Method for determining absolute density of cement slurry
View Patent ↗A method for determining absolute density of a slurry that typically contains entrained air, such as cement slurry, in a continuous mixing operation such those used in cementing a gas or oil well. The method obtains density measurements of a slurry at two different pressures and then uses the two density measurements and the two pressure measurements to compute absolute density of the slurry employing the following formula at isothermal conditions: Dabs=D 1 /(1−((D 1 /D 2 −1)/(P 1 /P 2 −1))), where Dabs=absolute density, D 1 =first density, D 2 =second density, P 1 =absolute pressure at which the first density was measured, and P 2 =absolute pressure at which the second density was measured.
1. A method for determining the absolute density of a liquid or slurry that contains entrained air comprising the following:
measuring a first density of a liquid or slurry at a first pressure,
measuring a second density of the liquid or slurry at a second pressure which is different from the first pressure,
calculating absolute density of the liquid or slurry employing the following derived formula that incorporates the polytropic process model of compressibility of gas:
absolute density of the liquid or slurry=first density/ (1−((first density/second density−1)/ ((first pressure/second pressure) 1/exponent for pressure-volume polytropic process relatonship −1))),
wherein first and second densities are continuosly measured by one or more densitometers and first and second pressures are continuously measured by one or more pressure transducers.
2. A method for determining the absolute density of a liquid or slurry that contains entrained air according to claim 1 wherein the density measurement and pressure measurements are constantly transmitted to a computer system that continuously calculates the absolute density of the liquid or slurry in real time.
3. A method for determining the absolute density of a liquid slurry that contains entrained air according to claim 2 wherein the first density and the first pressure are measured in a recirculation line of a cement mixing system by a first densitometer and a first pressure transducer and the second density and second pressure are measured in a transfer line of the cement mixing system by a second densitometer and a second pressure transducer.
4. A method for determining the absolute density of a liquid or slurry that contains entrained air according to claim 2 wherein the first density and the first pressure are measured in liquid or slurry line of a cement mixing system by a first densitometer and a first pressure transducer and the second density and second pressure are measured in the same liquid or slurry line downstream of the first densitometer by a second densitometer and a second pressure transducer that are provided in series with the first densitometer and first pressure transducer.
5. A method for determining the absolute density of a liquid or slurry that contains entrained air according to claim 4 wherein the liquid or slurry line where the densitometers and pressure transducers are measuring the liquid or slurry is the recirculation line.
6. A method for determining the absolute density of a liquid or slurry that contains entrained air according to claim 4 wherein the liquid or slurry line where the densitometers and pressure transducers are measuring the liquid or slurry is the transfer line.
7. A method for determining the absolute density of a liquid or slurry that contains entrained air according to claim 2 wherein both the first density and second density are measured in a liquid or slurry line of a cement mixing system by a first densitometer and wherein both the first pressure and second pressure are measured in the liquid or slurry line by a first pressure transducer.
8. A method for determining the absolute density of a liquid or slurry that contains entrained air according to claim 7 further comprising:
varying the pressure in the liquid or slurry line between the time of measurement of the first density and the time of measurement of the second density.
9. A method for determining the absolute density of a liquid or slurry that contains entrained air according to claim 8 wherein the pressure in the liquid or slurry line is varied by employing a pulsing pump.
10. A method for determining the absolute density of a liquid or slurry that contains entrained air according to claim 8 wherein the pressure in the liquid or slurry line is varied by employing a varying downstream flow restriction.
11. A method for determining the absolute density of a liquid or slurry that contains entrained air according to claim 2 wherein the pressure and density measurements are taken in a liquid or slurry transfer line.
12. A method for determining the absolute density of liquid or slurry that contains entrained air according to claim 11 wherein the pressure in the liquid or slurry transfer line is varied by employing a downstream manifold with a manifold valve that repetitiously opens and closes to provide a varying downstream flow restriction and varying upstream back pressure.
13. A method for determining the absolute density of liquid or slurry that contains entrained air according to claim 2 wherein the pressure and density measurements are taken in a liquid or slurry recirculation line.
14. A method for determining the absolute density of liquid or slurry that contains entrained air according to claim 13 wherein the pressure in the liquid or slurry recirculation line is varied by employing a downstream manifold with a manifold valve that repetitiously opens and closes to provide a varying downstream flow restriction and varying upstream back pressure.
15. A method for determining the absolute density of liquid or slurry that contains entrained air according under isothermal conditions comprising the following:
measuring a first density of a liquid or slurry at a first pressure,
measuring a second density of the liquid or slurry at a second pressure which is different from the first pressure, and
calculating absolute density of the liquid or slurry employing the following derived formula that incorporates the isothermal process model of compressibility of gas:
absolute density of the liquid or slurry=first density/ (1−((first density/second density −1)/ (first pressure/second pressure−1))),
wherein first and second densities are continuously measured by one or more densitometers and first and second pressures are continuously measured by one or more pressure transducers,
wherein the density measurement and pressure measurements are constantly transmitted to a computer system that continuously calculates the absolute density of the liquid or slurry in real time, and
wherein the first density and the first pressure are measured in a recirculation line of a cement mixing system by a first densitometer and a first pressure transducer and the second density and second pressure are measured in a transfer line of the cement mixing system by a second densitometer and a second pressure transducer.
16. A method for determining the absolute density of liquid or slurry that contains entrained air under isothermal conditions comprising the following:
measuring a first density of a liquid or slurry at a first pressure,
measuring a second density of the liquid or slurry at a second pressure which is different from the first pressure, and
calculating absolute density of the liquid or slurry employing the following derived formula that incorporates the isothermal process model of compressibility of gas:
absolute density of the liquid or slurry=first density/ (1−((first density/second density −1)/ (first pressure/second pressure−1))),
wherein first and second densities are continuously measured by one or more densitometers and first and second pressures are continuously measured by one or more pressure transducers,
wherein the density measurement and pressure measurements are constantly transmitted to a computer system that continuously calculates the absolute density of the liquid or slurry in real time,
wherein both the first density and second density are measured in a liquid or slurry line of a cement mixing system by a first densitometer and wherein both the first pressure and second pressure are measured in the liquid or slurry line by a first pressure transducer,
varying the pressure in the liquid or slurry line between the time of measurement of the first density and the time of measurement of the second density, and
wherein the pressure in the liquid or slurry line is varied by employing a pulsing pump.