All oil and gas reservoirs have water associated with them. Since it is a common part of the system, we will need to discuss how it is stored and moves in the reservoir.

### Water Formation Volume Factor, B_{w}

The water (or more correctly, the brine) *Formation Volume Factor*, B_{w}, (sometimes referred to as the FVF) is a pressure and temperature dependent property that relates the volume of 1.0 stock tank barrel, STB, of water to its volume in barrels, bbl, at another pressure. It has the units of bbls/STB. We have already discussed the use of the stock tank pressure and temperature as an oilfield reference system.

By definition, if we had 1.0 STB of water at p_{ST} and T_{ST}, and that same STB occupied 1.02 bbls at reservoir conditions, p_{r} and T_{r}, then it would have a formation volume factor of:

$${B}_{w}\left({p}_{r},{T}_{r}\right)=\frac{{V}_{w\text{}r}\text{}bbl}{{V}_{w\text{}ST}\text{}STB}=\frac{1.02\text{bbl}}{1.00\text{}STB}=1.02\text{}bbl/STB$$

We can also define the formation volume factor in terms of densities at stock tank conditions and at reservoir conditions. If we assume the mass of 1.0 STB, m_{1} _{STB}, then at reservoir conditions, we would have:

which implies:

Water Isothermal Compressibility, c_{w}

Water is considered to be a slightly compressible liquid with a very low value of compressibility. From **Equation 3.26** we have:

One correlation for water compressibility^{[5]} , c_{w}, is:

Where:

- p is the pressure, psi
- C is the salt concentration, gm/L
- T is temperature, °F

We can develop an explicit formula for the water formation volume factor based on the water compressibility. If we take 1.0 STB of water and its volume in barrels at a reservoir pressure and temperature, then we would have: V_{w} (bbl) = B_{w} (p_{r}, T_{r}) (bbl/STB) x 1.0 STB. Now,

or,

Water Viscosity, μ_{w}

In the laboratory, the water viscosity is measured with an apparatus called a Viscometer. The mechanics and test procedures for a viscometer are beyond the scope of this course, and we will work with known correlations. One correlation from McCain has the form:

with

and

where

- μ
_{w}_{14.7}_{psi}is the water viscosity at 14.7 psi and temperature, T °F - S is the salt concentration in weight percent, Wt% (note different unit from
**Equation 3.31**)

Once the viscosity at 14.7 psi and T °F are determined, the water viscosity at other pressures can be determined from:

Water Density, ρ_{w}

The density of water is also a property of interest in petroleum engineering. McCain^{[6]} provides the following correlation for estimating the water density at reference conditions:

where

- ρ
_{w}_{ST}is the water density at sock tank conditions, lb/ft^{3} - S is the salt concentration in weight percent, Wt%

The water density at reservoir conditions can then be calculated using **Equation 3.29**.

^{}[5]^{ }Petro Wiki: Produced water compressibility

^{}[6] McCain, W.D. Jr.: McCain, W.D. Jr. 1990. The Properties of Petroleum Fluids, second edition. Tulsa, Oklahoma: PennWell Books.