{"id":74,"date":"2020-10-11T04:23:40","date_gmt":"2020-10-11T04:23:40","guid":{"rendered":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/?post_type=chapter&p=74"},"modified":"2020-12-29T16:14:35","modified_gmt":"2020-12-29T16:14:35","slug":"total-porosity","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/chapter\/total-porosity\/","title":{"raw":"3.1 Total Porosity","rendered":"3.1 Total Porosity"},"content":{"raw":"Water below the land surface occurs in the spaces between solid particles of sediment and within fractures of rocks (Figure 3<\/a>). Total porosity<\/em> (n<\/em>) is the ratio of the volume of void space (V<\/em>V<\/em><\/small><\/sub>) in a sample of earth material to the total volume of the sample (V<\/em>T<\/em><\/small><\/sub>) including solids and void space. Total volume is enclosed within the entire box shown in Figure 3a<\/a>, while void volume includes only the blue zones. In some texts total porosity is referred to as porosity and both terms are used in this book. Total porosity is preferred here because of the need to distinguish it from effective porosity defined in this section.\r\n\r\nPorosity can be represented as a fraction of the total volume as shown in Equation 2, or as a percentage (if multiplied by 100%).\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle n=\\frac{V_V}{V_T}[\/latex]<\/td>\r\n(2)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nwhere:\r\n\r\n\r\n\r\n\r\n\r\n
n<\/em><\/td>\r\n=<\/td>\r\ntotal porosity (dimensionless)<\/td>\r\n<\/tr>\r\n
V<\/em>V<\/em><\/small><\/sub><\/td>\r\n=<\/td>\r\nvolume of void space in a sample (L3<\/sup>)<\/td>\r\n<\/tr>\r\n
V<\/em>T<\/em><\/small><\/sub><\/td>\r\n=<\/td>\r\ntotal volume of a sample (L3<\/sup>)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Measuring Porosity<\/h1>\r\nIt is difficult to measure the volume of voids directly. However, the relationship between sample density and total porosity provides a means of calculating the void volume because the bulk density of a sample is controlled by the proportion of solids and voids. That is, the bulk density<\/em> is equal to the fractional volume of solids (1 - n<\/em>) times the particle density<\/em> plus the fractional volume of voids (n<\/em>) times the fluid density<\/em>, as shown in Equation 3.\r\n\r\n\r\n\r\n
<\/td>\r\n\u03c1<\/em>b<\/em><\/sub> = (1 - n<\/em>) \u03c1<\/em>p<\/em><\/sub> + n \u03c1<\/em>f<\/em><\/sub><\/td>\r\n(3)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nwhere:\r\n\r\n\r\n\r\n\r\n\r\n\r\n
\u03c1<\/em>b<\/em><\/sub><\/td>\r\n=<\/td>\r\nbulk density (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
n<\/em><\/td>\r\n=<\/td>\r\ntotal porosity (dimensionless)<\/td>\r\n<\/tr>\r\n
\u03c1<\/em>p<\/em><\/sub><\/td>\r\n=<\/td>\r\nparticle density (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
\u03c1<\/em>f<\/em><\/sub><\/td>\r\n=<\/td>\r\nfluid density (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThus, the total porosity can be computed if the bulk density (\u03c1<\/em>b<\/em><\/sub>) of the sample is determined for either a fully saturated or a fully dried sample, and the fluid density (\u03c1<\/em>f<\/em><\/sub>) as well as the particle density (\u03c1<\/em>p<\/em><\/sub>) of the dominate mineral material making up the matrix (solid particles) of the sample are known, as shown in Equation 4. Typically, the fluid is air or water, so the fluid density is known.\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle n=\\frac{\\rho_b-\\rho_p}{\\rho_f-\\rho_p}[\/latex]<\/td>\r\n(4)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nTo determine the total porosity of a sample, the sample volume can be measured by fully saturating the sample then immersing it in water and noting the volume of displaced fluid. Then, the wet bulk density is determined by weighing the saturated sample and dividing that weight by the volume. When water is the fluid, the density is assumed to be 1 gram per cubic centimeter (g\/cm3<\/sup>), because this is its density at 4\u00b0C and the density does not noticeably change in the range of temperatures experienced in the field and lab. If the sample is dried and then weighed, the dry bulk density can be used to calculate porosity by assuming the air filling the pores to have a fluid density of 0 g\/cm3<\/sup>.\r\n\r\nFor example, the porosity for a sample volume of one cubic centimeter of loose quartz sand can be computed knowing that the dry bulk density of the sand sample is 1.43 g\/cm3<\/sup> and the density of a corresponding cubic centimeter of solid quartz with no pore space (i.e., the composition of the sand grain) has a density of 2.65 g\/cm3<\/sup> as shown in Figure 6.\r\n\r\n \r\n\r\n[caption id=\"attachment_86\" align=\"alignnone\" width=\"683\"]\"Schematic Figure 6 -<\/strong> Schematic of: a) dry bulk density of 1 cubic centimeter of loose quartz sand; and, b) density of 1 cubic centimeter of solid quartz, which provides the particle density of the quartz sand grains.[\/caption]\r\n\r\nBy using Equation 4, the total porosity can be calculated as 0.46 or 46%, as shown in Equation 5.\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle n=\\frac{1.43\\frac{\\textup{g}}{{\\textup{cm}}^3}-2.65\\frac{\\textup{\\textup{g}}}{{\\textup{\\textup{cm}}}^3}}{0\\frac{\\textup{g}}{{\\textup{cm}}^3}-2.65\\frac{\\textup{g}}{{\\textup{cm}}^3}}=0.46[\/latex]<\/td>\r\n(5)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nFor additional information on the densities of earth materials, <\/a>Click here to link to Box 1<\/a>.\r\n

