*Published in June 2024, by Ryan Olf, PhD and the Trisk team.*

I use a steel vacuum-insulated flask for my morning coffee every day, typically with just a rinse between uses. Over time, a layer of insoluble coffee-related residue builds up on the stainless interior. This daily cleaning routine is obviously lacking, but it’s good enough — most of the time. When I travel, I use the same flask primarily for drinking water, and even with the coffee scale, after a more thorough clean of the lid, the taste of the water is barely affected. After all, the scale is building up because it’s insoluble — not much of it comes off in water, so there’s not much to taste. If the taste were more evident, I’d be inclined to do a deep clean more frequently (pro tip: drop a dishwasher detergent pod in there with hot water and let it soak - the coffee scum peals right off). Then again, if the taste were more evident, the scale would be more likely to yield to my rinse regimen and build-up less in the first place.

But while typically the rinse water (or drinking water) is quite clean, sometimes the fact that my flask is not clean does become evident. Eventually, bits of the coffee residue start to peel off intermittently. This shows up not in the flavor of coffee or water, or the clarity of the rinse, but in the sudden unwelcome feel of a bit of slimy film on my tongue, or in the form of discrete specs in the rinse.

I thus understand why, in their guide to validation of cleaning processes, the FDA says of cleaning a dirty pot: “one does not look at the rinse water to see that it is clean; one looks at the pot.” It’s not just that the pot isn’t spotless, it’s that it’s inviting the sort of non-linear failure that I experience with my flask. Things come out OK until, without warning, they don’t.

In spite of this risk of non-linear failure and the FDA’s warning, conventional wisdom seems to be that if you have WFI-grade water coming out of your system after cleaning, the system must be at least pretty clean. The rinse doesn’t tell the whole story, sure, but limits on the level of soil in rinse water must at least *constrain* the level of soil that can remain in the system, right?

In general, no! In this post I’m going to share a simple model of equipment cleaning and soil wherein not only is the amount of residual soil unconstrained by cleanliness of the rinse, **the quality of the rinse can be improved when either the system or cleaning process deteriorates****.** I’ll discuss the potential impact of this on quality assurance and outline testing that might be done to make sure rinse samples are more useful.

## Toy model of cleaning kinetics

Let’s consider a situation where we flow a certain volume of solution through a system at a constant rate to clean it and then we retain the last bit of solution and analyze the soil quantity. Typically different solutions are used for cleaning and rinsing, but for simplicity let’s assume we can use the same fluid for both. We’ll call the soil “carbon” for simplicity.

An amount of carbon, $A$, exists in the system. As a small volume of solution $\mathrm{d}V$passes through the system, the amount of carbon that enters the solution and is removed is proportional to $A$. Thus, $A(V)$ is a function of the volume of solution that has passed, and $\mathrm{d}A/\mathrm{d}V = -kA$, with some rate constant $k$ that depends on a bunch of (ideally fixed) factors pertaining to the system and the cleaning process. This first-order system is easily solved and the solution is $A(V)=A_0 \exp(-kV)$ with $A_0$ the amount of carbon at $V=0$.

The amount of carbon, $\text{C}$, that comes out in a volume of solution between $V$ and $V+\mathrm{d}V$ is

$\text{C}(V,V+\mathrm{d}V) = A(V)-A(V+\mathrm{d}V)=A_0e^{-kV}\left(1-e^{-k\mathrm{d}V}\right).\tag{1}$This simple model is easily extended to include more than one compartment, surface, material, or whatever carbon source that elutes into the solution at a different rate, i.e. $A(V)=A_1 \exp(-k_1V) + A_2 \exp(-k_2V)$, leading to a spectral description of the cleanability of a system (under a particular cleaning process with fixed chemistry, flow rate, temperature, etc) in terms of the various constants. These model parameters $\{ A_i,k_i \}$ — which we can in principle determine by continuously analyzing the rinse — tell us a lot about our system, but as you’ll soon see, we’re mostly interested in the smallest $k$.

## Clean and cleanability

Each $A$ tells us about how much carbon is present in a given compartment — how dirty it is — and the $k$ tells us the fraction that comes off in each solution volume it is exposed to — how “cleanable” it is. When we talk about making something clean, we mean that the amount of soil left, $A(V)$, has fallen below some upper limit, $A_f$. The volume of rinse fluid required to achieve a certain cleanliness scales like $V\approx \log(A/A_f)/k$, with $k$ the smallest of the $k_i$ for which $A_i \equiv A \gg A_f$.

