Patent Grant
11841302
This application is the U.S. National Stage of International Application No. PCT/IB2019/000194, filed Feb. 19, 2019, which designates the U.S. and was published in English. The entire teachings of the above application are incorporated herein by reference.
The present invention relates to a method for determining the intrinsic viscosity of a polymer solution comprising at least one acrylamide-based polymer.
Hydrocarbons (such as crude oil) are extracted from a subterranean formation (or reservoir) by means of one or more production wells drilled in the reservoir. Before production begins, the formation, which is a porous medium, is saturated with hydrocarbons.
The initial recovery of hydrocarbons is generally carried out by techniques of “primary recovery”, in which only the natural forces present in the reservoir are relied upon. In this primary recovery, only part of the hydrocarbons is ejected from the pores by the pressure of the formation. Typically, once the natural forces are exhausted and primary recovery is completed, there is still a large volume of hydrocarbons left in the reservoir.
This phenomenon has led to the development of enhanced oil recovery (EOR) techniques. Many of such EOR techniques rely on the injection of a fluid into the reservoir in order to produce an additional quantity of hydrocarbons.
The fluid used can in particular be an aqueous solution (“waterflooding process”), such as brine, which is injected via one or more injection wells in order to maintain reservoir pressure and push the oil from the pores.
Large amounts of water can also be recovered from the production wells. This is called “produced water”. The produced water can be e.g. discharged to the environment (after treatment) or reinjected into the subterranean formation via the injection wells.
A polymer (for example an acrylamide-based polymer) can also be added to the water to increase its viscosity and increase its sweep efficiency in recovering hydrocarbons (“polymer flooding process”). In this case, the produced water contains part of the polymer, which can thus be recovered.
However, depending on the conditions inside the subterranean formation (temperature, salinity, permeability), the nature of the polymer (monomer composition, molecular weight) must be adapted, in order to be able to achieve a proper viscosification of the water used for the polymer flooding and ensure good propagation in the porous medium. The viscosity of a polymer depends on a number of factors such as the type of polymer, the composition of the polymer, the concentration of the polymer, the molecular weight of the polymer (which decreases when the polymer is degraded upon use), the distribution of its molecular weight, the salinity of the subterranean formation, the temperature of the subterranean formation, the shear rate at which the viscosity is measured.
Furthermore, an estimation of the viscosity of a polymer under the conditions of the subterranean formation is often necessary in order to characterize the polymer, to perform quality controls on the polymers or the polymer solutions used in the subterranean formations, or to provide data for studies, design of equipment or simulation procedures for estimating the incremental oil recovered. Nevertheless, until now the estimation of the viscosity of a polymer has been a difficult, expensive and long procedure which requires a series of steps, measurements and experiments which are complex, time consuming and sometimes inaccurate.
The article of Bouldin M. et al. (Prediction of the non-Newtonian viscosity and shear stability of polymer solutions), 1988 (doi.org/10.1007/BF01417863) relates to the prediction of the zero-shear viscosity and the shear rate dependent viscosity by using structure-property relationships.
The article of Szopinski D. et al. (Structure-property relationships of carboxymethyl hydroxypropyl guar gum in water and a hyperentanglement parameter), 2015, (doi.org/10.1016/j.carbpol.2014.11.050) describes the determination of the viscoelastic properties of carboxymethyl hydroxypropyl guar gum in aqueous solution as a function of concentration and molecular weight, using SEC/MALLS/dRI and viscometry.
The article of Kulicke W.-M. et al. (Description and forecast of rheological characteristics of semi-dilute polymer solutions as a function of the molecular weight, concentration and solvent quality), 1991 (Polymer News, volume 16, pages 39-48) describes the rheological properties which enable the prediction of the flow behavior of semi-dilute polymer solutions from a molecular point of view. By using scaling laws, it is possible to predict elastic and viscous characteristics with respect to molecular parameters.
The article of Grigorescu G. et. al. (Prediction of viscoelastic properties and shear stability of polymers in solution), 2000 (doi.org/10.1007/3-540-46778-5_1) describes the possibilities of predicting the viscoelastic properties and the shear stability using the entanglement and reputation concepts and exemplifying mainly with narrow distributed polystyrene samples.
