Beer and Brewing

This is a follow-up from the post on Priming. There’s also a calculator based on this work.

Carbonating beer is normally done by either priming with sugar or force carbonation. Force carbonation is actually just a short cut of priming. Sugar is fermented, generating CO2, which pressurises the headspace, forcing CO2 to be dissolved into the beer.

Force carbonation uses a high pressure cylinder that keeps the head pressure constant thus carbonating the beer to a pre-determined level. Existing priming calculators assume that the head space is so small (in relation to the volume of beer) that the amount of CO2 left is negligible compared to the amount dissolved into the beer. However, this assumption becomes less and less true as the volume of the head space increases.

My new approach should work for arbitrary sized head spaces (e.g. 10L of beer in a 25L barrel) but there are limits. As volume of beer decreases proportionately more sugar is required and at some point it’ll start to noticeable increase the ABV of the beer. Also the required head pressure may exceed the capabilities of a simple plastic barrel.

So, down the detail:

First work out how many moles per litre of CO2 are required in your beer:

   

where Ca is the concentration of CO2, L is the number of volumes per litre required (technically the number of litres of CO2 at 1 atm and 273.15K) and 22.4 is the number of litres of gas in one mole (at STP). CHECK!

From this we can work out the mass of dissolved CO2:

   

Ca from before, Vbeer is the volume of the beer in litres. 44 is the number of grams of CO2 in one mole (the atomic weight).

Then work out Henry’s Constant for CO2 at the temperature at which the beer is to be stored. Henry’s constant is per gas and not as constant as you might think. We use Van’t Hoff’s equation to work out the constant at a particular temperature because Henry’s Constant is defined to be at 298.15K.

   

Where 0.034 is Henry’s Constant at 298.15K, 2400 is Van’t Hoff’s coefficient for CO2.

Next step is to work out the head space pressure that would correspond the amount of dissolved CO2 that we require. We can work this out using Henry’s Law that gives the relationship between concentration of dissolved gas and the pressure of the gas above it.

   

Phead is the head pressure in atmospheres, Ca is the concentration from above and Hcp is Henry’s constant at the storage temperature. Subtract one because this pressure is in addition to atmospheric pressure.

Conversions from atmospheres to Pascals and PSI:

In Pascals:

   

In PSI:

   

Now we use the Ideal Gas equation (PV = nRT) to work out the mass of CO2 in the head space:

   

Mgas is the mass of gas in grams, Phead is the head pressure in Pascals, Vhead is the volume of the head space in litres, temperature is the beer temperature in K and 188 is the value of Ideal Gas Constant for CO2 (it replaces the R component and converts moles to grams).

Now we now the total amount of CO2 required Mgas + Mdiss. However, there’s one thing overlooked: any CO2 that is already dissolved in the beer from the fermentation process. This can be calculated using the same set of equations and assuming atmospheric pressure and using the temperature that the beer was fermented at (or kept at prior to priming).

   

   

   

So now we have all the masses necessary:

   

This mass of CO2 is the amount which we need to add to ensure that the right amount is dissolved in the beer and the right amount of head pressure is present. In the standard calculators Mgas is assumed to be << Mdiss and is left out.

Now to work out the amount of sugar (glucose) required to generate this amount of CO2. Chemistry tell us that 1 mole of Glucose generates 2 moles of CO2. So, working backwards:

   

Additionally, we can use all this information to work out something else. Some people want to force carbonate using just one additional of CO2 i.e. pressurise it to well above the standard pressure and, once the CO2 has dissolved, it’ll drop down to the ‘normal’ pressure thus maintaining the right level of carbonation.

Firstly, we calculate the number of moles of CO2 we need to provide:

   

Then we use the Ideal Gas equation to work out the pressure of that amount of CO2 at Storage Temperature for that head space

   

where Pco2 is the head pressure in atmospheres, Molco2 is the above, Tstore is the storage temperature in K and Vhead the head space in litres.

