Engineering task and calculation objective
The BTK module calculates the cooling of beer tanks – cylindroconical fermentation and storage tanks (CCTs) as used in breweries for fermentation, maturation, and cold storage. The tanks are temperature-controlled by external cooling zones, typically half-pipe cooling jackets on the cylindrical shell and on the cone, supplied with a glycol-water mixture or with directly evaporating ammonia (NH3).
From the tank geometry – diameter, working and total volume, cone angle, knuckle radius, wall thickness – and the cooling jacket data (hydraulic and equivalent diameter, half-pipe spacing, active cooling surfaces, and zone layout), the module determines whether the product is brought from the initial to the final temperature within the maximum allowable cooling time tmax. The coolant temperatures at the shell and cone inlets, the fouling resistance, the ambient conditions (air temperature, wind velocity), and the heat of fermentation from the extract degradation all enter the balance.
Anyone who wants to calculate the cooling duty of a beer tank obtains the design basis for the refrigeration plant and the cooling zone layout – decisive for product quality (defined cooling rates) and for sizing the refrigeration capacity in brewhouse and cellar operation.
Calculation workflow
- Record tank geometry and filling: Diameter DT, working volume Vb, total volume Vr, cone angle, and knuckle radius describe the tank; the wall thickness enters the overall heat transfer. The working volume yields the product mass to be cooled.
- Define the cooling task: The product temperature at the start (TPA) and at the end of cooling (TPE) and the maximum allowable cooling time tmax define the task. The extract degradation EA provides the additional heat of fermentation released during cooling; ambient temperature and wind velocity give the heat gain or loss across the tank surface.
- Define coolant and cooling zones: For the selected coolant (directly evaporating NH3 or glycol with its volume fraction), the inlet temperatures at the shell (TeM) and cone (TAK) and the outlet temperature TA are set. The cooling jackets on cone and shell are described by hydraulic and equivalent diameter, half-pipe spacing, and active surfaces per zone.
- Calculate heat transfer and overall heat transfer: On the product side, natural convection develops in the tank; on the coolant side, forced flow in the half-pipe jacket. From both heat transfer coefficients, the wall conduction, and the fouling resistance f follows the overall heat transfer coefficient of each cooling zone.
- Balance the cooling time and assess the zones: The heat to be removed from product cooling, heat of fermentation, and ambient gains is compared with the zone duties; from this the temperature profile over time results. If the achieved cooling time exceeds tmax, the cooling surfaces, number of zones, or coolant temperature are adjusted; the allowable pressure drop of the jackets is also checked.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| tP | tP | °C |
| tL | tL | °C |
| VB | VB | m³ |
| DT | DT | m |
| HT | HT | m |
| HF | HF | m |
| alphaiB | alphaiB | W/(m²·K) |
| ßiB | ßiB | m²·K/W |
| ßaB | ßaB | m²·K/W |
| alphaaB | alphaaB | W/(m²·K) |
| AB | AB | m² |
| tgB | tgB | °C |
| taB | taB | °C |
| QhB | QhB | W |
| QiB | QiB | W |
| QaB | QaB | W |
| ßiM | ßiM | m²·K/W |
| ßaM | ßaM | m²·K/W |
| alphaaM | alphaaM | W/(m²·K) |
| alphaiMb | alphaiMb | W/(m²·K) |
| AMb | AMb | m² |
| tgMb | tgMb | °C |
| taMb | taMb | °C |
| QhMb | QhMb | W |
Worked example
For a cylindroconical storage tank, the mean cooling duty for cooling the beer after completed primary fermentation is to be estimated – a worked example (pure sensible cooling; heat of fermentation and ambient heat gain not considered here).
Given values
| Working volume Vb | 200 hl (20 m³) |
| Density of beer ρ | ≈ 1,010 kg/m³ |
| Heat capacity of beer cp | ≈ 4.0 kJ/(kg·K) |
| Product temperature TPA → TPE | 12 °C → 0 °C |
| Maximum allowable cooling time tmax | 24 h |
Solution
Product mass
m = ρ · Vb = 1,010 kg/m³ · 20 m³ = 20,200 kg
Heat to be removed
Q = m · cp · (TPA − TPE) = 20,200 kg · 4.0 kJ/(kg·K) · 12 K = 969,600 kJ ≈ 970 MJ
Mean cooling duty
Q̇ = Q / tmax = 969,600 kJ / 86,400 s ≈ 11.2 kW
For sizing the refrigeration plant, the heat of fermentation from the extract degradation, ambient heat gains, and a simultaneity margin for tanks cooling in parallel are added; the actual zone duty must also cover the time profile (decreasing temperature difference to the coolant), so the installed capacity lies above the mean value.
Result
| Product mass m | 20,200 kg |
| Heat to be removed Q | ≈ 970 MJ |
| Mean cooling duty Q̇ | ≈ 11.2 kW |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Why are the cone and the shell treated as separate cooling zones?
In a cylindroconical tank, the beer stratifies during cooling: cold, denser product sinks into the cone, while the shell zones cool the layers above. Separately controllable zones on cone and shell make it possible to cool selectively – for example to keep the cone cold for yeast harvesting – and to maintain the natural convection loop in the tank. That is why inlet temperatures and surfaces are balanced individually per zone.
What role does the extract degradation play in the cooling balance?
When extract is fermented, heat is released – the heat of fermentation is on the order of 550 kJ per kg of fermented extract. As long as fermentation is still running, the cooling system must remove this heat in addition to the sensible cooling; for vigorously fermenting green beer it can constitute the main part of the cooling load. If the extract degradation is neglected, the refrigeration plant is undersized and the cooling time is exceeded.
What should be considered when choosing between direct NH3 cooling and glycol?
Directly evaporating ammonia provides an almost constant, low wall temperature with high heat transfer, but requires pressure-rated cooling jackets and the safety provisions of an ammonia system in the cellar. Glycol-water is easier to handle; however, with increasing glycol volume fraction the heat capacity drops and the viscosity rises, degrading heat transfer and pressure drop – the volume fraction should be only as high as frost protection requires.
Why must the wall temperature at the cooling surface not be arbitrarily low?
Beer freezes a few degrees below 0 °C, depending on original gravity and alcohol content. If the wall temperature of the cooling zone lies well below that, an ice layer forms on the inner wall, drastically degrading the overall heat transfer and potentially damaging the product locally. The coolant temperature is therefore chosen so that the cooling time is met without falling below the freezing limit at the wall.