Correcting for pH drift?

I've noticed that over an hour my pH meter read 3.97 in the 4.01 buffer and 7.04 in the 7.01 buffer. The pH meter was washed with DI water and most excess water was blotted away to avoid contaminating the calibration solutions. Calibration solutions were kept at constant temperature.

Is it accurate to correct for pH drift by determining a linear formula (y=mx+b) based on the actual readings? Example from my last mash:

Actual Reading = 3.97
Actual Reading = 7.04

m = (7.01-4.01)/(7.04-3.97) = 0.9772
b = 4.01-.9772*3.97 = 0.1305

Corrected pH = 0.9772*Measured pH + 0.1305

Measurements taken right after calibration need no correction. But checking for drift before or after a group of measurements could help determine the actual pH a little closer... The biggest error would be when BOTH ends of the calibration drift positive or negative (measured pH - calibration pH), unlike my example.

Can anyone comment if linear correction for drift is the best way?

I have often wondered how it is possible to build a pH meter with specified accuracy as bad as 0.05 or 0.1 pH given modern electronics and concluded, based on a check of one of these for a brewing friend, that the answer must be drift. Your post supports that hypothesis and is, therefore, very interesting to me. First question is which meter are you using?

Your meter electrode produces a voltage
E = Ei + s*(pH-7)
When you calibrate you measure 2 buffers which gives 2 equations
Eb1 = Ei + s*(pHb1 -7)
Eb2 = Ei + s*(pHb2 -7)
which can be solved for Ei and s (which is negative) and this is what your meter does. Subsequently, if presented with the voltage measured on a sample, Es, the meter is able to calculate
pH_ = (Es-Ei)/s + 7

What has happened here is that s and/or Ei have changed over the course of an hour. But you don't know when the change occurred or that it was uniform. It's probably a good bet that is is though. Assuming everything is at the same temperature you can calculate
a = (pb1_ - pb2_)/(pb1 - pb2)
and
b =( pb1_ + pb2_ - a*(pb2 - 7) - a*(pb1 -7) - 14 )/2
pb1_ and pb2_ are the values you measure for the buffers at the end of a sequence of measurements and pb1 and pb2 are the actual pH's of the buffers at the temperature of the measurements. If they are not on the buffer packaging you can get them from the formulas in the sticky on pH meter calibration. a has initial value 1 and b has initial value 0. For the example you gave and assuming everything was done at 20 °C
a = (7.04 - 3.97)/(7.016 - 4.002) = 1.01858
and
b = (3.97 + 7.04 - 1.01858*(7.0162 - 7) - 1.01858*(4.0022- 7) -14 )/2 = 0.0234991

You could assume a = 1 + 0.01858*t and b = 0.0235*t where t is the time since calibration in hours and correct any reading taken after calibration using that.

a and b are used in the formula

pH = (1/a)*(p_ - 7 - b) + 7

where p_ is the pH the meter reads after drifting and pH is the estimated pH. Taking your pH 7 reading of 7.04 after an hour and inserting that in the formula with the 1 hour values of a and b would give
pH = (1/1.01858)*(7.04 - 7 - .0234991) + 7 = 7.0162
which is the pH of pH7 buffer at 20 °C.

Seems frequent recalibration would be simpler than going through all this math. Note that the pH calibration sticky recommends checking a newly obtained meter for calibration stability over time. This is based on my (growing) suspicion that the difference between a $100 meter and a $1000 meter is based on more than the fact that the operator can enter his initials in an internal data base in the latter.

The meter is a fairly newly acquired Hanna pHep5 (HI 98128). Not a $1000 meter but I've been impressed with this gadget. Now that I know my meter's tendency to drift in an hour, recalibrating prior to measurements is great advice. I'm using packets of calibration solution and will reuse them on the brewing day only. I've studied your sticky about pH meters and follow it.

The picture below shows my EZ Water calculations and a test mash I did while heating up the mash water. The pH meter was calibrated 15 minutes into the test mash for the first reading, rinsed and used again about an hour later for the first reading 15 minutes into the actual mash without calibration. I checked the drift thinking I could linearly correct as in the original post.

The expected mash pH was 5.43. The test mash pH was 5.38 @15 minutes. I used that to determine the amount of acid malt for the actual mash. The actual mash pH was 5.35 @ 15 minutes. This was lower than I expected because I put 65 grams of acid malt instead of the full 85 grams of acid malt into the mash (calculations per pic below, test mash was done assuming the actual mash would have been 85 grams). I think my actual mash reading was affected by my pH meter's drift AND pre-crushing more acid malt at than needed at the store and then scooping out of that. Is the acid concentrated in a certain part of the grain/husk?

DSmith said:

The meter is a fairly newly acquired Hanna pHep5 (HI 98128). Not a $1000 meter but I've been impressed with this gadget.

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I am too. At the price point it is FM.

DSmith said:

Now that I know my meter's tendency to drift in an hour, recalibrating prior to measurements is great advice.

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I don't think that's too much to ask in return for good pH readings from a device that costs less than $100.

DSmith said:

I'm using packets of calibration solution and will reuse them on the brewing day only.

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You'd be amazed by the number of people that don't know those things are single use.

DSmith said:

The expected mash pH was 5.43. The test mash pH was 5.38 @15 minutes. I used that to determine the amount of acid malt for the actual mash.

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Given all the factors that introduce uncertainty into mash pH prediction calculations I think that's pretty good.

DSmith said:

I think my actual mash reading was affected by my pH meter's drift AND pre-crushing more acid malt at than needed at the store and then scooping out of that. Is the acid concentrated in a certain part of the grain/husk?

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That's not that much of a difference - within the range of expected 'noise'.

Where the acid lies in the sauemalz depends on how it was made. In some cases 'sauergut' (lactic fermented wort) is spayed onto base malt which is then dried. In another method the malt is steeped and stored at 47 °C so that L delbrueckii which are normally found on the surface can grow and ferment some of the sugars in the malt. In this case some of the acid would be deeper in the corn.

In any case, when using sauermalz it is a good idea to check the pH frequently from just after dough-in until such time as the pH is stable. Most people notice an abrupt climb in pH right after dough in with a gradual rise taking place over the next 20 - 30 minutes.