Material Balance Equations

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

The Material Balance Equation is:

V1W1 + V2W2 ..... = VFWF where: V1 + V2 ..... = VF

where: V1 = Volume of first material to be mixed together

W1 = Density of first material
V2 = Volume of second material to be mixed together
W2 = Density of second material
VF = Total or sum of all volumes mixed together
WF = Density of total mixture. Proportional average of all volumes mixed together
The most commonly used variables in material balance equations are:

Barite

1. Weight of a barrel of barite (BaSO4) s.g. = 4.2 g/cc
42 gal/bbl x 8.33 lb/gal x 4.2 = 1470 lb/bbl

* since barite comes in 100 lb sacks, one barrel contains 14.70

sacks

2. Weight of a gallon of barite
8.33 lb/gal x 4.2 = 34.9 lb/gal

Hematite

1. Weight of a barrel of hematite (Fe2O3) s.g. = 5.0 g/cc
42 gal/bbl x 8.33 lb/gal x 5.0 = 1749 lb/bbl
2. Weight of a gallon of hematite
8.33 lb/gal x 5.0 = 41.65 lb/gal

Light Oil

1. Example - (41° API Gravity) s.g. = 0.82 g/cc
2. Weight of a gallon of oil
8.33 lb/gal x 0.82 = 6.8 lb/gal


Example Problem #1-1:

Calculate how many sacks of barite are required to increase the density of an 800 barrel mud system from 12.7 lb/gal to 14.5 lb/gal.

Using: V1W1 + V2W2 = VFWF

where: V1 = 800 bbls
W1 = 12.7 lb/gal
V2 = unknown volume of barite
W2 = 34.9 lb/gal (density of barite)
VF = V1 + V2 (or 800 + V2 )
WF = 14.5 lb/gal

therefore: 800(12.7) + V2(34.9) = (800 + V2) x 14.5

10,160 + 34.9V2 = 11,600 + 14.5V2
20.4V2 = 1440
V2 = 70.6 bbls of barite
70.6 bbls x 14.7 sk/bbl = 1038 sacks of barite


Example Problem #1-2:

Calculate how much water and barite are required to make 800 barrels of a 10.5 lb/gal water-based drilling mud.

Using: V1W1 + V2W2 = VFWF

where: V1 = unknown volume of water

W1 = 8.33 lb/gal
V2 = unknown volume of barite or (800 - V1)
W2 = 34.9 lb/gal
VF = 800 bbls
WF = 10.5 lb/gal

therefore: V1(8.33) + (800 - V1)34.9 = 800(10.5)

8.33V1 + 27920 - 34.9V1 = 8400
-26.57V1 = -19520
V1 = 735 bbls of water
V2 = 800 bbls - 735 bbls = 65 bbls of barite @ 14.7 sk/bbl or 956 sacks