WO2015191091A1

WO2015191091A1 - Method and apparatus for measuring drilling fluid properties

Info

Publication number: WO2015191091A1
Application number: PCT/US2014/042639
Authority: WO
Inventors: Thomas Robert Larson; Lyndon Ray Stone
Original assignee: National Oilwell Varco, L.P.
Priority date: 2014-06-13
Filing date: 2014-06-17
Publication date: 2015-12-17

Abstract

A system (200) for measuring drilling fluid properties is disclosed that includes a capillary rheometer (234) and a pump (204) that is adapted to pump a fluid through the capillary rheometer (234) at a plurality of different flow rates. The capillary rheometer (234) includes a plurality of capillary tubes that are arranged for series flow of the fluid therethrough, each of the plurality of tubes having a different inside radius.

Description

METHOD AND APPARATUS FOR MEASURING DRILLING FLUID

PROPERTIES BACKGROUND

1. FIELD OF THE DISCLOSURE

The present disclosure is generally directed to drilling fluids that are used during drilling operations for oil and gas wells, and in particular, to methods and apparatuses for analyzing the properties of such drilling fluids. 2. DESCRIPTION OF THE RELATED ART

Drilling fluid, or“mud,” is a multicomponent fluid specially formulated to perform various functions during drilling of an oil or gas well. Examples of such functions include cooling the drill bit, lubricating and sealing the wall of the well, providing hydrostatic pressure in the well annulus to prevent formation fluid influx, clearing away drilled solids from the drill bit, and returning drilled solids to the surface. Circulation of the drilling fluid through the well typically involves pumping the drilling fluid down the bore of a drill string in the well, whereby the drilling fluid jets through nozzles in a drill bit at the end of the drill string into the bottom of the well. At the bottom of the well, the drilling fluid commingles with drilled solids and possibly other materials in the well such as gases and returns to the surface with the entrained materials. The return path is typically in an annulus between the wall of the well and the drill string. In dual bore drilling, the return path may be in the drill string. At the surface, a series of actions is taken to rid the drilling fluid of the entrained materials so that the drilling fluid can be pumped into the well again. Drilling fluid is generally an aqueous or non-aqueous suspension of one or more materials. The suspension medium may be water or brine, oil, or synthetic fluid combined with various chemical additives. The added materials can be minerals, such as barite or bentonite, or synthetic polymers in particulate form. At various stages of removing the entrained materials, it is important to analyze the properties of the drilling fluid in order to ascertain that the drilling fluid has the proper composition and rheology to achieve desired functions. The drilling fluid properties measured are typically specific weight, viscosity, and solids content. Currently, drilling fluid properties are measured using at least four devices, such as a mud balance, a Marsh funnel, a rotating cylinder viscometer, and a mud retort. The measurements are customarily made manually in that a technician collects a sample of drilling fluid, places the sample in the device, reads some type of physical indicator by eye, and records the measurement. These manual measurements are prone to errors that may prove costly in a drilling process. A mud balance is used to measure the specific weight of a drilling fluid. To measure the specific weight of a drilling fluid, a cup is overfilled with a sample of the drilling fluid while placing a lid over the sample in such a way that there are no bubbles in the volume of drilling fluid remaining in the cup. The cup is then placed at one end of a graduated beam having a bubble level. A slider weight is moved along the length of the beam until the bubble level indicates that the beam is level. The position of the slider weight along the length of the beam indicates the density of the drilling fluid. The accuracy of the specific weight measurement depends on how accurately the technician can read the bubble level and the position of the slider weight. Most mud balance beams are graduated in increments of 0.1 pounds/gallon. A Marsh funnel is used to measure drilling fluid viscosity. To measure drilling fluid viscosity, the funnel is held vertically while plugging the bottom of the funnel. The drilling fluid is then poured into the funnel through a filter, e.g., a 10 Mesh screen. The filter will prevent solids that can clog the funnel from entering the funnel. When a desired amount of the drilling fluid has been poured into the funnel, the bottom of the funnel is unplugged to allow the drilling fluid to flow into a graduated container. The technician uses a stopwatch to record the time needed for a predetermined volume of the drilling fluid to be released from the funnel into the container. The accuracy of the viscosity measurement depends on the ability of the technician to accurately read the volume of drilling fluid released into the container and to accurately start and stop the stopwatch. In the Marsh funnel method, filtering of the drilling fluid actually changes the drilling fluid so that the viscosity measured is more an apparent viscosity than a true viscosity. Also, particles in the drilling fluid may segregate inside the funnel while the bottom of the funnel is plugged, which may lead to variations in flow rate out of the funnel that would not be accounted for by merely measuring time and the amount of fluid released into the container. The range of application of the device is limited to those fluids that continue to flow freely as the level inside the funnel drops to very low values. Other fluids not having this property may result in clogging of the funnel by surface tension forces. A rotating cylinder viscometer is also used to measure drilling fluid viscosity. A typical rotating cylinder viscometer includes two concentric cylinders. The inner cylinder is often referred to as bob and is suspended on a torque measuring device. To measure drilling fluid viscosity, drilling fluid is poured into a chamber through a filter, e.g., a 200 Mesh screen. The filter will prevent solids that can lodge in between the concentric cylinders from entering the chamber. The cylinders are then submerged in the drilling fluid in the chamber, and the outer cylinder is rotated at various rotational speeds while the bob is held stationary. The force necessary to shear the fluid between the cylinders is read from the torque measuring device that holds the bob stationary. Viscosity is estimated using an expression that is a function of the shear torque, the geometry of the cylinders, the angular velocity of the outer cylinder, and the immersion depth of the inner cylinder or bob in the drilling fluid. The rotating cylinder viscometer provides additional value over the Marsh funnel in that multiple rotational speeds correspond to multiple strain rates, which allows non-Newtonian behavior to be recorded for the drilling fluid. The accuracy of the viscosity measurements made by the rotating cylinder viscometer depends on the accuracy of the rotational speed of the outer cylinder, on the accuracy of the reading of the indicator of the torque measuring device, and on the depth of immersion of the cylinders. In older versions of the device, a hand crank is used to rotate the outer cylinder. The normal procedure calls for turning the hand crank very evenly through a gearbox that allows for several specific speeds, if the handle is turning at a constant rotational speed. However, this constant rotational speed has to be achieved by hand, which can be very difficult. A more modern version of the device uses a motor to drive the outer cylinder at precisely correct rotational speeds, which results in better precision. The viscosity measurements made by the rotating cylinder viscometer are affected by filtering of the drilling fluid received in the chamber, i.e., the actual drilling fluid measured is different from the original drilling fluid that contained the solids removed by the filtering. There is also the possibility of particles settling within the chamber while the viscosity measurements are being made. Particle settling can introduce errors to the measured shear torque. A mud retort is used to measure the percent by volume of the solids and liquids, such as water and/or oil, in the drilling fluid. To make measurements with the mud retort, a known volume of fluid is heated in a retort chamber, typically to a temperature of over 900°F. Steam and vaporized oil exit the chamber and immediately pass through a condenser that returns the vapors to liquids and delivers the liquids to a graduated cylinder. The volumes of the liquids read from the cylinder are subtracted from the known volume to determine a percent volume of the solids in the drilling fluid. The weight of the solids can be determined, e.g., on a digital scale. The volume and weight of the solids are used to determine the specific weight of the solids. The present disclosure is directed to various methods and apparatuses for measuring the properties of drilling fluids that may address, at least in part, some of the above-described problems associated with prior art devices and methods that are used to evaluate drilling fluid properties. SUMMARY OF THE DISCLOSURE

