Starting volume of original mud (weight up with Calcium Carbonate)

You know how much volume will be increased due to adding calcium carbonate into the system; however, you sometimes are limited to total volume due to limit pit volume on the rig so you need to calculate starting volume to achieve the predetermined final volume of desired mud weight.
This formula below is used to determine the staring volume of mud (for calcium carbonate system).

Starting volume in bbl  = VF x (22.5 – W2) ÷ (22.5 – W1)

Note: 22.5 is density of calcium carbonate in ppg.

Where; W1 = current mud weight in ppg

W2 = new mud weight in ppg

VF = final volume of mud needed in bbl

Example: Determine the barrel of starting volume of 10.0 ppg (W1) mud required to achieve final volume of 100 bbl (VF) of 13.0 ppg (W2) mud with calcium carbonate:

Starting volume in bbl = VF x (22.5 – W2) ÷ (22.5 – W1)

Starting volume in bbl = 100 x (22.5 – 13.0) ÷ (22.5 – 10.0)

Starting volume = 76 bbl

In order to achieve  final mud volume of 100 bbl of 13.0 ppg mud weight up with calcium carbonate, you must have 76.0 bbl starting volume of 10.0 ppg mud.

Please find the Excel sheet for calculating Barrel of starting volume of original mud weight required to give a predetermined final volume of desired mud weight with CALCIUM CARBONATE.

Ref book: Formulas and Calculations for Drilling, Production and Workover, Second Edition