Values of Total Porosity<\/h1>\r\nTables of total porosity values for earth materials are included in publications provided by government agencies and researchers, as well as in hydrogeology textbooks. Examples of total porosity values for earth materials are presented in Table 1.\r\n\r\nGenerally, unconsolidated materials have higher porosities (20 to 55%) than consolidated sediments and igneous and metamorphic rocks. Though, some consolidated sedimentary rocks; and weathered and\/or fractured igneous and metamorphic rocks can also have high porosities. The porosity of vesicular basalt is a result of the degree of void creation during the solidification process.\r\n\r\n<\/a>Table 1 -<\/strong>Typical total porosity ranges of some common earth materials (after Rivera, 2014; with data from Freeze and Cherry, 1979 and Domenico and Schwartz, 1998).\r\n<\/small>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Total Porosity Range of Some Common Earth Materials (Percent)<\/strong><\/td>\r\n<\/tr>\r\n
Material<\/strong><\/td>\r\nRange Total Porosity (%)<\/strong><\/td>\r\n<\/tr>\r\n
Unconsolidated Sediments<\/strong><\/td>\r\n<\/td>\r\n<\/tr>\r\n
Clay<\/td>\r\n45 - 55<\/td>\r\n<\/tr>\r\n
Silt<\/td>\r\n35 - 50<\/td>\r\n<\/tr>\r\n
Fine-sand<\/td>\r\n26 - 50<\/td>\r\n<\/tr>\r\n
Coarse-sand<\/td>\r\n30 - 45<\/td>\r\n<\/tr>\r\n
Gravel<\/td>\r\n25 - 35<\/td>\r\n<\/tr>\r\n
Sand and gravel<\/td>\r\n20 - 30<\/td>\r\n<\/tr>\r\n
Glacial till<\/td>\r\n20 - 30<\/td>\r\n<\/tr>\r\n
Consolidated Sediments<\/strong><\/td>\r\n<\/td>\r\n<\/tr>\r\n
Shale<\/td>\r\n1 - 10<\/td>\r\n<\/tr>\r\n
Siltstone<\/td>\r\n20 - 40<\/td>\r\n<\/tr>\r\n
Sandstone<\/td>\r\n5 - 30<\/td>\r\n<\/tr>\r\n
Limestone and dolomite<\/td>\r\n1 - 25<\/td>\r\n<\/tr>\r\n
Karstic limestone<\/td>\r\n5 - 35<\/td>\r\n<\/tr>\r\n
Igneous and Metamorphic Rocks<\/strong><\/td>\r\n<\/td>\r\n<\/tr>\r\n
Fresh granite and gneiss<\/td>\r\n0.01 - 3<\/td>\r\n<\/tr>\r\n
Weathered granite and gneiss<\/td>\r\n5 - 25<\/td>\r\n<\/tr>\r\n
Fractured basalt<\/td>\r\n5 - 30<\/td>\r\n<\/tr>\r\n
Vesicular basalt<\/td>\r\n10 - 40<\/td>\r\n<\/tr>\r\n
Tuff<\/td>\r\n10 - 55<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>","rendered":"

