Method for determining a derived property of a medium and nuclear magnetic measuring device, computer program product and computer-readable storage medium for such

Abstract

A method includes the steps of: introducing a medium with a first temperature into a measuring volume; carrying out nuclear magnetic measurements on the medium with the first temperature; determining a property of the medium at the first temperature; determining a viscosity of the medium at the first temperature using the property; and determining a derived property of the medium at a second temperature using the property of the medium at the first temperature, the viscosity of the medium at the first temperature, the first temperature, and the second temperature. The property is at least one of a first spin-lattice relaxation time constant, a first spin-spin relaxation time constant, and a first diffusion time constant. The derived property is at least one of a second spin-lattice relaxation time constant, a second spin-spin relaxation time constant, and a second diffusion time constant.

Claims

1. A method for the determination of at least one derived property of a medium, comprising: introducing a medium with a first temperature (ϑ.sub.1) into a measuring volume; carrying out nuclear magnetic measurements on the medium with the first temperature (ϑ.sub.1) in the measuring volume; determining at least one property of the medium at the first temperature (ϑ.sub.1) from the nuclear magnetic measurements, the at least one property being at least one of a first spin-lattice relaxation time constant (T.sub.1(ϑ.sub.1)), a first spin-spin relaxation time constant (T.sub.2(ϑ.sub.1)), and a first diffusion time constant (D(ϑ.sub.1)); determining a viscosity (η(ϑ.sub.1)) of the medium at the first temperature (ϑ.sub.1) from the at least one property; and determining at least one derived property of the medium at a second temperature (ϑ.sub.2) using the at least one property of the medium at the first temperature (ϑ.sub.1), the viscosity (η(ϑ.sub.1)) of the medium at the first temperature, the first temperature (ϑ.sub.1), and the second temperature (ϑ.sub.2), the at least one derived property being at least one of a second spin-lattice relaxation time constant (T.sub.1(ϑ.sub.2)), a second spin-spin relaxation time constant (T.sub.2(ϑ.sub.2)), and a second diffusion time constant (D(ϑ.sub.2)).

2. The method according to claim 1, wherein the first spin-lattice relaxation time constant (T.sub.1(ϑ.sub.1)) of the medium (5) at the first temperature (ϑ.sub.1) is determined as the at least one property: wherein the method further comprises: determining a logarithmic average or a weighted average of the first spin-lattice relaxation time constant (T.sub.1,LM(ϑ.sub.1)); and determining the viscosity (η(ϑ.sub.1)) of the medium at the first temperature (ϑ.sub.1) from the logarithmic average or the weighted average of the first spin-lattice relaxation time constant using the first formula
T.sub.1,LM(ϑ.sub.1)≈k.sub.1(η(ϑ.sub.1)).sup.−k.sup.2+k.sub.3(η(ϑ.sub.1)).sup.k.sup.1; wherein 0.37831≤k.sub.1≤3.3887, 0.45419≤k.sub.2≤1.2055, 00.88616.Math.10.sup.−3≤k.sub.3≤26.547.Math.10.sup.−3, and −0.023116≤k.sub.4≤0.34519.

3. The method according to claim 1, wherein the first spin-spin relaxation time constant (T.sub.2(ϑ.sub.1)) of the medium at the first temperature (ϑ.sub.1) is determined as the at least one property; wherein the method further comprises: determining a logarithmic average or a weighted average of the first spin-spin relaxation time constant (T.sub.2,LM(ϑ.sub.1)); and determining the viscosity (η(ϑ.sub.1)) of the medium at the first temperature (ϑ.sub.1) from the logarithmic average or the weighted average of the first spin-spin relaxation time constant using the second formula
T.sub.2,LM(ϑ.sub.1)≈k.sub.5(η(ϑ.sub.1)).sup.−k.sup.6; wherein 0.37831≤k.sub.5≤3.3887 and 0.45419≤k.sub.6≤1.2055.

4. The method according to claim 1, wherein the first diffusion time constant (D(ϑ1)) of the medium at the first temperature (ϑ1) is determined as the first property; wherein the method further comprises determining the viscosity (η(ϑ1)) of the medium at the first temperature (ϑ1) from the diffusion time constant using the third formula
D(ϑ.sub.1)=k.sub.7η(ϑ.sub.1).sup.k.sup.8; wherein 0.2445.Math.10.sup.−9≤k.sub.7≤2.2005.Math.10.sup.−9 and 0.375≤k.sub.8≤0.650 when the first diffusion time constant (D(ϑ.sub.1)) of the medium at the first temperature (ϑ.sub.1) is less than or equal to 3.Math.10.sup.−11 m.sup.2/s; and wherein 0.05777.Math.10.sup.−9≤k.sub.7≤0.5199.Math.10.sup.−9 and 0.125≤k.sub.8≤0.375 when the first diffusion time constant (D(ϑ.sub.1)) of the medium at the first temperature (ϑ.sub.1) is greater than 3.Math.10.sup.−11 m.sup.2/s.