However, this is less useful than it might appear. You might think “Let’s just fill a keg, pressurise it to this level and leave it.” but for small head spaces the pressure required can get silly quickly. For 2 vol at 14C for 20L with a head space of 5L the required pressure is 85PSI, which exceeds typical CO2 cylinders.

Try with 18L in a 18.9L Corny keg (0.9L head space) and you’ll have to pressurise it to in excess of 370PSI. No chance. Look at it this way: 18L beer means 36L of CO2, the ratio of gaseous to aqueous CO2 is about 40:1. That means about 1500L of CO2 in a space of less than 1L.

We’ve suffered from under primed beer in the past and I’ve been trying to figure out why. I think that the problem is the head space in the barrels. Priming bottles seems to be quite reliable but we prefer to prime our barrels and let the carbonation happen in bulk. Regularly we finish up with under carbonated beers. Eventually they might carbonate in the bottle but it can take a while.

Anyway, I started thinking about the head space in the barrels. They’re designed for 20L brewers but have an extra head space of about 5L. Sometimes we only do 10L brewers but use the same barrels.

So, the way that carbonation works is down to some basic thermodynamic physics. If we consider forced carbonation for a moment: CO2 is pumped into a keg. Over time the CO2 ‘dissolves’ into the beer and when it’s dispensed it’s carbonated.

An equilibrium forms between the CO2 in gas form and the CO2 in the beer. That equilibrium depends on a few things: the pressure of the gas, the temperature of the system and the properties of the gas. CO2 happens to be very soluble (compared to N2, O2 and other common gases). It’s about 50 times more soluble at room temperature than N2.

Henry’s Law gives the relationship between the concentration in the liquid, the gas pressure and the solubility. Contentration = Solubility x Pressure. Basically the higher the pressure, the higher the concentration. No shock there.

Aside: The solubility for a gas is called Henry’s Constant but it’s only constant for a gas at one temperature. van ‘t Hoff’s equation allows us to calculate the Constant for any particular temperature. At room temperature it’s 29, at 3C it’s 52, for CO2. So CO2 is more soluble the colder it gets.

So, this is why we can calculate the CO2 pressure required to successfully carbonate a beer using a gas cylinder – we just turn the value until there’s 30psi (or whatever) in the Corny keg, easy. That’s just basic physics.

The chemistry comes in when you ‘re using priming sugar. As we all know yeast turns sugar into alcohol and CO2. And we know how much CO2 is produced from a particular amount of sugar. So this should be easy…

This is where the head space comes in. You might know the volume of CO2 produced but unless that translates into the right head pressure then the beer won’t carbonate properly. Boyle’s Law states that, at a fixed temperature, Pressure is inversely proportional to Volume. Thus a larger volume of head space means a lower pressure for the same amount of gas.

Aside: Equally Gay-Lussac’s Law tells us that the pressure will drop as the temperature drops.

Aside: During the brewing process the beer will be saturated with CO2 (atmospheric pressure will play its part).

What does this mean then? Firstly, that it’s easier to reliably carbonate with a cylinder than with priming sugar. Secondly, if we’re going to use priming sugar then we need to do some more calculations.

If we want to calculate the right amount of priming sugar then we’re going to need to know a few things: 1) Temperature at which the beer was fermentated (to calculate the amount of CO2 in the beer at atmospheric pressure; 2) volume of the head space; 3) required carbonation level.

From these we should be able to work out the required pressure of CO2 in the head space at the storage temperature, then work out how much CO2 is required to pressurize the head space to that level.

Simple right? We’ll see. I’ve not tried it yet.

Oh, and just to note that this doesn’t take into account two things: 1) Dalton’s Law – there will be other gases in the head space – hopefully no O2 but there will be ethanol fumes and water vapour; 2) Le Chatelier’s Principle – CO2 in solution reacts with the water to form other compounds and reaches an equilibrium based on the concentration.

