FermCalc - Fortification Calculators - Post-Fermentation Fortification Calculator
- Introduction
- Input Field Definitions
- Output Field Definitions
- Calculation Details
- Mass Balance Equations
- Specify Target Alcohol & Sugar > Calculate Additions and Volume
- Specify Target Alcohol, Sugar, & Volume > Calculate Additions
- Specify Additions > Calculate Resulting Alcohol, Sugar, & Volume
- Fortification Point Calculator
- Introduction
- Input Field Definitions
- Output Field Definitions
- Calculation Details
- Hackbarth SG Calculator
- Introduction
- Input Field Definitions
- Output Field Definitions
- Calculation Details
## Post-Fermentation Fortification Calculator## IntroductionThe Post-Fermentation Fortification Calculator determines the amounts of fortifier and sweetener to add to a given wine to yield a fortified wine with the desired alcohol content, sugar content, and volume. Alternatively, the resulting alcohol content, sugar content, and volume can be calculated from the specified fortifier and sweetener additions. The sweetener can be either sugar, honey, or concentrate. FermCalc offers three options for this calculation: - Specify Target Alcohol & Sugar > Calculate Additions and Volume – Specify the desired alcohol and sugar contents, and FermCalc will calculate the required additions of fortifier and sweetener to achieve the targets, as well as the resulting volume after the additions.
- Specify Target Alcohol, Sugar, & Volume > Calculate Additions – Specify the desired alcohol content, sugar content, and volume, and FermCalc will calculate the required amounts of wine, fortifier, and sweetener to achieve all three targets.
- Specify Additions > Calculate Resulting Alcohol, Sugar, & Volume – Specify the amounts of fortifier and sweetener to be added, and FermCalc will calculate the resulting alcohol content, sugar content, and volume.
All volumes and specific gravities have a temperature basis of 20°C (68°F). It is assumed that the fortifier contains only ethanol and water, and that the sweetener contains only sucrose and water. Specific gravities for all liquids containing both ethanol and sucrose are calculated using the Hackbarth model. Back to top## Input Field DefinitionsSweetener – 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. Fortifier Alcohol Content – The alcohol content of the fortifier being added. Target Alcohol Content – The desired alcohol content of the fortified wine. Target Sugar Content – The desired total solids content of the fortified wine. Wine Volume – The volume of the wine prior to fortification. Required only if either the first or third calculation option is selected. Target Volume – The desired volume of the wine after fortification. Required only if the second calculation option is selected. Wine Alcohol Content – The original alcohol content of the wine being fortified. Wine Sugar Content – The total solids content (true Brix) of the wine being fortified. Fortifier Added – The amount of fortifier added to the wine. Required only if the third calculation option is selected. Sugar (or Honey or Concentrate) Added – The amount of sweetener added to the wine. Required only if the third calculation option is selected. ## Output Field DefinitionsFortifier Required – The calculated amount of fortifier required to yield the desired alcohol content, sugar content, and volume. Reported only if either the first or second calculation option is selected. Sugar (or Honey or Concentrate) Required – The calculated amount of sweetener required to yield the desired alcohol content, sugar content, and volume. Reported only if either the first or second calculation option is selected. Wine Required – The volume of wine required to yield the desired alcohol content, sugar content, and volume. Reported only if the second calculation option is selected. Resulting Volume – The calculated volume of the fortified win after adding the specified amounts of fortifier and sweetener. Reported only if either the first or third calculation option is selected. Resulting Alcohol Content – The alcohol content of the fortified wine after adding the specified amounts of fortifier and sweetener. Reported only if the third calculation option is selected. Resulting Sugar Content – The total solids content of the fortified wine after adding the specified amounts of fortifier and sweetener. Reported only if the third calculation option is selected. Back to top## Calculation Details## Mass Balance EquationsTo derive the necessary equations for these calculations we need to perform a simple mass balance. In other words, we need to honor the constraint that the resulting or target mass of any component is equal to the initial mass of that component plus the added mass of that component. It is assumed that the fortifier contains only alcohol and water, and that the sweetener contains only sucrose and water. For water, sugar, and alcohol the mass balances are:
where:
We can also write a mass balance on the total mass as:
where:
We can relate the masses of the liquids to their volumes and specific gravities
as follows:
where:
Knowing the initial and target sugar (true Brix) levels we can then relate the initial and final sugar masses to the initial and final total masses as follows:
where:
Substituting equations (6) and (7) into equations (8) and (9) gives us:
If we're adding honey or concentrate as a sweetener, we'll need to account for the fact that they contain both sugar and water. We can express the amount of sugar added as:
Where Alcohol masses can be related to the volumes, specific gravities, and alcohol levels of the liquids as follows:
where:
Substituting equations (10) through (12) into equation (2) we get the sugar mass balance equation:
Substituting equations (13) through (15) into equation (3) we get the alcohol mass balance equation:
And substituting equations (5) through (7) into equation (4) we get the total mass balance equation:
Equations (16) through (18) form the basis for all of these calculations. They'll just be re-arranged and solved differently depending on what we're solving for. Back to top Back to top## Option 1: Specify Target Alcohol & Sugar > Calculate Additions and Volume
In this case the known values are sg, _{i}a,
_{wi}B, _{i}sg,
_{f}a, _{wf}B,
_{f}sg, and _{fa}a.
