### Introduction

Amelioration is the dilution of must with water in order to reduce the acidity or sugar content. When diluting to reduce the acidity, it is often necessary to add sugar to maintain the potential alcohol level of the must. When diluting to reduce sugar content, it is often necessary to add acid to bring the acidity up to an acceptable level.

The Amelioration Calculator determines the required additions of water, sugar, and acid to a must to meet the desired acidity and SG levels given the initial acidity, initial SG, and initial must volume. Alternatively, the target must volume can be specified, in which case FermCalc calculates the initial volume of must required, along with the required water, acid, and sugar additions.

### Input Field Definitions

Acid Type – The type of acid being added, either tartaric, malic, citric, or acid blend. Acid blend is assumed to be a blend of 40% tartaric, 40% malic, and 20% citric acids.

Sweetener – The type of sweetener to be added, either sugar, honey, or concentrate. The SG of the sweetener must be specified if honey or concentrate is selected.

Target Acidity – The desired acidity of the must after the water/sugar/acid additions. Range: 0 to 100 grams/liter.

Initial Acidity – The acidity of the must prior to the water/sugar/acid additions. Range: 0 to 100 grams/liter.

Target SG – The desired specific gravity of the must after the water/sugar/acid additions. Range: 0.77193 to 1.55454

Initial SG – The specific gravity of the must prior to the water/sugar/acid additions. Range: 0.77193 to 1.55454

Must Volume – The volume of the must prior to the water/sugar/acid additions.

Target Volume – The desired volume of the must after the water/sugar/acid additions.

### Output Field Definitions

Water Required – The volume of water required to meet the target acidity, SG, and volume.

Sugar Required – The mass of sugar required to meet the target acidity, SG, and volume.

Acid Required – The mass of acid required to meet the target acidity, SG, and volume.

Resulting Volume – The volume of the must after adding the water, sugar, and acid. Reported only if Must Volume is selected above.

Must Required – The volume of the juice required to meet the target acidity, SG, and volume. Reported only if Target Volume is selected above.

### Calculation Details

FermCalc first determines whether the acidity adjustment or the sugar adjustment requires the larger increase in volume. The increase in volume due to the acidity adjustment is calculated from an acid mass balance equation:

v = _{i}a_{i}v_{f}a_{f} |
(3-13) |

where:

*v _{i}* = initial must volume, liters

*v _{f}* = final must volume, liters

*a _{i}* = initial acidity, grams/liter tartaric

*a _{f}* = final acidity, grams/liter tartaric

Solving for *v _{f}* we get:

v = _{f}v / _{i}a_{i}a_{f} |
(3-14) |

Or if we’re solving for *v _{i}* we get:

v = _{i}v / _{f}a_{f}a_{i} |
(3-15) |

The increase in volume due to the sugar adjustment is calculated using the previously developed sugar mass balance equations (2-12) and (2-13), repeated here for completeness:

v = _{f}sg_{f}ρ_{w}B_{f}v + _{i}sg_{i}ρ_{w}B_{i}m_{sa}B_{s} |
(2-12) |

v = _{f}sg_{f}ρ_{w}v + _{i}sg_{i}ρ_{w}m + _{sa}v_{wa}ρ_{w} |
(2-13) |

where:

*v _{i}* = initial must volume, liters

*v _{f}* = final volume, liters

*sg _{i}* = initial specific gravity

*sg _{f}* = final specific gravity

*B _{i}* = initial Brix

*B _{f}* = final Brix

*B _{s}* = sugar Brix

*ρ _{w}* = density of water = 0.9982 kg/liter at 20ºC

*m _{sa}* = mass of sugar added, kg

*v _{wa}* = volume of water added, liters

If the target (final) SG is greater than or equal to the initial SG, then we won’t be adding any water for the sugar adjustment, so *v _{wa}* is zero. If we solve equation (2-13) for

*m*, substitute it into equation (2-12), and re-arrange to solve for

_{sa}*v*, we get:

_{f}v = _{f}v(_{i}sg_{i}B – _{s}B) / [_{i}sg(_{f}B – _{s}B)]_{f} |
(3-16) |

Or if we’re solving for *v _{i}* we get:

v = _{i}v(_{f}sg_{f}B – _{s}B) / [_{f}sg(_{i}B – _{s}B)]_{i} |
(3-17) |

If the target SG is less than the initial SG, then we won’t be adding sugar, so *m _{sa}* is zero. Solving equation (2-12) for

*v*, we get:

_{f}v = (_{f}v) / (_{i}sg_{i}B_{i}sg)_{f}B_{f} |
(3-18) |

Or if we’re solving for *v _{i}* we get:

v = (_{i}v) / (_{f}sg_{f}B_{f}sg)_{i}B_{i} |
(3-19) |

The value of *v _{f}* is taken as the maximum value calculated by equations (3-14), (3-16), and (3-18). If we’re solving for

*v*, its value is taken as the minimum value calculated by equations (3-15), (3-17), and (3-19). Now that we know both

_{i}*v*and

_{i}*v*, we can solve equation (2-13) for the mass of sugar to add, or:

_{f}m = (_{sa}v – _{f}sg_{f} ρ_{w}B_{f}v)_{i}sg_{i}ρ_{w}B_{i} / B_{s} |
(3-20) |

In the case of concentrate, the mass calculated from equation (3-20) is converted to a volume as:

v = _{ca}m / (_{sa}sg)_{c}ρ_{w} |
(3-21) |

where:

*v _{ca}* = volume of concentrate added, liters

*sg _{c}* = concentrate specific gravity

Knowing the amount of sweetener to add we can then re-arrange equation (2-13) to solve for the amount of water to add:

v = (_{wa}v – _{f}sg_{f}ρ_{w}v – _{i}sg_{i}ρ_{w}m) / _{sa}ρ_{w} |
(3-22) |

The amount of acid to add is then calculated by modifying equation (3-6) as:

m = (_{a}v – _{f}a_{f}v) (_{i}a_{i}i/_{t}mw) / (_{t}i/_{a}mw)_{a} |
(3-23) |