The following presents a simplified summary of the present disclosure in order to provide a basic understanding of some aspects disclosed herein. This summary is not an exhaustive overview of the disclosure, nor is it intended to identify key or critical elements of the subject matter disclosed here. Its sole purpose is to present some concepts in a simplified form as a prelude to the more detailed description that is discussed later. The present disclosure is generally directed to various methods and apparatuses for analyzing the properties of fluids, and in particular drilling fluids that may be used during oil and gas well drilling operations. In one illustrative embodiment, a system for measuring drilling fluid properties is disclosed that includes, among other things, a capillary rheometer and a pump that is adapted to pump a fluid through the capillary rheometer at a plurality of different flow rates. Furthermore, the capillary rheometer includes a plurality of capillary tubes that are arranged for series flow of the fluid therethrough, each of the plurality of tubes having a different inside radius. In another illustrative embodiment, a capillary rheometer for determining the rheology of a fluid is disclosed. The capillary rheometer includes, among other things, a first capillary tube having a first inside radius and a second capillary tube having a second inside radius that is different than said first inside radius, wherein the second capillary tube is arranged in series flow with the first capillary tube such that a fluid flowing through the capillary rheometer sequentially exits an outlet end of the first capillary tube and enters an inlet end of the second capillary tube. Furthermore, the illustrative capillary rheometer also includes a first pressure sensor that is positioned between the first and second capillary tubes, wherein the first pressure sensor is adapted to measure a pressure of the fluid flowing through the capillary rheometer. A further exemplary embodiment of the present disclosure is a method of determining the rheology of a fluid. The disclosed method includes, among other things, operatively coupling a pump to a capillary rheometer that includes a plurality of capillary tubes, wherein the plurality of capillary tubes are arranged for series flow and each of the plurality of capillary tubes has a different inside radius. Furthermore, the illustrative method also includes controlling the operation of the pump so as to pump a fluid through the capillary rheometer at a series of pre-determined flow rates and determining a pressure differential of the fluid flowing through the capillary rheometer across each of the plurality of capillary tubes for each of the series of pre-determined flow rates. Additionally, the disclosed method includes determining the rheology of the fluid for each of the pre-determined flow rates and each of the determined pressure differentials across each of the plurality of capillary tubes. BRIEF DESCRIPTION OF THE DRAWINGS The disclosure may be understood by reference to the following description taken in conjunction with the accompanying drawings, in which like reference numerals identify like elements, and in which: FIGS. 1A-1C schematically depict various exemplary configurations of a system for measuring drilling fluid properties in accordance with some illustrative embodiments of the present disclosure, wherein each of the disclosed systems includes a plurality of capillary tubes that are arranged in series; FIG. 2 schematically depicts one embodiment of an exemplary control system that may be used in conjunction with any one of the illustrative systems depicted in FIGS. 1A-1C; FIG. 3 is a graphical illustration of an exemplary drilling fluid rheology curve generated in accordance with the present disclosure; and FIG. 4 schematically illustrates yet another exemplary drilling fluid measurement system that includes a single capillary tube. While the subject matter disclosed herein is susceptible to various modifications and alternative forms, specific embodiments thereof have been shown by way of example in the drawings and are herein described in detail. It should be understood, however, that the description herein of specific embodiments is not intended to limit the invention to the particular forms disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention. DETAILED DESCRIPTION

