1.6 Estimating scale deposition rates (Water for coffee)

When calcium/magnesium carbonate precipitates out as scale, it
lowers the alkalinity and hardness measures by equal amounts (in the
CaCO3 equivalent units being used) until the LI drops to zero. At this
point, scaling stops until more hard water is introduced.
The calculation doesn't have a closed form solution. If you
have a programming language, write an iterative subroutine to solve
this equation for x, the milligram amount of scale per liter
throughput, for any H, A, & T you want:

```  0.9*log(H - x) + 2.465*log(A - x) = 39.61 - 13.12*log(T + 273)
or  log(H - x) + 2.365*log(A - x) = 39.61 - 13.12*log(T + 273)
```

Barring that, I've included two scaling tables:

Milligrams Scale At 95c Per Liter Throughput

```                                              Alkalinity
Hardness    25 50 75 100 125 150 175 200 225 250 275 300
--------------------------------------------------------
25     0  0  0   6  13  17  20  21  22  23  24  24
50     0  0  8  22  31  38  42  45  46  47  48  49
75     0  0 17  33  47  56  63  67  70  71  72  73
100     0  2 23  42  58  72  81  88  92  95  96  97
125     0  6 27  48  67  83  97 106 113 117 120 121
150     0  8 31  52  73  92 108 122 131 138 142 145
175     0 10 33  56  77  98 117 133 147 156 163 167
200     0 12 35  58  81 102 123 142 158 172 181 188
225     0 14 37  60  83 106 127 148 167 183 197 206
250     0 15 39  62  85 108 131 152 173 192 208 222
275     0 17 40  64  87 110 133 156 177 198 217 233
300     0 18 42  65  89 112 135 158 181 202 223 242
325     0 19 43  67  90 114 137 160 183 206 227 248
350     0 19 44  68  92 115 139 162 185 208 231 252
375     0 20 44  69  93 117 140 164 187 210 233 256
400     0 21 45  69  94 118 142 165 189 212 235 258
425     0 22 46  70  94 119 143 167 190 214 237 260
450     0 22 47  71  95 119 144 168 192 215 239 262
475     0 23 47  72  96 120 144 169 193 217 240 264
500     0 23 48  72  97 121 145 169 194 218 242 265
--------------------------------------------------------
```

Milligrams Scale At 125c Per Liter Throughput

```                                              Alkalinity
Hardness    25 50 75 100 125 150 175 200 225 250 275 300
--------------------------------------------------------
25     0  0 10  17  20  22  23  24  24  25  25  25
50     0  7 23  35  42  45  47  48  49  49  50  50
75     0 13 32  48  60  67  70  72  73  74  74  75
100     0 17 38  57  73  85  92  95  97  98  99  99
125     0 19 42  63  82  98 110 117 120 122 123 124
150     0 22 44  67  88 107 123 135 142 145 147 148
175     0 23 47  69  92 113 132 148 160 167 170 172
200     1 25 48  72  94 117 138 157 173 185 192 195
225     2 26 50  73  97 119 142 163 182 198 210 217
250     3 27 51  75  98 122 144 167 188 207 223 235
275     4 28 52  76 100 123 147 169 192 213 232 248
300     4 29 53  77 101 125 148 172 194 217 238 257
325     5 29 54  78 102 126 150 173 197 219 242 263
350     5 30 54  79 103 127 151 175 198 222 244 267
375     6 30 55  79 104 128 152 176 200 223 247 269
400     6 31 55  80 104 129 153 177 201 225 248 272
425     7 31 56  80 105 129 154 178 202 226 250 273
450     7 32 56  81 105 130 154 179 203 227 251 275
475     7 32 57  81 106 130 155 179 204 228 252 276
500     8 32 57  82 106 131 155 180 204 229 253 277
--------------------------------------------------------
```

Notes on the tables:
1. To obtain the composition of the water remaining in the
boiler, subtract the amount of scale from both the hardness and
alkalinity column
2. Results for 120C and 130C differ from the 125C table by 1
or 2 mg/l scale less or more respectively. Similarly for the 90C and
100C tables to the 95C one.
3. The 125C table applies only to cases when liquid water is
being extracted from the boiler. When steam is extracted, all minerals
are left behind. So, the entire lower value of the hardness or
alkalinity deposits as scale if the boiler water is fully saturated
with an LI of 0 or higher.
4. If boiler water is not saturated, the hardness and
alkalinity values rise in proportion to the proportion of steam
extracted tempered by the values of the feedwater replacing the lost
steam. Barring any water extraction, the hardness levels will
eventually climb to saturation. Therefore, even if the feedwater is
below the boiler's saturation point, scaling may still occur if a high
proportion of use is as steam.
Actual mineral concentrations in the boiler, if saturation
isn't reached, depend on the ratio of steam to water extraction and is
as follows:

Boiler Concentration = Feedwater Concentration/(1 - Steam Ratio)

No scaling occurs only if the boiler concentrations of
alkalinity and hardness yield a negative LI. Therefore boilers used
only or primarily for steaming must be flushed (blown down) regularly,
with the schedule depending on the mineral concentration of the
feedwater and the volume of steam use. Water treatments must be chosen
with these factors in mind.

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