# Water formation volume factor

## Water formation volume factor

The water formation volume factor represents the change in volume of the brine as it is transported from the reservoir conditions to surface conditions[1].

The units are reservoir barrels per surface barrel at standard conditions, res bbl/STB.

Water formation volume factor correlation in the PVT software at pengtools.com

## Math and Physics

$B_w = (1+\Delta V_{wP})(1+\Delta V_{wT})$[1]

where

$\Delta V_{wP} = -1.95301(10^{-9}) P T - 1.72834(10^{-13}) P^2 T - 3.58922(10^{-7}) P - 2.25341(10^{-10}) P^2$
$\Delta V_{wT} = -1.0001(10^{-2}) + 1.33391(10^{-4}) T + 5.50654(10^{-7}) T^2$

## Application range

The correlation is valid through the full range of solids concentrations, temperatures to 260F, and pressures to 5000psia[2].

## Example. Calculating water formation volume factor

Example source [1]

### Input data

Calculate water formation volume factor at 3176 psia and 165°F?

### Solution

$\Delta V_{wP} = -0.0047241$
$\Delta V_{wT} = 0.027$
$B_w = 1.022$

The solution is also available in the PVT software model at [The solution is available in the PVT calculator software model at www.pengtools.com

## Nomenclature

$B_w$ = water formation volume factor, res bbl/STB
$P$ = pressure, psia
$T$ = Temperature, °F
$\Delta V_{wP}$ = pressure correction, res bbl/STB
$\Delta V_{wT}$ = temperature correction, res bbl/STB

Water bubble point pressure
Water compressibility
Water density
Water formation volume factor
Water salinity from density equation
Water solids concentration
Water viscosity
Gas/Water Interfacial Tension

## References

1. McCain, W.D. Jr. (1990). Properties of Petroleum Fluids (2 ed.). Oklahoma: PennWell Corp. ISBN 978-0878143351.
2. McCain, W.D. Jr. (1991). . Society of Petroleum Engineers (SPE-18571-PA).