5. The method according to claim 1 further comprising determining at least one relaxation time constant (T.sub.i(ϑ.sub.2), i={1,2}) of the medium at the second temperature (ϑ.sub.2) from at least one of the second spin-lattice relaxation time constant (T.sub.1(ϑ.sub.2)) and the second spin-spin relaxation time constant (T.sub.2(ϑ.sub.2)) using a temperature coefficient (dT.sub.i/dϑ) of a relaxation time constant (T.sub.i) from at least one of the second spin-lattice relaxation time constant (T.sub.1(ϑ.sub.2)) and the second spin-spin relaxation time constant (T.sub.2(ϑ.sub.2)).

6. The method according to claim 5, further comprising determining the at least one relaxation time constant (T.sub.i(ϑ.sub.2), i={1,2}) of the medium at the second temperature (ϑ.sub.2) using the fourth formula
T.sub.i(ϑ.sub.2)=T.sub.i(ϑ.sub.1)e.sup.γϑ.sup.2, or using the Taylor polynomial of the fourth formula according to the fifth formula
T.sub.i(ϑ.sub.2)=T.sub.i(ϑ.sub.1)[1+γ(ϑ.sub.2−ϑ.sub.1)+ . . . ], or using the approximation formula of the fourth formula, according to the sixth formula $T_i\left({\vartheta }_2\right)\approx T_i\left({\vartheta }_1\right)+\frac{d{T}_i}{d\vartheta }\left({\vartheta }_2-{\vartheta }_1\right),$ which uses the seventh formula $\gamma =\frac{1}{T_i\left({\vartheta }_1\right)}\frac{{\mathrm{dT}}_i}{d\vartheta }$

7. The method according to claim 5, further comprising determining the temperature coefficient (dT.sub.i/dϑ) using the eighth formula $\frac{{\mathrm{dT}}_i}{d\vartheta }\approx k_9{e}^{-k_{10}\eta };$ wherein 0.013036≤k.sub.9≤0.11732 and 1.2604.Math.10.sup.−3≤k.sub.10≤5.0416.Math.10.sup.−3.

8. The method according to claim 7, further comprising using the viscosity (η(ϑ1)) of the medium at the first temperature (ϑ1).

9. The method according to claim 5, further comprising determining the second spin-lattice relaxation time constant (T.sub.1(ϑ.sub.2)) at the second temperature (ϑ.sub.2) of the medium: determining a logarithmic average or a weighted average of the second spin-lattice relaxation time constant (T.sub.1,LM(ϑ.sub.2)); and determining the viscosity (η(ϑ.sub.2)) of the medium at the second temperature (ϑ.sub.2) from the logarithmic average or the weighted average of the second spin-lattice relaxation time constant (T.sub.1,LM(ϑ.sub.2)) using the first formula.

10. The method according to claim 9, further comprising determining the second diffusion time constant (D(ϑ.sub.2)) of the medium at the second temperature (ϑ.sub.2) from the viscosity (η(ϑ.sub.2)) of the medium at the second temperature (ϑ.sub.2) using the third formula.

11. The method according to claim 5, further comprising: determining the second spin-spin relaxation time constant (T.sub.2(ϑ.sub.2)) at the second temperature (ϑ.sub.2) of the medium: determining a logarithmic average or a weighted average of the second spin-spin relaxation time constant (T.sub.2,LM(ϑ.sub.2)); and determining the viscosity (η(ϑ.sub.2)) of the medium at the second temperature (ϑ.sub.2) from the logarithmic average or the weighted average of the second spin-spin relaxation time constant (T.sub.2,LM(ϑ.sub.2)) using the second formula.

12. The method according to claim 5, further comprising: flowing the medium with the second temperature (ϑ.sub.2) through the measuring volume; carrying out nuclear magnetic measurements on the medium with the second temperature (ϑ.sub.2) in the measuring volume; and determining a flow of the medium with the second temperature (ϑ.sub.2) using the nuclear magnetic measurements, the second spin-lattice relaxation time constant (T.sub.1(ϑ.sub.2)) and/or the second spin-spin relaxation time constant (T.sub.2(ϑ.sub.2)) of the medium (5) at the second temperature (ϑ.sub.2).

13. The method according to claim 12, further comprising converting the flow of the medium with the second temperature (ϑ.sub.2) to a flow of the medium at the first temperature (ϑ.sub.1) or a further temperature (ϑ.sub.3).

