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Material Balance Equations

Material balance equations are used for calculating volumes and densities when two or moreinsoluble materials are mixed together.

The Material Balance Equation is:

V1W 1 V ! W ! ..... " V #W # where: V 1 V ! ..... " V #

where: V 1 " Volume of first material to be mixed together

W 1 " $ensit% of first material

V ! " Volume of second material to be mixed together

W ! " $ensit% of second material

V# " Total or sum of all volumes mixed together

W # " $ensit% of total mixture. &ro'ortional average of all volumes mixed together

Barite

1. Weight of a barrel of barite (Ba)*+, s.g. " +.! g-cc

+! gal-bbl x .// lb-gal x +.! " 1+0 lb-bbl

2 )ince barite comes in 1 lb sac3s4 one barrel contains 1+.0 sac3s

!. Weight of a gallon of barite

.// lb-gal x +.! " /+.5 lb-gal

Example Problem #1-1:

6alculate how man% sac3s of barite are required to increase the densit% of an barrel muds%stem from 1!.0 lb-gal to 1+.7 lb-gal.

8sing: V 1W 1 V ! W ! " V #W #

where: V1 " bbls

W 1 " 1!.0 lb-gal

V ! " un3nown volume of bariteW ! " /+.5 lb-gal (densit% of barite,

V# " V 1 V ! (or V ! ,

W # " 1+.7 lb-gal

therefore: (1!.0, V ! (/+.5, " ( V ! , x 1+.7

1 419 /+.5V! " 1149 1+.7V !

! .+V ! " 1++

V ! " 0 .9 bbls of barite

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0 .9 bbls x 1+.0 s3-bbl " 1 / sac3s of barite

Example Problem #1-2:

6alculate how much water and barite are required to ma3e barrels of a 1 .7 lb-gal water based drilling mud.

8sing: V 1W 1 V ! W ! " V #W #

where: V 1 " un3nown volume of water

W 1 " .// lb-gal

V ! " un3nown volume of barite or ( V 1,

W ! " /+.5 lb-gal

V# " bbls

W # " 1 .7 lb-gal

therefore: V 1( .//, ( V 1,/+.5 " (1 .7,

.//V 1 !05! /+.5V 1 " +

!9.70V 1 " 157!

V1 " 0/7 bbls of water

V ! " bbls 0/7 bbls " 97 bbls of barite ; 1+.0 s3-bbl or 579 sac3s