Accurate correlations exist for the density of pure water. An example is the model of Keyes et al. [1], which is used in PVTsim Nova. Formation water produced together with gas and oil is not pure, but contains dissolved salts, and these salts can have a significant effect on the density.
The importance of water density for the design of pipelines and process equipment increases with the water cut. There are cases where oil is produced with a water cut as high as 90%. Also when designing water-based drilling fluids, it is of much importance to be able to calculate how much dissolved salts affect the density of the water phase.
In PVTsim, the salt concentration can either be input as mg/l or the concentration of each individual salt can be entered. In both cases, the model by Laliberté and Cooper [2] is used to correct the density for salt content. When the amount of salt is given as mg/l, it is assumed that all salt is sodium chloride (NaCl).
The correlation of Laliberté and Cooper takes the form:
.PNG)
where
ρbrine Density of salt water (brine)
wH2O Weight fraction of water
ρH2O Density of pure water
wi Weight fraction of salt number i
ρApp,i Density of salt number i when dissolved in water (apparent salt density)
The apparent density (in kg/m3) of a salt dissolved in water is calculated from
where c0-c4 are salt specific constants and t the temperature in oC. PVTsim Nova handles the effect of the below salts on the water phase density:
– Sodium Chloride (NaCl)
– Potassium Chloride (KCl)
– Sodium Bromide (NaBr)
– Potassium Bromide (KBr)
– Calcium Chloride (CaCl2)
– Calcium Bromide (CaBr2)
– Zinc Bromide (ZnBr2)
– Sodium Formate (HCOONa)
– Potassium Formate (HCOOK)
– Cesium Formate (HCOOCs)
Table 1 shows the constants to be used for NaCl.
| Constant | Value for NaCl |
| c0 | 0.00433 |
| c1 | 0.06471 |
| c2 | 1.0166 |
| c3 | 0.014624 |
| c4 | 3315.6 |
Figure 1 shows measured and simulated densities of NaCl brine at four different temperatures at 1 bar and at four different pressures at 50 oC. An almost perfect match is seen between the experimental densities and those simulated using the correlation of Laliberté and Cooper.
Figure 1 Measured and simulated densities of NaCl salt water at four different temperatures at 1 bar and at four different pressures at 50 oC.
It has also been verified that the correlation of Laliberté and Cooper works well for mixed salts. Densities were simulated of water with NaCl and NaBr. The data covered NaCl weight%’s from 0 – 14.8 and NaBr weight%’s from 0 – 24.0 in several mixing ratios. The match of the data is shown in Figure 2 as Calculated versus Experimental densities. With a perfect match, all the points on the plot should follow the diagonal, which is very close to being the case.
Figure 2 Calculated versus experimental densities of salt water solutions with NaCl and NaBr at 25 oC and 1 bar.
References
Keyes, F.G., Keenan, J.H., Hill, P.G. and Moore, J.G., ”A Fundamental Equation for Liquid and Vapor Water”, presented at the Seventh International Conference on the Properties of Steam, Tokyo, Japan, Sept. 1968.
Laliberté, M. and Cooper, W.E., “Model for Calculating the Density of Aqueous Electrolyte Solutions”, J. Chem. Eng. Data 49, 2004, pp. 1141-1151.
