Method for determining the viscosity of a polymer solution

1. A method for determining intrinsic viscosity [η] of an aqueous polymer solution at a temperature T, wherein the aqueous polymer solution comprises at least one acrylamide-based polymer in an aqueous solvent, the aqueous solvent having a salinity of from 6 to 250 g/L, the method comprising:

providing a single universal relation R 1 between (i), product of polymer concentration and intrinsic viscosity C·[η], and (ii) specific viscosity at zero shear rate η sp ;

performing a measurement of dynamic viscosity of the aqueous polymer solution at one polymer concentration C 1 , at temperature T and at various shear rates;

determining from said measurement zero-shear viscosity η 0 of the aqueous polymer solution at polymer concentration C 1 and at temperature T;

calculating specific viscosity at zero shear rate of the aqueous polymer solution at polymer concentration C 1 and at temperature T as η sp =(η 0 −η s )/η s , where η s is zero-shear viscosity of the aqueous solvent; and

estimating the intrinsic viscosity [η] of the aqueous polymer solution at temperature T by applying the universal relation R 1 to the calculated specific viscosity at zero shear rate η sp and polymer concentration C 1 .

2. The method according to claim 1 , wherein one or more measurements of the dynamic viscosity of the aqueous polymer solution at various shear rates are performed only at the polymer concentration C 1 .

3. The method according to claim 1 , further comprising:

performing a measurement of dynamic viscosity of the aqueous polymer solution, at at least another polymer concentration C 2 , at temperature T, and at various shear rates;

determining zero-shear viscosity η 0 of the aqueous polymer solution at least the polymer concentrations C 1 and C 2 and at temperature T, from the measurement of the dynamic viscosity of the aqueous polymer solution at the polymer concentration C 1 and the measurement of the dynamic viscosity of the aqueous polymer solution at the polymer concentration C 2 ;

calculating specific viscosity at zero shear rate of the aqueous polymer solution at least the polymer concentrations C 1 and C 2 and at temperature T as η sp =(η 0 −η s )/η s , where η s is the zero-shear viscosity of the aqueous solvent; and

estimating an average intrinsic viscosity [η] of the aqueous polymer solution at temperature T by fitting the calculated specific viscosity at zero shear rate of the aqueous polymer solution at least the polymer concentrations C 1 and C 2 and at temperature T with the universal relation R 1 .

4. The method according to claim 1 , wherein the single universal relation R 1 is obtained by:

providing a number of acrylamide-based polymers;

for each acrylamide-based polymer, performing several measurements of dynamic viscosity of aqueous solutions of the acrylamide-based polymer in an aqueous solvent, the aqueous solvent having a salinity of from 6 to 250 g/L, at various shear rates and various polymer concentrations, at one or several temperatures;

deriving specific viscosity at zero shear rate and intrinsic viscosity of each aqueous solution, at each concentration and temperature, from said several measurements, so as to obtain a set of specific viscosity at zero shear rate data associated with product of intrinsic viscosity and polymer concentration data; and

providing a mathematical fit for the specific viscosity at zero shear rate data as a function of the product of intrinsic viscosity and polymer concentration data.

5. The method according to claim 1 , wherein the single universal relation R 1 is defined as η sp =C·[η]+0.56 (C·[η]) 2.17 +0.0026 (C·[η]) 4.72 or as any other function where η sp deviates from C·[η]+0.56 (C·[η]) 2.17 +0.0026 (C·[η]) 4.72 at any value of C·[η] by less than 20%.

6. A method for determining dynamic viscosity of an aqueous polymer solution as a function of shear rate, at a temperature T and at a polymer concentration C′, wherein the aqueous polymer solution comprises at least one acrylamide-based polymer in an aqueous solvent, the aqueous solvent having a salinity of from 6 to 250 g/L, the method comprising:

providing a single universal relation R 2 between (i) product of polymer concentration and intrinsic viscosity C·[η] and (ii) Carreau coefficient n;

providing a single universal relation R 3 between (i) the product of polymer concentration and intrinsic viscosity C·[η] and (ii) ratio of relaxation time to diluted regime-relaxation time λ/λ d ;

