Different types of limestone (including chalk, travertine, marble, wacke stone and packstone-grainstone) commonly used as building stones in Jordan with porosity ranging from around 1% to less than 30% have been covered in this study. The total porosity has been split into matrix and secondary porosity. Types (fracture/moldic) and amounts of secondary porosity have also been defined. The relationships of the different porosity types with the other measured or derived properties have been delineated using correlation. Mathematical formulae have been presented to derive complicated or difficult to measure properties from easily measured ones. As indicated by the calculated cementation exponent value m and documented petrographically, tight limestones are dominated by fracture porosity, whereas highly porous limestones are dominated by moldic porosity. This is well exemplified by Siwaqa travertine where vugs are dominant in the high porosity varieties and fractures in the low porosity samples. Practical implications of the present work and its limitations have also been discussed.
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Sound propagation and porosity of limestone have many economic applications in the exploration and exploitation of mineralized ores (and their mining), construction materials and oil and water (Anderson and Nevenst, 1952; Wantland, 1953; Mamillan, 1954; Sutherland, 1962; Belikov, 1967; Duncan, 1969; Griffiths and King, 1969; Atkinson, 1970; Fourmaitraux, 1976; Bell, 1980; Goodman, 1980; Christensen, 1982; Leary, 1983; North, 1985; Odent, 1993; Gueguen, 1994; Mohd, 1996).
The term total porosity was used in this work to indicate the porosity measured in the laboratory using a vacuum pump (without pulverizing the sample) and to differentiate it from other types of porosity mentioned in the text, although it is known that the only true total porosity is that obtained by pulverizing the sample (Brown, 1981).
Porosity is defined as the percentage of voids in a rock to its total volume (including solid and voids). Unfortunately, in many practical applications including fluid flow in rock, as well as, many technical and industrial problems total porosity alone is not sufficient to give complete and satisfactory answers for many questions. Consequently, there is a need to know the type of porosity present along with its amount.
Carbonates as nearly as all other sedimentary rocks, have high values of porosity at the time of their formation referred to as primary porosity where the pores usually occur between their particles or crystals. With progress of time, the passage of solutions through the rock occasionally may diminish its porosity to less than 5%, as is the case in marbles and tight limestones. Tectonic and dissolution diagenetic processes may lead to fracture and vug porosities. This type of porosity, which forms long after the rocks deposition, is referred to as secondary porosity. For further details on the classification of limestone porosity refer to Choquette and Pray (1970).
Microcracks can be introduced into, or removed from, a rock by a variety of processes. Some processes such as pressure relief from erosion, meteorite shock impact and cementation from circulating water have a geological cause. Other processes could be due to drilling, hammering or blasting. Despite its importance, there is, so far, little convincing and easy to carry out quantitative work on microcrack characterization (Edet, 1992). However, the research of Aguilera and Aguilera (2003) used seems to be a breakthrough in this field. Using total porosity and cementation exponent, it can quantify the fracture and moldic porosities. The dual porosity concept, a simple version of Aguilera and Aguilera (2003) in comparison with the triple porosity model was used in the present study.
In developing countries, such as Jordan, where sophisticated laboratory tests are rarely performed due to lack of facilities, there is the need to develop simple estimation schemes by which different porosity types and quantities are defined. This will be of importance for exploration projects for oil, water and minerals currently carried out in Jordan mainly by the National Oil Company, Water Authority and Natural Resources Authority. In this context, the present author (Mohd, 2002) has previously published a paper on deriving some pore-related properties from water absorption and water saturation.
The present research aims at characterizing the secondary porosity of the studied limestones into fracture and moldic (vuggy) types along with their amounts using only Vp, total porosity and water saturation. Of course, for calculating the cementation exponent m, there is a need to know water resistivity (Rw). This value was assumed to be 0.005 ohm m.
MATERIALS AND METHODS
The geology of Jordanian building stones is summarized in Table 1 and the petrography of those selected for the present study is shown in Table 2 (Mohd, 2002). The petrographic nomenclature is following one or more of the following: Folk (1959, 1962), Dunham (1962) and Fookes and Higginbottom (1975).
The porosity, degree of saturation and sound velocity (Vp) tests were carried out at BRE (UK) and NRA (Jordan) following the BRE testing procedures (Ross and Butlin, 1989).
Derived properties include
Modified saturation: This was obtained by multiplying total porosity with degree of saturation.
Cementation exponent m: This was calculated using Archie formula and assuming that water resistivity as 0.005 where m = log (0.005/water saturation squared)/log total porosity. This parameter can also be estimated from total and sonic porosity for fractured (Rasmus, 1983) and vuggy carbonates (Nugent, 1983).
Permeability: Was obtained using Jorgensen (1988) equation by multiplying 84105 by porosity index = Φm+2/(1-Φ)2. The obtained values were found to correlate well with measured air permeability using API standards.
