The formula for continuous dilution is:

Percent Required = -100% * ln(1 - (% Dilution / 100%))

To achieve a 25% dilution requires -100% * ln(1 - 25%/100%) = 28.8% of the total pool water volume being replaced.

To achieve a 50% dilution requires -100% * ln(1 - 50%/100%) = 69.3%.

To achieve a 75% dilution requires -100% * ln(1 - 75%/100%) = 139%.

So you can see that continuous dilution becomes very inefficient to produce significant dilution. Other methods such as using a large plastic sheet covering the pool, draining from underneath and filling from the top, or using large silage bags draining from outside and filling the inside, are more effective and do not waste water.

TECHNICAL DERIVATION (ignore if not interested)

This comes from the fact that continuous dilution is essentially from a small partial incremental dilution done repeatedly

Diluted Fraction Remaining = (1 - f)^n

where "f" is the fraction of new water and "n" is the number of times this is repeated so "n*f" is the total amount of water replaced. This can be rewritten as

Diluted Fraction Remaining = ( (1 + 1/x)^x )^(-n*f)

where x=-1/f and if we let x go to infinity (f goes to zero) for smaller and smaller water replacement done more and more frequently, then this becomes

Diluted Fraction Remaining = e^(-n*f) = e^(-(Total Water Volume Replaced Through Continuous Dilution))

so solving for total water volume we get

Total Water Volume Replaced Through Continuous Dilution = -ln(Diluted Fraction Remaining)

The % Dilution is 100% * (1 - Diluted Fraction Remaining).