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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

Introduction

The 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.

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.

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 Definitions

Fortifier 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.

Calculation Details

Mass Balance Equations

To 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:

m_wf = m_wi + m_wfa + m_wsa (1)

m_sf = m_si + m_ssa (2)

m_af = m_ai + m_afa (3)

where:

m_wf = final water mass, kg
m_wi = wine initial water mass, kg
m_wfa = mass of water in the fortifier added, kg
m_wsa = mass of water in the sweetener (sugar, honey, or concentrate) added, kg
m_sf = final sugar mass, kg
m_si = wine initial sugar mass, kg
m_ssa = mass of sugar in the sweetener (sugar, honey, or concentrate) added, kg
m_af = final alcohol mass, kg
m_ai = wine initial alcohol mass, kg
m_afa = mass of alcohol in the fortifier added, kg

We can also write a mass balance on the total mass as:

m_tf = m_ti + m_fa + m_sa (4)

where:

m_tf = final total mass, kg
m_ti = wine initial total mass, kg
m_fa = mass of fortifier added, kg
m_sa = mass of sweetener added, kg

We can relate the masses of the liquids to their volumes and specific gravities as follows:

m_fa = v_fasg_faρ_w (5)

m_ti = v_isg_iρ_w (6)

m_tf = v_fsg_fρ_w (7)

where:

v_fa = volume of fortifier added, liters
v_i = wine initial volume, liters
v_f = final volume, liters
sg_fa = fortifier specific gravity
sg_i = wine initial specific gravity
sg_f = final specific gravity
ρ_w = density of water = 0.9982 kg/liter at 20ºC

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:

m_si = m_tiB_i/100 (8)

m_sf = m_tfB_f/100 (9)

where:

B_i = initial wine Brix
B_f = final Brix

Substituting equations (6) and (7) into equations (8) and (9) gives us:

m_si = v_isg_iρ_wB_i/100 (10)

m_sf = v_fsg_fρ_wB_f/100 (11)

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:

m_ssa = m_saB_s/100 (12)

Where B_s is the Brix of the sweetener.

Alcohol masses can be related to the volumes, specific gravities, and alcohol levels of the liquids as follows:

m_ai = v_isg_iρ_wa_wi/100 (13)

m_af = v_fsg_fρ_wa_wf/100 (14)

m_afa = v_fasg_faρ_wa_wfa/100 (15)

where:

a_wi = wine initial alcohol level, % by weight
a_wf = final alcohol level, % by weight
a_wfa = fortifier alcohol level, % by weight

Substituting equations (10) through (12) into equation (2) we get the sugar mass balance equation:

v_fsg_fρ_wB_f = v_isg_iρ_wB_i + m_saB_s (16)

Substituting equations (13) through (15) into equation (3) we get the alcohol mass balance equation:

v_fsg_fρ_wa_wf = v_isg_iρ_wa_wi + v_fasg_faρ_wa_wfa (17)

And substituting equations (5) through (7) into equation (4) we get the total mass balance equation:

v_fsg_fρ_w = v_isg_iρ_w + v_fasg_faρ_w + m_sa (18)

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.

Option 1: Specify Target Alcohol & Sugar > Calculate Additions and Volume

In this case the known values are v_i, sg_i, a_wi, B_i, sg_f, a_wf, B_f, sg_fa, and a_wfa. We need to solve for v_fa, m_sa, and v_f.

If we solve equation (18) for m_sa and solve equation (17) for v_fa and then substitute them into equation (16) we can solve for v_f:

v_f = [v_isg_i(B_i - B_s + B_sa_wi/a_wfa)] / [sg_f(B_f - B_s + B_sa_wf/a_wfa)] (19)

Then we can re-arrange equation (17) to solve for the amount of fortifier to add:

v_fa = (v_fsg_fa_wf - v_isg_ia_wi) / (sg_faa_wfa) (20)

Knowing how much fortifier we're adding we can then re-arrange equation (18) to solve for the amount of sweetener to add:

m_sa = (v_fsg_f - v_isg_i - v_fasg_fa)ρ_w (21)

In the case of concentrate, the mass calculated from equation (21) is converted to a volume as:

v_ca = m_sa / (sg_cρ_w) (22)

where:

v_ca = volume of concentrate added, liters
sg_c = concentrate specific gravity

Option 2: Specify Target Alcohol, Sugar, & Volume - Calculate Additions

In this case the known values are sg_i, a_wi, B_i, v_f, sg_f, a_wf, B_f, sg_fa, and a_wfa. We need to solve for v_fa, m_sa, and v_i.

