Determination of Permeability and Velocity Information of Oil Reservoir Using Well Log Data (S-Field)

Abstract

Permeability information is a necessary requirement to assess the migration and accumulation of fluids in the reservoir. Three well data (A, B, C) were available for this investigation. Microsoft Excel was used for the analysis and computation of results. Spurious values were noted and removed. Porosity was first determined and their average results for Wells A, B and C are 17.26604%, 22.83019% and 13.35095% respectively. These values of porosity indicate the reservoir classes of Wells A, B and C as good, good and fair correspondingly. This information enables the determination of average permeability of wells A, B and C corresponding to 80975.24 Darcy, 105407.1 Darcy and 65580.38 Darcy. Therefore, the reservoir of wells A and B are highly porous and permeable for the storage and migration of fluids. They should be developed for hydrocarbon exploration. This is because the porosity and permeability values of these wells are reasonable as they have met the standard. However, well C is permeable but not reasonably porous as it belongs to a fair class. The velocity information would give account of the rock elastic properties in terms of strength.

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Malaysian Journal of Geosciences (MJG) 8(2) (2024) 47-52
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DOI:
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Cite the A rticle:
Umor en, E.B.,
Atat, J.G., Aka nkpo, A.O ., Uzoewu lu, R.O. (2024). Det erminatio n of Per meability and Velo city
Infor mation of Oil Rese rvoir Usi ng Well Lo g Data (S-Field).
Mala ysian Jo urnal of Geosciences, 8(2): 47-52.
ISSN: 2521-0920 (Print)
ISSN: 2521-0602 (Online)
CODEN: MJGAAN
RESEARCH ARTICLE
Malaysian Journal of Geosciences (MJG)
DOI: http://doi.org/10.26480/mjg.02.2024.47.52
DETERMINATION OF PERMEABILITY AND VELOCITY INFORMATION OF OIL
RESERVOIR USING WELL LOG DATA (S-FIELD)
Umoren, E.B., Atat, J.G*., Akankpo, A.O., Uzoewulu, R.O.
Department of Physics, University of Uyo, Uyo, Nigeria.
*Corresponding Author Email: josephatat@uniuyo.edu.ng
This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.
ARTICLE DETAILS ABSTRACT
Article History:
Received 20 January 2024
Revised 24 February 2024
Accepted 29 March 2024
Available online 05 April 2024
Permeability information is a necessary requirement to assess the migration and accumulation of fluids in
the reservoir. Three well data (A, B, C) were available for this investigation. Microsoft Excel was used for the
analysis and computation of results. Spurious values were noted and removed. Porosity was first determined
and their average results for Wells A, B and C are 17.26604%, 22.83019% and 13.35095% respectively. These
values of porosity indicate the reservoir classes of Wells A, B and C as good, good and fair correspondingly.
This information enables the determination of average permeability of wells A, B and C corresponding to
80975.24 Darcy, 105407.1 Darcy and 65580.38 Darcy. Therefore, the reservoir of wells A and B are highly
porous and permeable for the storage and migration of fluids. They should be developed for hydrocarbon
exploration. This is because the porosity and permeability values of these wells are reasonable as they have
met the standard. However, well C is permeable but not reasonably porous as it belongs to a fair class. The
velocity information would give account of the rock elastic properties in terms of strength.
KEYWORDS
Permeability, Fluid, well data, Reservoir, Density, Porosity
1. INTRODUCTION
Permeability is the property of rock formations that determines the flow
of fluids like oil, gas and water (that is, a significant property of several
media; it is a critical parameter in the fields of reservoir engineering,
hydrogeology and environmental science (Xiao et al., 2019; Xiao et al.,
2018; Peng and Nelson, 2006). Precise permeability information is vital
for understanding fluid behavior in the subsurface reservoirs, improving
resource extraction, and making up-to-date decisions about
environmental remediation and groundwater management (Sudicky,
2006). Permeability determination may involve mining rock samples from
the subsurface and subjecting them to laboratory tests for measurement
(Kleppe et al., 1999). Well logging approach offers a cost-effective and
efficient means of assessing permeability of a reservoir. Well logs
generated by appropriate tools and sensors lowered into boreholes during
drilling or logging operations, offer continuous measurements of
petrophysical properties as a function of depth. These properties include
gamma-ray, resistivity, sonic, velocity, density, among others (Johansen
and Joshi, 2019).
Petrophysicists and geoscientists have developed empirical equations,
correlations and mathematical models that relate well log responses to
rock properties (Kenneth, 2010). By examining well log data with core
data, where available, it is likely to estimate permeability with a high
degree of accuracy. A group researcher had worked on a mathematical
model to predict the evolution of rock permeability depending on effective
pressure during oil production (Kozhevnikov et al., 2021). The model
developed enables the prediction of the change in permeability of rocks
during oil production. Some researchers worked on the permeability
characteristics of tight oil reservoir through high-pressure mercury
injection and established the correlation between the pore radius
distribution and the permeability contribution rate (Hao et al., 2023). A
group researcher investigated the permeability disparity and its influence
on oil recovery from unconsolidated sand heavy-oil reservoirs during
steam flooding process (Zhong et al., 2021). Their result showed that the
permeability and porosity of sand tube decrease with increase in
overburden pressure.
The rewards of using well log data for permeability estimates is that, it
permits for real-time monitoring of reservoir behavior, helps in well
placement optimization, and supports the development of Enhanced Oil
Recovery (EOR) techniques. It also curtails the environmental influence by
minimizing the need for wide core sampling (Swar and Cluff, 2009). This
research will contribute to facts regarding permeability information in the
Niger Delta basin which is adequate and reliable for well development
(Massoud et al., 2015). The accuracy of permeability estimates influenced
by the quality and consistency of well log data. Variability in logging tools,
data acquisition techniques and data interpretation can introduce errors
and uncertainties in the results. Permeability investigation is considered
to assess the flow ability of reservoir fluids in the S-Field of the Niger Delta
Basin using the approach of (Coates, 1981). The outcome would be
adequate for the recommendation on development of these wells for
hydrocarbon exploration.
1.1 Location and Geology of the Study Area
S-Field is seen as one of the Fields in the Niger Delta Basin where crude oil
is in appreciable amount, and its production plays a vital role in ensuring
a stable supply of petroleum products to the industries. It is location in the
southern part of Rivers State, Niger Delta (Figure 1). The oil Fields in the
Niger Delta Basin is located in the southern part of Nigeria, along the Gulf