The article of Kulicke W.-M. et al. (The shear viscosity dependence on the concentration, molecular weight, and shear rate of polystyrene solutions), 1984 (doi.org/10.1007/BF01333878) relates to the solution viscosity of narrow molecular weight distribution polystyrene samples dissolved in toluene and trans-decalin. In this article, the effect of polymer concentration, molecular weight and shear rate on viscosity was determined.
There is thus a need for a method for determining the viscosity of an aqueous polymer solution, notably a polymer solution comprising an acrylamide-based polymer, in a variety of conditions, in an easy, rapid and cost-effective manner. There is also a need for a method for determining the molecular weight of an acrylamide-based polymer without performing any complex and lengthy measurements.
It is a first object of the invention to provide a method for determining the 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 the steps of:
In some variations, one or more measurements of the dynamic viscosity of the aqueous polymer solution at various shear rates are performed only at the single polymer concentration C1.
In some variations, the method comprises:
In some variations, the single universal relation R1 is obtained by:
In some variations, the single universal relation R1 is defined as ηsp=C·[η]+0.56 (C·[η])2.17+0.0026 (C·[η])4.72 or as any other function where ηsp 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%, preferably by less than 10%, more preferably by less than 5%.
The invention also relates to a method for determining the 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:
In some variations, the single universal relation R2 is obtained by:
In some variations, the single universal relation R2 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%, preferably by less than 10%, more preferably by less than 5%.
In some variations, the single universal relation R3 is obtained by:
In some variations, the single universal relation R3 is defined as λ/λd=1+0.04 (C·[η])2.4 or as any other function where λ/λd deviates from 1+0.04 (C·[η])2.4 at any value of C·[η] by less than 20%, preferably by less than 10%, more preferably by less than 5%.
In some variations, the one or more measurements of the dynamic viscosity of the aqueous polymer solution is/are 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; and preferably C·[η] is within the range of 2 to 5 and C′·[η] is out of the range of 2 to 5.
The invention also relates to a method for determining the 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:
In some variations, the single universal relation R2 is obtained by:
In some variations, the single universal relation R2 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%, preferably by less than 10%, more preferably by less than 5%.
In some variations, the single universal relation R3 is obtained by:
In some variations, the single universal relation R3 is defined as λ/λd=1+0.04(C·[η])2.4 or as any other function where λ/λd deviates from 1+0.04(C·[η])2.4 at any value of C·[η] by less than 20%, preferably by less than 10%, more preferably by less than 5%.
The invention also relates to a method for determining the viscosimetric molecular weight of an acrylamide-based polymer, the method comprising:
In some variations, the single universal relation R3 is obtained by:
In some variations, the single universal relation R3 is defined as λ/λd=1+0.04(C·[η])2.4 or as any other function where λ/λd deviates from 1+0.04(C·[η])2.4 at any value of C·[η] by less than 20%, preferably by less than 10%, more preferably by less than 5%.
In some variations of any of the above methods, the polymer comprises units derived from one or more monomers selected from acrylamide, sodium acrylate, N-vinyl pyrrolidone and 2-acrylamide-2-methylpropane sulfonate, and wherein the polymer is preferably selected from the homopolymer of 2-acrylamide-2-methylpropane sulfonate, copolymers of acrylamide and sodium acrylate, copolymers of acrylamide and 2-acrylamide-2-methylpropane sulfonate, copolymers of acrylamide and N-vinyl pyrrolidone, terpolymers of acrylamide, sodium acrylate and N-vinyl pyrrolidones and terpolymers of acrylamide, sodium acrylate and 2-acrylamide-2-methylpropane sulfonate.
The present invention makes it possible to address the need expressed above. In particular, the invention provides a method for determining the viscosity of an aqueous polymer solution, notably a polymer solution comprising an acrylamide-based polymer, in a variety of conditions, in an easy, rapid and cost-effective manner. The invention also provides a method for determining the molecular weight of an acrylamide-based polymer without performing any complex and lengthy measurements.