We can see from this that how much soil is initially present doesn’t matter much, as the volume of solution required (and the cleaning time, since we’re assuming constant cleaning conditions, i.e. constant flow rate) appears in the logarithm. Thus, to make the system cleanable we maximize the minimum $k_i$ in the system for which $A_i$ is non-neglibile compared to $A_f$. If we are using rinse solution to evaluate cleanliness, the target level (a concentration expressed as $\text{C}$ per final rinse volume $\mathrm{d}V$, which we’ll denote $\text{TOC}_f$) will depend on this minimum $k$. Plugging in $A_f$ for $A_0e^{-kV}$ in Eq. 1, and using the fact that $k\mathrm{d}V$ is small, we find the target TOC level for the rinse should be

$\text{C}_f/\mathrm{d}V \equiv\text{TOC}_f=A_f\left(1-e^{-k\mathrm{d}V}\right)/\mathrm{d}V\approx kA_f. \tag{2}$We can only count on the rinse to tell us we’re meeting the $A_f$ spec if $k$ is sufficiently large — i.e. the system is sufficiently cleanable — otherwise the TOC target will fall below the limit of detection. As the pot (and my coffee mug) teach us, the cleanliness of the rinse doesn’t tell us *anything* about carbon left in the system without knowledge of the system and how it interacts with the carbon soil: in this model, $k$.

In reality, we don’t typically know $k$, so we have to find some other reasonable way to set a limit for the rinse, for example by comparing the TOC levels in rinse samples from systems that are deemed clean (and not) by direct sampling or inspection.

## When worse is better

Imagine we were given a fixed rinse TOC target concentration that was meant to apply to any equipment. Solving Eq. 1 for $V$ in the limit of small $\mathrm{d}V$, we find that the volume of cleaning fluid required to achieve this target TOC in the rinse is

At first glance, this makes intuitive sense. When $k$ is large — the system is easily cleaned — the amount of solution that needs to flow to achieve the clean rinse decreases with increasing $k$, i.e. as the system becomes more cleanable.

But something somewhat interesting happens when $k$ is small. In this regime, the amount of solution that needs to flow to achieve the clean rinse decreases with *decreasing* k, i.e. as the system becomes *less* cleanable. **The cleaning solution volume formula has a maximum.*** *Whereas the cleaning challenge gets harder and harder as $k\rightarrow0$, the* clean-rinse *challenge does not, and in fact gets easier. Moreover, since $V\rightarrow-\infty$ as $k\rightarrow 0^+$, there is always some $k$ below which $V\le0$: with a fixed TOC concentration target — however low — and sufficiently *uncleanable* systems (e.g. one that traps an insoluble soil), no cleaning is required.

That $V$ has a finite maximum means * there is a maximum amount of cleaning fluid required to hit a certain rinse TOC target independent of the cleanability of the system! *The worst-case cleaning solution volume for the worst-case $k$ depends only on the initial amount of soil and the target cleanliness of the rinse:

where $e$ is the Euler constant (base of the natural log). This limit is independent of system size, geometry, and even the cleaning/rinse flow parameters! These factors all impact the parameter $k$ and the actual volume that may be needed in a given case, but that volume will always be less than $V_\text{max}$. (Important caveat: our model assumes that the system is filled with cleaning solution, so all of this is only valid when the cleaning solution volume is much greater than the system volume. Easier if you’re running small bioreactors!) One way to make this seem less crazy than it might at first is to note that $V_\text{max}$ is just a small factor ($e$) less than the volume required to dilute all the initial carbon soil to the target TOC concentration.

Of course in the real world, *worse* cleanability should not make cleaning targets *easier* to hit. It’s tempting to pin the discrepancy on the model being wrong — it’s a toy! The model certainly is lacking and limited, but it isn’t the deep issue here. **I think the model is reasonable in the right limits, and these limits are not too far from realistic.** The dissonance between reality and our observations here comes from the premise of this section: that achieving any particular rinse TOC concentration relates to the cleanliness of the system, irrespective of the system. **Rinse targets ****must**** be set with a good understanding of the system and what it means for it to be clean.**

## Real consequences for quality assurance?

Typically one would not rely on *only* rinse samples in assessing and validating a cleaning process. But once a process has been validated, rinse samples might be a primary means of quality assurance (QA). In this case, the TOC target for the rinse is likely well justified, but Eq. 3 is still relevant and couches potentially important lessons.

