
??
0.6402
?
0.309
???? = ??(???? ) ??????????? = 98.78 ? 63.27 ? 1?
? 292.3 ??????
??
125.32
Engineering analysis
In experiment 10, Water/Air had an absolute surface tension of 63.27 dynes per cm. While,
VegetarianOil/Air had an absolute surface tension of 44.80 dynes per cm. By comparing both
values, Water/Air has a higher absolute surface tension than VegetarianOil/Air. In experiment 11,
capillary pressure curves for all samples were plotted in figures 4. In figure 4, sample 1 appeared
to be shifted far to the right from the other samples, otherwise the capillary pressure curves for all
samples behaves in a normal pattern. In figures 6 and 7, both capillary pressure curves for core
sample 4C and 4D behaves in a norm…
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