{"id":2354,"date":"2026-01-23T16:01:49","date_gmt":"2026-01-23T21:01:49","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/hydrometallurgy\/?post_type=chapter&p=2354"},"modified":"2026-03-23T16:29:13","modified_gmt":"2026-03-23T20:29:13","slug":"thickener-design","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/hydrometallurgy\/chapter\/thickener-design\/","title":{"raw":"3. Thickener Design","rendered":"3. Thickener Design"},"content":{"raw":"

Overflow Quality and Thickener Depth<\/h2>\r\nThe depth of a thickener depends on the rate of settling of the solids. The objective is a clear overflow solution. Even so, very fine solids might still be present. Flocculation is the process of particles coming together. Hence the growth of a floc requires interaction of two particles. This then may be expected to obey second order kinetics,\r\n\r\n\\[\\ce{\\frac{dC}{dt} = -kC^2} \\tag{31}\\]\r\n\r\nwhere C is the concentration of particles, k is the rate constant for flocculation and t is time. Rearranging,\r\n\r\n\\[\\ce{-\\frac{dC}{C^2} = k\\,dt} \\tag{32}\\]\r\n\r\nThis may be integrated over the limits C0 to C and 0 to t,\r\n\r\n\\[\\ce{-\\int_{C_0}^{C} \\frac{dC}{C^2} = k \\int_{0}^{t} dt} \\tag{33}\\]\r\n\r\nThen,\r\n\r\n\\[\\ce{\\frac{1}{C} = kt + \\frac{1}{C_0}} \\tag{34}\\]\r\n\r\nThe overflow quality is indicated by 1\/C = Z. When C is small, the overflow is largely free of solids and 1\/C is large. The volumetric flow rate of slurry is designated Q0, e.g. m3\/hr. The residence time in the thickener is volume \/ flow rate,\r\n\r\n\\[\\ce{t = \\frac{Q_0}{A h}} \\tag{35}\\]\r\n\r\nwhere A is the thickener surface area and h is the depth. Then,\r\n\r\n\\[\\ce{Z = \\frac{1}{C} = \\frac{kAh}{Q_0} + \\frac{1}{C_0}} \\tag{36}\\]\r\n\r\nIf k is large then h can be small to achieve a given quality. But, if k is small, i.e. flocculation is slow, then h must be large to achieve the same quality.\r\n

Surface Area Determination<\/h2>\r\nIn order to determine the required surface area for a thickener settling tests are performed. These involve mixing up a slurry of the required solids with varying additions of flocculant. The mixture is poured into a large graduated cylinder (e.g. 1 L) and inverted several times to ensure it is well mixed. Then it is allowed to stand for about a day. As the solids fall a definite interface appears. Above is clear solution. Below is a bed of slurry. Theinterface drops over time as the solids settle. A plot of slurry bed depth with time is the settling curve. This may be analyzed by a number of methods that involve geometric constructions to estimate the required thickener area per unit flow rate. The methods vary widely, some over-estimating and some under-estimating the required area. In practice it is better to over-estimate than under-estimate. Mineral processing textbooks may be consulted for details of the methods.","rendered":"

Overflow Quality and Thickener Depth<\/h2>\n

The depth of a thickener depends on the rate of settling of the solids. The objective is a clear overflow solution. Even so, very fine solids might still be present. Flocculation is the process of particles coming together. Hence the growth of a floc requires interaction of two particles. This then may be expected to obey second order kinetics,<\/p>\n

\\[\\ce{\\frac{dC}{dt} = -kC^2} \\tag{31}\\]<\/p>\n

where C is the concentration of particles, k is the rate constant for flocculation and t is time. Rearranging,<\/p>\n

\\[\\ce{-\\frac{dC}{C^2} = k\\,dt} \\tag{32}\\]<\/p>\n

This may be integrated over the limits C0 to C and 0 to t,<\/p>\n

\\[\\ce{-\\int_{C_0}^{C} \\frac{dC}{C^2} = k \\int_{0}^{t} dt} \\tag{33}\\]<\/p>\n

Then,<\/p>\n

\\[\\ce{\\frac{1}{C} = kt + \\frac{1}{C_0}} \\tag{34}\\]<\/p>\n

The overflow quality is indicated by 1\/C = Z. When C is small, the overflow is largely free of solids and 1\/C is large. The volumetric flow rate of slurry is designated Q0, e.g. m3\/hr. The residence time in the thickener is volume \/ flow rate,<\/p>\n

\\[\\ce{t = \\frac{Q_0}{A h}} \\tag{35}\\]<\/p>\n

where A is the thickener surface area and h is the depth. Then,<\/p>\n

\\[\\ce{Z = \\frac{1}{C} = \\frac{kAh}{Q_0} + \\frac{1}{C_0}} \\tag{36}\\]<\/p>\n

If k is large then h can be small to achieve a given quality. But, if k is small, i.e. flocculation is slow, then h must be large to achieve the same quality.<\/p>\n

Surface Area Determination<\/h2>\n

In order to determine the required surface area for a thickener settling tests are performed. These involve mixing up a slurry of the required solids with varying additions of flocculant. The mixture is poured into a large graduated cylinder (e.g. 1 L) and inverted several times to ensure it is well mixed. Then it is allowed to stand for about a day. As the solids fall a definite interface appears. Above is clear solution. Below is a bed of slurry. Theinterface drops over time as the solids settle. A plot of slurry bed depth with time is the settling curve. This may be analyzed by a number of methods that involve geometric constructions to estimate the required thickener area per unit flow rate. The methods vary widely, some over-estimating and some under-estimating the required area. In practice it is better to over-estimate than under-estimate. Mineral processing textbooks may be consulted for details of the methods.<\/p>\n","protected":false},"author":1076,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2354","chapter","type-chapter","status-publish","hentry"],"part":2336,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/hydrometallurgy\/wp-json\/pressbooks\/v2\/chapters\/2354","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/hydrometallurgy\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/hydrometallurgy\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/hydrometallurgy\/wp-json\/wp\/v2\/users\/1076"}],"version-history":[{"count":6,"href":"https:\/\/pressbooks.bccampus.ca\/hydrometallurgy\/wp-json\/pressbooks\/v2\/chapters\/2354\/revisions"}],"predecessor-version":[{"id":3875,"href":"https:\/\/pressbooks.bccampus.ca\/hydrometallurgy\/wp-json\/pressbooks\/v2\/chapters\/2354\/revisions\/3875"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/hydrometallurgy\/wp-json\/pressbooks\/v2\/parts\/2336"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/hydrometallurgy\/wp-json\/pressbooks\/v2\/chapters\/2354\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/hydrometallurgy\/wp-json\/wp\/v2\/media?parent=2354"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/hydrometallurgy\/wp-json\/pressbooks\/v2\/chapter-type?post=2354"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/hydrometallurgy\/wp-json\/wp\/v2\/contributor?post=2354"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/hydrometallurgy\/wp-json\/wp\/v2\/license?post=2354"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}