### Introduction

Accurate chaptalization calculations require accurate values of initial juice volumes. In situations involving pulp fermentations, the assumed initial volume is often a rough estimate based on an assumed juice yield for the specific fruit and must characteristics. If the actual juice yield is less than expected, the initial volume might be over-estimated, which could result in over-chaptalization. To avoid over-chaptalization, Pambianchi (2021) recommends a two-step approach. First, the required sweetener addition is estimated based on the assumed initial juice volume, but only a portion of that sweetener addition (say half) is made. Next, the initial juice volume is re-calculated based on the observed change in specific gravity resulting from the sweetener addition. Finally, the required sweetener addition is re-calculated based on the revised initial juice volume estimate, and any remaining additions are made.

### Input Field Definitions

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 SG – The desired SG (20°C/20°C) of the must after chaptalization or dilution. Required only if either the first or second calculation option is selected. Range: 0.77193 to 1.55454

Initial SG – The SG (20°C/20°C) of the must prior to chaptalization or dilution. Range: 0.77193 to 1.55454

Target Volume – The desired volume of the must after chaptalization or dilution. Required only if the second calculation option is selected.

Initial Volume – The volume of the must prior to chaptalization or dilution. Required only if either the first or third calculation option is selected.

Sugar (or Honey or Concentrate) Added – The amount of sweetener added to the must. Required only if the third calculation option is selected.

Water Added – The amount of water added to the must. Required only if the third calculation option is selected.

### Output Field Definitions

Sugar (or Honey or Concentrate) Required – The calculated amount of sweetener required to yield the desired specific gravity and volume. Reported only if either the first or second calculation option is selected.

Water Required – The calculated amount of water required to yield the desired specific gravity and volume. Reported only if either the first or second calculation option is selected.

Resulting SG – The SG (20°C/20°C) of the must after adding the specified amounts of sweetener and water. Reported only if the third calculation option is selected.

Initial Volume – The volume of the must prior to chaptalization or dilution. Required only if either the first or third calculation option is selected.

Resulting Volume – The calculated volume of the must after adding the specified amounts of sweetener and water. Reported only if the third calculation option is selected.

### Calculation Details

The multi-step chaptalization calculations are based on the previously developed mass balance equations (2-12) and (2-13), which are repeated below 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

To begin we’ll need to assume an initial juice volume *v _{i}* and a target specific gravity

*sg*, and then estimate the sweetener and water additions. We’ll start with equation (2-24) which we developed by substituting the right-hand side of equation (2-13) into equation (2-12) to get:

_{f}( v + _{i}sg_{i}ρ_{w}m + _{sa}v)_{wa}ρ_{w}B = _{f}v + _{i}sg_{i}ρ_{w}B_{i}m_{sa}B_{s} |
(2-24) |

If the target gravity is greater than the initial gravity, we know we’ll be adding a sweetener and no water, so we can solve equation (2-24) the amount of sweetener to add:

m = [_{sa}v(_{i}sg_{i}ρ_{w}B – _{i}B) – _{f}v] / (_{wa}ρ_{w}B_{f}B – _{f}B)_{s} |
(2-27) |

If the target gravity is less than the initial gravity, we know we’ll need to add water to reduce the gravity, so we can solve equation (2-24) the amount of water to add:

v = [_{wa}v(_{i}sg_{i}ρ_{w}B – _{i}B) + _{f}m(_{sa}B – _{s}B)] / (_{f}ρ)_{w}B_{f} |
(2-28) |

The multi-step chaptalization procedure calls for making a partial sugar and/or water addition, allowing the must to equilibrate, then measuring the resulting specific gravity *sg _{f}*, and then re-calculating the initial juice volume

*v*based on the observed change in specific gravity. We can solve equation (2-24) above for

_{i}*v*to get:

_{i}v = [_{i}m – (_{sa}B_{s}m + _{sa}v)_{wa}ρ_{w}B] / [_{f}sg(_{i}ρ_{w}B – _{f}B)]_{i} |
(2-29) |

With the new estimate of initial volume, we can then recalculate the required sugar or water additions using equations (2-27) and (2-28), and then subtract the additions that have already been made to determine the remaining additions required to achieve the desired specific gravity.

Knowing how much sweetener we’re adding we can then use equation (2-26) to calculate the final volume after the addition of the sweetener:

v = (_{f}v + _{i}sg_{i}ρ_{w}m + _{sa}v) / (_{wa}ρ_{w}sg)_{f}ρ_{w} |
(2-26) |