Characterization of Density and Porosity of Rocks Samples from Ogun State of Nigeria

Knowledge of densities of rocks is essential in petrological and geological studies, interpretation of gravity anomalies and ground water exploration. Fifty samples were collected from Abeokuta, Sagamu, Odeda, Ewekoro, Ibese Yewa North Local Government, Ijebu East Local Government and Obafemi Owode in Ogun State and dry bulk density, saturated density, porosity and particle density were determined. Results showed that Ewekoro shale has the lowest mean density of 1.35g/cm while Ibese, Yewa North Local Government limestone has the highest mean density of 3.9g/cm.Porosity ranges from 0.030 to 0.640 with the granite in Odeda local government having the highest porosity and the shale in Ewekoro local government having the lowest porosity. Mean porosity for all the rocks samples in the seven Local Government Areas was 0.34. Test of significance revealed that there is significant relationship in the values of density of rock samples within the state.


Introduction
In geology, rock density has particular value as a theme that connects the properties of minerals and rocks to topics such as seismic velocity, isostasy and porosity (Robert and Robert, 2000).According to Caravaca et al. (2001) and Shrestha et al. (2007) study of bulk density, particle density, saturated density, porosity, organic matter content and size distribution of soil samples from an area reveal some vital soil physical properties of the area.Knowledge of densities of rocks is essential in petrological and geological studies and more so for a meaningful structural interpretation of gravity anomalies Ajakaiye (1975).It was also stated by Horgan (1996) that the gravity reduction is computed by taking the density as a constant (2.67g/cm 3 ) which represents the topographical density.
The effect of density on porosity follows a mixing law.The porosity, φ, is the fractional pore volume of a rock.The total mass of a volume of rock V T is made up of the mass of the pore fluid, of density , plus the mass of the matrix minerals of density ρ ma the density measured is the bulk density .
The total mass then becomes: which gives a formula for the bulk density in terms of the porosity, pore fluid density and the matrix density.The mixing law for density is given as follows: From the mixing law we can then find the porosity via: (3)

Geology of Study Area
Ogun State is entirely in the tropics, located in the Southwest Zone of Nigeria with a total land area of  (1979).
The sedimentary rock unit of Ogun state consists of Abeokuta formation lying directly above the basement complex.This is in turn overlain by Ewekoro, Oshosun and llaroformations, which are themselves overlain by the coastal plain sands (Benin formation).The flood plains of the major rivers and streams are covered by the alluvial sands (Kehinde, 1992).Using an electronic weighing balance, 20g of rock samples were collected in 50 different crucibles and each crucible was labeled according to the sample description.The rock samples were heated in an oven at a temperature of 100 o C for 18 hours and later weighed separately in air (w d ) and in water (w w ) (after adding 40ml of water to the samples).The samples were then saturated in water for 24 hours and weighed again in water (w s ) and in air (w t ).The weight in air after saturation (w t ) was measured by draining off the water remaining in the crucible and then weighing, using an electronic balance.
From the results obtained, that is, the value of W d , W w , W t and W s , the dry bulk density (ρ d ), saturated density (ρ s ) and particle or grain density (ρ g ) for the fifty rock samples was calculated using the following mathematical expression (Ajakaiye, 1975).

Results
Table 1 shows the densities of the fifty rock samples collected from the different locations of the study areas.
Table 2 is the Analysis of variance of studied parameters while Table 3 shows the mean densities and porosity of the rock samples.
The map of Ogun State within which the study areas located is shown in Figure 1. Figure 2   Obafemi-Owode was 1.48g/cm 3 .From Figures 2 and 3, granite in Odeda LGA has the highest dry bulk density (3.12 g/cm 3 ) among rocks samples while shale in Ewekoro LGA has the lowest dry bulk density (1.00 g/cm 3 ).

Saturated Density
Saturated density of granite from Odeda LGA ranges from 1.85g/cm 3 to 7.61g/cm 3 while the saturated density of pegmatite ranges from 1.22g/cm 3 to 2.20g/cm 3 .Quartzite from Odeda has its saturated density determined to be 2.43g/cm 3 , while the saturated density of the limestone from Sagamu ranges from 1.82g/cm 3 to 2.76g/cm 3 .The saturated densities of limestone and shale in Ewekoro LGA range from 1.95g/cm 3 to 3.40g/cm 3 ,and from 1.61g/cm 3 to 2.19g/cm 3 respectively.In Yewa North LGA saturated density of limestone ranges from 2.26g/cm 3 to 2.38g/cm 3 , while granites from Ijebu East LGA have saturated density ranging from 1.45g/cm 3 to 1.94g/cm 3 .Two rock types collected In Obafemi-Owode were granite and kaolin.The saturated density of granite in Obafemi-Owode ranges from 2.05g/cm 3 to 3.13g/cm 3 , while for kaolin in the same Local Government, saturated density was determined as 2.16g/cm 3 .Analysis of samples from Abeokuta North LGA shows that granite has the highest saturated density of 2.37g/cm 3 followed by quartzite, kaolitic clay and feldspar with 1.78g/cm 3 .Figures 1 to 8 revealed that granite has the highest and lowest saturated density among all rock samples considered.Granite with highest saturated density (3.5 g/cm 3 ) was in Odeda LGA while the one with least value (1.45 g/cm 3 ) was found in Ijebu East LGA.

