My assumption is that the coke drum water storage tank is common for the drum quench water and for the drum cutting water. Taking as sample off of the quench water pumps is easier than taking it off of the suction of the cutting water pump.
I believe it is generally acceptable to have a suspended solids content in the cutting water system of up to 500 ppm without excess erosion or plugging or equipment wear. Above 2000 ppm suspended solids is very dirty water and the cutting water system will experience plugging, erosion, equipment wear and poor system reliability. In between these two values, the issues are the same, just less severe.
It is possible to maintain the cutting water solids content at less than 100 ppm suspended solids with proper management of the maze and routine purging of the cutting water storage tank. I think the benefits of going lower than 100 ppm suspended solids are limited. If you can get there, lower solids is better.
Flowserve and RuhrPumpen have guidance on the suspended solids content the cutting water should contain, so you should consult them on this problem.