14. The method according to claim 13, further comprising using the density (ρ) and/or the viscosity (η) of the medium for the conversion.

15. The method according to claim 1, further comprising determining a density (ρ) of the medium from the viscosity (η) of the medium.

16. The method according to claim 15, wherein the density (ρ) is determined from the viscosity using the formula $\rho \approx k_{11}-\frac{k_{12}}{{\eta }^{k_{13}}};$ wherein 941.82≤k.sub.11≤1025.8, 180.65≤k.sub.12≤264.61, and 0.15921≤k.sub.13≤0.37899.

17. A non-transitory computer program product including instructions which, when the program is executed by a computer, cause the computer to execute the method according to claim 1.

18. A nuclear magnetic flowmeter, comprising: a measuring tube having a measuring volume; a measuring device designed to carry out nuclear magnetic measurements; and a computer designed to carry out a method including the following steps: carrying out nuclear magnetic measurements on a medium with the first temperature (ϑ1) in the measuring volume; determining at least one property of the medium at the first temperature (ϑ1) from the nuclear magnetic measurements, the at least one property being at least one of a first spin-lattice relaxation time constant (T1(ϑ1)) a first spin-spin relaxation time constant (T2(ϑ1)), and a first diffusion time constant (D(ϑ1)); determining a viscosity (η(ϑ1)) of the medium at the first temperature (ϑ1) from the at least one property; and determining at least one derived property of the medium at a second temperature (ϑ2) using the at least one property of the medium at the first temperature (ϑ1), the viscosity (η(ϑ1)) of the medium at the first temperature, the first temperature (ϑ1) and the second temperature (ϑ2), the at least one derived property being at least one of a second spin-lattice relaxation time constant (T1(ϑ2)), a second spin-spin relaxation time constant (T2(ϑ2)), and a second diffusion time constant (D(ϑ2)).

19. A non-transitory computer-readable storage medium including instructions which, when the program is executed by a computer, cause the computer to execute a method including the following steps: carrying out nuclear magnetic measurements on a medium with a first temperature (ϑ1) in a measuring volume of a measuring tube; determining at least one property of the medium at the first temperature (ϑ1) from the nuclear magnetic measurements, the at least one property being at least one of a first spin-lattice relaxation time constant (T1(ϑ1)), a first spin-spin relaxation time constant (T2(ϑ1)), and a first diffusion time constant (D(ϑ1)); determining a viscosity (η(ϑ1)) of the medium at the first temperature (ϑ1) from the at least one property; and determining at least one derived property of the medium at a second temperature (ϑ2) using the at least one property of the medium at the first temperature (ϑ1), the viscosity (η(ϑ1)) of the medium at the first temperature, the first temperature (ϑ1), and the second temperature (ϑ2), the at least one derived property being at least one of a second spin-lattice relaxation time constant (T1(ϑ2)), a second spin-spin relaxation time constant (T2(ϑ2)), and a second diffusion time constant (D(ϑ2)).

Description

DESCRIPTION OF THE DRAWINGS

(1) In detail, there is a plurality of possibilities for designing and further developing the method, the nuclear magnetic flowmeter, the computer program product and the computer-readable storage medium. For this, reference is made to the following description of preferred embodiments in connection with the drawings.

(2) FIG. 1 illustrates a first embodiment of a nuclear magnetic flowmeter.

(3) FIG. 2 illustrates a flow chart of an embodiment of a method for the determination of a derived property of a medium.

DETAILED DESCRIPTION

(4) FIG. 1 shows an embodiment of a nuclear magnetic flowmeter 1, comprising a measuring tube 2 with a measuring volume, a measuring device 3 and a computer 4. The measuring device 3 is designed to carry out nuclear magnetic measurements. During operation of the nuclear magnetic flowmeter 1, a medium 5 flows through the measuring tube 2 and the computer 4 carries out the method described below, wherein the computer 4 also controls the measuring device 3 and the measuring device carries out nuclear magnetic measurements on the medium 5 in the measuring volume. The method is stored as a program on a storage medium readable by the computer 4 and is read into the computer 4 by the computer 4 when operation is started and comprises commands which cause the computer 4 to execute the method.

(5) Referring to FIG. 2, in a first method step 6, the medium 5 has a first temperature ϑ.sub.1 and is introduced into the measuring volume by flowing through the measuring tube 2.

(6) In a second method step 7, nuclear magnetic measurements are carried out on the medium 5 in the measuring volume. The medium 5 has the first temperature ϑ1 during the measurements.

(7) In a third method step 8, a spin-lattice relaxation time constant T.sub.1(ϑ.sub.1) is determined from the nuclear magnetic measurements as a property of the medium at the first temperature ϑ.sub.1.