determining intrinsic viscosity [η] of the aqueous polymer solution at temperature T by:

providing a single universal relation R 1 between (i), the product of polymer concentration and intrinsic viscosity C·[η], and (ii) specific viscosity at zero shear rate η sp ;

performing a measurement of dynamic viscosity of the aqueous polymer solution at one or more polymer concentrations other than C′, at temperature T and at various shear rates;

determining from said measurement zero-shear viscosity η 0 of the aqueous polymer solution at the one or more polymer concentrations other than C′ and at temperature T;

calculating specific viscosity at zero shear rate of the aqueous polymer solution at the one or more polymer concentrations other than C′ and at temperature T as η sp =(η 0 −η s )/η s , where η s is zero-shear viscosity of the aqueous solvent; and

estimating the intrinsic viscosity [η] of the aqueous polymer solution at temperature T by applying the universal relation R 1 to the calculated specific viscosity at zero shear rate η sp and the one or more polymer concentrations other than C′;

estimating diluted regime-relaxation time λ d of the aqueous polymer solution at temperature T by:

determining relaxation time λ 1 of the aqueous polymer solution at temperature T and at a single polymer concentration C 1 , from a measurement of dynamic viscosity of the aqueous polymer solution at polymer concentration C 1 and at temperature T, and then applying the universal relation R 3 to the determined relaxation time λ 1 , polymer concentration C 1 and the determined intrinsic viscosity [η] at temperature T; or

determining at least two relaxation times λ 1 and λ 2 of the aqueous polymer solution at temperature T and at at least two respective polymer concentrations C 1 and C 2 , from respective measurements of dynamic viscosity of the aqueous polymer solution at the at least two polymer concentrations C 1 and C 2 and at temperature T, and applying the universal relation R 3 to the at least two determined relaxation times λ 1 and λ 2 , respective polymer concentrations C 1 and C 2 and the determined intrinsic viscosity [η] at temperature T so as to provide an average value of λ d at temperature T;

estimating relaxation time λ′ of the aqueous polymer solution at temperature T and polymer concentration C′ by applying the universal relation R 3 to the estimated diluted-regime relaxation time λ d , the polymer concentration C′ and the determined intrinsic viscosity [η] at temperature T;

estimating Carreau coefficient n′ of the aqueous polymer solution at temperature T and polymer concentration C′ by applying the universal relation R 2 to polymer concentration C′ and the determined intrinsic viscosity [η] at temperature T;

estimating specific viscosity at zero shear rate η sp ′ of the aqueous polymer solution at polymer concentration C′ and at temperature T by applying the universal relation R 1 to (i) the determined intrinsic viscosity [η] at temperature T and (ii) polymer concentration C′;

estimating a zero-shear viscosity η 0 ′ of the aqueous polymer solution at polymer concentration C′ and at temperature T as η 0 ′=η s ·(η sp ′+1); and

estimating the dynamic viscosity η′ of the aqueous polymer solution as a function of shear rate {dot over (γ)}, at temperature T and at polymer concentration C′ by applying Carreau's equation: η′=η s +(η 0 ′−η s )·[1+(λ′−{dot over (γ)}) 2 ] (n′−1)/2 .

7. The method according to claim 6 , wherein the single universal relation R 2 is obtained by:

providing a number of acrylamide-based polymers;

for each acrylamide-based polymer, performing several measurements of dynamic viscosity of aqueous solutions of the acrylamide-based polymer in an aqueous solvent, the aqueous solvent having a salinity of from 6 to 250 g/L, at various shear rates and various polymer concentrations, at one or several temperatures;

deriving a Carreau coefficient and intrinsic viscosity of each aqueous solution, at each concentration and temperature, from said several measurements, so as to obtain a set of Carreau coefficient data associated with product of intrinsic viscosity and polymer concentration data; and

providing a mathematical fit for the Carreau coefficient data as a function of the product of intrinsic viscosity and polymer concentration data.

8. The method according to claim 6 , wherein the single universal relation R 2 is defined as n=1−(0.796−0.687×exp (−0.059×C·[η]) or as any other function where n deviates from 1−(0.796−0.687×exp (−0.059×C·[η]) at any value of C·[η] by less than 20%.

