Forms of metrics

Chlorine cannot be stored economically or moved long distances. International movements of bulk chlorine are more or less limited to movements between Canada and the United States. In 1987, chlorine moved in the form of derivatives was 3.3 million metric tons or approximately 10% of total consumption (3). Exports of ethylene dichloride, vinyl chloride monomer, poly(vinyl chloride), propylene oxide, and chlorinated solvents comprise the majority of world chlorine movement. Countries or areas with a chlorine surplus exported in the form of derivatives include Western Europe, Bra2il, USA, Saudi Arabia, and Canada. Countries with a chlorine deficit are Taiwan, Korea, Indonesia, Vene2uela, South Africa, Thailand and Japan (3). 

The ores of most importance are fluorspar, CaF2 fluorapatite, Ca (P0 2Fj cryoHte [15096-52-3], Na AlF. Fluorspar is the primary commercial source of fluoiine. Twenty-six percent of the world s high quaHty deposits of fluorspar are ia North America. Most of that is ia Mexico. United States production ia 1987—1991 was 314,500 metric tons, most of which occurred ia the Illinois-Kentucky area. Imported fluorspar ia 1990—1991 represented about 82% of U.S. consumption 31% of U.S. fluorspar imports were from Mexico and 29% from China compared to 66% from Mexico ia the 1973—1978 period. The majority of the fluorine ia the earth s cmst is ia phosphate rock ia the form of fluorapatite which has an average fluorine concentration of 3.5%. Recovery of these fluorine values as by-product fluorosiHcic acid from phosphate production has grown steadily, partially because of environmental requirements (see Phosphoric acid and THE phosphates). 

Phthahc anhydride (1) is the commercial form of phthaUc acid (2). The worldwide production capacity for the anhydride was ca 3.5 x 10 metric tons ia 1993, and it was used ia the manufacture of plasticizers (qv), unsaturated polyesters, and alkyd resins (qv) (see Polyesters, unsaturated). Sales of terephthahc acid (3) and its dimethyl ester are by far the largest of any of the benzenepolycarboxyhc acids 14.3 x 10 t were produced in 1993. This is 80% of the total toimage of ah. commercial forms of the benzenepolycarboxyhc acids. Terephthahc acid is used almost exclusively for the manufacture of poly(ethylene terephthalate), which then is formed into textiles, films, containers, and molded articles. Isophthahc acid (4) and trimehitic anhydride (5) are commercial products, but their worldwide production capacities are an order of magnitude smaller than for terephthahc acid and its dimethyl ester. Isophthahc acid is used primarily in the production of unsaturated polyesters and as a comonomer in saturated polyesters. Trimehitic anhydride is used mainly to make esters for high performance poly(vinyl chloride) plasticizers. Trimesic acid (6), pyromehitic dianhydride (7), and hernimehitic acid (8) have specialized commercial apphcations. The rest of the benzenepolycarboxyhc acids are not available commercially. 

The estimated worldwide production of various forms of amorphous siHca and the principal suppHers as of the early 1990s are given ia Table 4. The aimual U.S. productioa of sand is about 27 million metric tons (72). 

Since its development in cosmetics in the 1940s, thioglycolic acid has become a widespread thiochemical, used all over the world as the acid or in the form of its salts or esters. Because of the several derivatives of thioglycolic acid used, the market size for this chemical is often expressed in terms of thioglycolic acid equivalents. In 1994 the total world market was estimated at around 15,000 to 20,000 metric tons of thioglycolic acid equivalents. Some mercaptocarboxyhc acid and esters available are compiled in Table 2. 

World production ia the late 1990s of both natural and synthetic forms of vitamin E is estimated at 22,000 metric tons and growth is expected to keep pace with increasing need. The 1993 U.S. production was 14,096 metric tons (47) with an additional 1080 metric tons from imports. The principal U.S. producers of the natural form are Eastman Chemical Company, Archer Daniels Midland Company, and Henkel, and of synthetic vitamin E, Hoffmaim-La Roche and BASE. International producers include Hoffmaim-La Roche, BASE, Eisai, and Rhc ne-Poulenc. 

The largest consumption of beryUium is in the form of aUoys, principally the copper—beryUium series. The consumption of the pure metal has been quite cycHc in nature depending on specific governmental programs in armaments, nuclear energy, and space. The amount of beryUium extracted from bertrandite has tanged between 200 and 270 metric tons pet year since 1986 (14). SmaU quantities of beryl were also processed during this period. 

The Systeme International (SI) is the internationally accepted form of the metric system. It defines seven base units in terms of which all physical quantities can be expressed ... 

The above development considers Ho to be an entity, and develops the nonsym-metric form of RSPT accordingly [18]. 

Approximations thus must be introduced that involve modeling both the XC potential and the metric tensor, and a truncation of the space within which to choose the unknown functions v, to finite dimension r < >. The modeling is based on the restt-icted ansatz chosen for the form of states used to determine paths that approximate D (p), D](p) and ). It can be carried... 

Similar expressions can be derived for second spatial derivatives. The final form of the equations that result after a generalized coordinate transformation depends on the degree of differentiation by using the chain rule, i.e. on the treatment of the metrics x, x, and y. For more details we refer to the... 

One can see that the forms of equations (4.4) and (4.5) are identical. It is clear that RME (AE) and Em (Emw) describe material efficiency from different points of view, the former with respect to the target product and the latter with respect to the waste products. Figure 4.1 shows the interconnections between the key material green metrics presented above. 

A Microsoft Excel (Version 5.0 or higher) spreadsheet template form has been developed which allows the calculation of the complete reaction mass efficiency (RME) according to equation (4.1) and raw material cost (RMC) for any chemical transformation. Lines are numbered and line instructions are embedded in the same manner as a personal income tax form. Green metrics are evaluated to determine the greermess of the experiment in a rigorous quantitative way and to determine the bottom line cost of carrying out the experiment. Formula entries are inserted in appropriate cells to facilitate computation. Any... 

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