The invention relies on the surprising finding by the inventors that acrylamide-based polymers in aqueous solutions having a salinity between 6 and 250 g/L behave according to a number of universal relations, which are valid for any polymer in this family, in a large variety of conditions. This makes it possible to predict a number of useful properties of a polymer solution based on a very limited set of measurements on the polymer.
In particular, a single universal relation R1 between the product of polymer concentration and intrinsic viscosity, and the specific viscosity at zero shear rate of these polymer solutions has been found. By using this relation, the intrinsic viscosity of the polymer may be determined for a wide range of concentrations and temperatures, without carrying out complex measurements for each concentration of polymer. The determination of this intrinsic viscosity makes it possible in turn, using further universal relations, to determine other parameters such as the dynamic viscosity of a polymer solution in any set of conditions, or even the molecular weight of the polymer.
. The dynamic viscosity can be read on the Y-axis and the shear rate can be read on the X-axis.
The invention will now be described in more detail without limitation in the following description.
Polymer Solution
The polymer solution referred to in the present application comprises at least one acrylamide-based polymer in an aqueous solvent.
The acrylamide-based polymer may comprise units derived from one or more monomers selected from acrylamide, sodium acrylate, N-vinyl pyrrolidone and 2-acrylamide-2-methylpropane sulfonate. Preferably the polymer is selected from the homopolymer of 2-acrylamide-2-methylpropane sulfonate, copolymers of acrylamide and sodium acrylate, copolymers of acrylamide and 2-acrylamide-2-methylpropane sulfonate, copolymers of acrylamide and N-vinyl pyrrolidone, terpolymers of acrylamide, sodium acrylate and N-vinyl pyrrolidone and terpolymers of acrylamide, sodium acrylate and 2-acrylamide-2-methylpropane sulfonate.
According to some embodiments, only one acrylamide-based polymer is present in the polymer solution.
According to other embodiments, more than one acrylamide-based polymers, for example two, or three, or four, or more than four acrylamide-based polymers are present in the polymer solution.
The polyamide polymer(s) may be present in the polymer solution at a concentration from 20 to 20000 ppm by weight and preferably from 50 to 17000 ppm by weight. For example, the polyamide polymer(s) may be present in the polymer solution at a concentration from 20 to 50 ppm; or from 50 to 100 ppm; or from 100 to 200 ppm; or from 200 to 500 ppm; or from 500 to 1000 ppm; or from 1000 to 1500 ppm; or from 1500 to 2000 ppm; or from 2000 to 2500 ppm; or from 2500 to 3000 ppm; or from 3000 to 3500 ppm; or from 3500 to 4000 ppm; or from 4000 to 4500 ppm; or from 4500 to 5000 ppm; or from 5000 to 5500 ppm; or from 5500 to 6000 ppm; or from 6000 to 6500 ppm; or from 6500 to 7000 ppm; or from 7000 to 7500 ppm; or from 7500 to 8000 ppm; or from 8000 to 8500 ppm; or from 8500 to 9000 ppm; or from 9000 to 9500 ppm; or from 9500 to 10000 ppm by weight.
The aqueous solvent in which the acrylamide-based polymer is dissolved may be or may derive from produced water, fresh water, sea water or aquifer water.
The aqueous solvent has a salinity from 6 to 250 g/L. For example, the aqueous solvent may have a salinity from 6 to 10 g/L; or from 10 to 20 g/L; or from 20 to 30 g/L; or from 30 to 40 g/L; or from 40 to 50 g/L; or from 50 to 60 g/L; or from 60 to 70 g/L; or from 70 to 80 g/L; or from 80 to 90 g/L; or from 90 to 100 g/L; or from 100 to 120 g/L; or from 120 to 140 g/L; or from 140 to 160 g/L; or from 160 to 180 g/L; or from 180 to 200 g/L; or from 200 to 220 g/L; or from 220 to 240 g/L; or from 240 to 250 g/L. Salinity is defined herein as the total concentration of dissolved inorganic salts in water, including e.g. NaCl, CaCl2, MgCl2 and any other inorganic salts.
The polymer solution may further comprise additives such as surfactants, salts, sacrificial agents, pH adjustment agents, solvents and/or marking agents.
The polymer solution according to the invention may be used in a hydrocarbon recovery process, and more preferably in an enhanced oil recovery process. The polymer solution may therefore be injected into a subterranean formation via one or more injection wells.