For example, it might seem reasonable to assume that any cleaning process failure or deviation that negatively impacts the system cleanliness would also negatively impact the cleanliness of the rinse water, which implies that rinse samples are quite powerful in assuring quality. However, this is not necessarily the case. In fact, if the cleaning process changes for the worse (e.g. flow rates slow down) or the system becomes less cleanable (e.g. some surfaces are scratched), the rinse samples may in fact be improved or not change at all, in spite of the system being less clean than it should be. This could lead the clean rinse to give *false* quality assurance.

This can be seen by solving Eq. 3 for TOC, which shows us how the rinse quality depends on the system cleanability $k$ and starting carbon soil level given a cumulative volume of solution:

As with Eq. 3, this equation has a single peak as a function of $k$. For systems or cleaning conditions to the right of the peak (better cleaning or cleanability), reducing $k$ (deteriorating cleaning or cleanabiilty) increases the TOC of the rinse. But for systems to the left, reducing $k$ *decreases the TOC of the rinse — *the system is less clean, but the rinse is *more *clean*.* At the peak, where $k=1/V$, changing $k$ has no impact on the TOC of the rinse.

From the perspective of doing QA, it might be nice to know which regime our systems are in. To learn this we can run the cleaning and rinse program on a soiled system twice: once with normal flow rates, and once with low (deteriorated) flow rates. Importantly, each run should use the same *volume* of cleaning solution and rinse. (If we fix the time instead of volume, the situation is less readily generalized as changing flow rate would change both $k$ and $V$.) If the rinse sample is *worse* in the second case, then that suggests we’re in the favorable regime, $k>1/V$, and at least under this model, the rinse is likely to be more meaningful in QA.

We should certainly be cautious and careful taking a toy model like this into the real world where important boundary conditions and assumptions may not be sufficiently maintained. However, toy models can be a good check on our intuition, which also readily misleads, and point towards assumptions that warrant a second look and additional testing.

## Fun with numbers: justifying my coffee flask cleaning routine

Just for fun, let’s put some numbers into Eq. 4 to see what volume of WFI we’d need to rinse through some systems before it comes out clean, starting with my coffee flask.

Coffee is roughly 1-2% dissolved solids (assume I take it black), of which about 50% is probably carbon, and my coffee flask holds about half a liter. Most of those solids end up in my belly, but let’s generously say 0.1% of those solids end up stuck to the walls. This means $A_0$, the initial amount of carbon, is 5 mg. WFI is 0.5 mg/L = 0.5 ppm TOC at worst. Eq. 4 then tells us that regardless of the material or surface condition of my flask, the water will taste clean and probably still qualify as WFI (at least initially — if the water sits for a while it’s a different question with different kinetics) if I rinse it with $5\,\text{mg}/(e\cdot0.5\,\text{mg/L})= 3.5\,\text{L}$ of water. That’s a lot of rinse water, but not a crazy amount. I’d estimate in reality I rinse with 0.5 liter in several stages, and my guess is if I doubled that there would still be some improvement. Maybe to be safe I should adopt the full 3.5 L treatment.

More relevant for our work at Trisk is cleaning bioprocess equipment. Say we have a 3L bioprocess with $10^7$ cells/mL, the soils of which will be spread throughout the system. With each cell weighing 3 ng and comprised of 70% water, this is a carbon density of about 9000 mg/L. In the 3L process we have 27000 mg of possible carbon soil. Regardless of the cleanability and cleaning process for our system, what is the maximum possible amount of cleaning solution required according to Eq. 4?

Realistically, most of the cell debris will come out very quickly (i.e. it will drain with the bulk contents) and only a small amount will be left on worst-case surfaces. Let’s conservatively assume the entire surface of the bioreactor is a worst-case surface. If the bioreactor were a 3L sphere, it would have a radius of about 9 cm. Let’s say that after draining, 100 micron of the original solution remains adhered to the bioreactor surfaces. The volume of this layer is just 0.3% of the bioreactor volume, so there is 81 mg of carbon soil on a worst-case surface. In this case, the maximum amount of cleaning solution required would be $81\, \text{mg}/(e\cdot0.5\, \text{mg/L}) \approx 60\,\text{L}$. If the layer is only 10 micron thick, or the worst case surface is 10x smaller, it’s 6L. Fill it up, swish it around. Drain. Repeat. And you’re done!

Of course, that doesn’t mean it’s *actually* clean! It could still eventually look like my coffee flask.