We need to solve for _{wfa}v, _{fa}m,
and _{sa}v.
_{f}
If we solve equation (18) for v and then substitute them into equation
(16) we can solve for _{fa}v:
_{f}
Then we can re-arrange equation (17) to solve for the amount of fortifier to add:
Knowing how much fortifier we're adding we can then re-arrange equation (18) to solve for the amount of sweetener to add: Back to top ## Option 2: Specify Target Alcohol, Sugar, & Volume - Calculate Additions
In this case the known values are a, _{wi}B,
_{i}v, _{f}sg,
_{f}a, _{wf}B,
_{f}sg, and _{fa}a.
We need to solve for _{wfa}v, _{fa}m,
and _{sa}v.
_{i}
Again we solve equation (18) for v and then substitute them
into equation equation (16), but this time we solve for _{fa}v:
_{i}
Then we can solve equations (20) and (21) for the amounts of fortifier and sweetener to add. Back to top## Option 3: Specify Additions - Calculate Resulting Alcohol, Sugar, & Volume
In this case the known values are sg, _{i}a,
_{wi}B, _{i}v,
_{fa}sg, _{fa}a, and
_{wfa}m. We need to solve for _{sa}
v, _{f}sg, _{f}a,
and _{wf}B.
_{f}
We can easily solve for
We can solve for
We can then determine
B and _{f}a using the
Hackbarth model and solve equation
(18) for _{wf}v to get:_{f}Back to top ## Fortification Point Calculator## IntroductionPort wine is traditionally made by adding a fortifier to a fermenting grape must at a specific point during the fermentation. The addition of the fortifier stops the fermentation by elevating the alcohol content of the must above the alcohol tolerance ot the yeast, thereby leaving the desired amount of residual sugar. The fortifier is traditionally a distilled wine spirit, known as aguardente or brandy, with an alcohol content of 76-78% v/v. The Fortification Point Calculator determines 1) the specific gravity (SG) at which to stop an active fermentation to yield the desired level of residual sugar in a fortified wine, and 2) the amount of fortifier required yield the desired alcohol level. It accounts for the alcohol produced during fermentation, and for the dilution of the residual sugar by the addition of the fortifier. After this "ideal" fortification point is calculated, the user has the option to override the calculated value of SG at the fortification point in order to model the impact of fortifying at a different SG. If the entered SG is lower than the ideal value, then there is not enough residual sugar to achieve the target sugar content, so the sweetener addition required to achieve the target sugar content is calculated. If the entered SG is higher than the ideal value, the sugar content will exceed the target sugar content after fortification, so the resulting sugar content after the addition of fortifier is calculated. All volumes and specific gravities have a temperature basis of 20°C (68°F). It is assumed that the fortifier contains only ethanol and water, and that the sweetener contains only sucrose and water. ## Input Field DefinitionsSweetener – 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. This is only used if the user enters a value of wine SG at fortification that is less than the "ideal" value, in which case the addition of a sweetener is required to achieve the target sugar content. Fortifier Alcohol Content – The alcohol content of the fortifier being added. Wine Volume – The volume of the fermenting wine at the time of fortification. If this volume option is selected, the resulting volume after fortification is calculated. Target Volume – The volume of the fortified wine after the addition of the calculated fortifier and sweetener additions. If this volume option is selected, the required wine volume at the fortification point is calculated. Initial Must SG – The SG of the must prior to the start of fermentation. Target Alcohol Content – The desired alcohol content of the fortified wine. Target Sugar Content – The desired total solids content of the fortified wine after the addition of fortifier and sweetener. Wine SG at Fortification – The SG of the fermenting wine at the time of fortification. This field can serve either as an input field or an output field. Initially the "ideal" fortification point SG is calculated based on the