Systems and methods for determining a fluid characteristic

1. A method for determining a first fluid characteristic and a second fluid characteristic of a fluid within a flow region of a pipe viscometer, comprising:

pumping the fluid at a first flow rate of a plurality of flow rates;

measuring, across the flow region of the pipe viscometer, a first differential pressure of the fluid flowing at the first flow rate, wherein the flow region comprises an area inside a conduit, an annulus, or a combination thereof;

pumping the fluid at a second flow rate of the plurality of flow rates, wherein the second flow rate is different from the first flow rate;

measuring, across the flow region of the pipe viscometer, a second differential pressure of the fluid flowing at the second flow rate;

receiving, using a processing device, the first and second flow rates and the first and second differential pressure measurements;

storing, using the processing device, the first and second flow rates and the first and second differential pressure measurements;

determining, using the processing device, shear stress values and first shear rate values of the fluid at each of the first and second flow rates;

determining, using the processing device, the first fluid characteristic of the fluid using the shear stress values at each of the first and second flow rates, wherein the first fluid characteristic comprises a friction factor, a Reynolds number, or a combination thereof;

determining, using the processing device, flow behavior index values of the fluid at each of the first and second flow rates based on the shear stress and first shear rate values at each of the first and second flow rates;

determining, using the processing device, second shear rate values based on the flow behavior index values at each of the first and second flow rates, wherein the second shear rate values represent the shear rate at a wall of the flow region;

determining, using the processing device, the second fluid characteristic of the fluid using a rheological model that relates the shear stress and second shear rate values at each of the first and second flow rates; wherein the rheological model comprises the Yield Power Law Model; and wherein the second fluid characteristic comprises at least one of a consistency index, a yield stress, a fluid behavior index, or a combination thereof;

determining, using the processing device, Reynolds number values of the fluid at each of the first and second flow rates;

determining, using the processing device, friction factor values of the fluid at each of the first and second flow rates;

determining, using the processing device, parameters of a model relating the Reynolds number and friction factor values at each of the first and second flow rates;

determining, based on the model, one or more additional friction factor values of the fluid at downhole conditions of a well; and

providing the one or more additional friction factor values to a hydraulic model of the well.

2. The method of claim 1 , wherein measuring the first and second differential pressure measurements of the fluid flowing within the flow region comprises:

measuring, at each of the first and second flow rates, a first pressure of the fluid flowing within the flow region using a first pressure sensor at a first location within the flow region;

measuring, at each of the first and second flow rates, a second pressure of the fluid flowing within the flow region using a second pressure sensor at a second location within the flow region, the second location being different from the first location; and

calculating, using the processing device, the first and second differential pressure measurements of the fluid flowing within the flow region using the first and second pressure measurements measured by the first and second pressure sensors at each of the first and second flow rates.

3. The method of claim 1 , wherein the flow region comprises an area inside a conduit.

4. The method of claim 3 , wherein the conduit is situated at or above the Earth's surface.

5. The method of claim 3 , wherein the conduit is situated within a wellbore and the first and second flow rates and the first and second differential pressure measurements are obtained at downhole conditions of the wellbore.

6. The method of claim 3 , wherein the conduit comprises a wired drill pipe.

7. The method of claim 1 , wherein the flow region comprises an annulus.

8. The method of claim 7 , wherein the annulus is a region between a conduit and a wellbore.

9. The method of claim 8 , wherein the first and second flow rates and the first and second differential pressure measurements are obtained at downhole conditions of the wellbore.

10. The method of claim 8 , further comprising correcting, using the processing device, the first and second differential pressure measurements of the fluid for eccentricity between the conduit and the wellbore.

11. The method of claim 1 , further comprising determining a temperature of the fluid.

12. The method of claim 1 , wherein the fluid comprises a non-Newtonian fluid, a drilling fluid, or a combination thereof.

13. The method of claim 1 , further comprising:

generating a logarithmic plot of the shear stress and first shear rate values, wherein determining the flow behavior index values includes determining a slope of the logarithmic plot at each of the first and second flow rates.

