where Vv is the volume of voids (pores), VT is the total (bulk) volume, and VS is the volume of the solids. Note that porosity is a dimensionless quantity.
Void Ratio (commonly used in engineering) (also dimensionless)
Exercise to do: express the void ratio as a function of total porosity.
Another definition of porosity as a function of dry bulk density and solids density
Solids densities of some common (and less common) mineral groups (in g/cm3)
quartz and feldspars 2.6-2.7
calcite and dolomite 2.7-2.8
amphiboles and pyroxenes 2.9-3.9
Another exericse: show that
Wet bulk density
Note that the density of water is 1 g/cm3 or 1 g/ml.
Final exercise: derive an equation for total porosity as a function of wet bulk density and dry bulk density.
II. Factors affecting porosity of unconsolidated materials.
Note that Table 3.1 in S&Z suggests that porosity increases with decreasing grain size. But size alone cannot explain this (as was illustrated by cubes filled with different size marbles).
A. Packing - see figure 3.2 in S&Z (theoretical values for cubic packing of spheres is about 48%, for hexagonal closest packing about 26%).
B. Sorting - well sorted (or poorly graded) sediments tend to have higher porosity than poorly sorted (well grades) sediment because with a range of grain sizes the small grains can fill pores.
C. Shape - platy clasts such as clays can form highly porous "house-of-cards" type deposits, although these can be rearranged and compacted during burial or dewatering. Angularity of larger clasts can also affect packing and porosity.
III. Precision, Accuracy and Significant Digits (information that you will need for labs and problems this semester)
Precision of measurements depends on the resolution of the measuring tool (smallest increment that can be read on a ruler, smallest unit of mass on a scale, etc.)
Accuracy refers to how well the measured value approximates the true value, and depends on calibration of the measuring instrument.
A measurement may be precise but inaccurate, or accurate but not very precise. (Of course we would like our measurements to be both accurate and precise.) Measurement error, uncertainties associated with assumptions, and round-offs during calculations can also affect the precision and accuracy of a result.
When making a series of calculations and expressing results to the correct number of significant digits (essentially an issue of "precision") there are three basic rules.
1. For addition or subtraction, the result should be rounded to the decimal unit of the number that terminates with a significant digit farthest to the left (largest value). For example, adding 1.15 (significant to the .01 position) to 100 (significant to the 1 position), the answer should be rounded to 101, not 101.15.
2. For multiplication or division, the result should be rounded to include only number of the significant digits in the measured value with the least signficant digits. For example, multiplying 100 (3 sig. dig assuming significant to the 1 position) by 1.1 (2 sig dig assuming significant to the 0.1 position), the answer should be expressed as 1.1 x 10^2 (indicating 2 signficant digits).
3. Carry all digits through multistep calculations and round at the end of the process to avoid introducing additional round-off errors.
IV. Pores in rocks (illustrated by slides, see also Fig. 3.1 in S&Z and Table 3.1
Primary and Secondary Porosity
Primary porosity (as defined in class) results from the intial processes that deposited sediments or formed rocks from liquid magma. Primary porosity can be reduced by cementation, compaction.
Secondary porosity (e.g. fractures,dissolution features) results from processes that occurred after the rocks formed.
1. Pores and fractures in "sandstone" (actually also includes other sedimentary rocks too).
This contain both primary and secondary porosity. Permeability may be due to either primary or secondary pore network, or both. Fracturing may be more intense in folded sedimentary rocks.
2. Solution openings in carbonate (and sometimes evaporite) rocks. Solution openings create high permeability.
3. Fractures and other openings in basalt. These include cooling cracks, vesicles and lava tubes. All these are considered primary porosity and can create high permeability.
4. Fractures in crystalline igneous and metamorphic rocks. These rocks have virtually no primary porosity and are generally of low permeability.
V. Effective porosity - refers to the interconnected pore space. Table 3.2 of S&Z indicates that this can be much lower than total porosity.