9. The method according to claim 6 , wherein the single universal relation R 3 is obtained by:

providing a number of acrylamide-based polymers;

for each acrylamide-based polymer, performing several measurements of dynamic viscosity of aqueous solutions of the acrylamide-based polymer in an aqueous solvent, the aqueous solvent having a salinity of from 6 to 250 g/L, at various shear rates and various polymer concentrations, at one or several temperatures;

deriving relaxation time, diluted regime-relaxation time and intrinsic viscosity of each aqueous solution, at each concentration and temperature, from said several measurements, so as to obtain a set of relaxation time-to-diluted regime-relaxation time ratio data associated with product of intrinsic viscosity and polymer concentration data; and

providing a mathematical fit for the relaxation time-to-diluted regime-relaxation time ratio data as a function of the product of intrinsic viscosity and polymer concentration data.

10. The method according to claim 6 , wherein the single universal relation R 3 is defined as λ/λ d =1+0.04 (C·[η]) 2.4 or as any other function where λ/λ d deviates from 1+0.04 (C·[η]) 2.4 at any value of C·[η] by less than 20%.

11. The method of claim 6 , wherein each measurement of the dynamic viscosity of the aqueous polymer solution is performed at one or more polymer concentrations C such that C·[η] is within the range of 1 to 10 and C′ [η] is out of the range of 1 to 10.

12. A method for determining dynamic viscosity of an aqueous polymer solution as a function of shear rate, at a temperature T′ and at a polymer concentration C′, wherein the aqueous polymer solution comprises at least one acrylamide-based polymer in an aqueous solvent, the aqueous solvent having a salinity of from 6 to 250 g/L, the method comprising:

providing a single universal relation R 2 between (i) product of polymer concentration and intrinsic viscosity C·[η] and (ii) Carreau coefficient n;

providing a single universal relation R 3 between (i) the product of polymer concentration and intrinsic viscosity C·[η] and (ii) ratio of relaxation time to diluted regime-relaxation time λ/λ d ;

determining intrinsic viscosity [η] of the aqueous polymer solution at a plurality of temperatures different from T′, wherein each determination of the intrinsic viscosity is performed by:

providing a single universal relation R 1 between (i), the product of polymer concentration and intrinsic viscosity C·[η], and (ii) specific viscosity at zero shear rate η sp ;

performing a measurement of dynamic viscosity of the aqueous polymer solution at the polymer concentration C 1 , at a given temperature from amongst the plurality of temperatures different from T′ and at various shear rates;

determining from said measurement zero-shear viscosity η 0 of the aqueous polymer solution at polymer concentration C 1 and at the given temperature;

calculating specific viscosity at zero shear rate of the aqueous polymer solution at polymer concentration C 1 and at the given temperature as η sp =(η 0 −η s )/η s , where η s is zero-shear viscosity of the aqueous solvent; and

estimating the intrinsic viscosity [η] of the aqueous polymer solution at the given temperature by applying the universal relation R 1 to the calculated specific viscosity at zero shear rate η sp and polymer concentration C 1 ;

evaluating intrinsic viscosity [η] of the aqueous polymer solution at temperature T′ based on the determined intrinsic viscosity [η] of the aqueous polymer solution at the plurality of temperatures, by a mathematical fit;

estimating diluted regime-relaxation time λ d of the aqueous polymer solution at one or more temperatures T from amongst the plurality of temperatures by:

determining relaxation time λ 1 of the aqueous polymer solution at a temperature T, from amongst the one or more temperatures, and at the polymer concentration C 1 , from the measurement of the dynamic viscosity of the aqueous polymer solution at polymer concentration C 1 and at said temperature T, and then applying the universal relation R 3 to the determined relaxation time λ 1 , polymer concentration C 1 and the determined intrinsic viscosity [η] at this temperature T; or

determining at least two relaxation times λ 1 and λ 2 of the aqueous polymer solution at temperature T and at at least two respective polymer concentrations C 1 and C 2 , from respective measurements of dynamic viscosity of the aqueous polymer solution at the at least two polymer concentrations C 1 and C 2 and at temperature T, and applying the universal relation R 3 to the at least two determined relaxation times λ 1 and λ 2 , respective polymer concentrations C 1 and C 2 and the determined intrinsic viscosity [η] at temperature T so as to provide an average value of λ d at temperature T;

estimating the diluted regime-relaxation time λ d of the aqueous polymer solution at temperature T′ as:

λ d ( T )×(η s ( T ′)×[η]( T ′)× T )/(η s ( T )×[η]( T )× T ′)

where λ d (T) is the diluted regime-relaxation time λ d of the aqueous polymer solution at temperature T, η s (T′) and η s (T) are respectively zero-shear viscosities of the aqueous solvent at temperatures T′ and T, and [η](T′) and [η](T) are respectively intrinsic viscosities of the aqueous polymer solution at temperatures T′ and T;

estimating relaxation time λ′ of the aqueous polymer solution at temperature T′ and polymer concentration C′ by applying the universal relation R 3 to the estimated diluted regime-relaxation time λ d at temperature T′, the polymer concentration C′ and the evaluated intrinsic viscosity [η] at temperature T′;

estimating Carreau coefficient n′ of the aqueous polymer solution at temperature T′ and polymer concentration C′ by applying the universal relation R 2 to polymer concentration C′ and the evaluated intrinsic viscosity [η] at temperature T′;

estimating specific viscosity at zero shear rate η sp ′ of the aqueous polymer solution at polymer concentration C′ and at temperature T′ by applying the universal relation R 1 to (i) the evaluated intrinsic viscosity [η] at temperature T′ and (ii) polymer concentration C′;

estimating zero-shear viscosity η 0 ′ of the aqueous polymer solution at polymer concentration C′ and at temperature T′=η 0 ′=η s ·(η sp ′+1); and

estimating the dynamic viscosity η′ of the aqueous polymer solution as a function of shear rate {dot over (γ)}, at temperature T′ and at polymer concentration C′ by applying Carreau's equation: η′=η s+ (η 0 ′−η s )·[1+(λ′·{dot over (γ)}) 2 ] (n′−1)/2 .

13. The method according to claim 12 , wherein the single universal relation R 2 is obtained by:

providing a number of acrylamide-based polymers;

for each acrylamide-based polymer, performing several measurements of dynamic viscosity of aqueous solutions of the acrylamide-based polymer in an aqueous solvent, the aqueous solvent having a salinity of from 6 to 250 g/L, at various shear rates and various polymer concentrations, at one or several temperatures;

deriving a Carreau coefficient and intrinsic viscosity of each aqueous solution, at each concentration and temperature, from said several measurements, so as to obtain a set of Carreau coefficient data associated with product of intrinsic viscosity and polymer concentration data; and

providing a mathematical fit for the Carreau coefficient data as a function of the product of intrinsic viscosity and polymer concentration data.

14. The method according to claim 12 , wherein the single universal relation R 2 is defined as n=1−(0.796−0.687×exp (−0.059×C·[η]) or as any other function where n deviates from 1−(0.796−0.687×exp (−0.059×C·[η]) at any value of C·[η] by less than 20%.

15. The method according to claim 12 , wherein the single universal relation R 3 is obtained by:

providing a number of acrylamide-based polymers;

for each acrylamide-based polymer, performing several measurements of dynamic viscosity of aqueous solutions of the acrylamide-based polymer in an aqueous solvent, the aqueous solvent having a salinity of from 6 to 250 g/L, at various shear rates and various polymer concentrations, at one or several temperatures;

deriving relaxation time, diluted regime-relaxation time and intrinsic viscosity of each aqueous solution, at each concentration and temperature, from said several measurements, so as to obtain a set of relaxation time-to-diluted regime-relaxation time ratio data associated with product of intrinsic viscosity and polymer concentration data; and

providing a mathematical fit for the relaxation time-to-diluted regime-relaxation time ratio data as a function of the product of intrinsic viscosity and polymer concentration data.

