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# Oilfield water compressibility

The following topic describes the compressibility of produced water.

## Compressibility

The compressibility of formation water at pressures above the bubblepoint is defined as the change in water volume per unit water volume per psi change in pressure. This is expressed mathematically as

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

or

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

or

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

where

 cw = water compressibility at the given pressure and temperature, bbl/bbl-psi, = average water compressibility within the given pressure and temperature interval, bbl/bbl-psi, V = water volume at the given pressure and temperature, bbl, = average water volume within p and T intervals, bbl, p1 and p2 = pressure at conditions 1 and 2 with p1 > p2, psi, Bw1 and Bw2 = water formation volume factor (FVF) p1 and p2, bbl/bbl , = average water FVF corresponding to V, bbl/bbl.

Water compressibility also depends on the salinity. In contrast to the literature, laboratory measurements by Osif[1] show that the effect of gas in solution on compressibility of water with NaCl concentrations up to 200 g/cm3 is essentially negligible. Osif’s results show no effect at gas/water ratios (GWRs) of 13 scf/bbl. At GWRs of 35 scf/bbl, there is probably no effect, but certainly no more than a 5% increase in the compressibility of brine.

Laboratory measurements[2] of water compressibility resulted in linear plots of the reciprocal of compressibility vs. pressure. The plots of l/cw vs. P have a slope of m1 and intercepts linear in salinity and temperature. Data points for the systems tested containing no gas in solution resulted in Eq. 2.

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

where cw = water compressibility, psi−1; p = pressure, psi; C = salinity, g/L of solution; T = temperature, °F; m1 = 7.033; m2 = 541.5; m3 = −537; and m4 = 403.3 × 103. Eq. 2 was fit for pressures between 1,000 and 20,000 psi, salinities of 0 to 200 g/L NaCl, and temperatures from 200 to 270°F. Compressibilities were independent of dissolved gas.

When conditions overlap, the agreement with the results reported by both Dorsey[3] and Dotson and Standing[4] is very good. Results from the Rowe and Chou[5] equation agree well up to 5,000 psi (their upper pressure limit) but result in larger deviations with increasing pressure. In almost all cases, the Rowe and Chou compressibilities are less than that of Eq. 2.

## References

1. Osif, T.L.: "The Effects of Salt, Gas, Temperature, and Pressure on the Compressibility of Water," SPERE (February 1988) 175.
2. Kriel, B.G., Lacey, C.A., and Lane, R.H.: "The Performance of Scale Inhibitors in the Inhibition of Iron Carbonate Scale," paper SPE 27390 presented at the 1994 SPE International Symposium and Exhibition on Formation Damage Control, Lafayette, Louisiana, 7–10 February.
3. Dorsey, N. E.: Properties of Ordinary Water Substances, Monograph Series, American Chemical Soc. (1940) 208, No. 81, 246.
4. Dotson. C.R. and Standing, M.B.: "Pressure, Volume, Temperature and Solubility Relations for Natural Gas-Water Mixtures," Drill. & Prod. Prac., API (1944) 173.
5. Rowe, A.M. Jr. and Chou, J.C.S.: "Pressure-Volume-Temperature-Concentration Relations of Aqueous NaCl Solutions," J. Chem. Eng. Data (1970) 15, 61.