Not sure how much difference 1) makes as Dalton’s Law says that the partial pressures are independent. As for 2), it means that some of the CO2 will disappear as other compounds, again, not sure what impact this has.

We attempted our first Attobrew last night. It was based on the Magnum Blonde recipe we’ve done before. It’s essentially just Maris Otter Pale Ale Malt and a single hop in the boil. Normally the hop is Magnum but we used an open packet of old Northdown for this test so as not to have open a packet of the good stuff.

It went pretty much according the plan. 121g of malt plus 363ml of water at 75C filled a 500ml metal flask. After 5 minutes the mash was at about 68C so I’ll drop the temperature of the strike water a degree next time.

Left it 15 minutes, drained the wort out through a small sieve. Refilled the flask with more hot water, left it for another 10 minutes. Drained it. Refilled it. Shook it. Drained it.

So at that point we had about 700ml of wort. Put it in a pan with 1.8g of Northdown and boiled it for 15 minutes. The boil was a bit vigorous so we finished with about 400ml of wort after cooling. The cooling was pretty quick: no more than 5 minutes.

Poured it into a 1.5L Coke bottle through the sieve and a funnel. Added a pinch of yeast nutrient, shook it up to aerate and added a dash of Safale T-58 yeast.

The whole process took about 1.5 hours from gathering the components to putting the Coke bottle to one side to ferment. Could probably get this down to an hour if both of us were doing things.

The OG was a bit low (1.040 as opposed to the desired 1.049). The wort was quite murky, as you’d expect from a mash which had been drained quickly. It might clear in the ferment.

Lessons learned

• Using 3:1 water to grain was pushing the flask volume. 2.5:1 would work better.
• An infrared thermometer is very useful for checking water temperature. As is a digital probe thermometer for the mash temperature.
• Calibrating the “mash tun’s” thermal profile in advance is a good idea. The strike temperature should have been 73.4C but it hit 75C and, as a result, the mash temperature was a degree C or so too high.
• A bigger pan of strike water might give more stable water temperature.
• Draining the wort through a tiny sieve really could do with two sets of hands. A bigger sieve might work better.
• The grain blocked the mouth of the flask when tipped upside down. Tilting gently might work better.
• A longer mash might be necessary as the sugar extraction was a bit low. Or that might just be the characteristics of such a small mash.
• Hitting the pre-boil volume (1.1L) this way is going to be difficult. Either accept a lower volume, or tip the grain into a big sieve and rinse into the pan.
• Don’t boil too vigorously, or for as long, as there isn’t much wort to begin with.

A normal brew day is about 6-7 hours. How can we make it shorter?

Our usual time saving activities:

• Measure and weight malts, hops and chemical the day before.
• Fill the HLT the day before with strike and sparge water to allow any chlorine to escape.
• On the day heat the water while doing other things (sleeping, breakfast etc.).
• Ensuring that tasks that can be done in parallel are (e.g. activating yeast while the wort is aerating).

New ideas (for us):

• Mash for as short a time as possible as the malt allows. Well modified malts (base malts) don’t need much time – about 20 minutes to convert.
• Use the sparging as extra mash time.
• Collect as little wort as possible (low strike to grain ratio/minimal sparging). This reduces the heating and cooling times.
• Draining directly into a heating boiler will cut down on the time to reach a boil.
• Boiling doesn’t need to be for more than 15 minutes. Just enough time to extract and isomerise the alpha acids from the hops. Less time means more hops but the extraction is not linear and most of the extraction is done earlier.
• Fast cooling can be done using a plate chiller straight into the fermentor.
• Remember to aerate the wort as it’s draining into the fermentor and activate your yeast at the same time.

So the numbers: Heating 20L is about 40m. Mash 15m. Drain 10m. Wait 10m. Drain 10m. Heat for 20m. Boil 15m. Cool 15m. Add 15m for ancillary bits and pieces.

Total: 2.5h. Less than 2h after the water is heated the yeast can be pitched.