Cite the A rticle:
Umor en, E.B.,
Atat, J.G., Aka nkpo, A.O ., Uzoewu lu, R.O. (2024). Det erminatio n of Per meability and Velo city
Infor mation of Oil Rese rvoir Usi ng Well Lo g Data (S-Fi eld).
Mala ysian Jo urnal of Geosciences, 8(2): 47-52.
Malaysian Journal of Geosciences (MJG) 8(2) (2024) 47-52
of Guinea coast. This region is situated approximately within longitudes
5°E and 8°E and latitudes 3°N and 6°N (Balogun, 2013; Akpabio et al.,
2023a; Umoren et al., 2019; Reijers et al., 1996). The wet and the dry
seasons are the major seasons in the province; with average monthly
rainfall of 0.135 m noted during the wet season, to about 0.065 m as dry
season approaches (Atat et al., 2023a; Ejoh et al., 2023; Atat et al., 2020a;
George et al., 2017; Atat et al., 2012; George et al., 2010). The total space
occupy by the sediment is almost 5.0 x 105km3 (Atat et al., 2020b; Umoren
et al., 2020; Atat et al., 2020c). The petroleum system is the Tertiary Niger
Delta (Akata-Agbada). Petroleum occurs throughout the Agbada
formation of the Niger Delta (Udo et al., 2017). According to Atat and
Umoren, the Niger Delta is the youngest Sedimentary basin in the Beune
Trough system (Atat and Umoren, 2016). According to a study,
groundwater is found at the top of the stratigraphic arrangement (George
et al., 2017). It generates substantial revenue and contributes to the
economic development of the region (Hunt, 1996).
Figure 1: Map showing the location of study
2. THEORETICAL BASIS
Permeability relates with porosity. Porosity relates with density and to
know more on the stability of the formation, velocity information is vital.
2.1 Permeability
Permeability is a fundamental parameter in reservoir characterization and
hydrocarbon production, playing a critical role in the evaluation and
management of oil and gas reservoirs; it is a key parameter used to assess
the ability of a reservoir rock to transmit fluids (Wu et al., 2008). It is
essential for reservoir characterization because it helps to determine the
potential flow capacity of the subsurface formation (Sudicky, 2006).
Moreso, permeability may be defined as a measure of the Connectivity of
pores in the reservoir. It is measured in millidarcy (mD) or Darcy of the
narrow throats. The sand in the reservoir, has narrow pore throats
between large pores that allow fluid to transmit. The Common
permeability in the range of 100 to 500md is a reasonable value for a
petroleum reservoir rock (Satter and Igbal, 2016; Tiab and Donaldson,
2016). Mathematically permeability may be expressed as defined in
Equation 1.
   󰇛󰇜
 