inputs above. If the calculated value is overridden by the user, then either the target sugar content or the required sweetener addition are calculated, depending on whether the entered SG value is greater than or less than the ideal value. ## Output Field DefinitionsWine Alcohol Content – The calculated alcohol content of the fermenting wine at the fortification point. Wine Sugar Content – The calculated total solids content (true Brix) of the fermenting wine at the fortification point. Wine Required – The volume of fermenting wine required to yield the desired alcohol content, sugar content, and volume. Reported only if target volume is selected as the volume option above. Fortifier Required – The calculated amount of fortifier required to yield the desired alcohol content, sugar content, and volume. Sugar (or Honey or Concentrate) Required – The calculated amount of sweetener required to yield the desired alcohol content, sugar content, and volume. This will be zero unless the user enters a wine SG at fortification that is less than the "ideal" value. Resulting Volume – The calculated volume of the fortified wine after adding the specified amounts of fortifier and sweetener. Reported only if wine volume is selected as the volume option above. ## Calculation Details
We'll need to specify the initial specific gravity of the must
In this case the known values are v), _{f}sg,
_{m}a, _{wf}B,
_{f}sg, _{f}sg,
_{fa}a, and _{wfa}m.
Since we're not adding a sweetener in this case we can eliminate the terms
_{sa}m and _{sa}B.
We need to solve for _{s}v (or _{f}v),
_{i}sg, _{i}a,
_{wi}B, and _{i}v.
Since _{fa}sg, _{i}a,
and _{wi}B are all interdependent, we'll need to iterate
to find a solution.
_{i}
We start by substituting equation (18) into equation (17) to eliminate
v:
_{f}
Or, if we're solving for
In these equations the subscript B:
_{i}
Next we update the estimate of B and
_{i}a, and then repeat the calculations in equations
(26) through (28) until we converge on a solution. Then we can solve equation
(18) for the volume of fortifier to add:
_{wi}
After the "ideal" fortification point is calculated, the user has the
option to override the calculated value of a using
the Balling method and the value of
_{wi}B using the Hackbarth model.
_{i}
If the value of
If the value of B.
To do this we'll follow an iterative procedure similar to the one described above utilizing
equations (26) through (29), but we'll use a starting value of 1.0 for
_{f}sg, and instead of equation (28) we'll solve equation (16)
for _{f}B:
_{f}
Below the results of the FermCalc Fortification Point calculator are compared to the classic work of Pato & Miranda (1938) and to the fortification calculator found on the Australian Wine Research Institute (AWRI) web site. The density at fortification and the amount of fortifier to add were calculated to yield a fortified wine with an alcohol content of 20% v/v and a density of 1028.51 g/L using a fortifying spirit with an alcohol content of 77% v/v. The FermCalc results generally fall between the two other methods, and show better agreeement with the Pato & Miranda results. (The forumulas used by the AWRI calculator aren't documented on their site, but it apparently uses the formulas found on the Monash Scientific site because they give identical results.)
## Hackbarth SG Calculator## IntroductionThe Hackbarth SG Calculator utilizes the Hackbarth model to estimate SG from given values of alcohol content and sugar content. Its purpose is mainly to test and validate the Hackbarth calculation in FermCalc, but it is also useful in the preparation of fortified wines and liqueurs. ## Input Field DefinitionsAlcohol Content – Alcohol content of the solution. Range: 0% to 100% vol/vol. Sugar Content – Sugar content of the solution. Range: 0% to 100% by wt. ## Output Field DefinitionsCalculated SG – The calculated specific gravity (20°C/20°C) of the solution. ## Calculation DetailsSpecific gravity is calculated using the Hackbarth model for calculating the specific gravity of ethanol-sucrose solutions. The model has a temperature basis of 20°C (68°F). Back to top
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