Posted tagged ‘Brewhouse Calculations’

Day 462

December 11, 2012

First day of exams. Fever. Cough. I felt not quite bad enough to stay in bed but reasonably wretched for the Brewhouse Calculations exam, which started–of course–at 8:30 a.m.

Writing an exam is never a pleasant experience, and today especially so. Strangely enough, despite how I felt, I got through the calculations part of the exam with no problem. Grain weights, krausening, raising mash temperature via infusion, they all fell before my pencil and calculator. One would think that aceing the calculations in Brewing Calculations would guarantee me a good mark, but there were also several non-calculation type questions that my fuzzy mind had to contend with, and the old memory banks were clearly having a hard time. (“Name eight factors a brewer has to keep in mind when making a high-gravity brew”  was worth an astounding 16% of the final mark).

Oh well, on to History of Beer. The final exam for this was a bit more straightforward until I got to the last page. The final three questions asked my opinion about the course, what I found useful, and any changes I would suggest. Yes, I got marks for course feedback. Hmmm.

Another final exam tomorrow, so off to bed for some restorative sleep.

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Day 455

December 3, 2012

This is the second-last week of the term, and as we start to review what we have learned, it is surprising how far back into the distant mists of time the start of the semester seems.

Brewhouse Calculations, for example:

“Who can give the formula for calculating grain weight?”

Blank stares. We learned how to calculate grain weight?

“Week One. Remember? Grain weight? Anyone? Okay, how about the formula for determining strike water temperature?”

My mind raced furiously. I momentarily considered, then discarded the concept of simply sticking my pinkie finger into the mash and adding hot water until the temperature felt right. That didn’t sound like the correct answer for a calculations exam.

“All right, how about the first step in calculating yeast additions?”

Yeast. Hey, I remembered them. Facultative anaerobic single-celled critters. Pitching rates. Hectolitres. Cells per millilitre. Slowly the gears started to grind.

The best news of the day was that a sheet of formulae will be included with the exam. Now all we have to do is remember how to use the formulae.

Good thing we have seven days to study…

On to History of Beer, where we listened to the last batch of student presentations, including Probibition on both sides of the border, brewing in ancient Egypt, and Trappist breweries. Bill White finished the course with a look at brewing in the 21st century, and some trends for the future. Seven days until that exam too…

Day 441

November 20, 2012

You know you’re getting deep into the semester in Brewhouse Calculations when it takes you a solid hour just to review last week’s class. Finished with review, we moved on to some basic fluid mechanics. Liquids and semi-solids are moved all around the brewery in pipes, so an understanding of flow rates and turbulence would seem to be fairly important.

First, we learned that (in the metric world), a force of one newton pressing on one square metre equals a pressure of one pascal. That’s not much pressure, by the way–typical barometric pressure on a nice day is about 101,325 pascals (or about 101.3 kilopascals).

(Isaac Newton, by the way, was an English mathemetician who undoubtedly put many newtons of pressure on the seat of his chair when he sat down despite the fact that he was only one Newton. Blaise Pascal was a French mathemetician, which just goes to show that if you want something named after you, become a mathemetician. But I digress…)

We reviewed the various types of pressure gauges, then moved on to flow meters–the instruments that measure how fast fluid is moving through a pipe.

Due to friction with the pipe walls, fluid near the walls always moves slowest, while fluid in the middle of the pipe always moves fastest. If there is a gradual gradient between the two extremes and little in the way of eddying and break-up, then the flow is said to be smooth or “laminar”. If there is a lot of eddying and mixing of the liquid, the flow is turbulent. This is represented by something called a “Reynolds number”, and the formula for calcualting it is

Re = pud/µ

where

  • Re = the Reynolds number: less than 2100 is laminar, more than 4000 is turbulent, somewhere in between is transitional
  • p =  density of fluid (kg/m3)
  • u = velocity of the liquid (metres per second)
  • d = diameter of the pipe (metres)
  • µ = fluid dynamnic viscosity (kg per metre-second)

If you want to determine the minimum diameter pipe you need to ensure laminar flow, or conversely, the maximum diameter needed for turbulent flow, you can rearrange this formula:

d = (Re µ) / (p u)

For instance, if you want to move some wort that has a density of 1034 kg/m3 and a dynamic viscosity of 5 x 10-3 kg/ms, and your pump is going to move the wort at 5 m/s, then to ensure laminar flow (a Reynolds number of 2100):

d = (2100 x 5 x 103) / (5 x 1034) = 0.002 m = 2 millimetres

So to ensure laminar flow, your pipe can be no smaller than 2 mm in diameter. Since most pipes carrying wort are much larger than 2 mm, it seems you won’t have any trouble maintaining a laminar flow with this particular wort.

