# is water filter log reduction multiplicative?

Two water filters each provide a 4 log (99.99%) reduction for some pathogen.

If I pass the water through both filters (or one filter twice), have I now achieved an 8 log reduction?

For example:

MSR advertises their Guardian Gravity Purifier as achieving 99.99% reduction of viruses.

For the sake of argument, assume another device (say MSR Trailshot) was measured to achieve 90% reduction (not enough to be certified). If water were filtered through it four times, would it achieve a similar 4 log reduction?

An immediate thought is that the virus size would affect the results - in worst case, perhaps the 90% initially removed were all large, and everything that remained is too small to be filtered at all.

• or perhaps "additive" instead of "multiplicative"
– jhnc
Feb 26 at 15:13

No. Filters don't work like that, though there can be some benefit to double filtration as I'll explain below. I don't know the mathematics of it though.

Basically what happens inside a filter is that the filtering component (dependent on type) is composed of a membrane with tiny tunnels through it. These tunnels are called pores and are an intrinsic property of the manufacturing process. If you think of it like a very small-scale dish sponge, you'll get the idea of how the pores look in reality.

Usually, the filtration pore size of the filter is the average size of the holes/tunnels, though sometimes they will give an absolute size. The average size means that sometimes you will get some pores that are larger than the rated size and some that are smaller. This means you don't get an absolute filtration down to the rated size; some particles will pass through due to the random pore size. The range of pore sizes and the physical properties (e.g. electrostatic charge for N-95 respirators) of the filter contribute to the efficiency This is where you get the efficiency rating of a filter from. A lower efficiency rating generally means there is more spread in the range of pore sizes.

The CDC has a good image and explanation of water filters:

Image source: Centers for Disease Control and Prevention, National Center for Emerging and Zoonotic Infectious Diseases (NCEZID), Division of Foodborne, Waterborne, and Environmental Diseases (DFWED)

You can think of it as like having fishing net - you'll only catch fish that are larger than the holes, anything smaller will pass through, no matter how often you cast the net.

So; if you have a filter with a 0.1 micrometre/3.94x10-6 inches (AKA "micron", this is a common size for influenza virus and Covid virus (SARS-CoV-2)), with a 90% efficiency, then it will filter out 9 out of 10 particles with a size of 0.1 micrometres and let 1 particle through.

If you passed the same water back through the same filter, you run the risk of dislodging some of the captured particles (water filters are generally mechanical removal rather than a physical property of the filter that actually binds to the particles), and having these pass through the filter onto the clean side of the filter.

This means you could double filter using two of the same type of filter, but you still have the same pore size so you have the same risk of a particle passing through. The most efficient way to filter water is to have your first filter set to catch large particles and then have a secondary filter that catches the things you might be worried about. The first is there to prevent the second getting clogged with large particles and becoming inoperable.

• Related: depending on the particular size I suspect that you can pre-filter with just something like cloth. I’ve experienced the issue you mentioned in the last paragraph when filtering quite silty water - it made a near-new filter gum up awfully quickly. It still worked, but significantly slower with more effort. Feb 26 at 21:18
• @fyrepenguin Yes, that's absolutely possible. In fact an emergency filter you can make consists of several layers of materials stacked in a plastic bottle or tube. This often starts with gravel or cloth at the top and has charcoal at the bottom. Works pretty well to clean dirt and bacteria out of water.
– bob1
Feb 26 at 21:42
• Yeah, I’ve seen designs for those, they’re pretty neat. I was considering more of an impromptu prefilter w/ cloth; my main concern was how effective it would be on something like fine silt (hence my minor prevarication). The pump I’ve used has its own mesh to stop larger particles like sand, at least, but does nothing to help with silty water. Feb 27 at 0:48
• @fyrepenguin Silt is pretty small - 4-62 micron according to Wikipedia and will clog filters very easily. 4 micron is bacteria size. Most cloths are too loose weave to filter it out. You might be able to get away with multiple layers of cloth or something like lens-cleaning cloths and gravity feed, but it won't be very efficient. Perhaps (lots of) layers of tissue paper/toilet paper with cloth to support?
– bob1
Feb 27 at 1:40
• @jhnc what I mean by that is that the water isn't made more clean by repeatedly filtering. You get physical chunks of filtrate accumulating that break off and re-enter suspension. There is no more risk than passing another lot of dirty water through, but in that scenario you are going from dirty -> clean, rather than clean -> maybe slightly more clean.
– bob1
Feb 27 at 2:42

I wrote to MSR, Sawyer and Lifestraw. Also NSF.

Sawyer replied that they have not tested this, and don't intend to do so since it is very expensive. Their opinion was that there would not be an additive effect because "what has got [through] the filter the first time around is still small enough to get through the second time".

MSR were brief: "No, it will still only be a 4 log reduction."

LifeStraw seems to disagree (if I am parsing the third paragraph, and infographic correctly):

Our lab did some research and didn't find any significant scientific studies or academic articles on the effects of repeated filtration through a membrane microfilter like the Mission Gravity Purifier.

Based on theory, if you re-filtered water through a similar purifier of the same type, the log reduction would depend on the virus concentration in the water in the initial batch of initial influent water.

Please see this infographic as a demonstration where there is a further reduction in the log count after the second filtration that would be more closely related to the concentration of the original amount not be additive to the log count.

• influent water (10^7 virus/L)
• filter through 1st LifeStraw Mission
• 1st effluent water ( <=100 virus/L, equal >=5log reduction)
• filter through 2nd LifeStraw Mission
• 2nd effluent water (<=1 virus/L, equal >=7log reduction)

However, more importantly:

Please note that per the NSF P231- 2014 standard and the US EPA 1987 Guide standard and protocol for testing microbiological water purifiers (Appendix A -page 22, 23), it was stated that in reality highest virus concentration in US raw water is about 10^4/L (case of US raw sewage water - worst case of natural water source) and the requirement of 4 log reduction on virus is enough to ensure the “target effluent level of less than one virus in 1 liters of water means safe.

I will update if I hear more.

• it may be relevant that my question to each organisation was slightly different from the question here: I customised with a product from the company I wrote to (protozoa for sawyer, viruses for the other two; for NSF I just asked about "particular contaminant"). I also asked if they had pointers to scientific research
– jhnc
Mar 16 at 2:44

GearSkeptic on Youtube believes that log reduction is in fact additive but has no specific research to back up their opinion:

Transcript from 52:57:

one last idea is the possibility of filtering your water twice

you could carry two filters i suppose but i'm talking about running the water through a given filter a second time

now i did not find any studies on this but the filter has no idea whether a batch of water is raw or it's been through once already

reduction rates are just percentages so if the source water had 100 germs in it and your removal was 90 you'd have 10 germs left

we'll run that batch back through the same filter and i'm not aware of any reason why you don't get another ninety percent reduction and that brings the germ count down to one

you could theoretically repeat this process as many times as it takes for you to feel comfortable so put six log filtration on top of six logs so to speak

for good lab practices though you should probably separate containers for each stage of the process for example one bag labeled dirty for your source water another marked one for your first filtration and a last bag identified as two

you could vary the operational tactics of it all but i just wanted to point out that something like that is an option