14. A system for determining a first fluid characteristic and a second fluid characteristic of a fluid within a flow region, the system comprising:

a conduit;

a flow meter configured to measure, during different time intervals, first and second flow rates of a plurality of flow rates of the fluid flowing within the flow region, wherein the first and second flow rates are different from each other, and wherein the flow region comprises an area inside the conduit, an annulus, or a combination thereof;

a pressure sensor configured to measure, across the flow region, first and second differential pressures corresponding to the first and second flow rates of the fluid flowing within the flow region; and

a processing device configured to:

receive the first and second flow rates of the fluid from the flow meter;

receive the corresponding first and second differential pressure measurements of the fluid from the pressure sensor;

store the first and second flow rates and the corresponding first and second differential pressure measurements;

determine shear stress values and wall shear rate values of the fluid at each of the first and second flow rates;

determine the first fluid characteristic of the fluid using the shear stress values at each of the first and second flow rates, wherein the first fluid characteristic comprises a friction factor, a Reynolds number, or a combination thereof;

determine the second fluid characteristic of the fluid using a rheological model that relates the shear stress and wall shear rate values at each of the first and second flow rates; wherein the rheological model comprises the Yield Power Law Model; and wherein the second fluid characteristic comprises at least one of a consistency index, a yield stress, a fluid behavior index, or a combination thereof;

determine Reynolds number values of the fluid at each of the first and second flow rates;

determine friction factor values of the fluid at each of the first and second flow rates;

determine parameters of a model relating the Reynolds number and friction factor values at each of the first and second flow rates;

determine, based on the model, one or more additional friction factor values of the fluid at downhole conditions of a well; and

provide the one or more additional friction factor values to a hydraulic model of the well.

15. The method of claim 14 , wherein the processing device is further configured to:

determine nominal Newtonian shear rate values at each of the first and second flow rates using the first and second flow rates and the corresponding first and second differential pressure measurements; and

determine flow behavior index values of the fluid at each of the first and second flow rates based on the shear stress and nominal Newtonian shear rate values at each of the first and second flow rates; and

wherein determining the wall shear rate values includes using the flow behavior index values of the fluid at each of the first and second flow rates.

16. A method for determining rheological parameters of a fluid within a flow region, comprising:

pumping the fluid at a first flow rate of a plurality of flow rates;

measuring, across the flow region, a first differential pressure of the fluid at the first flow rate;

pumping the fluid at a second flow rate of the plurality of flow rates, wherein the second flow rate is different from the first flow rate;

measuring, across the flow region, a second differential pressure of the fluid at the second flow rate;

receiving, using a processing device, the first and second flow rates and the first and second differential pressure measurements;

determining, using the processing device, shear stress values and first shear rate values of the fluid at each of the first and second flow rates;

determining, using the processing device, flow behavior index values of the fluid at each of the first and second flow rates based on the shear stress and first shear rate values at each of the first and second flow rates;

determining, using the processing device, second shear rate values based on the flow behavior index values at each of the first and second flow rates, wherein the second shear rate values represent the shear rate at a wall of the flow region;

determining, using the processing device, a rheological parameter of the fluid using a rheological model that relates the shear stress and second shear rate values at each of the first and second flow rates;

determining, using the processing device, Reynolds number values of the fluid at each of the first and second flow rates;

determining, using the processing device, friction factor values of the fluid at each of the first and second flow rates;

determining, using the processing device, parameters of a model relating the Reynolds number and friction factor values at each of the first and second flow rates;

determining, based on the model, one or more additional friction factor values of the fluid at downhole conditions of a well; and

providing the one or more additional friction factor values to a hydraulic model of the well.

17. The method of claim 16 , further comprising

generating a logarithmic plot of the shear stress and wall shear rate values, wherein determining the flow behavior index values includes determining a slope of the logarithmic plot at each of the first and second flow rates.