Again we solve equation (18) for m_sa and solve equation (17) for v_fa and then substitute them into equation equation (16), but this time we solve for v_i:

v_i = [v_fsg_f(B_f - B_s + B_sa_wf/a_wfa)] / [sg_i(B_i - B_s + B_sa_wi/a_wfa)] (23)

Then we can solve equations (20) and (21) for the amounts of fortifier and sweetener to add.

Option 3: Specify Additions - Calculate Resulting Alcohol, Sugar, & Volume

In this case the known values are v_i, sg_i, a_wi, B_i, v_fa, sg_fa, a_wfa, and m_sa. We need to solve for v_f, sg_f, a_wf, and B_f.

We can easily solve for B_f by dividing equation (16) by equation (18):

B_f = (v_isg_iρ_wB_i + m_saB_s) / (v_isg_iρ_w + v_fasg_faρ_w + m_sa) (24)

We can solve for a_wf by dividing equation(17) by equation (18):

a_wf = (v_isg_iρ_wa_wi + v_fasg_faρ_wa_wfa) / (v_isg_iρ_w + v_fasg_faρ_w + m_sa) (25)

We can then determine sg_f from B_f and a_wf using the Hackbarth model and solve equation (18) for v_f to get:

v_f = (v_isg_iρ_w + v_fasg_faρ_w + m_sa) / (sg_fρ_w) (26)

Fortification Point Calculator

Introduction

Port 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 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. 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 Definitions

Wine 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 sg_m in order to calculate the alcohol produced during the fermentation from the drop in specific gravity. We'll use the Balling Method to calculate the amount of alcohol produced because it's simple to apply and seems to be just as accurate as the other SG-drop methods.

In this case the known values are v_i (or v_f), sg_m, a_wf, B_f, sg_f, sg_fa, a_wfa, and m_sa. Since we're not adding a sweetener in this case we can eliminate the terms m_sa and B_s. We need to solve for v_f (or v_i), sg_i, a_wi, B_i, and v_fa. Since sg_i, a_wi, and B_i are all interdependent, we'll need to iterate to find a solution.

We start by substituting equation (18) into equation (17) to eliminate v_fa and solve for v_f:

v_f = [v_isg_i(a_wfa - a_wi)] / [sg_f(a_wfa - a_wf)] (27)

Or, if we're solving for v_i:

v_i = [v_fsg_f(a_wfa - a_wf)] / [sg_i(a_wfa - a_wi)] (28)

In these equations the subscript i denotes values at the fortification point. For the first iteration we'll assume a value of 1.0 for sg_i. After solving equation (27) or (28) we can solve equation (16) for B_i:

B_i = v_fsg_fB_f / v_isg_i (29)

Next we update the estimate of sg_i using Hackbarth model with the calculated values of B_i and a_wi, and then repeat the calculations in equations (27) through (29) until we converge on a solution. Then we can solve equation (18) for the volume of fortifier to add:

v_fa = (v_fsg_f - v_isg_i) / (sg_fa) (30)

After the "ideal" fortification point is calculated, the user has the option to override the calculated value of sg_i in order to model the impact of fortifying at a different SG. When this is done, we first calculate the resulting value of a_wi using the Balling method and the value of B_i using the Hackbarth model.

If the value of sg_i entered by the user is lower than the ideal value, then there is not enough residual sugar to achieve the target sugar content. In this case we can then solve equation (19) or (23) above, depending on whether the initial volume or the target volume were specified, and then solve equations (20) and (21) to determine the required additions of fortifier and sugar.

If the value of sg_i entered by the user is higher than the "ideal" fortification point, then the sugar content of the wine will be too high to yield the target sugar content. In this case, no sweetener will be added and we'll need to calculate the resulting sugar content B_f. To do this we'll follow an iterative procedure similar to the one described above utilizing equations (27) through (30), but we'll use a starting value of 1.0 for sg_f, and instead of equation (29) we'll solve equation (16) for B_f:

B_f = v_isg_iB_i / v_fsg_f (31)

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.)

aguardente

Hackbarth SG Calculator

Introduction

The 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 Definitions

Alcohol 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 Definitions

Calculated SG – The calculated specific gravity (20°C/20°C) of the solution.

Calculation Details

Specific 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).