he reactions are stochiometric:
HCL disassociates into H+ and Cl-
 
The effect of H+ addition on alkalinity is
H2CO3 ↔ H++HCO3- which further disassociates to H+ +CO3= depending upon pH
The best way to find out is to test the system with titration of 1/50 N HCl on samples and see what works.
 
 
The easiest way to explain the effect is the system diagram attached.

 

The carbonate chemistry is complex, and because it has two reactions associated with it, it does not lend itself to easy computation.

There is a formula but it’s about two pages worth of computation, and at the risk of blowing my own horn, it’s found in my book Practical Wastewater Treatment, which is available in both Chinese and now in Spanish from John Wiley.  Look on pages 72-80 for complex solution to the reactions.

Hope that helps.