(1)
Where K is permeability,  is the porosity, = 0.3 is the irreducible
water saturation (Coates, 1981).
2.2 Density
Density is one of the critical parameters used in petrophysics and
geophysics to characterize and understand the composition and
properties of rock formations. This property aids in identification of
reservoir rock by lithology delineation (Atat et al., 2020b). If there is no
accuracy in the estimation of fluid density, the porosity will not be
appreciable (Atat et al., 2020c). Density logs provide data that can be used
to estimate porosity which permeability depends on. The relationship
between density and porosity is indirect but significant. Permeability is
influenced by various factors, including porosity and the arrangement of
pore spaces within the rock. Density is closely related to porosity as the
ratio of pore volume to total rock volume (Kenneth, 2010). As porosity
decreases (that is, the rock becomes denser), permeability typically
decreases as well. This is because a denser rock has fewer and smaller
interconnected pores through which fluids can flow.
2.3 Porosity
Porosity measures the void spaces within rocks, is closely related to
permeability. Porosity of a formation is crucial in valuation of fluid
content, potentiality of fluids flow and recaptures volumes in a pool (Atat
et al., 2023b; Akankpo et al., 2015; Akpabio et al., 2023b). Well logs can be
used to estimate porosity, allowing for indirect assessment of
permeability. Porosity may be estimated using Equation 2 (Atat et al.,
2022).
   
   

(2)
 is the porosity
 is the density of the grain matrix
 is the density of the fluid
 is the bulk density of the formation (Atat et al., 2022).
Porosity 󰇛󰇜 is also the ratio of the volume of voids to total volume
(Equation 3). It is also possible to porosity 󰇛󰇜 with particle density 󰇛󰇜
and bulk density 󰇛󰇜 as stated in Equation 4 (Flint and Flint, 2002; Nimmo,
2004; Nimmo, 2013; Nabayi et al., 2021).
   
   
(3)
   
 
(4)
Where  is the porosity,  is the particle density and  is the bulk density.
The particle density is a measure of the mass of solid particles per given
volume in g/; pore space density is approximated as 2.65g/. This
may vary if the sample has a high concentration of organic matter
(Passchier and Kleinhans, 2005).
2.4 Velocity
Some other possible deductions from the well data include compressional
waves velocity (Vp) and Shear wave velocity (Vs). If neither velocity
information is available, Vp may be obtained from the sonic log and Vs
determined using Castagna Equation (Equation 5) with local fits constants
obtained by a group researchers (that is, constants in Equation 6) which is
adequate for Niger Delta basin processes (Atat et al., 2021). Compressional
waves also known as P-waves, are acoustic waves that travel through
subsurface formations by compressing and expanding the rock in the
direction of their propagation. They are the fastest acoustic waves and
typically arrive at the detection sensors before shear waves. P-wave
velocity is directly related to the elastic modulus of the rock, which is a

Cite the A rticle:
Umor en, E.B.,
Atat, J.G., Aka nkpo, A.O ., Uzoewu lu, R.O. (2024). Det erminatio n of Per meability and Velo city
Infor mation of Oil Rese rvoir Usi ng Well Lo g Data (S-Fi eld).
Mala ysian Jo urnal of Geosciences, 8(2): 47-52.
Malaysian Journal of Geosciences (MJG) 8(2) (2024) 47-52
measure of a rock's resistance to compression. Elastic modulus is inversely
proportional to porosity and permeability. Shear waves (S-waves) are
acoustic waves that propagate by causing shearing or side-to-side
movement of rock particles perpendicular to their direction of travel.
Shear wave velocity is related to the shear modulus of the rock, which is
another measure of a rock's mechanical properties. Shear modulus is also
inversely related to porosity and permeability. These waves are pulses of
energy caused by the sudden breaking of rocks within the earth or an
explosion and propagates through the earth (Atat and Umoren, 2016).

