Method for determining the viscosity of a polymer solution

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 R2 between (i) product of polymer concentration and intrinsic viscosity C·[η] and (ii) Carreau coefficient n;
• providing a single universal relation R3 between (i) the product of polymer concentration and intrinsic viscosity C·[η] and (ii) ratio of relaxation time to diluted regime-relaxation time λ/λd;
• determining intrinsic viscosity [η] of the aqueous polymer solution at temperature T by:
• providing a single universal relation R1 between (i), the product of polymer concentration and intrinsic viscosity C·[η], and (ii) specific viscosity at zero shear rate ηsp;
• 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 η0 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 ηsp=(η0−ηs)/ηs, where ηs 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 R1 to the calculated specific viscosity at zero shear rate ηsp and the one or more polymer concentrations other than C′;
• estimating diluted regime-relaxation time λd of the aqueous polymer solution at temperature T by:
• determining relaxation time λ1 of the aqueous polymer solution at temperature T and at a single polymer concentration C1, from a measurement of dynamic viscosity of the aqueous polymer solution at polymer concentration C1 and at temperature T, and then applying the universal relation R3 to the determined relaxation time λ1, polymer concentration C1 and the determined intrinsic viscosity [η] at temperature T;
• or
• determining at least two relaxation times λ1 and λ2 of the aqueous polymer solution at temperature T and at at least two respective polymer concentrations C1 and C2, from respective measurements of dynamic viscosity of the aqueous polymer solution at the at least two polymer concentrations C1 and C2 and at temperature T, and applying the universal relation R3 to the at least two determined relaxation times λ1 and λ2, respective polymer concentrations C1 and C2 and the determined intrinsic viscosity [η] at temperature T so as to provide an average value of λd at temperature T;
• estimating relaxation time λ′ of the aqueous polymer solution at temperature T and polymer concentration C′ by applying the universal relation R3 to the estimated diluted-regime relaxation time λd, 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 R2 to polymer concentration C′ and the determined intrinsic viscosity [η] at temperature T;
• estimating specific viscosity at zero shear rate ηsp′ of the aqueous polymer solution at polymer concentration C′ and at temperature T by applying the universal relation R1 to (i) the determined intrinsic viscosity [η] at temperature T and (ii) polymer concentration C′;
• estimating a zero-shear viscosity η0′ of the aqueous polymer solution at polymer concentration C′ and at temperature T as η0′=ηs·(ηsp′+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′=ηs+(η0′−ηs)·[1+(λ′−{dot over (γ)})2](n′−1)/2.

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 R2 between (i) product of polymer concentration and intrinsic viscosity C·[η] and (ii) Carreau coefficient n;
• providing a single universal relation R3 between (i) the product of polymer concentration and intrinsic viscosity C·[η] and (ii) ratio of relaxation time to diluted regime-relaxation time λ/λd;
• 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 R1 between (i), the product of polymer concentration and intrinsic viscosity C·[η], and (ii) specific viscosity at zero shear rate ηsp;
• performing a measurement of dynamic viscosity of the aqueous polymer solution at the polymer concentration C1, 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 η0 of the aqueous polymer solution at polymer concentration C1 and at the given temperature;
• calculating specific viscosity at zero shear rate of the aqueous polymer solution at polymer concentration C1 and at the given temperature as ηsp=(η0−ηs)/ηs, where ηs 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 R1 to the calculated specific viscosity at zero shear rate ηsp and polymer concentration C1;
• 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 λd of the aqueous polymer solution at one or more temperatures T from amongst the plurality of temperatures by:
• determining relaxation time λ1 of the aqueous polymer solution at a temperature T, from amongst the one or more temperatures, and at the polymer concentration C1, from the measurement of the dynamic viscosity of the aqueous polymer solution at polymer concentration C1 and at said temperature T, and then applying the universal relation R3 to the determined relaxation time λ1, polymer concentration C1 and the determined intrinsic viscosity [η] at this temperature T;
• or
• determining at least two relaxation times λ1 and λ2 of the aqueous polymer solution at temperature T and at at least two respective polymer concentrations C1 and C2, from respective measurements of dynamic viscosity of the aqueous polymer solution at the at least two polymer concentrations C1 and C2 and at temperature T, and applying the universal relation R3 to the at least two determined relaxation times λ1 and λ2, respective polymer concentrations C1 and C2 and the determined intrinsic viscosity [η] at temperature T so as to provide an average value of λd at temperature T;
• estimating the diluted regime-relaxation time λd of the aqueous polymer solution at temperature T′ as:
• λd(T)×(ηs(T′)×[η](T′)×T)/(ηs(T)×[η](T)×T′)
• where λd(T) is the diluted regime-relaxation time λd of the aqueous polymer solution at temperature T, ηs(T′) and ηs(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 R3 to the estimated diluted regime-relaxation time λd 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 R2 to polymer concentration C′ and the evaluated intrinsic viscosity [η] at temperature T′;
• estimating specific viscosity at zero shear rate ηsp′ of the aqueous polymer solution at polymer concentration C′ and at temperature T′ by applying the universal relation R1 to (i) the evaluated intrinsic viscosity [η] at temperature T′ and (ii) polymer concentration C′;
• estimating zero-shear viscosity η0′ of the aqueous polymer solution at polymer concentration C′ and at temperature T′=η0′=ηs·(ηsp′+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′=ηs+(η0′−ηs)·[1+(λ′·{dot over (γ)})2](n′−1)/2.

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 R3 between (i) product of polymer concentration and intrinsic viscosity C·[η] and (ii) ratio of relaxation time to diluted regime-relaxation time λ/λd;
• determining intrinsic viscosity [η] of the aqueous polymer solution at a temperature T by:
• providing a single universal relation R1 between (i), product of polymer concentration and intrinsic viscosity C·[η], and (ii) specific viscosity at zero shear rate ηsp;
• performing a measurement of dynamic viscosity of the aqueous polymer solution at one polymer concentration C1, at temperature T and at various shear rates;
• determining from said measurement zero-shear viscosity η0 of the aqueous polymer solution at polymer concentration C1 and at temperature T;
• calculating specific viscosity at zero shear rate of the aqueous polymer solution at polymer concentration C1 and at temperature T as ηsp=(η0−ηs)/ηs, where ηs 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 R1 to the calculated specific viscosity at zero shear rate ηsp and polymer concentration C1;
• estimating diluted regime-relaxation time λd of the aqueous polymer solution at temperature T by:
• determining relaxation time λ1 of the aqueous polymer solution at temperature T and polymer concentration C1, from the measurement of the dynamic viscosity of the aqueous polymer solution at polymer concentration C1 and at temperature T, and then applying the universal relation R3 to the determined relaxation time λ1, polymer concentration C1 and the determined intrinsic viscosity [η] at temperature T;
• or
• determining at least two relaxation times λ1 and λ2 of the aqueous polymer solution at temperature T and at at least two respective polymer concentrations C1 and C2, from respective measurements of dynamic viscosity of the aqueous polymer solution at the at least two polymer concentrations C1 and C2 and at temperature T, and applying the universal relation R3 to the at least two determined relaxation times λ1 and λ2, respective polymer concentrations C1 and C2 and the determined intrinsic viscosity [η] at temperature T so as to provide an average value of λd at temperature T;
• estimating the viscosimetric molecular weight of the polymer according to the equation M=(λd·T)/([η]·ηs)/1.474 where ηs is the zero-shear viscosity of the aqueous solvent at temperature T.