In History of Beer, it was more student presentations, including a history of glassware, brewing in Ontario, and the Aztec production and use of pulque, an intoxicating spirit made from the agave plant.

Instructor Bill White also covered brewing in North America in the 20th century (although at times I felt like it was Bill’s history of Labbatt’s in the 20th century.)

Day 434

November 13, 2012

Ooops. I discovered in Brewhouse Calculations, to my chagrin, that I had made a boo-boo. Turns out when mixing water and grain together, you need to multiply the grain’s weight by 40%, since the grain holds back a lot of its heat during mixing. (In the formula I posted last week, I left this out.) So to calculate the resultant temperature when we mix 200 kg of grain at 20°C into 300 L of water at 69°C, the formula should be:

c = [(0.4 x Aa) + (Bb)]/(0.4A + B)

where

  • A = grain weight
  • a = grain temperature
  • B = water weight (1 L of water = 1 kg. Yay, metric system!)
  • b = water temperature
  • c = resultant temperature

Plugging in all the right values:

c= [(0.4 x 200 kg x 20°C) + (300 kg x 69°C)]/(0.4 x 200) + 300 =

= [1600 + 20,700]/380 kg = 58.7°C

(Last week’s answer was 49.4°C. As I said, oops. Hope you weren’t using that blog post to study for an exam.)

Review finished, we had a real grab bag of calculations this week. First up was carbonation, which is interesting because we just learned some calculations for carbonation last week in FCF. Huh. Calculating when to close up the fermenter and allow CO2 being produced by fermentation to naturally carbonate the beer:

  1. Determine how many grams of CO2 are required (remembering that 1 g of CO2 = 0.506 volumes)
  2. Divide this by 0.46 to determine how much extract will be needed
  3. Convert grams of extract to degrees Plato
  4. Close up the fermenter when the gravity of the beer equals the number reached in Step 3 plus the desired final gravity.

So, if we want to naturally carbonate our beer with 2.5 volumes of CO2, and expect the yeast to attentuate the wort to 2.5°P:

Step 1: 2.5 volumes of CO2 desired/0.506  = 4.94 g/L desired

Step 2: Extract needed to produce that much CO2 = 4.94/0.46 = 10.74 g/L

Step 3: Extract needed converted to degrees Plato = (10.74/1000) x 100 [to convert to percent] = 1.1°P

Step 4: Close up fermenter when gravity reaches 2.5°P + 1.1°P = 3.6°P

OK, seems to work the same as what we learned in FCF. On to calculating how much wort to hold back in order to induce a secondary fermentation (i.e. krausening):

  1. Calculate the Apparent Degree of Fermentation (ADF): [original gravity – final gravity]/original gravity
  2. However, the Real Degree of Fermentation (RDF) will be lower because of the less dense alcohol in the mixture: RDF = ADF x 0.82
  3. Calculate the Real Final Extract (RFE) that is unfermentable: RFE = OG x (1 – RDF)
  4. Finally, calculate the percentage of wort that should be reserved: [(Desired g/100 mL of CO2 – existing g/100 mL of CO2)/0.46]/[OG – RFE]

Seem simple? Let’s assume we have 10 hL of 13°P wort all ready to be fermented at 20°C. We eventually want it to be carbonated with 6.5 g/L of CO2, and we believe the wort will eventually attenuate to 4°P. (We know from consulting a table that fermenting it at 20°C will cause 1.69 g/L of CO2 to be dissolved in the beer.)

Step 1: ADF = [OG – FG]/OG = (13-4)/13 = 69.2%

Step 2: RDF = ADF x 0.82 = 69.2% x 0.82 = 56.7%

Step 3: RFE = OG x (1 – RDF) = 13 x (1 – 0.567) = 5.63

Step 4: Percent of wort to be reserved = [(Desired g/100 mL of CO2 – existing g/100 mL of CO2)/0.46]/OG – RFE = [(0.65 – 0.169)/0.46]/(13 – 5.63) = 1.1/7.37 = 0.147 = 14.7%

From our 10 hL of wort, we should reserve 14.7% of it, or 147 L, to be added later in order to induce a secondary fermenttion that will produce 2.5 volumes of CO2 in the final product.