 
 
(5)
With a and b being values deduced by for Niger Delta basin, this yields
Equation 6 (Atat et al., 2021).

(m/s) = 0.611  
(m/s) + 0.2862
(6)
Where 
(m/s) is the share wave

(m/s) is the compressional wave
3. MATERIALS AND METHODS
The well location, raw well data and geology were data obtained for three
wells from the onshore Niger delta oilfield. Microsoft Excel was used for
data loading, processing, plots/curves and other computations. These data
were used to generate suites of logs such as depth, gamma ray, density and
other necessary data. Figure 2 presents the research workflow. Data were
loaded, conditioned and processed with Microsoft Excel. Sand and shale
lithologies were identified. Sonic (s/ft), Vp (m/s), Vs (m/s),  (kg/m3),
Porosity (%) and permeability (mD) was determined. The dominant
lithology at the top of the reservoir was noted as shale with API value
greater than 65; the dominant lithology in the reservoir was sand with API
values less than 65. Software used was Microsoft Excel most suitable
package.
4. RESULT AND DISCUSSION
4.1 Results
In order to determine permeability, three wells were analyzed in this
research. Figures 3 to 8 show the results; a page of the tabulated result for
each well is presented in Tables 1 to 3.
Figure 2: Research Workflow
Table 1: Well A velocity information and other parameters
S/N
Depth (ft)
Sonic (s/ft)
Vp (m/s)
Vs (m/s)
 (kg/m3)
Porosity (%)
1
5900
0.000126
2420.635
1479.294
2245.2
15.27547
2
5910
0.000127
2401.575
1467.648
2269.7
14.35094
3
5920
0.000127
2401.575
1467.648
2216.9
16.3434
4
5930
0.000125
2440
1491.126
2258.5
14.77358
5
5940
0.000114
2675.439
1634.979
2307.7
12.91698
6
5950
0.000111
2747.748
1679.16
2277.1
14.0717
7
5960
0.000118
2584.746
1579.566
2317.5
12.54717
8
5970
0.000115
2652.174
1620.764
2318.7
12.50189
9
5980
0.000131
2328.244
1422.843
2246.3
15.23396
10
5990
0.000111
2747.748
1679.16
2260.2
14.70943
11
6000
0.000104
2932.692
1792.161
2119.1
20.03396
12
6010
0.000107
2850.467
1741.922
2123.9
19.85283
13
6020
0.000109
2798.165
1709.965
2122.6
19.90189
14
6030
0.000104
2932.692
1792.161
2147.2
18.97358
15
6040
0.000104
2932.692
1792.161
2134.8
19.44151
16
6050
0.000108
2824.074
1725.795
2178.3
17.8
17
6060
0.000116
2629.31
1606.795
2102.1
20.67547
18
6070
0.000109
2798.165
1709.965
2102.9
20.64528
19
6080
0.000108
2824.074
1725.795
2122.2
19.91698
20
6090
0.000102
2990.196
1827.296
2118.2
20.06792