The temperature within the subterranean formation may range from 25 to 140° C., preferably from 40 to 140° C. and more preferably from 50 to 120° C.
The injection of the polymer solution may be performed at a pressure from 30 to 1000 bar, preferably from 50 to 350 bar.
The permeability of at least a portion of the subterranean formation may range from 2 to 20000 md, preferably from 10 to 20000 md and more preferably from 100 to 10000 md, as estimated by well log.
Method for Determining the Intrinsic Viscosity of a Polymer Solution
The invention first relates to a method for determining the intrinsic viscosity [η] of the polymer solution described above, at a given temperature T.
Unless specified otherwise, by “viscosity” η of a polymer solution is meant herein the dynamic viscosity of a polymer solution. The viscosity of the polymer solution depends on the applied shear rate, and physicochemical conditions such as the nature of the polymer, molecular weight of the polymer, concentration of the polymer, nature of the aqueous medium present in the solution (notably salinity), temperature, etc. It can be expressed for example in Pa·s.
A viscosity measurement at a given shear rate can be performed for example by using a rotational viscometer with a cone and plate, parallel plates or cup and bob (coaxial cylinders) geometry. This measurement consists in measuring the torque required to rotate, at a given angular velocity, an object immersed in the fluid or in contact with the fluid. Through the calculation of a form factor which depends on the specific dimensions of the used geometry, torque is converted to shear stress and angular velocity to converted in shear rate.
The viscosity is the ratio between the shear stress and the shear rate. A value of viscosity is thus obtained from the torque measurement at each angular velocity. Some viscometers work in deformation, meaning that a shear rate is applied and the corresponding torque is measured, while other viscometers impose the shear stress (torque) and the shear rate is measured. The graph “Viscosity” vs. “Shear rate” is called a flow curve.
The typical aspect of such a flow curve for a given polymer solution is shown in
At low shear rate, the curve has a first plateau meaning that viscosity does not depends on shear rate; the fluid is said to have a “Newtonian behavior”. The value of the viscosity at this plateau is called “zero-shear rate viscosity” η0.
Starting at a given shear rate which depends on all the physicochemical conditions previously listed, the viscosity η starts to decrease with shear rate and follows a power law of the form η=K
(x−1) where K is the flow consistency index and x is the flow behavior index. Both K and x depend on all the physicochemical conditions previously listed.
At a high shear rate, the curve reaches a second plateau. In this area, the viscosity η of the polymer solution approaches the viscosity of the aqueous solution devoid of polymer, ηs.
Practically, a flow curve is measured by applying a given shear rate to the solution and waiting until a constant viscosity value is measured by the viscometer. Once this value is obtained, the shear rate is changed and a new equilibrium value is measured.
Overall, viscosity as a function of shear rate approximately follows the following Carreau equation: η=ηs+(η0−ηs)·[1+(λ·)2](n−1)/2, wherein
is the shear rate (for example expressed in s−1), λ is the relaxation time (for example expressed in s) and n is the Carreau coefficient which is close to the flow behavior index x of the power law equation. Parameters λ and n depend on a number of factors related to physicochemical conditions (temperature, polymer concentration, nature and molecular weight of the polymer, salinity of the aqueous medium etc.). λ roughly corresponds to the inverse of the shear rate at which viscosity starts to decrease with the shear rate.
The “specific viscosity at zero shear rate” ηsp is defined as ηsp=(η0−ηs)/ηs wherein η0 is the zero-shear rate viscosity and ηs is the viscosity of the aqueous solution devoid of polymer (in the same conditions and particularly at the same temperature). It is a dimensionless parameter.
The “intrinsic viscosity” of the polymer is defined as the limit of the specific viscosity at zero shear rate divided by the mass concentration of the polymer in the solution, when said mass concentration approaches zero. It can be expressed for instance in L/g. It represents in fact the effective volume under which 1 gram of polymer in solution counters the flow of liquid. The intrinsic viscosity of the polymer is characteristic of a given polymer combined with a given aqueous solution since it depends on polymer/polymer and polymer/solvent interactions. It slightly varies according to the temperature.