Water below the land surface occurs in the spaces between solid particles of sediment and within fractures of rocks (Figure 3<\/a>). Total porosity<\/em> (n<\/em>) is the ratio of the volume of void space (V<\/em>V<\/em><\/small><\/sub>) in a sample of earth material to the total volume of the sample (V<\/em>T<\/em><\/small><\/sub>) including solids and void space. Total volume is enclosed within the entire box shown in Figure 3a<\/a>, while void volume includes only the blue zones. In some texts total porosity is referred to as porosity and both terms are used in this book. Total porosity is preferred here because of the need to distinguish it from effective porosity defined in this section.<\/p>\n

Porosity can be represented as a fraction of the total volume as shown in Equation 2, or as a percentage (if multiplied by 100%).<\/p>\n\n\n\n
<\/td>\n\"\displaystyle n=\frac{V_V}{V_T}\"<\/td>\n(2)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

where:<\/p>\n\n\n\n\n\n
n<\/em><\/td>\n=<\/td>\ntotal porosity (dimensionless)<\/td>\n<\/tr>\n
V<\/em>V<\/em><\/small><\/sub><\/td>\n=<\/td>\nvolume of void space in a sample (L3<\/sup>)<\/td>\n<\/tr>\n
V<\/em>T<\/em><\/small><\/sub><\/td>\n=<\/td>\ntotal volume of a sample (L3<\/sup>)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Measuring Porosity<\/h1>\n

It is difficult to measure the volume of voids directly. However, the relationship between sample density and total porosity provides a means of calculating the void volume because the bulk density of a sample is controlled by the proportion of solids and voids. That is, the bulk density<\/em> is equal to the fractional volume of solids (1 – n<\/em>) times the particle density<\/em> plus the fractional volume of voids (n<\/em>) times the fluid density<\/em>, as shown in Equation 3.<\/p>\n\n\n\n
<\/td>\n\u03c1<\/em>b<\/em><\/sub> = (1 – n<\/em>) \u03c1<\/em>p<\/em><\/sub> + n \u03c1<\/em>f<\/em><\/sub><\/td>\n(3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

where:<\/p>\n\n\n\n\n\n\n
\u03c1<\/em>b<\/em><\/sub><\/td>\n=<\/td>\nbulk density (M\/L3<\/sup>)<\/td>\n<\/tr>\n
n<\/em><\/td>\n=<\/td>\ntotal porosity (dimensionless)<\/td>\n<\/tr>\n
\u03c1<\/em>p<\/em><\/sub><\/td>\n=<\/td>\nparticle density (M\/L3<\/sup>)<\/td>\n<\/tr>\n
\u03c1<\/em>f<\/em><\/sub><\/td>\n=<\/td>\nfluid density (M\/L3<\/sup>)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Thus, the total porosity can be computed if the bulk density (\u03c1<\/em>b<\/em><\/sub>) of the sample is determined for either a fully saturated or a fully dried sample, and the fluid density (\u03c1<\/em>f<\/em><\/sub>) as well as the particle density (\u03c1<\/em>p<\/em><\/sub>) of the dominate mineral material making up the matrix (solid particles) of the sample are known, as shown in Equation 4. Typically, the fluid is air or water, so the fluid density is known.<\/p>\n\n\n\n
<\/td>\n\"\displaystyle n=\frac{\rho_b-\rho_p}{\rho_f-\rho_p}\"<\/td>\n(4)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

To determine the total porosity of a sample, the sample volume can be measured by fully saturating the sample then immersing it in water and noting the volume of displaced fluid. Then, the wet bulk density is determined by weighing the saturated sample and dividing that weight by the volume. When water is the fluid, the density is assumed to be 1 gram per cubic centimeter (g\/cm3<\/sup>), because this is its density at 4\u00b0C and the density does not noticeably change in the range of temperatures experienced in the field and lab. If the sample is dried and then weighed, the dry bulk density can be used to calculate porosity by assuming the air filling the pores to have a fluid density of 0 g\/cm3<\/sup>.<\/p>\n

For example, the porosity for a sample volume of one cubic centimeter of loose quartz sand can be computed knowing that the dry bulk density of the sand sample is 1.43 g\/cm3<\/sup> and the density of a corresponding cubic centimeter of solid quartz with no pore space (i.e., the composition of the sand grain) has a density of 2.65 g\/cm3<\/sup> as shown in Figure 6.<\/p>\n