Various illustrative embodiments of the present subject matter are described below. In the interest of clarity, not all features of an actual implementation are described in this specification. It will of course be appreciated that in the development of any such actual embodiment, numerous implementation-specific decisions must be made to achieve the developers’ specific goals, such as compliance with system-related and business-related constraints, which will vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming, but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of this disclosure. The present subject matter will now be described with reference to the attached figures. Various systems, structures and devices are schematically depicted in the drawings for purposes of explanation only and so as to not obscure the present disclosure with details that are well known to those skilled in the art. Nevertheless, the attached drawings are included to describe and explain illustrative examples of the present disclosure. The words and phrases used herein should be understood and interpreted to have a meaning consistent with the understanding of those words and phrases by those skilled in the relevant art. No special definition of a term or phrase, i.e., a definition that is different from the ordinary and customary meaning as understood by those skilled in the art, is intended to be implied by consistent usage of the term or phrase herein. To the extent that a term or phrase is intended to have a special meaning, i.e., a meaning other than that understood by skilled artisans, such a special definition will be expressly set forth in the specification in a definitional manner that directly and unequivocally provides the special definition for the term or phrase. In the following detailed description, various details may be set forth in order to provide a thorough understanding of the various exemplary embodiments disclosed herein. However, it will be clear to one skilled in the art that some illustrative embodiments of the invention may be practiced without some or all of these such various disclosed details. Furthermore, features and/or processes that are well-known in the art may not be described in full detail so as not to unnecessarily obscure the disclosed subject matter. In addition, like or identical reference numerals may be used to identify common or similar elements. FIG. 1A schematically illustrates one embodiment of an exemplary system 200 that may be used for measuring the properties of a drilling fluid. The system 200 may include a pump unit 204 that is used to pump an inlet flow 201 of drilling fluid through the various components of the system 200, as will be further described in detail below. As shown in FIG. 1A, a suction line 206 may be coupled to the pump unit 204 for delivering the inlet flow 201 thereto. Additionally, a discharge line 208 may also be coupled to the pump unit 204 for directing the flow 201 of drilling fluid to the remainder of the system 200. The pump unit 204 may be any suitable type of pump known in the art that is capable of generating a desired range of volumetric flow rates to the system 200. For example, the pump unit 204 may be adapted to generate volumetric flow rates that range from between approximately 5.7 and 37.8 liters per minute (1.5 to 10.0 gallons per minute), although such flow rates are exemplary only and not intended to limit the design of the system 200 or the scope of the present disclosure. In at least some embodiments, the pump unit 204 may be, for example, a positive-displacement pump, such as a progressive cavity pump, a peristaltic (or diaphragm) pump, a piston pump, and the like, although it should be appreciated that other known types of pumps may also be used provided the selected pump is suitable for generating the requisite range of volumetric flow rates. As shown in FIG. 1A, the pump unit 204 may be coupled to (and driven by) a drive motor 210. In certain embodiments, the drive motor 210 may in turn be operatively coupled to, and adapted to receive control signals from, an external control system 260. Furthermore, the drive motor 210 may be, for example, a variable speed drive motor and the like, which may be controlled by the external control system 260 to operate over an appropriate range of rotational speeds so as to enable to the pump unit 204 to provide volumetric flow rates to the system 200 within a specified range, as will be further described in conjunction with FIG. 2 below. As noted previously, the discharge line 208 may provide fluid communication between the pump unit 204 and the remainder of the system 200. Furthermore, in some embodiments a fluid analyzer system 262 that is adapted to perform various different fluid analyses on the fluid as it flows through the system 200 may be coupled to the discharge line 208, as is shown in FIG. 1A. For example, in certain embodiments, the fluid analyzer system 262 may be adapted to perform temperature measurement, pH measurement, and the like. As depicted in FIG. 1A, the discharge line 208 may be coupled to a capillary rheometer 234. In some illustrative embodiments of the system 200, the capillary rheometer 234 may include a plurality of capillary tubes arranged in series, such as the three capillary tubes 245, 246, and 247. However, it should be understood by one of ordinary skill after a full and complete reading of the present disclosure that the quantity of three capillary tubes, e.g., tubes 245, 246, and 247, shown in FIG. 1A is exemplary only. In some embodiments the capillary rheometer 234 may include only two capillary tubes, whereas in other embodiments the capillary rheometer 234 may include four or more capillary tubes, as may be required for the specific types of fluid and measurements required of the system 200. Accordingly, while the following description of the system 200 and the capillary rheometer 234 is directed to the three- capillary tube arrangement depicted in FIG. 1A, such description should not be construed as limiting in any way to the scope of the present disclosure. In some illustrative embodiments, the capillary rheometer 234 may be oriented and arranged such that the flow 201 of fluid through the capillary rheometer 234 is nominally in a vertically upward direction. That is, the fluid flow 201 enters the lowermost (bottom, or inlet) end 234b of the capillary rheometer 234 and flows vertically upward to the uppermost (top, or outlet) end 234t of the capillary rheometer 234, which is positioned at a height 234h above the bottom end 234b. In this way, the capillary rheometer 234 may be substantially completely filled with fluid during the operation of the system 200. As previously noted, the capillary tubes 245, 246, and 247 are arranged in a series configuration such that the fluid flowing through the capillary rheometer 234 initially enters the bottom, or lowermost, capillary tube 245, flows next into an intermediate capillary tube 246, and then the top, or uppermost, capillary tube 247. Accordingly, the capillary tube 245 is positioned at the bottom, or inlet, end 234b of the capillary rheometer 234 and the capillary tube 247 is positioned at the top, or outlet, end 234t. Additionally, the capillary tube 245 has an inside radius 245r and a tube length 245L, the capillary tube 246 has an inside radius 246r and a tube length 246L, and the capillary tube 247 has an inside radius 247r and a tube length 247L. In certain illustrative embodiments, the inside radius 245r/246r/247r of each respective capillary tube 245/246/247 may be different from that of the other respective capillary tubes. Furthermore, the length 245L/246L/247L of each respective capillary tube 245/246/247 may also be different from that of the other respective capillary tubes. For example, the inside radius 245r may be less than the inside radius 246r, and the inside radius 246r may be less than the inside radius 247r. Similarly, the tube length 245L may be less than the tube length 246L, and the tube length 246L may be less than the tube length 247L. For example, in at least one exemplary embodiment, the inside radius 245r may be in the range of approximately 6 to 10 mm (1/4” to 3/8”), the radius 246r may be approximately 15 to 21 mm (9/16” to 13/16”), and the radius 247r may be approximately 27 to 33 mm (1-1/16” to 1-5/16”), although it should be appreciated that other capillary tube radii may also be used. Moreover, each of the respective tube lengths 245L/246L/247L may be adjusted as required based upon the specific inside radius and the anticipated flow rate of fluid through the system 200. In this way, data may be obtained on the flow of fluid through each of the capillary tubes 245, 246, and 247, which can then be used to determine a fluid rheology curve for the fluid based upon a variety of corresponding fluid strain rates and fluid shear stresses, as will be further described in conjunction with FIGS. 2 and 3 below. It should be understood that even though the capillary rheometer 234 shown in FIG. 1A depicts a configuration wherein each successive capillary tube has both a greater inside radius and greater tube length than the immediately preceding capillary tube– e.g., wherein the capillary tube 246 is longer and has a greater inside radius than the capillary tube 245, etc.