The present method of determining the intrinsic viscosity [η] of the polymer solution at temperature T comprises a step of providing a single universal relation R1 between (i), the product of polymer concentration C and intrinsic viscosity [η], namely C·[η], and (ii) specific viscosity at zero shear rate ηsp.
The single universal relation R1 may be obtained by:
The acrylamide-based polymers which are provided preferably have different molecular weight distributions.
Preferably, at least some of the acrylamide-based polymers which are provided have been degraded from a higher molecular weight to a lower molecular weight, using mechanical devices such as mixers, rotor stators or valves.
In the above, the specific viscosity at zero shear rate ηsp of each polymer solution, at each temperature, is derived from the measurements of the low shear viscosity η0 through the formula ηsp=(η0−ηs)/ηs.
In the above, the intrinsic viscosity of each polymer solution, at each temperature, is obtained by plotting specific viscosity ηsp divided by concentration C and extrapolating at zero concentration. The ordinate of such extrapolation is the intrinsic viscosity of the polymer/solvent system. Such method is based on the Huggins equation ηsp=C·[η]+kH·[η]2·C2 where C is the polymer concentration and kH the Huggins constant which depends on the polymer/solvent system.
Preferably, in the above steps, several different polymers (including preferably polymers with different degrees of degradation) are used as well as several different aqueous media (having different salinities) and several temperatures, so as to ensure that the set of data better represents the diversity of possible polymer solutions.
The single universal relation R1 may thus be defined as a mathematical fit for the data of
R1: ηsp=C·[η]+0.56(C·[η])2.17+0.0026(C·[η])4.72
Of course, it is also possible to define R1 as a slightly different fit based on the same data.
Therefore, R1 may also be defined as any other function where ηsp 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%, preferably by less than 10%, more preferably by less than 5%, most preferably by less than 2% or even by less than 1%.
If R1 is determined based on a different set of data from the data of
The method for determining the intrinsic viscosity [η] of a given polymer solution comprises a step of performing a measurement of the dynamic viscosity of the polymer solution at (at least) one polymer concentration C1, at temperature T and at various shear rates, so as to deduce the zero-shear viscosity η0 of the polymer solution at polymer concentration C1 and at temperature T (as described above) and then the specific viscosity at zero shear rate ηsp.
According to some embodiments, a single measurement of the dynamic viscosity of the polymer solution at various shear rates is performed, so that a single specific viscosity at zero shear rate ηsp at polymer concentration C1 and at temperature T is determined.
The intrinsic viscosity [η] of the polymer solution at temperature T is then directly determined by applying universal relation R1 to this single specific viscosity at zero shear rate ηsp.
According to other embodiments, more than one measurements of the dynamic viscosity of the polymer solution at various shear rates are performed at at least two polymer concentrations C1, C2 (etc.) at temperature T.
In this case, the specific viscosity at zero shear rate ηsp of the polymer solution is determined at the plurality of polymer concentration C1, C2 (etc.) and at temperature T. Then, the intrinsic viscosity [η] is adjusted so as to obtain the best fit of specific viscosities at C1, C2 with the universal relation R1, for instance using the method of least squares.
Using a single flow curve “viscosity vs. shear rate” measurement at a single polymer concentration makes the determination of the intrinsic viscosity easier and quicker.
Using several viscosity vs. shear measurements at various polymer concentrations may make the determination of the intrinsic viscosity more accurate and reliable.
Accuracy can be increased by performing different individual measurements in the same conditions (i.e. at the same polymer concentration C1).
Method for Determining the Dynamic Viscosity of a Polymer Solution at a Polymer Concentration C′ and at a Temperature T, Based on Measurements Performed at Temperature T but at (One or more) Polymer Concentrations other than C′
Based on the intrinsic viscosity of the polymer solution at temperature T, determined as described above, the dynamic viscosity of the polymer solution at this temperature T and at any shear rate and at any concentration can in turn be determined.
As a result, based on a single or a few viscosity vs. shear rate measurements, either at a single polymer concentration C1 or at at least two polymer concentrations C1, C2 (etc.), the viscosity of the polymer solution as a function of shear rate may be directly calculated at any given polymer concentration C′, and still at temperature T.