Without a plate chiller about another 30m is required. Using ice can help though. 1L of ice at -20C in 10L of wort at about 30C will drop the temperature by about 6 or 12C. Given that the longest part of the cool is the last 15-20C then this can save quite a bit of time. Adding ice also helps to top up the low wort volume.

We brew as a couple so there are certain things that one can be doing while the other is doing something else but it’s worth understanding your own ‘critical path’. One of our limitations is that our HLT is also our Copper so the wort sits in buckets waiting until the sparging is over before it can be heated and boiled. A separate Copper would mean that the heating and boiling could start as soon as the vorlaufing is over (although it would make sense to have a reasonable volume of wort first to avoid burning anything).

The usual critical path is something like:

Filling HLT -> Heating liquor -> Mashing -> Vorlaufing -> Sparging -> Heating wort -> Boiling wort -> Cooling wort -> Fermenting -> Conditioning -> Bottling.

There’s no way to change the order and only some overlap is possible (e.g. heating while filling).

In a larger set up, where there’s multiple pieces of the same equipment, there are savings to be made. e.g. reusing the (warmed) water used to cool the wort as liquor, or conditioning one brew while fermenting, cooling, boiling, sparging and/or mashing others (pipelining).

We’re running out of prefixes to describe small brews. This idea is about trying to brew a single pint of beer in a simple, quick and repeatable way. Why? Firstly, it’s just interesting, secondly, it’s a quick way of prototyping a beer (assuming it works!) using common equipment that’s easy to clean (just dump it all in the dishwasher!).

So, it would start with mashing a small amount of grain with water at the right temperature (heated on the hob) in a Thermos flask. Ideally the flask should have been calibrated so that our strike water calculator works properly.

It would be nice to be able to knock together a container that can be heated and use a PID to keep the mash temperature at the required point but that’s beyond me at the moment.

Once mashed it’s easy to just pour out the wort into a pan. Add a small amount of hops and then boil for 15 minutes. Boiling for longer could reduce it too much.

Cooling can be accomplished by dipping the pan in a sink of cold water for a few minutes.

Ferment in a sanitised 1-2L drinks bottle with a small amount of yeast, nutrient and a loose lid. Shake to aerate.

Add dry hops to the bottle. After a week decant/syphon/syringe off the beer into a 500ml bottle primed with a carbonation drop/sugar.

Wait. Drink.

Notes: Currently untried. Not sure how much liquid is required at each stage to achieve the required single pint. Working backwards: 500ml in bottle -> 550ml in fermentor -> 1L pre-boil -> 1.125L for strike and sparge – assuming 125g of grain -> strike of about 350ml -> sparge with about 780ml. Less sparge water would mean less to boil (which could be risky as evaporation rate is proportional to the input heat (and pan size), not the volume of liquid) and would require a top up.

Scaling: This was written around making a single 500ml bottle of beer but, depending on the sizes of your various equipment it can scaled up a little. Our Thermos flasks are 500ml so that’s our limit on the mash tun. A larger Thermos means more wort. It would be a strange household that didn’t have pans which could hold 3-4L of wort and 2L bottles are easy enough to find (just remember not to fill them or things will get messy – leave about 30% headroom).

Arran from the home brew group brews this lovely Imperial Russian Stout and he let us have the recipe – thanks Aaron. Finally we’ve got around to brewing it. We managed to fit this in between Christmas and New Year 2018.

Obviously this requires a considerable grain bill. For 12L it totalled over 6kg (which is more than a typical 20L brew needs). A mixutre of Maris, Roasted barley, oats, crystal, Special B, Oat flakes and chocolate malts, bittered with Cluster, Fuggle and Target. Fermented with two lots of Safale S04 to ensure a nice strong fermentation.

The day went well. No mistakes, no failures, no problems. The mash and boil were both long ones (90m each) but we managed to finish at a sensible time and then head out to see friends.

So far it’s fermented quickly and with some vigour. It’ll be primed, kegged and conditioned for a couple of weeks to carbonate and then bottled.