Sonic porosity: Is equivalent to velocity of sound-141/ (28.59); where 28.59 is the inverse of 100/(3000-141); 141 and 3000 are transit time (in μ s/m) in calcite crystal and air, respectively.
Vug porosity and Fracture porosity: Are estimated from the dual porosity chart of Aguilera and Aguilera (2003).
Matrix porosity: Is the total porosity minus the sum of vug and fracture porosities.
Dry density: Is calculated using the following equation
Dry density = grain density (1-fractional porosity)
Test results of measured and derived properties are summarized in Table 3. The studied stones are arranged in ascending order based on the value of their cementation exponent m. The lower part of Table 3 is a correlation matrix for the different studied properties.
|Table 1:||Stratigraphy of Cretaceous to early Tertiary in Jordan|
|*Units with good potential as sources of building stones|
|Table 2:||Petrographic classification of the stones studied|
|? Classes not known in Folk or Dunhams classifications|
|Table 3:||Measured and derived properties of the studied stones listed and correlated|
|Table 4:||A list of significant relationships seen in the correlation matrix and illustrated in Fig. 1 to 17|
|Fig. 1:||Deriving sonic porosity from Vp|
|Fig. 2:||Deriving vug porosity from Vp|
|Fig. 3:||Vp versus total porosity|
|Fig. 4:||Vp versus modified saturation|
|Fig. 5:||Vp versus cementation exponent (m)|
|Fig. 6:||Vp versus matrix porosity|
|Fig. 7:||Deriving secondary porosity from total porosity|
|Fig. 8:||Deriving secondary porosity from total porosity|
|Fig. 9:||Deriving modified saturation from total porosity. Area below best-fit line represents bimodal and polymodal pores|
|Fig. 10:||Deriving matrix porosity from total porosity|
|Fig. 11:||Deriving vug porosity from total porosity|
|Fig. 12:||Deriving sonic porosity from total porosity|
|Fig. 13:||Deriving fracture porosity from degree of saturation|
|Fig. 14:||Deriving cementation exponent M from modified saturation|
|Fig. 15:||Deriving secondary porosity from modified saturation|
|Fig. 16:||Deriving sonic and matrix porosity from modified saturation|
Significant correlations between different parameters as seen in the correlation matrix assume linear best-fit lines (better in case of non-linear relationships) are plotted in Fig. 1 to 17 and summarised in Table 4.
|Fig. 17:||Deriving secondary porosity from cementation exponent M|
When there is no secondary porosity, values of cementation exponent (m) will be equal to or around 2 indicating inter-particle or inter-crystalline porosity. Consequently, the total porosity will be wholly of the matrix type. When m values are less than 2 then part of the total porosity will be secondary and of fracture type, whereas, m values much higher than 2 reflect the existence of secondary porosity in the form of moldic or vuggy porosity. Lucia (1983) considered that the higher the value of m above 2, the higher the ratio of separate vug porosity to total porosity. An idea about the uni- or bi-modality of pore-size distribution can be easily gained from plotting modified saturation against total porosity (Fig. 9). Modified saturation used in the present work is the same as bulk water used in petroleum engineering literature. It is important here to mention that the relationships achieved to in the present work are restricted to clean limestones (with very little dolomite, quartz or clay) and should not be generalized to other lithologies without further experimental work. Also, the database is very small and to be generalized for other areas much larger data bases are needed to check the validity of conclusions arrived at during this work. The importance of the present work lies in pinpointing parameters that have strong correlations with other difficult to measure parameters.
In case of clean limestone and when it is difficult to have access to sophisticated equipment the easiest parameter to measure is bulk density, which can be inverted to total porosity (Mohd, 2002). This can be used to derive cementation exponent, secondary, matrix and vug porosity, as well as, modified saturation. Water saturation can be obtained from total porosity and modified saturation and consequently fracture porosity may be derived. Fracture porosity can also be calculated by subtracting the sum of matrix and vug porosity from total porosity. Permeability can be estimated from total porosity and cementation exponent using Jorgensens (1988) equation.
Despite its limited size, the present database shows that some easily measured parameters can be used in deriving other parameters with correlation coefficients mostly more than 0.9. Thus, Vp can be used to derive sonic porosity and similarly total porosity can give cementation exponent, secondary, matrix and vug porosity, as well as, modified saturation. The latter can be used to derive cementation exponent, secondary and matrix porosities. Degree of saturation is a good indicator of fracture porosity.
There is a need of larger database to check the validity of relationships deduced by the present study and to restrict its use to clean limestone.
- Aguilera, M.S. and R.F. Aguilera, 2003. Improved models for petrophysical analysis of dual porosity reservoirs. Petrophysics, 44: 21-35.
- Choquette, P.W. and L.C. Pray, 1970. Geologic nomenclature and classification of porosity in sedimentary carbonates. AAPG Bull., 54: 207-250.
- Folk, R.L., 1959. Practical petrographic classification of limestone. AAPG Bull., 43: 1-38.