This method thus comprises a step of providing a single universal relation R2 between (i) the product of polymer concentration and intrinsic viscosity C·[η] and (ii) the Carreau coefficient n. The single universal relation R2 may be obtained by:
The acrylamide-based polymers which are provided preferably have different molecular weight distributions.
Preferably, at least some of the acrylamide-based polymers which are provided have been degraded from a higher molecular weight to a lower molecular weight, using mechanical devices such as mixers, rotor stators or valves.
In the above, the intrinsic viscosity of each polymer solution, at each temperature, is derived from the measurements by extrapolating the specific viscosity at zero shear rate divided by polymer concentration vs. polymer concentration at zero polymer concentration. Alternatively, it can be determined by applying universal relation R1 to the specific viscosity at zero shear rate and polymer concentration data.
In the above, the Carreau coefficient n of each polymer solution, at each polymer concentration and temperature, is derived from the measurements by fitting the viscosity vs. shear rate data to the Carreau equation η=ηs+(η0−ηs)·[1+(λ·)2](n−1)/2. η0 corresponds to viscosity at zero shear rate, ηs is the solvent viscosity (which depends on temperature and salinity), and λ and n are two adjustable parameters obtained by the method of least squares. Preferably, in the above steps, several different polymers are used as well as several different aqueous media (having different salinities) and different temperatures so as to ensure that the set of data better represents the diversity of possible polymer solutions.
The set of data used for generating universal relation R2 may optionally be obtained from the same measurements as those from which the set of data used for generating universal relation R1 are obtained. Alternatively, different measurements may be used for generating universal relation R1 and universal relation R2.
The single universal relation R2 may thus be defined as a mathematical fit for the data of
R2: n=1−(0.796−0.687×exp(−0.059×C·[η])
Of course, it is also possible to defined R2 as a slightly different fit based on the same data.
Therefore, the single universal relation R2 may also be defined 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%, preferably by less than 10%, more preferably by less than 5%, most preferably by less than 2% or even by less than 1%.
If R2 is determined based on a different set of data from the data of
The method for determining the dynamic viscosity of the polymer solution as a function of shear rate at temperature T and at a polymer concentration C′ also comprises a step of providing a single universal relation R3 between (i) the product of polymer concentration and intrinsic viscosity C·[η] and (ii) the ratio of relaxation time to diluted regime-relaxation time λ/λd. The single universal relation R3 may obtained by:
The acrylamide-based polymers which are provided preferably have different molecular weight distributions.
Preferably, at least some of the acrylamide-based polymers which are provided have been degraded from a higher molecular weight to a lower molecular weight, using mechanical devices such as mixers, rotor stators or valves.
In the above, the intrinsic viscosity of each polymer solution, at each temperature, is derived from the measurements by extrapolating the specific viscosity at zero shear rate divided by polymer concentration vs. polymer concentration at zero polymer concentration (polymer concentration approaching zero). Alternatively, it can be determined by applying universal relation R1 to the specific viscosity at zero shear rate and polymer concentration data.
In the above, the relaxation time λ of each polymer solution, at each polymer concentration and temperature, is derived from the measurements by fitting the viscosity vs. shear rate data to the Carreau equation η=ηs+(η0−ηs)·[1+(λ·)2](n−1)/2 where η0 corresponds to viscosity at zero shear rate, ηs is the solvent viscosity (which depends on temperature and salinity), and λ and n are two adjustable parameters obtained by the method of least squares.
For values close to the diluted regime (C[η]<1), the relaxation time λ becomes independent from polymer concentration. We call this relaxation time in the diluted regime λd.
In the above, the diluted regime-relaxation time λd of each polymer solution, at each temperature, is derived from the measurements by plotting the relaxation time λ as a function of polymer concentration, and by extrapolating the relaxation time at low polymer concentration (polymer concentration approaching zero).
Preferably, in the above steps, several different polymers are used as well as several different aqueous media (having different salinities) and different temperatures so as to ensure that the set of data better represents the diversity of possible polymer solutions.
The set of data used for generating universal relation R3 may optionally be obtained from the same measurements as those from which the set of data used for generating universal relation R1 are obtained. Alternatively, different measurements may be used for generating universal relation R3 and universal relation R1.