– it is within the scope of the present disclosure to arrange the capillary tubes 245/246/247 in any configuration of relative tube lengths and/or inside radii. For example, the bottom, or lowermost, capillary tube 245 may have a greater inside radius 245r and/or tube length 245L than the intermediate and/or top capillary tubes 246 and 247. In similar fashion, the capillary tube 246 may have a greater tube length 246L and/or inside radius 246r than either or both of the capillary tubes 245 and 247. In some illustrative embodiments, the capillary rheometer 234 may include a plurality of pressure sensors 224a-d coupled thereto that may be adapted to measure the pressure of the fluid as it flows through the system 200. For example, as shown in FIG. 1A, a pressure sensor 224a may be positioned at the bottom end 234b of the capillary rheometer 234 (and the capillary tube 245), a pressure sensor 224b may be positioned between the capillary tube 245 and the capillary tube 246, a pressure sensor 224c may be positioned between the capillary tube 246 and the capillary tube 247, and a pressure sensor 224d may be positioned at the top end of the capillary rheometer 234 (and of the capillary tube 247). Additionally, the pressure sensor 224b may be positioned at a height 245h above the pressure sensor 224a, the pressure sensor 224c may be positioned at a height 246h above the pressure sensor 224b, and the pressure sensor 224d may be positioned at a height 247h above the pressure sensor 224c. Furthermore, in at least some embodiments, each of the pressure sensors 224a-d may be adapted to provide pressure data on the fluid flowing through capillary rheometer 234 to the control system 260 (see, FIG. 2), which may then be used to determine the properties of the fluid, as will be described in further detail below. As shown in FIG. 1A, the discharge line 208 may be coupled to the bottom end 234b of the capillary rheometer 234, for example, at the bottom, or lowermost, pressure sensor 224a. Additionally, a fluid line 207 may also be coupled to the upper end 234t of the capillary rheometer 234, e.g., at the top, or uppermost, pressure sensor 224d, and may be used to discharge a flow 203 of fluid from the system 200. Furthermore, in some illustrative embodiments, a flow discharge device 225 that is adapted to maintain the capillary rheometer 234 substantially completely full of fluid may be positioned in the fluid line 207. As shown in FIG. 1A, the flow discharge device 225 may include, for example, an overflow weir or deflector plate 225d, which may be arranged and positioned so that the entirety of the capillary rheometer 234 may be maintained substantially full of fluid even when the flow 201 of fluid to the system 200 may be temporarily interrupted. In other illustrative embodiments, a choke valve 226 may be positioned in the fluid line 207. Depending on the pressure-sensing range and/or sensitivity of the pressure sensors 224a-d, the choke valve 226 may be operated in such a manner as to create a back-pressure on the system 200, and in particular on the capillary rheometer 234, thereby increasing the measured pressure at each of the sensors 224a-d during operation of the system 200. Furthermore, in certain exemplary embodiments, both a flow discharge device 225 and a choke valve 226 may both be positioned in the fluid line 207, as is illustrated in FIG. 1A. The flow 203 of fluid through the fluid line 207 is then discharged out of the system 200 at substantially atmospheric, or zero gauge, pressure conditions. The system 200 of FIG. 1A may be used, among other things, to determine the rheology of the flow 201 of fluid flowing through the system 200. This may be accomplished based on the different pressure readings obtained from the various pressure sensors 224a-d of the capillary rheometer 234, as will be described in further detail below. As may be appreciated by a person of ordinary skill after a complete reading of the present disclosure, the differential pressure between any two of the pressure sensors 224a-d may be attributed to two primary factors: 1) the static pressure differential due to hydrostatic head of fluid in each of the capillary tubes 245/246/247; and 2) the dynamic pressure differential due to the shear (drag) force between the fluid and the inside surface of the capillary tubes 245/246/247 as the fluid moves through the tubes. For some configurations of the system 200, and depending on the type of fluid and the sizes the various capillary tubes 245/246/247, the static pressure differential between adjacent pressure sensors may be substantially greater than the dynamic pressure differential between those same sensors. This may be particularly the case when the inside radius of the capillary tube (or tubes) between pressure sensors becomes larger and the corresponding shear force becomes smaller. In such cases, it may sometimes be necessary to increase the length of a given capillary tube based on the sensitivity of the adjacent pressure sensors so that the dynamic pressure differential across that capillary tube can be more accurately sensed. FIG. 1B is a schematic illustration of a further modified embodiment of the system 200 of FIG. 1A in which the tube length of one or more of the capillary tubes 245, 246, and/or 247 may be increased in the manner described above. In certain embodiments, an extension loop or “U-bend” may be included in a given capillary tube in order to increase the overall tube length of the capillary tube so as to address the low dynamic pressure and pressure sensor sensitivity issues described above. Such capillary tube length modifications may be used in those embodiments where space and/or system size limitations may prevent the use of continuous vertically oriented substantially straight capillary tubes, such as are generally depicted in FIG. 1A. For example, as shown in FIG. 1B, the capillary tube 245 may include an extension loop so that the overall tube length 245L' is increased above that of a comparative capillary tube that is otherwise substantially straight and vertically oriented, such as the capillary tube 245 shown in FIG. 1A having a tube length 245L. Furthermore, the length of the extension loop in the capillary tube 245 may be further increased as necessary based on the type of fluid and/or the size of the inside radius 245r so that the capillary tube 245 has a modified overall tube length 245L'', as indicated by dashed lines in FIG. 1B. Moreover, the capillary tube 246 may be modified in similar fashion so as to have an increased overall tube length of 246L' or even 246L''. In other illustrative embodiments, the overall tube length of a given capillary tube may be increased as required by modifying the capillary so as to include multiple extension loops or coils. As noted above, such a modification may be suitable in those embodiments where space and/or system size limitations may limit the capillary tube orientation and configuration. For example, as shown in the illustrative embodiment depicted in FIG. 1B, the capillary tube 247 may be modified to include a plurality of coils (three shown) so as to provide an overall tube length 247L', as compared to the tube length 247L of the substantially straight and vertically oriented capillary tube 247 shown in FIG. 1A. Other than the presence of the increased capillary tube lengths 245L', 246L', and 247L' (or 245L'', 246L'', and 247L') in the capillary rheometer 234, operation of the system 200 as shown in FIG. 1B may be substantially the same as for the system 200 shown in FIG. 1A, although calculation adjustments will typically be made by the control system 260 in determining the rheology of the fluid flowing through the system 200, as will be further described below. It should be understood that the extension loops and/or coil configurations for the various capillary tubes 245, 246, and 247 depicted in FIG. 1B are exemplary only, and should not be construed as otherwise limiting in any way to the present disclosure, as other capillary tube extension configurations may also be used. Furthermore, the series-arranged capillary tubes 245, 246, and 247 of the capillary rheometer 234 may also be arranged such that the fluid flow therethrough is nominally in a vertically upward direction, and where each successive series- arranged pressure sensor is positioned vertically higher than– i.e., above–the immediately previous pressure sensor so that the static pressure differential of the fluid across each individual capillary tube 245/246/247 may be determined. FIG. 1C schematically illustrates yet another modified embodiment of the system 200 of FIG. 1A in which the capillary rheometer 234 includes only three pressure sensors 224a-c and where the fluid flowing out of the top end 234t exits the capillary rheometer 234 at substantially atmospheric pressure conditions, i.e., zero gauge pressure. As shown in the illustrative embodiment of FIG. 1C, the flow discharge device 225 is positioned at and coupled to the top end 234t of the capillary rheometer 234 in lieu of the pressure sensor 224d shown in the embodiments depicted in FIGS. 1A and 1B. As with the flow discharge device 225 shown in FIG. 1A, the flow discharge device 225 of FIG. 1C may also include an overflow weir or deflector plate 225d, which may be arranged and positioned so as to substantially maintain the entirety of the capillary rheometer 234 full of fluid. Additionally, the flow discharge device 225 may also allow the flow 203 of fluid to pass to the fluid line 207 and out of the system 200 to atmospheric pressure conditions. Accordingly, the system 200 depicted in FIG. 1C may be operated in substantially similar fashion to the system 200 of FIGS. 1A and 1B, wherein however there is no back pressure imposed on the system 200 as would be the case when the choke valve 226 may be positioned in the fluid line 207. Thus, in such embodiments there would be no need to include an additional pressure sensor at the top end 234t of the capillary rheometer 234, such as the pressure sensor 224d shown in FIGS. 1A and 1B, as the pressure at the top end 234t will generally remain substantially constant at atmospheric, or zero gauge, pressure. During operation of any of the systems 200 shown in FIGS. 1A-1C, the pump unit 204 is initially operated so as to pump the flow 201 of fluid through the system 200 at least until the capillary rheometer 234 is substantially completely full of fluid, after which the pump unit 204 is turned off and the system 200 is allowed to come to static equilibrium. The pressure sensors 224a, 224b, and 224c (and the pressure sensor 224d when used in the system 200 as shown in FIGS. 1A and 1B) may then be used to determine the static pressure at each respective pressure sensor location. From the static pressure values thus determined, the specific weight of the fluid that is being pumped through the system 200 may then be calculated by any one or all of the following equations:

For a fluid having a substantially uniform specific weight, each of the calculations shown in equations (1) through (5) should provide substantially similar values for the fluid specific weight. In the event that the deviation between the specific weight values provided by each equation (1) through (5) is less than a pre-determined amount of acceptable deviation, the fluid specific weight value y_c that is used for the subsequent fluid property calculations as outlined below may be based on any appropriate statistical assessment of the values, such as average, median, and the like. However, in the event that the deviation between specific weight values is not within a pre-determined amount, it may be indicative of one or more faulty pressure sensor readings, in which case an alternative approach for determining the specific weight value used for subsequent calculations may be used, such as re-performing the static pressure operation, either with or without performing maintenance evaluations of the pressure sensors.

Once the static pressures at each pressure sensor 224a-c (and 224d, when used) have been measured and a specific weight of the fluid has been determined as outlined above, the pump unit 204 is then turned on and the flow 201 of fluid through the system 200 is restarted, additional pressure measurements are obtained from each pressure sensor 224a-c (and 224d, when used) at different specified volumetric flow rates. Based on the pressure data obtained from each pressure sensor 224a-c (and 224d, when used), a differential dynamic pressure across each individual capillary tube 245, 246, and 247 (i.e., between each pressure sensor 224a-c and 224d when used) due to the shear (drag) force between the fluid and the inside surface of each capillary tube 245/246/247 may then be determined based on the following equations:

is the dynamic pressure differential between the pressure sensors 224c and 224d for

the systems 200 of FIGS. 1A and IB, or between the pressure sensor 224c and atmospheric pressure for the system 200 of FIG. 1C; and

H₁ , H₂, and H₃ are height differentials as noted above.

The capillary rheometer 234 of any one of the systems 200 described herein may be used to determine the rheology of a drilling fluid flowing through the system 200, based on the corresponding flow rates of the fluid and the dynamic pressure differentials across the capillary tubes 245, 246, and 247. These measurements may in turn be converted to corresponding shear stresses and strain rates, as will now be described below.

Viscosity is defined in terms of shear stress and the rate of change of shearing strain, as follows:

where:

μ is viscosity;

τ is the shear stress existing between laminae of moving fluid; and

γ is the rate of change of shearing strain (i.e., strain rate) between laminae of

For a pressure-driven flow through a circular tube, the Hagen-Poiseuille law states that:

where:

Q is volumetric flow rate;

μ is tube radius;

ΔΡ is pressure drop;

μ is viscosity; and

L is tube length. In a laminar flow through a circular tube, the shear stress at the wall of the tube is:

From the Hagen-Poiseuille law in equation (10) and the definition of viscosity in equation (9), the strain rate at the wall of the tube is then given by:

The shear stress and strain rate equations (11) and (12) are set forth in terms of pressure drop, fluid flow rate, and tube geometry. Pressure drop can be calculated as shown in equations (6), (7), and (8) above from the pressure sensor data obtained from the capillary rheometer 234, fluid flow rate is known from the operation of the pump unit 204, and the geometry of each capillary tube 245, 246, and 247 is known from the construction of the capillary rheometer 234. From these parameters, shear stress and strain rate can be determined from equations (11) and (12), respectively, and once the shear stress and strain rate are known, viscosity can be determined using equation (9).

As noted earlier, the Hagen-Poiseuille law holds for steady, laminar, Newtonian flow. However, due to the typical non-Newtonian and/or non-laminar flow characteristics of most drilling fluids, the Hagen-Poiseuille equation should be corrected to obtain the correct shear stress and strain rate for non-Newtonian and/or non-laminar flow. One illustrative methodology that may be used to correct or calibrate the Hagen-Poiseuille equation is described below.

In at least some exemplary embodiments, the Hagen-Poiseuille equation may be calibrated using measurements taken of a reference fluid, or of a set of various different reference fluids, having well-known rheological behavior. Initially, the Hagen-Poiseuille equation (10) may be re-arranged using simple algebra as follows:

The natural logarithm of both sides of equation (13) are taken to obtain:

The natural logarithm function is then distributed throughout the right side of equation (14) to obtain:

A standard linear regression may then be applied to equation (15) using a large number of data points that are obtained from pressure sensors 224a-c (and 224d, when used) of the capillary rheometer 234 while a fluid having a known rheological behavior flows through the system 200. Furthermore, in at least some embodiments, the regression analysis may be performed using a set of various different fluids each having well-known rheological behavior, wherein each one of the set of fluids may be used to obtain respective sets of fluid-specific data points. In this way, the coefficients that lead to the minimum least squares of error may be obtained for the following relationship:

where:

C is a constant term used in the regression analysis.