Cite the A rticle:
Umor en, E.B.,
Atat, J.G., Aka nkpo, A.O ., Uzoewu lu, R.O. (2024). Det erminatio n of Per meability and Velo city
Infor mation of Oil Rese rvoir Usi ng Well Lo g Data (S-Fi eld).
Mala ysian Jo urnal of Geosciences, 8(2): 47-52.
Malaysian Journal of Geosciences (MJG) 8(2) (2024) 47-52
Table 2: Well B velocity information and other parameters
S/N
Depth (ft)
Sonic (s/ft)
Vp (m/s)
Vs (m/s)
 (kg/m3)
Porosity (%)
1
6560
0.0001
3050
1863.836
2327.2
12.1811321
2
6570
0.000103
2961.165
1809.558
2170.5
18.0943396
3
6580
0.000106
2877.358
1758.352
2134
19.4716981
4
6590
0.000106
2877.358
1758.352
2128.5
19.6792453
5
6600
0.000105
2904.762
1775.096
2128.4
19.6830189
6
6610
0.000109
2798.165
1709.965
2168.7
18.1622642
7
6620
0.000106
2877.358
1758.352
2082.9
21.4
8
6630
0.000103
2961.165
1809.558
2073.9
21.7396226
9
6640
0.0001
3050
1863.836
2034.5
23.2264151
10
6650
0.000102
2990.196
1827.296
2073.5
21.754717
11
6660
0.000109
2798.165
1709.965
2183
17.6226415
12
6670
0.000109
2798.165
1709.965
2265.3
14.5169811
13
6680
0.00011
2772.727
1694.423
2118.3
20.0641509
14
6690
0.000117
2606.838
1593.064
2136.9
19.3622642
15
6700
0.000101
3019.802
1845.385
2121
19.9622642
16
6710
0.000104
2932.692
1792.161
2012.6
24.0528302
17
6720
0.000096
3177.083
1941.484
2072.2
21.8037736
18
6730
0.000094
3244.681
1982.786
2041.2
22.9735849
19
6740
0.0001
3050
1863.836
2056.2
22.4075472
20
6750
0.000101
3019.802
1845.385
2085.4
21.3056604
Table 3: Well C velocity information and other parameters
S/N
Depth (ft)
Sonic (s/ft)
Vp (m/s)
Vs (m/s)
 (kg/m3)
Porosity (%)
1
7100
8.88E-05
3434.197
2098.581
2340.1
11.6943396
2
7110
8.88E-05
3434.197
2098.581
2355.4
11.1169811
3
7120
8.03E-05
3797.585
2320.611
2459.9
7.17358491
4
7130
9.21E-05
3310.705
2023.127
2300.3
13.1962264
5
7140
8.79E-05
3469.004
2119.847
2250.7
15.0679245
6
7150
8.92E-05
3419.835
2089.805
2319
12.490566
7
7160
9.19E-05
3317.789
2027.455
2264.9
14.5320755
8
7170
9.08E-05
3359.405
2052.882
2207.2
16.709434
9
7180
9.24E-05
3302.524
2018.128
2251.8
15.0264151
10
7190
8.99E-05
3392.089
2072.852
2277.3
14.0641509
11
7200
9.49E-05
3212.988
1963.422
2194.6
17.1849057
12
7210
9.31E-05
3277.392
2002.773
2187.6
17.4490566
13
7220
9.2E-05
3316.064
2026.402
2172.3
18.0264151
14
7230
9.41E-05
3242.842
1981.663
2323.4
12.3245283
15
7240
9.09E-05
3353.963
2049.558
2238.8
15.5169811
16
7250
8.81E-05
3461.802
2115.447
2234.3
15.6867925
17
7260
8.57E-05
3557.469
2173.9
2319.3
12.4792453
18
7270
8.7E-05
3506.904
2143.005
2212.7
16.5018868
19
7280
9.36E-05
3257.562
1990.657
2228.4
15.909434
20
7290
8.2E-05
3718.882
2272.523
2357.6
11.0339623
Figure 3: Well Log Information (green for sonic and red for gamma) of Well A indicating sand and shale lithology.

Cite the A rticle:
Umor en, E.B.,
Atat, J.G., Aka nkpo, A.O ., Uzoewu lu, R.O. (2024). Det erminatio n of Per meability and Velo city
Infor mation of Oil Rese rvoir Usi ng Well Lo g Data (S-Fi eld).
Mala ysian Jo urnal of Geosciences, 8(2): 47-52.
Malaysian Journal of Geosciences (MJG) 8(2) (2024) 47-52
Figure 4: The result of porosity (purple), permeability (brown) and sonic (green) obtained from sand/shale formation of well A.
Figure 5: Well Log Information (green for sonic and red for gamma) of Well B indicating sand and shale lithology.
Figure 6: The result of porosity (purple), permeability (brown) and sonic (green) obtained from sand/shale formation of well B.