The set of data used for generating universal relation R3 may optionally be obtained from the same measurements as those from which the set of data used for generating universal relation R2 are obtained. Alternatively, different measurements may be used for generating universal relation R3 and universal relation R2.
It can be readily seen that, for each polymer solution at a certain temperature, the relaxation time plateaus at low C·[η], which makes it possible to determine by extrapolation the diluted regime-relaxation time λd.
The single universal relation R3 may thus be defined as a fit for the data of
R3: λ/λd=1+0.04(C·[η])2.4
Of course, it is also possible to defined R3 as a slightly different fit based on the same data.
Therefore, R3 may also be defined as any other function where λ/λd deviates from 1+0.04(C·[η])2.4 at any value of C·[η] by less than 20%, preferably by less than 10%, more preferably by less than 5%, most preferably by less than 2% or even by less than 1%.
If R3 is determined based on a different set of data from the data of
The method for determining the dynamic viscosity of the polymer solution as a function of shear rate at temperature T and at a polymer concentration C′ comprises a step of determining the intrinsic viscosity [η] of this polymer solution at temperature T according to the method for determining the intrinsic viscosity described above. In this case, the one or more measurements of the dynamic viscosity of the aqueous polymer solution used for determining the intrinsic viscosity is/are performed at one or more polymer concentrations other than C′ in the range 1<C·[η]<10.
According to
Preferentially, the one or more measurements is/are performed in the range 2<C·[η]<5, corresponding to 5.6<ηs<30, as viscometers are usually more accurate and reliable for determining the whole flow curve in this viscosity range.
Thus, the viscosity at lower or higher concentrations may be determined based one or more measurements in the preferred concentration ranges.
For a given concentration C and at temperature T, the intrinsic viscosity is first determined by applying universal relation R1 to the specific viscosity obtained from the viscosity at zero shear rate. Knowing the product C·[η], the shear thinning index n is determined by applying universal relation R2, and the ratio λ/λd is determined by applying universal relation R3. λd is obtained by adjusting the parameter λ so as to fit e.g. by the least squares method the flow curve determined experimentally. This determination can be performed at a single concentration or at several concentrations C1, C2, . . . for which all the flow curves will be fitted with one adjustable parameter λd.
Advantageously, the same measurements are used for determining the intrinsic viscosity [η] of the polymer solution at temperature T and the diluted regime-relaxation time λd of the polymer solution at stake, at temperature T.
If a single measurement, at polymer concentration C1 and temperature T, is used, then:
If at least two measurements, at polymer concentrations C1, C2, etc. and temperature T, are used, the same steps are performed except that the diluted regime-relaxation time λd is determined as an average based on the simultaneous fit of all the flow curves by one single λd value. The best fit is e.g. obtained through the method of least squares.
Using a single viscosity vs. shear measurement at a single polymer concentration makes the entire method easier and quicker.
Using several viscosity vs. shear measurements at various polymer concentrations may render the method more accurate or reliable.
Averaging may also be performed in a similar manner based on different individual measurements in the same conditions (i.e. at the same polymer concentration C).
Method for Determining the Dynamic Viscosity of a Polymer Solution at a Polymer Concentration C′ and at a Temperature T′, Based on Measurements Performed at Different Temperature T and at (One or more) Polymer Concentrations
The method described above for determining the intrinsic viscosity of a polymer solution at a given temperature can be repeated several times at different temperatures, so as to determine the dependence of the intrinsic viscosity of the polymer solution as a function of temperature.
An example is illustrated in
Based on such a graph, it is then possible to evaluate (without performing any further measurement) the intrinsic viscosity of a polymer solution at any given temperature, and in particular at a temperature T′ at which no measurement data is available, for example by fitting the data with a power law or exponential law.
It then becomes possible to determine the dynamic viscosity at zero shear rate of the polymer solution at this temperature T′ and at any concentration—based on measurements performed at a different temperature T.