The significance of each regression coefficient is thereafter tested using the standard t- test of the coefficients, and any unnecessary coefficients are removed from equation (16). The natural logarithm functions of equation (16) may then be disassembled using algebra to obtain:

Further simplifying, the term C₁ is defined as a function of the constant term C :

The definition of coefficient C₁ from equation (18) is then applied to equation (17) to obtain the final relationship for viscosity:

where:

μ is the calculated viscosity of the fluid;

is the dynamic differential pressure determined from equations

(6), (7), or (8) above;

R is the inside radius 245r, 246r, or 247r of the respective capillary tubes 245, 246, or

247;

L is the tube length 245L (or 245L* or 245L"), 246L (or 246L* or 246L"), or 247L (or 247L') of the respective capillary tubes 245, 246, or 247; and

al, a2, a3 and a4 are regression coefficients.

It should be understood that the above-described correction/calibration methodology for applying the Hagen-Poiseuille equation to the non-Newtonian and/or non-laminar flow characteristics of a fluid may be utilized in those embodiments wherein the data (obtained on a reference fluid, or on a set of several different reference fluids, having well-known rheological behavior) that is used to perform the regression analysis is based upon independently known and/or measured fluid viscosity values. However, as may be appreciated by one of ordinary skill after a complete reading of the present disclosure, other simplified methodologies may also be used to correct and or calibrate the systems 200 disclosed herein. For example, in some embodiments the above-described methodology may be modified in such a manner that the external reference data used for the regression analysis is based upon, e.g., measured fluid shear stress values rather than measured fluid viscosity values. In such embodiments, the disclosed methodology may be directly applied to the fluid shear stress equation (1 1) above, in which case the relevant strain rate parameters, i.e., flow rate and tube radius, of equation (12) would be used as-measured for the regression analysis, the strain rate obtained from these parameters would be accepted and used as-calculated, and the calculated shear stresses may then be calibrated so as to substantially correlate to the known shear stresses of the reference fluid, or of each of the set of several different reference fluids, i.e., having well-known rheological properties. Accordingly, such a simplified methodology may be considered adequate and/or acceptable for at least some embodiments of the systems 200 disclosed herein based upon a given drilling fluid application, provided the simplified approach is found to be sufficiently precise. In some exemplary embodiments, there may be other additional parameters that are relevant to the rheological properties of a fluid as it flows through a system 200 as disclosed herein, and which, if included, may improve the correction/calibration methodology described above. Accordingly, well-known statistical methods may also be used to determine and/or include additional terms in the linear regression analysis based on such additional relevant parameters, provided such additional terms can be shown to be linearly independent of the other terms in, for example, equation (16) above. For example, fluid temperature is one parameter that can have a significant influence on the rheological properties of a fluid. Accordingly, provided a proper statistical analysis shows that a term based on fluid temperature is linearly independent of the other terms in equation (16) and improves the overall correlation, then a temperature term may also be included in the regression analysis. Similarly, it is generally recognized that the velocity profile of a flow of fluid inside of a pipe or tube may have an influence on the strain rate at the wall of the tube, and as such, the velocity profile may therefore be relevant to the strain rate portion of the Hagen-Poiseuille equation. As would be understood one of ordinary skill, the Reynolds number is a dimensionless quantity that is used in fluid mechanics as an indicator of different flow regimes (commonly known as laminar flow, turbulent, flow, and transitional flow), and may be also used to help predict similar flow patterns in different fluid flow situations. Therefore, as with a temperature term, a term based on the flow regimes may also be included in the linear regression, provided the statistical analysis of the calibration data shows that the flow regime term is both relevant and linearly independent of other the terms in equation (16). In those embodiments of the present disclosure wherein both a temperature correlation term and a flow regime correlation term are included in the correction/calibration methodology outlined above, the resulting relevant equations will take the following form:

In order to determine the rheology of a drilling fluid using any one of the systems 200 disclosed herein, the pump unit 204 may be used to pump the drilling fluid into the capillary rheometer 234 through the bottom end 234b. After the pump unit 204 has been shut off and static pressure measurements through the capillary rheometer 234 have been obtained in the manner previously described, the pump unit 204 may then be re-started and dynamic pressure measurements may be obtained while the drilling fluid is pumped through the system 200. Furthermore, once the dynamic pressure differentials have been determined from the dynamic pressure measurements as set forth above, the respective dynamic pressure differentials along each of the capillary tubes 245, 246, and 247 the volumetric flow rate through the capillary rheometer 234 may then be used to determine the rheology of the drilling fluid in the manner previously described. In at least some embodiments, the pump speed of the pump unit 204 may be adjusted so as to achieve a sequence of multiple (e.g., three to seven, or even more) different flow rates of drilling fluid through the system 200. Furthermore, since the strain rate is a function of only flow rate and capillary tube radius (see, i.e., equation (12) above) each of the multiple different flow rates generated by the pump unit 204 corresponds to a different strain rate that is imparted to the drilling fluid within each of the different capillary tubes 245, 246, and 247, based on the different tube radii 245r, 246r, and 247r, respectively. This allows the fluid rheology to be determined over a relatively wide range of strain rates, thereby more effectively capturing and recording any non-Newtonian and/or non-laminar behavior of the drilling fluid as it circulates through the system 200. FIG. 2 schematically illustrates one exemplary external control system 260 that may be used in conjunction with any of the systems 200 described above and illustrated in FIGS. 1A- 1C. As shown in FIG.2, the control system 260 may be operatively coupled to receive signals from and send signals to various elements of the system 200. In certain embodiments, the control system 260 may be adapted to receive signals from the pressure sensors 224a, 224b, and 224c (and 224d of the system 200 shown in FIGS. 1A and 1B, shown by dashed lines in FIG. 2) of the capillary rheometer 234. Furthermore, the control system 260 may also be adapted to send signals to the controller of the drive motor 210 of the pump unit 204 and receive signals from the fluid analyzer system 262, which, as previously described, may be adapted to perform various fluid analyses, such as temperature and/or pH measurement, on the fluid as it flows through the system 200. In at least some embodiments, the control system 260 may be implemented as, for example, a computer system and the like, which may be adapted to receive and send signals through a communications interface 264 utilizing wired and/or wireless communication protocols. The control system 260 may further include a processor (or processors) 266, memory 268, a display (or displays) 270, and an input interface (or device(s)) 272. Additionally, the instructions for controlling the operation of the system 200 may be stored in, for example, the memory 268, or in another appropriate storage media that is accessible to the control system 260. In at least some illustrative embodiments, the control system 260 may be adapted to automatically control the operation of the system 200– that is, without any direct intervention with personnel– so as to continuously perform a series of operational steps that are directed to determining the rheological properties of the fluid flowing through the system 200. As a first step in the series of automatically controlled operations, the control system 260 may initially send a signal to a controller (not shown) of the drive motor 210 so as to drive the pump unit 204 and generate a flow of fluid through the system 200 for a sufficient length of time until substantially the entirety of the capillary rheometer 234, e.g., each of the series-arranged capillary tubes 245, 246, and 247, is completely full of fluid. Once the pump unit 204 has been operated for a sufficient length of time so that the capillary rheometer 234 is substantially completely full of fluid, the control system 260 may then automatically send another signal to the controller of the drive motor 210 so as to stop the pump unit 204 and allow the fluid in the system 200 to come to a static (non-flowing) fluid equilibrium. Thereafter, the control system 260 may receive signals indicative of a hydrostatic pressure from each of the pressure sensors 224a-c (and 224d, when used), and the control system 260 may then relay the signals from the pressure sensors 224a-c (and 224d, when used) to the processor 266. In some embodiments, the processor 266 may then in turn perform a series of specific weight calculations, such as the calculations represented by equations (1) through (5) above, so as to determine the specific weight of the fluid in the system 200. After the fluid specific weight has been determined in the manner described above, the control system 260 may then send a further signal to controller of the drive motor 210 so as to operate the pump unit 204 at a series of specific rotational speeds that correspond to a series of pre-determined volumetric flow rates. As the pump unit 204 is being operated at each specific rotational speed/flow rate, the control system 260 is adapted to receive signals from each of the pressure sensors 224a-c (and 224d, when used) and relay the received signals to the processor 266. The processor 266 may then utilize the pressure signals from each of the pressure sensors 224a-c (and 224d, when used) in conjunction with the pertinent geometry of the capillary rheometer 234 to calculate various viscosities of the fluid using the formula of equation (19) above for each of the various flow rates and corresponding dynamic pressure differentials across each of the capillary tube 245, 246, and 246. A rheology curve may then be generated from the various viscosities using equations (9) and (12) above, such as the rheology curve 301 shown in FIG. 3, described in further detail below. As noted previously, the series of pre-determined volumetric flow rates that are used to generate a given fluid rheology curve may include from three to seven, or even more, discretely different flow rates. Furthermore the range and magnitude of the volumetric flow rates that make up the series of pre-determined flow rates may depend on various different fluid testing parameters, such as the configuration of the system 200 and/or the capillary rheometer 234, the type of fluid being evaluated, and the like. For example, in at least one exemplary embodiment, the series of pre-determined flow rates generated by the pump unit 204 may include seven different flow rates ranging between approximately 6.4 and 25.3 liters per minute (lit/min) (1.7 and 6.7 gallons per minute (gpm)), wherein each discrete flow rate may be approximately as follows:

Flow rate #1 = 6.4 lit/min (1.7 gpm)

Flow rate #2 = 8.3 lit/min (2.2 gpm)

Flow rate #3 = 9.8 lit/min (2.6 gpm) Flow rate #4 = 12.8 lit/min (3.4 gpm)

Flow rate #5 = 19.6 lit/min (5.2 gpm)

Flow rate #6 = 21.8 lit/min (5.8 gpm)

Flow rate #7 = 25.3 lit/min (6.7 gpm)

