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# Produced water formation volume factor

The produced water formation volume factor (FVF), Bw, is defined as the volume at reservoir conditions occupied by 1 stock tank barrel (STB) of formation water plus its dissolved gas. It represents the change in volume of the formation water as it moves from reservoir conditions to surface conditions.

Three effects are involved:

• Liberation of gas from water as pressure is reduced
• Expansion of water as pressure is reduced
• Shrinkage of water as temperature is reduced.

## Effect of pressure on formation volume factor of water

Fig. 1 is a typical plot of water FVF as a function of pressure. As the pressure is decreased to the bubblepoint, pb, the FVF increases as the liquid expands. At pressures below the bubblepoint, gas is liberated, but, in most cases, the FVF still will increase because the shrinkage of the water resulting from gas liberation is insufficient to counterbalance the expansion of the liquid. This is the effect of the small solubility of natural gas in water.

## Measuring formation volume factor

The most accurate source of the FVF is laboratory data. It also can be calculated from density correlations if the effects of solution gas have been accounted for properly. Eq. 1 is used to estimate B w if solution gas is included in the laboratory measurement or correlation of ρrc.

....................(1)

where

 Vrc = volume occupied by a unit mass of water at reservoir conditions (weight of gas dissolved in water at reservoir or standard conditions is negligible), ft3, Vsc = volume occupied by a unit mass of water at standard conditions, ft3, ρsc = density of water at standard conditions, lbm/ ft3, ρrc = density of water at reservoir conditions, lbm/ ft3.

The density correlations and the methods of estimating ρsc and ρrc were described previously. The FVF of water can be less than one if the increase in volume resulting from dissolved gas is not great enough to overcome the decrease in volume caused by increased pressure. The value of FVF is seldom higher than 1.06.

An alternative expression for the FVF of brine may be calculated from McCain: [1][2]

....................(2)

where

....................(3)

and

....................(4)

where p = pressure in psia, and T = temperature in °F. McCain reported that this correlation agrees with a limited set of published experimental data to within 2%. The correlation is considered valid for temperatures to 260°F, and pressures to 5,000 psia. An increase in dissolved solids causes a slight increase in ΔVwT and a slight decrease in ΔVwp, which offset each other to within 1%.

## Nomenclature

 Bw = Water formation volume factor Vrc = volume occupied by a unit mass of water at reservoir conditions (weight of gas dissolved in water at reservoir or standard conditions is negligible), ft3, Vsc = volume occupied by a unit mass of water at standard conditions, ft3, ρsc = density of water at standard conditions, lbm/ ft3, ρrc = density of water at reservoir conditions, lbm/ ft3

## References

1. McCain, W.D. Jr.: McCain, W.D. Jr. 1990. The Properties of Petroleum Fluids, second edition. Tulsa, Oklahoma: PennWell Books.
2. McCain Jr., W.D. 1991. Reservoir-Fluid Property Correlations-State of the Art (includes associated papers 23583 and 23594). SPE Res Eng 6 (2): 266-272. SPE-18571-PA. http://dx.doi.org/10.2118/18571-PA