Measurement of properties of fluids using MRI

1. A method for determining rheological properties of a fluid, comprising the steps of:

a. providing an open-bore tube and defining within said bore a three dimensional grid (3DG) of voxels, with each voxel Vox i having a position (x i , y i , z i ) in said 3DG; defining at least two different cross sections, namely inlet cross section (ICS) and outlet cross section (OCS); and defining a volume of interest (VOI) within said bore between said ICS and said OCS;

b. obtaining a database of rheological properties of said fluid;

c. applying a pressure gradient to said bore between said ICS and said OCS, thereby flowing said fluid through said tube;

d. NMR imaging said fluid within said VOI, said image having a plurality p of slices, each slice comprising a plane within said 3DG;

e. from said image, for each of said voxels Vox i , determining a velocity for said fluid v i ;

f. for each of said voxels Vox i , from said velocity v i , calculating shear rate values (SRV); whilst, before or after determining a pressure gradient between said at least one ICS and said at least one OCS and thereby calculating shear stress values (SSV) for each voxel Vox i , from said SRV and said SSV determining at least one rheological property RP i for each voxel Vox i ;

g. comparing, for said at least one rheological property, RP i calculated for voxel Vox i to stored RP i for voxel Vox i from said database, thereby determining the difference in rheological property DRP i for voxel Vox i ; and

h. from the set of said DRP i , calculating 3D variations in said rheological property, therefrom determining the difference in rheological property DRP i as a function of position (x i ,y i ,z i ) in said grid;

wherein the resolution of said difference in rheological property DRP i is multiplied by about p compared to the per-slice resolution.

2. The method of claim 1 , comprising an additional step of selecting said rheological properties from a group consisting of fluid type, fluid density, fluid viscosity, fluid yield stress, and any combination thereof.

3. The method of claim 1 , comprising an additional step of selecting said fluid type from a group consisting of Newtonian fluid, pseudoplastic fluid, dilatant fluid, Bingham plastic fluid, and Herschel-Bulkley fluid.

4. The method of claim 1 , comprising an additional step of identifying inhomogeneous regions in said fluid.

5. The method of claim 4 , wherein said inhomogeneous regions in said fluid are selected from a group consisting of gas bubbles, liquid bubbles, regions of stratification, regions of settlement, regions of broken-down emulsion, and regions of incomplete mixing.

6. The method of claim 1 , comprising an additional step of identifying regions of turbulence by irregularities in the shape of the flow front.

7. The method of claim 1 , comprising an additional step of identifying regions of turbulence by the presence of eddies in the velocity field.

8. The method of claim 1 , further comprising a step of displaying said 3D velocity image on a display device.

9. A method for determining rheological properties of a fluid flowing through a tube, comprising the steps of:

a. providing an open-bore tube and defining within said bore a three dimensional grid (3DG) of voxels, with each voxel Vox i having a position (x i , y i , z i ) in said 3DG;

defining at least two different cross sections, namely inlet cross section (ICS) and outlet cross section (OCS); and defining a volume of interest (VOI) within said bore between said ICS and said OCS);

b. applying a pressure gradient to said bore between said ICS and said OCS, thereby flowing said fluid through said tube;

c. NMR imaging said fluid within said VOI, said NMR image having a plurality p of slices, each slice comprising a plane within said 3DG;

d. from said image, for each of said voxels Vox i ; determining a velocity for said fluid v i ;

e. for each of said voxels Vox i , from said velocity v i , calculating shear rate values (SRV); whilst, before or after determining a pressure gradient between said at least one ICS and said at least one OCS and thereby calculating shear stress values (SSV) for each voxel Vox i , from said SRV and said SSV determining at least one rheological property RP i for each voxel Vox i ;

f. creating at least two sets of voxels, set {Vox A } comprising at least one voxel Vox A,I and set {Vox B } comprising at least one voxel Vox B,i , locations of voxels in set {Vox A } differing from locations of voxels in set {Vox B } in a systematic way, each voxel Vox A,i , in set {Vox A } having a corresponding voxel Vox B,i , in set {Vox B };

g. comparing, for said at least one rheological property, for said at least two sets of voxels, rheological property RP A,i , for each voxel Vox A,i , in set {Vox A } to rheological parameter RP B,j for corresponding voxel Vox B,j in set {Vox B } thereby determining differences in rheological property DRP ij at relative position (x k , y k , z k ); and

h. from the set of said DRP ij , calculating 3D variations in said rheological property, therefrom determining the relative difference in rheological property DRP ij as a function of relative position (x k , y k , z k ) in said grid

wherein the resolution of said difference in rheological property DRP ij is multiplied by about p compared to the per-slice resolution.

10. The method of claim 9 , comprising an additional step of selecting said rheological properties from a group consisting of fluid type, fluid density, fluid viscosity, fluid yield stress, and any combination thereof.

11. The method of claim 9 , comprising an additional step of selecting said fluid type from a group consisting of Newtonian fluid, pseudoplastic fluid, dilatant fluid, Bingham plastic fluid, and Herschel-Bulkley fluid.

12. The method of claim 9 , comprising an additional step of identifying inhomogeneous regions in said fluid.

13. The method of claim 12 , wherein said inhomogeneous regions in said fluid are selected from a group consisting of gas bubbles, liquid bubbles, regions of stratification, regions of settlement, regions of broken-down emulsion, and regions of incomplete mixing.

14. The method of claim 9 , comprising an additional step of identifying regions of turbulence by irregularities in the shape of the flow front.

15. The method of claim 9 , comprising an additional step of identifying regions of turbulence by the presence of eddies in the velocity field.

16. The method of claim 9 , further comprising a step of displaying said 3D velocity image on a display device.