concentrations of the calcium and magnesium ions in the effluent are [Ca2+]meq and [Mg2+]meq, respectively. From this information, the total mass of calcium in the effluent is [Ca2+]meq[(Ca/2)/1000(1000)](1000)¥ = 0.02[Ca2+]meq ¥ kg. Similarly, the total mass of magnesium in the effluent is [Mg2+]meq[(Mg/2)/1000(1000)] (1000)¥ = 0.012 [Mg2+]meq ¥ kg. Therefore, f = ! 0.02 [ Ca2+] meq¥ J 1 = 1--

MjCa + CCa^CCOO^ MrCaHC0:

MtMg + w ,MIL , Mt lT Ms^Mg ( HC03)2 T MgHC03 + °.99

To derive the equation for f, it is important that the calcium and magnesium be expressed in terms of equivalents. The total equivalents of calcium, TEC a, and the total equivalents of magnesium, TEMg, are, respectively, equal to

Thus, f equals

f 1 U-.a(HC03)2/2 + Ca/2J f 2l.Mg(HC03)2/2 Mg/2J f _jm-t<^cc001_ + Mlcca) + f j^Ir:Mi^-^c(03 + M^A

U-.a(HC03)2/2 Ca/2J Uig(HC03)2/2 Mg/2J = /1(°.0123Mtchc03 + °.°5Mrea) + f2(°.°137MrMgHC03 + °.°82M7.MgI = (aO^M^^ + °.°5MrCa) + (°.°137MmgHœ3 + °.°82M7.Mg)

In the design of the water softening process, the various removal fractions need to be assumed. Normally, the desired effluent quality is known, thus knowing the value of f. It depends upon the designer how to apportion the respective removal fractions for the calcium and magnesium ions. Magnesium in excess of 40 mg/L as CaCO3 deposits as scales on heat exchange elements. In addition, CaSO4 tends to deposit at high temperatures. These two constraints should be considered in making assumptions regarding the various fractional removals.

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