But wait, there’s more! On to balancing draught systems. In any bar’s draught system, the gas pressure needed to force beer from keg to tap is balanced by the resistance of the beer line, and can be helped or hindered by gravity, depending on whether the keg is above or below the level of the tap.

Gravity either adds or subtracts 0.5 psi per foot of rise or fall. As we saw last year in Packaging, various types of lines have various resistances, measured as psi/ft. I won’t go into the formulae; it is pretty basic–simply balance the pressure of the gas to the calculated resistance of the line. If there’s too much pressure, add some restrictor line near the tap to increase resistance. If there’s too much resistance, increase the gas pressure. If the gas pressure needed gets to be excessive, switch to a nitrogen/CO2 mix so that the nitrogen pushes the beer and the CO2 gas keeps the dissolved CO2 in the beer.

In History of Beer, some more student presentations today, including a history of the beer can. Bill White’s lecture that followed was about Beer in Art.

Day 427

November 5, 2012

Another week, another three hours of brewing calculations. Today was all about mixing and the subsequent effect on temperature. The main formula for the morning was

Aa + Bb = Cc

where

  • A = the volume of one substance (say, grain)
  • a = some quality of A, say temperature
  • B = the volume of a second substance (say, water)
  • b = the same quality as “a”
  • C = the volume of the two substances mixed together
  • c = the resultant new quality of the mixture

We can rearrange this to solve for any of the variables. For instance, if we wanted to solv for “c”, we could rearrange the formula to look like

c = (Aa + Bb)/C

So if we mix 200 kg of grain at 20°C into 300 L of water at 69°C, the new temperature of the mash (“c”) will be:

[(200 kg x 20°C) + (300 kg x 69°C)]/500 kg = 49.4°C

[EDIT: I discovered one week later that I have missed one factor in this formula. See the correct formula and the correct answer on Day 434.]

Many home brewers do not have any external heat source for their mash tuns, such as steam. Instead, when they want to raise the temperature of the mash in order to mash out, they have to add hot water to the mash tun. How much would Mr. Homebrewer have to add to the above mash to raise the temperature from 58°C to 63°C? Can we use the above formula to determine the resultant temperature of the mash? Well, sort of. First we have to do an in-between calculation, because it turns out that grain doesn’t transfer heat nearly as well as water. In fact, grain only transfers 40% of its heat. So we need to determine the Mash Heat Capacity (MCH), which will tell us how much heat is represented by the mash.

MCH = [(volume of grain x 40%) + volume of water]/volume of grain + volume of water

or, for the above example

[(200 x 0.4) + 300]/(200 + 300) = 0.76 = 76%

Since we want to find out the volume of water needed, we can rearrange our old friend Aa + Bb = Cc so it looks like this:

B = [((MCH x C) x (c – a)]/(b – c)

where B is the volume of the water to be added. In this case

B = [(0.76 x 500 L)(63°C – 58°C)]/(95°C – 63°C) = 59.4 L

Those of you are actually following along will notice that I have used 95°C for the temperature of the boiling water instead of 100°C, since by the time you transfer the water from the boiler, it probably loses 5 degrees.

If you are planning a decoction mash–where a portion of mash is removed, heated up and then returned to the mash tun to raise the mash tun temperature, this formula will also work to calculate how much mash has to be removed. As a matter of fact, it’s even easier than calcualting additions of hot water, since you don’t have to calculate the Mash Heat Capacity–you are adding grain and water to grain and water, so the MCH of one cancels out the MCH of the other.

We also learned how to calculate evaporation losses per hour during the boil. This was relatively simple compared to the above:

Step 1  – Calculate the percentage of volume that evaporates: (Finishing volume – starting volume)/starting volume

Step 2 – Determine the evaporation rate per hour: % volume evaporated (from Step 1)/length of boil in hours

Step 3 – Calculate the volume of wort lost per hour: evaporation rate/hr (from Ste 2) x starting volume

So if we do a boil of 1h 15min, start with a volume of 1100 L and end with 1000 L:

  1. (1100 – 1000)/11 = 9% evaporation loss
  2. 9%/1.25 hrs = 7.2 %/hr
  3. 7.2% x 1100 L = 79.2 L per hour evaporation loss

On to History of Beer. Today we had more student presentations, including The History of Molson, E.P. Taylor’s Effect on the Canadian Beer Industry, and Beer in Art. We also had a special guest, beer historian Ian Bowering, who also writes a column for the Great Lakes Brewing News called “The Jolly Giant”.