16. The method according to claim 12 , wherein the single universal relation R 3 is defined as λ/λ d =1+0.04 (C·[η]) 2.4 or as any other function where λ/λ d deviates from 1+0.04 (C·[η]) 2.4 at any value of C·[η] by less than 20%.

17. A method for determining viscosimetric molecular weight of an acrylamide-based polymer, the method comprising:

providing an aqueous polymer solution, the aqueous polymer solution comprising the acrylamide-based polymer in an aqueous solvent, the aqueous solvent having a salinity of from 6 to 250 g/L;

providing a single universal relation R 3 between (i) product of polymer concentration and intrinsic viscosity C·[η] and (ii) ratio of relaxation time to diluted regime-relaxation time λ/λ d ;

determining intrinsic viscosity [η] of the aqueous polymer solution at a temperature T by:

providing a single universal relation R 1 between (i), product of polymer concentration and intrinsic viscosity C·[η], and (ii) specific viscosity at zero shear rate η sp ;

performing a measurement of dynamic viscosity of the aqueous polymer solution at one polymer concentration C 1 , at temperature T and at various shear rates;

determining from said measurement zero-shear viscosity η 0 of the aqueous polymer solution at polymer concentration C 1 and at temperature T;

calculating specific viscosity at zero shear rate of the aqueous polymer solution at polymer concentration C 1 and at temperature T as η sp =(η 0 −η s )/η s , where η s is zero-shear viscosity of the aqueous solvent; and

estimating the intrinsic viscosity [η] of the aqueous polymer solution at temperature T by applying the universal relation R 1 to the calculated specific viscosity at zero shear rate η sp and polymer concentration C 1 ;

estimating diluted regime-relaxation time λ d of the aqueous polymer solution at temperature T by:

determining relaxation time λ 1 of the aqueous polymer solution at temperature T and polymer concentration C 1 , from the measurement of the dynamic viscosity of the aqueous polymer solution at polymer concentration C 1 and at temperature T, and then applying the universal relation R 3 to the determined relaxation time λ 1 , polymer concentration C 1 and the determined intrinsic viscosity [η] at temperature T; or

determining at least two relaxation times λ 1 and λ 2 of the aqueous polymer solution at temperature T and at at least two respective polymer concentrations C 1 and C 2 , from respective measurements of dynamic viscosity of the aqueous polymer solution at the at least two polymer concentrations C 1 and C 2 and at temperature T, and applying the universal relation R 3 to the at least two determined relaxation times λ 1 and λ 2 , respective polymer concentrations C 1 and C 2 and the determined intrinsic viscosity [η] at temperature T so as to provide an average value of λ d at temperature T;

estimating the viscosimetric molecular weight of the polymer according to the equation M=(λ d ·T)/([η]·η s )/1.474 where η s is the zero-shear viscosity of the aqueous solvent at temperature T.

18. The method according to claim 17 , wherein the single universal relation R 3 is obtained by:

providing a number of acrylamide-based polymers;

for each acrylamide-based polymer, performing several measurements of dynamic viscosity of aqueous solutions of the acrylamide-based polymer in an aqueous solvent, the aqueous solvent having a salinity of from 6 to 250 g/L, at various shear rates and various polymer concentrations, at one or several temperatures;

deriving relaxation time, diluted regime-relaxation time and intrinsic viscosity of each aqueous solution, at each concentration and temperature, from said several measurements, so as to obtain a set of relaxation time-to-diluted regime-relaxation time ratio data associated with product of intrinsic viscosity and polymer concentration data; and

providing a mathematical fit for the relaxation time-to-diluted regime-relaxation time ratio data as a function of the product of intrinsic viscosity and polymer concentration data.

19. The method according to claim 17 , wherein the single universal relation R 3 is defined as λ/λ d =1+0.04 (C·[η]) 2.4 or as any other function where λ/λ d deviates from 1+0.04 (C·[η]) 2.4 at any value of C·[η] by less than 20%.

20. The method of claim 1 , wherein the at least one acrylamide-based polymer comprises units derived from one or more monomers selected from acrylamide, sodium acrylate, N-vinyl pyrrolidone and 2-acrylamide-2-methylpropane sulfonate.