(8) In a fourth step 9, a viscosity η(ϑ.sub.1) of the medium 5 at the first temperature ϑ.sub.1 is determined from the spin-lattice relaxation time constant T.sub.1(ϑ.sub.1).

(9) The viscosity η(ϑ.sub.1) is determined by first determining a logarithmic average of the spin-lattice relaxation time constant T.sub.1,LM(ϑ.sub.1). Then the viscosity η(ϑ.sub.1) is determined from the logarithmic average of the spin-lattice relaxation time constant T.sub.1,LM(ϑ.sub.1) using the first formula
T.sub.1,LM(ϑ.sub.1)≈k.sub.1(η(ϑ.sub.1)).sup.−k.sup.2+k.sub.3(η(ϑ.sub.1)).sup.k.sup.4.

(10) Here, k.sub.1=1.1348, k.sub.2=0.80942, k.sub.3=2.6592.Math.10.sup.−3 and k.sub.4=0.24243.

(11) In a fifth method step 10, the spin-lattice relaxation time constant T.sub.1(ϑ.sub.2) of the medium 5 at a second temperature ϑ.sub.2 is determined as a derived property using the spin-lattice relaxation time constant T.sub.1(ϑ.sub.1) of the medium at the first temperature ϑ.sub.1, the viscosity η(ϑ.sub.1) of the medium at the first temperature ϑ.sub.1, the first temperature ϑ.sub.1 and the second temperature ϑ.sub.2.

(12) The determination of the spin-lattice relaxation time constant T.sub.1(ϑ.sub.2) at the second temperature ϑ.sub.2 is carried out using the approximate formula

(13) $T_i\left({\vartheta }_2\right)\approx T_i\left({\vartheta }_1\right)+\frac{d{T}_i}{d\vartheta }\left({\vartheta }_2-{\vartheta }_1\right)$

(14) In the approximation formula a temperature coefficient dT.sub.1/dϑ of the spin-lattice relaxation time constant T.sub.1 is used. The temperature coefficient is determined using the formula

(15) $\frac{{\mathrm{dT}}_i}{d\vartheta }\approx k_9{e}^{-k_{10}\eta }.$

(16) In this, k.sub.9=0.039107 and k.sub.10=2.5208.Math.10.sup.−3. The viscosity η is used as viscosity η(ϑ.sub.1) at the first temperature ϑ.sub.1.

(17) Although only nuclear magnetic measurements on the medium 5 with the first temperature ϑ.sub.1 were carried out in the previously described method steps, the spin-lattice relaxation time constant T.sub.1(ϑ.sub.2) could be determined at the second temperature ϑ.sub.2. A time-consuming carrying out of nuclear magnetic measurements, from which the spin-lattice relaxation time constant T.sub.1(ϑ.sub.2) of the medium 5 is determined again at the second temperature ϑ2 of the medium 5 as at the first temperature of the medium, is no longer necessary, resulting in a shorter time requirement. Instead, the spin-lattice relaxation time constant T.sub.1(ϑ.sub.2) at the second temperature of medium 5 is derived from that at the first temperature ϑ.sub.1.

(18) In a supplement to the method, the following method steps are also carried out:

(19) In a sixth method step 11, the medium 5 has a second temperature ϑ.sub.2 and is introduced into the measuring volume by flowing through the measuring tube 2.

(20) In a seventh method step 12, nuclear magnetic measurements are performed on the medium 5 in the measuring volume. The medium 5 has the second temperature ϑ.sub.2 during the measurements.

(21) In an eighth method step 13, a flow rate of the medium 5 with the second temperature ϑ.sub.2 is determined through the measuring tube 2 using the nuclear magnetic measurements performed in the previous method step and the previously determined spin-lattice relaxation time constant T.sub.1(ϑ.sub.2) of the medium 5 at the second temperature ϑ.sub.2.

(22) Although the medium 5 now has the second temperature ϑ.sub.2 different from the first temperature ϑ.sub.1 and the value of the spin-lattice relaxation time constant T.sub.1 has changed due to the temperature change Δϑ=ϑ.sub.2−ϑ.sub.1, the determination of the flow rate of the medium 5 through the measuring tube 2 is possible because the spin-lattice relaxation time constant T.sub.1(ϑ.sub.2) at the second temperature ϑ.sub.2 of the medium 5 has been derived from spin-lattice relaxation time constant T.sub.1(ϑ.sub.1) of the medium 5 at the first temperature ϑ.sub.1. A time-consuming carrying out of nuclear magnetic measurements, from which the spin-lattice relaxation time constant T.sub.1(ϑ.sub.2) of the medium 5 is again determined at the second temperature ϑ.sub.2 of medium 5 as at the first temperature ϑ.sub.1 of the medium 5, is no longer necessary, resulting in a reduced time requirement.