Particle Density
Particle densities of granite and pegmatite in Odeda LGA range from 1.85g/cm 3 to 7.63g/cm 3 and from 3.40g/cm 3 to 3.66g/cm 3 respectively, while particle density for quartzite in the same LGA was 3.76g/cm 3 .The particle density of the limestone in Sagamu LGA ranges from 2.90g/cm 3 to 3.92g/cm 3 , while the particle density of limestone In Ewekoro LGA ranges from 2.00g/cm 3 to 3.44g/cm 3 .The particle density of shale from Ewekoro LGA ranges from 1.72g/cm 3 to 4.96g/cm 3 , while particle density of limestone from Yewa North LGA ranges from 3.74g/cm 3 to 4.10g/cm 3 .Particle density of granites from Ijebu East ranges from 2.30g/cm 3 to 3.18g/cm 3 , while the particle density of granite from Obafemi-Owode ranges from 3.18g/cm 3 to 3.90g/cm 3 .The particle density of kaolin for Obafemi-Owodewas 2.96g/cm 3.In Abeokuta North LGA, granite has the highest particle density of 3.80g/cm 3 followed by quartzite, kaolitic clay and feldspar with 2.48g/cm 3 .Figures 1 to 8 revealed that particle density was consistently high for all rocks from the state.It also shows that granite from Obafemi-Owode LGA has the highest particle density (3.9g/cm 3 ) among all rock samples, while shale from Ewekoro LGA has the least particle density (1.72 g/cm 3 ).

Porosity
Mean porosity of granite from Odeda LGA was determined to be 0.341.For the pegmatite rock samples, the mean porosity was 0.302 while the mean porosity of all the rock samples in Odeda LGA was found to be 0.302.In Odeda LGA granite rock samples has the highest (0.640) and the lowest (0.088) porosity.The porosity of five samples of limestone rock from Sagamu LGA ranges from 0.060 -0.453, while mean porosity was 0.321.The four different rock samples from Abeokuta North LGA are; Quartzite, kaolictic clay, feldspar and two granite rock samples with porosity of 0.392, 0.509, 0.532, 0.336 and 0.268 respectively.It is clearly seen that the granite samples have lowest porosity when compared to other rock samples for this area.The mean porosity for the local government area was 0.407.Mean porosity of limestone and shale from Ewekoro LGA was 0.354 while the mean porosity of limestone and shale rock samples was 0.396 and 0.312 respectively.The porosity of limestone rock samples ranges from 0.351 -0.453 while that of shale ranges from 0.030 -0.623.The highest and lowest porosity was recorded by shale in this local government area.The porosity of granite from Obafemi-Owode LGA ranges from 0.264 -0.316.The mean porosity for the granite was 0.316; the porosity for the Kaolin rock sample was 0.442.The mean porosity of all the rock samples collected in this area was 0.330.
Considering the mean porosity of all the seven local government areas, the mean porosity ranges from 0.302 -0.472.The lowest mean porosity (0.302) was in Odeda local government area while the highest porosity (0.472) was in Ijebu-East local government area.Figures 1 to 8 compared the porosity of the samples and place of origin, it can be deduced that granite from Odeda LGA has the highest porosity (0.64) while shale from Ewekoro LGA has the least porosity (0.03).

Test of Significance
To test the trend of the densities and porosity in seven selected local government areas, null hypothesis, Ho and alternative hypothesis, H1 were set for saturated density as follows: Ho: There is no significant trend between saturated densities obtained from seven Local Government Areas H1: There is significant trend between saturated densities obtained from seven Local Government Areas From Table 2, F RATIO (0.718) calculated for saturated density is greater than F TABULATED (0.637) at 5%, therefore suggesting that there is significant relationship between saturated densities obtained within the state.
Similarly for dry bulk density and particle density significant relationships exist between the dry bulk densities and also between the particle densities within the state.This is because F RATIO (1.408) of dry bulk density is greater than F TABULATED (0.637) and also F RATIO (0.896) of particle density is greater than F TABULATED (0.506).
Figure 2 also revealed that F RATIO (1.002) calculated for Porosity is greater than F TABULATED (0.436) at 5% which suggests that there is significant relationship between porosity within the state.

Conclusion
The Limestone rock sample from Ibese, Yewa North Local Government area has the highest mean density value of 3.9g/cm 3 while the shale rock sample from Ewekoro has the lowest mean density of 1.35g/cm 3 .The highest porosity was from granite in Odeda local government area with a value of 0.640 and the lowest porosity was from Shale in Ewekoro Local Government Area.The mean porosity of all the rock samples is 0.34 which shows that all the location does not have the same mean porosity when one location is compared with the other locations.It was observed that significant relationship exists between densities within the state, as well as between porosity within the state.

Figure 1 .
Figure 1.Geological Map of Ogun State

Figure 2 .
Figure 2. Bar chart of densities and porosity of samples from Odeda LG

Table 1 .
The densities of the fifty rock samples collected from the selected locations are given below is the bar chart of the dry bulk density, saturated density, particle density and porosity of the rock samples taken from Odeda Local government area.The samples collected from Odeda local government area are pegmatite, granite and quartzite.Figure3is the bar chart of saturated density, dry bulk density, particle density and porosity of limestone being the only rock samples collected from Sagamu LGA.Figures4, 5, 6, 7 and 8 are the bar charts showing the dry bulk density, saturated densities, particle density as well as porosity of rock samples respectively from Abeokuta North, Ewekoro, Yewa North ,Ijebu East and Obafemi-Owode local government area.Rock samples from Abeokuta North are quartzite, kaolin, feldspar and granite while limestone and granite were taken from Yewa North and Ijebu East Local Government Area.Also granite and kaolin were collected from Obafemi-Owode local government area and limestone and shale from Ewekoro Local Government Area.

Table 2 .
Table of the analysis of variance of studied parameters

Table 3 .
The table below shows the mean densities of the rock samples