More specifically, the intrinsic viscosity [η] of the polymer solution at temperature T′ is evaluated based on a mathematical fit applied to data corresponding to determined intrinsic viscosity [η] of the polymer solution at a plurality of temperatures T other than T′ (as illustratively shown in
The method described above for determining the diluted-regime relaxation time of a polymer solution at a given temperature can be repeated several times at different temperatures, so as to determine the dependence of the diluted-regime relaxation time of the polymer solution as a function of temperature.
An example is illustrated in
R4 may be defined as a mathematical fit for the data of
R4: λd=1.474×ηs×[η]×M/T
Of course, it is also possible to define R4 as a slightly different fit based on the same data.
Therefore, R4 may also be defined as any other function where λd deviates from 1.474×ηs×M/T at any value of ηs, [η], M and T by less than 20%, preferably by less than 10%, more preferably by less than 5%, most preferably by less than 2% or even by less than 1%.
If R4 is determined based on a different set of data from the data of
From the knowledge of λd at temperature T, λd at temperature T′ can be predicted from R4 as follows, using relation R5:
R5: λd(T′)=λd(T)×(ηs(T′)×[η](T′)×T)/(ηs(T)×[η](T)×T′)
Where [η](T′) is the intrinsic viscosity at temperature T′ and ηs(T′) is the solvent viscosity at T′.
If a single measurement, at polymer concentration C1 and temperature T, is used, then:
If at least two measurements, at polymer concentrations C1, C2, etc. and temperature T, are used, the same steps are performed except that the diluted regime-relaxation time λd is determined as an average based on at least two estimates. This is similar to what has already been described above.
Method for Determining the Molecular Weight
By determining the intrinsic viscosity of the polymer solution, as described above, the determination of the (unknown) viscosimetric molecular weight of the polymer becomes possible. By molecular weight is herein meant the average viscosimetric molecular weight which lies between the number-average molecular weight Mn and the weight-average molecular weight Mw.
Indeed, the molecular weight of the polymer can be estimated by using universal relation R4: M=(λd·T)/([η]·ηs)/1.474, where [η] and ηs are considered at temperature T.
The intrinsic viscosity of the polymer solution at temperature T and the diluted-regime relaxation time λd of the polymer solution at temperature T may be determined as already described in detail above, based on a single or a few viscosity vs. shear rate measurements, either at a single polymer concentration C1 or at at least two polymer concentrations C1, C2, etc.
This makes it possible to determine the molecular weight M of the polymer based on said single or few viscosity vs. shear rate measurements, without knowing the polymer type/composition (provided it is an acrylamide based polymer) and the brine composition.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/IB2019/000194 | 2/19/2019 | WO |
| Publishing Document | Publishing Date | Country | Kind |
|---|---|---|---|
| WO2020/169999 | 8/27/2020 | WO | A |
| Number | Name | Date | Kind |
|---|---|---|---|
| 4814096 | Evani | Mar 1989 | A |
| Number | Date | Country |
|---|---|---|
| 2020169999 | Aug 2020 | WO |
| Entry |
|---|
| International Search Report and Written Opinion for International Application No. PCT/IB2019/000194, entitled “Method for Determining the Viscosity of a Polymer Solution,” consisting of 8 pages, dated Oct. 29, 2019. |
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| Kulicke W., et al. “Description and Forecast of Rheological Characteristics of Semi-Dilute Polymer Solutions as a Function of the Molecular Weight, Concentration and Solvent Quality,” Polymer News, vol. 16, pp. 39-48, Gordon and Breach Science Publishers S.A. (1991). |
| Grigorescu G., et al., “Prediction of Viscoelastic Properties and Shear Stability of Polymers in Solution,” Advances in Polymer Science, vol. 152, Spring-Verlag Berlin Heideberg (doi.org/10.1007/3-540-46778-5_ 1) (2000). |
| Kulicke W., et al., “The shear viscosity dependence on concentration, molecular weight, and shear rate of polystyrene solutions,” Rheol Acta vol. 23, No. 1, pp. 75-83 (doi.org/10.1007/BF01333878) (1984). |
| Tam, K. C., et al. “Comments on the Accuracy of Zero Shear Intrinsic Viscosity of High Molecular Weight Polyacrylamide”, Polymer International 24 (1991) 15-22. |
| Number | Date | Country | |
|---|---|---|---|
| 20220155201 A1 | May 2022 | US |