 <\/p>\n

\"Schematic
Figure 6 –<\/strong> Schematic of: a) dry bulk density of 1 cubic centimeter of loose quartz sand; and, b) density of 1 cubic centimeter of solid quartz, which provides the particle density of the quartz sand grains.<\/figcaption><\/figure>\n

By using Equation 4, the total porosity can be calculated as 0.46 or 46%, as shown in Equation 5.<\/p>\n\n\n\n
<\/td>\n\"\displaystyle n=\frac{1.43\frac{\textup{g}}{{\textup{cm}}^3}-2.65\frac{\textup{\textup{g}}}{{\textup{\textup{cm}}}^3}}{0\frac{\textup{g}}{{\textup{cm}}^3}-2.65\frac{\textup{g}}{{\textup{cm}}^3}}=0.46\"<\/td>\n(5)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

For additional information on the densities of earth materials, <\/a>Click here to link to Box 1<\/a>.<\/p>\n

Values of Total Porosity<\/h1>\n

Tables of total porosity values for earth materials are included in publications provided by government agencies and researchers, as well as in hydrogeology textbooks. Examples of total porosity values for earth materials are presented in Table 1.<\/p>\n

Generally, unconsolidated materials have higher porosities (20 to 55%) than consolidated sediments and igneous and metamorphic rocks. Though, some consolidated sedimentary rocks; and weathered and\/or fractured igneous and metamorphic rocks can also have high porosities. The porosity of vesicular basalt is a result of the degree of void creation during the solidification process.<\/p>\n

<\/a>Table 1 –<\/strong>Typical total porosity ranges of some common earth materials (after Rivera, 2014; with data from Freeze and Cherry, 1979 and Domenico and Schwartz, 1998).
\n<\/small><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Total Porosity Range of Some Common Earth Materials (Percent)<\/strong><\/td>\n<\/tr>\n
Material<\/strong><\/td>\nRange Total Porosity (%)<\/strong><\/td>\n<\/tr>\n
Unconsolidated Sediments<\/strong><\/td>\n<\/td>\n<\/tr>\n
Clay<\/td>\n45 – 55<\/td>\n<\/tr>\n
Silt<\/td>\n35 – 50<\/td>\n<\/tr>\n
Fine-sand<\/td>\n26 – 50<\/td>\n<\/tr>\n
Coarse-sand<\/td>\n30 – 45<\/td>\n<\/tr>\n
Gravel<\/td>\n25 – 35<\/td>\n<\/tr>\n
Sand and gravel<\/td>\n20 – 30<\/td>\n<\/tr>\n
Glacial till<\/td>\n20 – 30<\/td>\n<\/tr>\n
Consolidated Sediments<\/strong><\/td>\n<\/td>\n<\/tr>\n
Shale<\/td>\n1 – 10<\/td>\n<\/tr>\n
Siltstone<\/td>\n20 – 40<\/td>\n<\/tr>\n
Sandstone<\/td>\n5 – 30<\/td>\n<\/tr>\n
Limestone and dolomite<\/td>\n1 – 25<\/td>\n<\/tr>\n
Karstic limestone<\/td>\n5 – 35<\/td>\n<\/tr>\n
Igneous and Metamorphic Rocks<\/strong><\/td>\n<\/td>\n<\/tr>\n
Fresh granite and gneiss<\/td>\n0.01 – 3<\/td>\n<\/tr>\n
Weathered granite and gneiss<\/td>\n5 – 25<\/td>\n<\/tr>\n
Fractured basalt<\/td>\n5 – 30<\/td>\n<\/tr>\n
Vesicular basalt<\/td>\n10 – 40<\/td>\n<\/tr>\n
Tuff<\/td>\n10 – 55<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"author":1,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-74","chapter","type-chapter","status-publish","hentry"],"part":54,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/74","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":58,"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/74\/revisions"}],"predecessor-version":[{"id":1170,"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/74\/revisions\/1170"}],"part":[{"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/parts\/54"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapters\/74\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/wp\/v2\/media?parent=74"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/pressbooks\/v2\/chapter-type?post=74"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/wp\/v2\/contributor?post=74"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow\/wp-json\/wp\/v2\/license?post=74"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}