End of a long day, but assignments are starting to pile up again, so time to burn some midnight oil…

Day 420

October 30, 2012

Back to class. Somehow those two papers never got done. Huh.

And what better way to start the second half of the semester than with a few brewing calculations? First, a review of water chemistry, especially converting calcium and magnesium to equivalents of calcium carbonate, and calculating residual alkalinity. With our brains sufficiently woken up from their 10-day nap, we moved on to a few brewhouse design considerations: given the density of mash, what size of mash tun would we need for a given volume? Also, the difference between the angle of rest of a given substance (how steep a cone it forms when poured into a pile) and the angle of slide (how high you have to tilt a board holding a layer of a given substance before it starts to slide off the board.) Both of these angles will have a bearing on brewhouse equipment dsign. For instance, how steep does the cone at the bottom of a fermenter have to be to encourage descending yeast to fall to the bottom of the cone?

We also spent some time taking up the mid-term exam. Although I did reasonably well, I was annoyed that I thrown away 3 marks on simple arithmetic errors like misplaced decimal places, and another 2 marks for the complete mind blank of only completing the first part of a three-part question. D’ohh! Obviously I need to load up on more caffeine for those 8:30 a.m. exams.

Speaking of mid-terms, we wrote the History of Beer exam today. Well, not so much wrote it as checked it off, since it was 100 multiple choice questions. Afterwards, Bill White delivered a lecture on laws and beer–how the legal system has affected the production and consumption of beer through the ages. The four key dates seemed to be 1770 B.C., 1516, 1920 and 1979, which correspond to the establishment of Hammurabi’s Code in Mesopotamia (the first legal code that mentions penalties for serving bad beer, cheating customers and allowing seditious talk within the bar), the Rheinheitsgebot (the famous Bavarian Purity Law that only allowed beer to be made from malt, barley and water), Prohibition in the U.S., and the legalization of  homebrewing in the U.S. (which likely kickstarted the entire craft beer movement).

And now to make the perilous journey home in the face of Tropical Storm Sandy.

Day 405

October 17, 2012

What better way to start mid-term week than with a 90-minute Brewing Calculations mid-term at 8:30 am on a Monday.

Erk.

…followed by a one-hour lecture on predicting residual alkalinity and pH of the mash.

Erk Erk.

So here’s the thing. Water hardness–the amount of calcium and magnesium in the water–is desirable. Water softness or alkalinity (an overabundance of free CO32- ions, aka carbonates) is not, since it will not only raise the pH of the mash, but also acts as a pH buffer, resisting the efforts of the brewer to lower the pH. Since low pH is good for enzymes, good for yeast, limits extraction of phenols from malt husks, improves the quality of hop bitterness, improves filterability of the mash, and improves coagulation of proteins in the kettle, a low pH is very desirable.

Being able to predict when our mash pH is going to be too high before we even start brewing is better than discovering that our mash pH is too high in mid-brew and trying to correct it after the fact.

Both hardness and alkalinity can be characterized by the presence of calcium carbonate (CaCO3), since it contains both hardness in the form of calcium (Ca2+) and alkalinity in the form of carbonate (CO32-). So if we take all the calcium and magnesium ions in brewing water and convert them to equivalent amounts of CaCO3, and then take all the carbonates and bicarbonates present and also express them as an equivalent amount of CaCO3, we will then be able to see what the total hardness and alkalinity of the water is as expressed by the presence of CaCO3, calculate how this will affect our mash pH, and then make suitable adjustments to the brewing water.

The first step is to convert the calcium and magnesium into equivalent units (called milli-Equivalents or mEq). The conversion formula is

milliEquivalents (mEq) = amount of ion (in ppm) ÷ equivalent weight (calculated as molecular weight of ion/absolute valence of ion)

For instance, water here at Niagara-on-the-Lake has 34.8 ppm of calcium (Ca2+, valence of 2, molecular weight of 40) and 8.7 ppm of magnesium (Mg2+, molecular weight of 23.4 and valence of 2). First of all, the equivalent weight of calcium would be (molecular weight of 40/valence of 2) = 20. The equivalent weight of magnesium would be (molecular weight of 24.3/valence of 2) = 12.2. The millEquivalents of both of them would be

(34.8 ppm Ca ÷ 20) + (8.7 ppm Mg ÷ 12.2)

= 1.74 + 0.71 = 2.45 mEq

The next step is to convert this value to an equivalent amount of CaCO3 in parts per million, which is done by multiplying the mEq by the molecular weight of CaCO3 (which happens to be 50). Therefore, 2.45 mEq x 50 = an equivalent value of 122.5 ppm of CaCO3 in the local water.