Cite the A rticle:
Umor en, E.B.,
Atat, J.G., Aka nkpo, A.O ., Uzoewu lu, R.O. (2024). Det erminatio n of Per meability and Velo city
Infor mation of Oil Rese rvoir Usi ng Well Lo g Data (S-Fi eld).
Mala ysian Jo urnal of Geosciences, 8(2): 47-52.
Malaysian Journal of Geosciences (MJG) 8(2) (2024) 47-52
Figure 7: Well Log Information (green for sonic and red for gamma) of Well C indicating sand and shale lithology.
Figure 8: The result of porosity (purple), permeability (brown) and sonic (green) obtained from sand/shale formation of well C
4.2 Discussion
Well-log data were obtained from wells A, B and C and analyzed to
determine permeability of oil reservoir. Microsoft Excel was used for the
processing and computation of the results. The results were achieved after
spurious values have been removed from the data. Figures 3, 5 and 7 were
generated in order to identify sand lithology with API index less than 65
and shale lithology whose API is greater than 65. This information enables
the identification of the portions of interest and concentrate on these
reservoir thicknesses. Density, gamma ray and sonic with depth curves
were obtained. Compressional wave velocity was determined from the
sonic data; Equation 6 was used to calculate the shear wave velocity.
Density was converted to system international unit. Tables 1, 2 and 3 show
the results of compressional and shear wave velocities with their
corresponding depths. Porosity was estimated using Equation 4 and
Equation 1 was adequate for the determination of permeability. Figures 4,
6 and 8 have this information for wells A, B and C respectively.
The thicknesses of sand/shale formation have been marked as 1500ft
(5900 to 7400ft), 840ft (6560 to 7400ft) and 590ft (7100 to 7690)
corresponding to wells A, B and C. The lowest porosity value of well A is
10.2717% and the highest is 24.26038%, resulting in the average of
17.26604%. This classifies the pores space information as good. Well B has
the lowest porosity of 18.18113% and 27.47925% as the highest. The
average porosity of this well is 22.83019% belonging to the good class. The
lowest and highest values of porosity correspond to 3.211321% and
23.49057% for well C. The average value of porosity noted from well C is
13.35095%. It shows that it is permeable but not reasonably porous as it
belongs to a fair class.
Permeability as earlier stated is reasonable if it has values ranging from
100 to 500mD for a petroleum reservoir rock. The value obtained in this
research as the lowest is 24618.48D and the highest value is 137332.00D
for well A. The average permeability of this well with respect to the
marked thickness is 80975.24D. The lowest and highest value values from
well B are 34622.00D and 176192.10D respectively. Well B has the
average permeability of 105407.10D. Well C information on permeability
is as stated: Lowest value = 2406.27D, highest value = 128754.50D and the
average = 65580.38D. It is observed that the permeability results
determined are in the reasonable and accepted value of its ability to
migrate and accumulate petroleum as porosity information is also
appreciable. The connectivity of pores is adequate. The velocity
information in Tables 1 – 3 are necessary for further investigation of the
rock elastic properties.
5. CONCLUSION
Permeability has been determined using well-log data. Well C has the
highest average value of 97626.33D, well B has 71788.42D and well A has
the lowest average value of 52961.35D. These results are within

Cite the A rticle:
Umor en, E.B.,
Atat, J.G., Aka nkpo, A.O ., Uzoewu lu, R.O. (2024). Det erminatio n of Per meability and Velo city
Infor mation of Oil Rese rvoir Usi ng Well Lo g Data (S-Fi eld).
Mala ysian Jo urnal of Geosciences, 8(2): 47-52.
Malaysian Journal of Geosciences (MJG) 8(2) (2024) 47-52
reasonable value for a petroleum reservoir rock. The average porosity
value obtained for the three wells is 17.33481% which is an indication of
a good class. Therefore, the reservoir of wells A, B and C can accumulate
and transmit or migrate fluids. The velocity information obtained would
aid other investigation on the rock elastic properties.
ACKNOWLEDGMENTS
Acknowledgement is made to the competent Reviewers for their inputs.
The Authors also thank the Editorial board of this Journal for the
acceptance and publication of this research article without any publication
fees.
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