3

where r is the radius of a spherical particle (cm); i is the viscosity of the suspending medium in poises; d is the settling distance (cm); pl and p2 are the specific gravities of the particles and the suspending medium, respectively; g is the gravitational constant, 981 cm/sec2, and i is the time from the start of the test (sec.). It has been found that by calculating particle size as the edge length or width of a cube of the same volume as a sphere of radius r, particle sizes conform to sieve analysis.34 Results of sedimentation tests are. therefore, reported as equivalent spherical diameters (esd) which are equal to 1.612 r.

Sometimes drilling mud technologists forget that Stokes' law is based on the premise that the sedimenting particles do not interfere with each other To avoid interference, the concentration of the suspension must not he greater then 0.5",, by volume, or 1 to 2°;, by weight, depending on the specific gravity of the particles.

Settling velocities of heterogeneous suspensions cannot be determined by the rate at which sediment accumulates at the bottom of a graduate, because coarse particles which started at the top arrive at the bottom at the same lime as fine particles which started near the bottom. Sedimentation tests arc therefore based on the principle of measuring the concentration of particles in a narrow zone at a known depth below the surface, at various time intervals after settling commences. The difference between the initial concentration of the suspension and the concentration at depth d after time t gives the concentration of particles whose settling velocity is greater than dit.

The simplest and quickest method of measuring concentrations is to use a Boyoucos soil hydrometer, which is available from laboratory supply houses, and which measures concentrations directly in grams per liter. The method has a disadvantage, however, in that the suspension is disturbed every lime the hydrometer is inserted. A better practice is to use a pipet to withdraw 10 cm3 from a known depth, evaporate the liquid, and weigh the residue. The Andreasen pipet (see Figure 3-19) is the most accurate and convenient apparatus to use for this purpose,34 but a 500 era3 cylinder and 10 cm pipet will serve.

After mixing with water, samples must be agitated long enough to break down aggregates into individual particles, and a suitable deflocculant, such as 0.5"o of a polyphosphate, must be added. The diluted suspension is then transferred to the sedimentation vessel, shaken briefly, and 10 cm3 aliquots withdrawn by the pipet after a series of increasingly greater time intervals. Intervals ranging from 2 minutes to 96 hours will measure particle sizes from aboul 32 microns to 0.6 micron esd, assuming that the specific gravity of the particles is 2.65; the temperature of the water is 25 C: and the setting depth is 20 cm.

Particles less than 0.5 micron esd do not settle according to Stokes' law. Colloidal clays may be separated into size fractions in a supercentrifugc'' and the size and shape of the particles in each fraction may be determined by electron microscopy or electro-optical birerefringence techniques.36

An electronic sensing device known as the Coulter counter provides a quick method of determining particle size distribution from 400 to 0.6 micron esd. ° A particle size analyzer that uses a laser beam has been found suitable for water base muds.' Oil muds may also be analyzed, but the solids must first be extracted from the oil and redispersed in water. An automated laser-beam particle size analyzer has been used by Mohnot37b to measure 1 to 192 micron particles in clay suspensions and field muds. The samples are not deflocculated before analysis. and the results therefore reflect the degree of flocculation and loose particle association. This procedure provides useful information, but means that the results obtained are affected by aging and degree of prior agitation. Standard procedures must therefore be adopted in order to get comparative results, and field samples must be tested immediately after collection. In the appendix Mohnot provides a useful comparison of the different types of automated particle size analyzers and lists their advantages and disadvantages.

The mineral constituents of clays and shales are identified semi-quantitatively by X-ray diffraction techniques. Clay minerals can also be identified by differential thermal analysis, and by electron microscopy. These methods require elaborate instruments and procedures which have been summarized by van Olphen.38

Identification of Mineral Constituents

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