So what, you say? We’re not done yet, I reply.

A German researcher discovered that 3.5 equivalents of calcium or 7 equivalents of magnesium would offset the pH raising effects of 1 equivalent of carbonate. Therefore, if we simply subtract the equivalent of calcium (divided by 3.5) and the equivalent of magnesium (divided by 7) from the carbonate equivalent, we can see how much Residual Alkalinity is left in the water–that amount of alkalinity that will resist any attempted lowering of pH.

First, we can quickly calculate the mEq of CaCO3, using the same formula we used above. The concentration of CaCO3 in our local water is 85.9 ppm, and its molecular weight is 50, so

mEq of CaCO3 = 85.9/50 = 1.72

Since

RA = (mEq of CaCO3) – [(mEq of calcium/3.5) + (mEq of magnesium/7)]

then

RANiagara-on-the-Lake = 1.7 – [(1.74/3.5) + (0.71/7)]

 = 1.72 – (0.50 + 0.10) = 1.12  mEq

If we then convert this back into CaCO3 (1.12 mEq x equivalent weight of 50), we get a Residual Alkalinity of 55.95 ppm. This is right on the edge of being too alkaline for brewing.

But wait, we’re not done yet. The same German researcher discovered that one degree of Residual Hardness as measured in units called German Hardness Units or °dHa in a 12°P mash will increase the pH of the mash by 0.03. (No, I am not making this up!) So now that we know the Residual Alkalinity of our water, we can calculate its effect on the pH of the mash. First we can look on the malt analysis sheet provided by the maltster to discover the pH rating of the grain we are using (which is calculated in a lab by making a “congress” mash using distilled water). We can then convert our RA to German Hardness Units by dividing the RA by ppm per °dHa of CaCO3, which happens to be 17.85:

55.95/17.85 = 3.13°dHa

So if our grain has a malt pH rating of 5.8, then

Predicted pH of mash = malt pH rating  + (RA as  °dHa x 0.03)

= 5.8 + (3.13°dHa x 0.03) = 5.8 + 0.09 = 5.9

(If you are using multiple grains, then you would use the above forumla for each grain multiplied by the percentage of that grain in the mash. Add the weighted pH’s together and you get a prediction of the eventual mash pH.)

But wait, there’s more…

Alas, my brain had melted by this time, so my notes are meaningless scribbles highlighted by phrases like “acidulated malts” and “acid additions”. Some day this will all make sense.

As if this wasn’t enough for one day, it was also the first day of class presentations in History of Beer. Yours truly was the third presenter, speaking for 12 minutes on Russian Imperial Stout: Being a moft excellent and entertaining Recital of the Hiftory of the Exportation of Strong Beers from London to Russia with divers scholarly Addenda and learned Afides by the Author.

This was actually a very educational topic from my point of view. I had previously understood that Russian Imperial Stout was so named because it was made by English brewers for the court of Catherine the Great, and that it was stronger and hoppier than normal so that it wouldn’t freeze as it was being shipped across the icy Baltic Sea. What I discovered was that trade in strong porter had started six decades before Catherine the Great, during the reign of Tsar Peter (also “the Great”), who discovered English beer on a trip to London in 1698. He liked dark London porter so much that, during his visit, he became a prodigious party animal who had to be wheeled back to his lodgings in a wheelbarrow each night. Upon his return to Russia, he ordered a shipload of the stuff to be sent to his new court at St. Petersburg. Alas, the 4-month voyage proved too much for the low-gravity English beer, and brewers were forced to increase the bitterness and strength not so that it wouldn’t freeze, but so that it would arrive in Russia in a drinkable state. The export of strong stout continued for the next 300 years, until the First World War and the Russian Revolution put an end to the beer export market. However, the name “Russian Imperial Stout” actually wasn’t given to the stuff until 1934–twenty years afterwards–as a marketing gimmick to attract English drinkers.

But wait! There was more. Bill White then gave a one-hour lecture on technology and its effect on beer, from the water canal and the steam engine to the microscope.

Finally, the end of a long day. But hark! I sense another mid-term…


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