Script to calculate water salt additions

doobliebop · 01-12-2011, 09:36 PM

I wrote this script to calculate the optimal amount of brewing salts to add to your water profile to end up with a target profile. I grabbed most of my numbers from ProMash, and so far this seems to be working well for me.

It is a python script, so you'll need the python interpreter with numpy, and the PyIMSL numerical libraries (freely available here: http://www.imslaps.com/products/imsl/pyimsl/)

Code:

from numpy import *
from imsl.math.linLsqLinConstraints import linLsqLinConstraints
from imsl.math.writeMatrix import writeMatrix
from imsl.math.vectorNorm import vectorNorm

#Replace the values in base_water with your water profile
base_water = [26.0, 3.6, 13.2, 28.0, 12.2, 68]
#################Values taken from ProMash################
burton_on_trent = [268., 62., 30., 638., 36., 141.]
calistoga_mineral = [11.1, 62., 30., 638., 36., 141.]
distilled_water = [0.,0.,0.,0.,0.,0.]
dortmund = [260.,23.,69.,240.,206.,270.]
dublin = [118., 4., 12., 54., 19., 319.]
edinburgh = [140., 36., 92., 231., 60., 270.]
london = [90., 4., 24., 58., 18., 123.]
marin_county_ca = [12., 10., 15., 17., 13., 74.]
munich = [76., 18., 1., 10., 2., 152.]
pilsen = [7., 3., 3.2, 5.8, 5., 9.]
vienna = [200., 60., 8., 125., 12., 120.]
yorkshire = [105., 17., 23., 66., 30., 153.]
###########################################################
target = burton_on_trent

#Salt contents (PPM / (grams per gallon))
caso4 =  [61.5, 0.0, 0.0, 147.4, 0.0, 0.0]
mgso4 =  [0.0, 26.1, 0.0, 103.0, 0.0, 0.0]
nacl =   [0.0, 0.0, 103.9, 0.0, 160.3, 0.0]
nahco3 = [0.0, 0.0, 72.0, 0.0, 0.0, 189.0]
cacl2 =  [72.0, 0.0, 0.0, 0.0, 127.4, 0.0]
caco3 =  [105.8, 0.0, 0.0, 0.0, 0.0, 158.4]

# The overall goal here is to find x ST: 
# Ax =~ b 
# x >= 0

a = transpose([caso4, mgso4, nacl, nahco3, cacl2, caco3])
b = array(target) - array(base_water)
xlb = [0.] * 6
xub = [-1.0e30] * 6
c = []
con_type = [] 
bu = [] 
bl = [] 
residual = []
x = linLsqLinConstraints(a, b, c, bl, bu, con_type,  xlb, xub, residual=residual) 

ion_labels = ['', 'Ca', 'Mg', 'Na', 'SO4', 'Cl', 'HCO3'] 
salt_labels = ['', 'CaSO4', 'MgSO4', 'NaCl', 'NaHCO3', 'CaCl2', 'CaCO3']
writeMatrix("Salt amounts to add \n(Grams per Gallon)", x, colLabels=salt_labels)
writeMatrix("Target Profile \n(PPM)", target, colLabels=ion_labels)
writeMatrix("Base Water + Recomended Salt Additions \n(PPM)", dot(a,x) + array(base_water), colLabels=ion_labels)
writeMatrix("Residuals \n(PPM)", residual, colLabels=ion_labels)
print ("\nNorm of residual = %f" % (vectorNorm(residual)))

Here's a run calculating additions from my water to Burton on Trent. Plugging these numbers back into ProMash I get these exact totals.

Code:

ryan@ubuntu-desktop:~/Desktop$ python water.py
 
                            Salt amounts to add 
                             (Grams per Gallon)
      CaSO4        MgSO4         NaCl       NaHCO3        CaCl2        CaCO3
      2.888        1.817        0.106        0.000        0.083        0.489
 
                               Target Profile 
                                    (PPM)
         Ca           Mg           Na          SO4           Cl         HCO3
        268           62           30          638           36          141
 
                   Base Water + Recomended Salt Additions 
                                    (PPM)
         Ca           Mg           Na          SO4           Cl         HCO3
      261.3         51.0         24.2        640.8         39.8        145.5
 
                                 Residuals 
                                    (PPM)
         Ca           Mg           Na          SO4           Cl         HCO3
      -6.67       -10.98        -5.81         2.78         3.77         4.45

Norm of residual = 15.513117

Hope somebody finds this useful!