As noted, the that flow rate range and the number for pre-determined flow rates listed above are exemplary only, as both wider and narrow flow rate ranges and both a fewer and a greater number of pre-determined flow rates may be used, depending on the specific configuration of the system 200 being utilized and the type of fluid being evaluated. Accordingly, the specific flow rates and flow rate ranges listed herein should not be construed as limiting in any way to the scope of the present disclosure. While each of the systems 200 depicted in FIGS. 1A-1C above are configured such that the flow of fluid through the capillary rheometer 234 is nominally in a vertically upward direction (i.e., wherein the top end 234t of the capillary rheometer 234 is positioned at a height level 234h above the bottom end 234b), it should be understood that any of the systems 200 disclosed herein may be arranged in a such a manner that the flow through the capillary rheometer 234 is in a nominally horizontal direction, and so that all of the pressure sensors 224a- c (and 224d, when used) of the capillary rheometer 234 are at substantially the same height level. When the capillary rheometer 234 is arranged in this fashion, the static pressure differential between each of the pressure sensors 224a-c (and 224d, when used) may therefore be substantially negligible, e.g., zero, and as such the additional operational and calculation steps described above that are used for determining and correcting for the static pressure differential between pressure sensors may be eliminated from the overall fluid viscosity evaluations. Moreover, in certain embodiments, a flow discharge device, such as the flow discharge devices 225 shown in FIGS. 1A-1C, may be included in the systems 200 that are configured in this manner so that each of the tubes 245, 246, 247 are substantially full of fluid during the operation of the systems 200. Accordingly, in such embodiments, the pressure differentials measured between each of the various pressure sensors 224a-c (and 224d, when used) may be substantially a function of the shear (drag) force between the fluid and the inside surface of each capillary tube 245/246/247. Furthermore, it should also be understood that each of the systems 200 disclosed herein may be configured such that the flow of fluid through the capillary rheometer 234 is nominally in a vertically downward direction, i.e., wherein the inlet end of the capillary rheometer 234 is the top end 234t, the outlet end of the capillary rheometer 234 is the bottom end 234b, and the top (inlet) end 234t is positioned at the height level 234h above the bottom (outlet) end 234b. In such embodiments, the arrangement of the various elements of the system 200 may be substantially reversed, such that the pump unit 204 is positioned upstream of the top (inlet) end 234t of the capillary rheometer and, when used, a flow discharge device, such as the flow discharge device 225, would be positioned downstream of the bottom (outlet) end 234b so as to maintain each of the capillary tubes 245, 246, 247 substantially full of fluid during system operation. Furthermore, the capillary tube 245 and the pressure sensor 224a would be positioned proximate to the top (inlet) end 234t of the capillary rheometer and the capillary tube 247 and the pressure sensor 224d (when used) would be positioned proximate the bottom (outlet) end 234b. When the capillary rheometer 234 is arranged in this fashion, e.g., such that the fluid flow through each of the capillary tubes 245/246/247 is in a substantially vertically downward direction, the pressure sensor 224b would then be positioned at a distance 245h below the pressure sensor 224a, the pressure sensor 224c would be positioned at a distance 246h below the pressure sensor 224b, and the pressure sensor 224d would be positioned at a distance 247h below the pressure sensor 224c. Therefore, the calculation steps described above that are used for determining and correcting for the static pressure differential between each of the pressure sensors 224a-d would still remain relevant to the data obtained during the operation of the system 200, however the formulas shown in equations (1 ) through (5) above should be adjusted as required in order to address the revised configuration of the capillary rheometer 234. During the above-described series of specific flow-rate operations and fluid viscosity calculations, the control system 260 may also receive signals from the fluid analyzer 262, such as, for example, signals indicative of fluid temperature, fluid pH, polar liquid content, solids constituency, and the like. Furthermore, in at least some embodiments, at least some of the signals sent to the control system 260 by the fluid analyzer 262 may be used to generate appropriate correction factors for the various equations used to perform fluid specific weight and viscosity calculations, such as temperature corrections and the like. It should be appreciated by those of ordinary skill after a complete reading of the present disclosure that the viscosity of the flow 201 of fluid being pumped through the system 200 may be substantially continuously monitored and evaluated by the control system 260 by continuously and repeatedly performing the above-described series of system operations and control system calculations. In this way, any changes over time in the rheology of a given fluid may be passively monitored, e.g., via the display 270, on substantially a real-time basis. Furthermore, in those illustrative embodiments wherein the fluid being analyzed by the system 200 is, for example, a drilling fluid that is being returned from a down-hole drilling operation, such real-time assessment of the drilling fluid properties may provide drilling rig personnel with a valuable real-time drilling fluid analysis tool. FIG. 3 depicts an illustrative graph 300 of a representative fluid rheology curve 301 that may be generated from the data that is obtained by operating any one of the above-disclosed systems 200 in accordance with the methods described herein. As shown in FIG. 3, the X-axis of the graph 300 represents fluid strain rate and the Y-axis of the graph 300 represents fluid shear stress. Recall that, as previously noted, the viscosity of a fluid is defined as the ratio of the shear stress to the rate of change of shearing strain (i.e., strain rate). See equation (9) and the associated description above. Accordingly, the rheology of a given fluid may be plotted as a curve from the various data points obtained and calculations made during the operation and monitoring of the system 200, such as is indicated by the representative rheology curve 301 of FIG. 3. As will be noted from in FIG. 3, the representative rheology curve 301 takes a substantially curvilinear shape having a substantially constantly changing slope– which is indicative of a fluid (such as a drilling fluid) having non-Newtonian properties– rather than a substantially linear shape having a substantially linear slope– which, without a yield point would be indicative of a Newtonian fluid, or, with a yield point would be indicative of a Bingham fluid. Furthermore, it should also be noted that between a strain rate of approximately 500 sec^-1 and a strain rate of approximately 1000 sec^-1 the rheology curve 301 has a relatively near-constant slope, however below approximately 300 sec^-1 the slope of the rheology curve 301 greatly increases. Accordingly, it is well recognized by those having skill in the art that the lower end of a rheology curve, such as the rheology curve 301, may provide valuable information on the performance of the fluid under low to very low strain rate conditions. It should be appreciated by those having ordinary skill in the art after a complete reading of the present disclosure that at least some fluid rheological properties that are obtained by using one or more of the prior art devices described above– e.g., rheological properties that are known and used by those having skill in the art– may also be obtained from the data that is used to generate curve 301 of FIG. 3. For example, one such well-known fluid rheological property, often referred to as the“plastic viscosity” of a fluid, is commonly obtained by using a rotating cylinder, or rotating bob, viscometer. Typically, the plastic viscosity of a fluid is calculated by determining the slope of line passing through the two shear stress/strain rate data points that are obtained by operating the rotating cylinder viscometer on a fluid sample, e.g., drilling fluid sample, at 300 RPM and 600 RPM, such as the slope 302s of the straight line 302 passing through points 301a and 301b on the rheology curve 301. Furthermore, based on the known geometry of a standard rotating cylinder viscometer, the RPM parameter of a rotating cylinder viscometer test can be directly related to the strain rate parameter, such that 1 RPM corresponds to 1.703 sec^-1. Therefore, as is shown in FIG. 3, the Y-value difference 301y between the Y- value of line 302 at point 301a (i.e., the shear stress/strain rate data point for 600 RPM) and the Y-value of line 302 point 301b (i.e., the shear stress/strain rate data point for 300 RPM) on the rheology curve 301 corresponds to the commonly known“plastic viscosity” of the tested fluid. Another rheological property known and used by those skilled in the art that is obtained using a rotating cylinder viscometer is commonly referred to as the“yield point” of a fluid, which may also be obtained from data that is used to generate curve 301 of FIG. 3. The yield point of a fluid is commonly understood to be the Y-axis intercept of the straight line passing through the 600 RPM and 300 RPM shear stress/strain rate data points obtained during the rotating cylinder viscometer tests performed on a fluid, which represents a theoretical linear shear stress of the fluid at a theoretical“zero strain rate.” Accordingly, using the shear stress/strain rate data points 301a and 301b on the rheology curve 301– which, as noted above, correspond to the equivalent 600 RPM and 300 RPM rotating cylinder viscometer data points– the Y-axis intercept point 302y of the straight line 302 passing through points 301a and 301b corresponds to the commonly known“yield point” of the tested fluid. Therefore, in addition to providing a true rheology curve of a fluid, such as the representative rheology curve 301 plotted in graph 300 of FIG. 3, in at least some embodiments of the present disclosure, any of the systems 200 disclosed herein can provide the traditional and commonly known“plastic viscosity” and‘yield point” of a tested fluid. In this way, personnel monitoring any of the systems 200 disclosed herein will have immediate feedback on traditional fluid properties that are presented in a manner that is known to those having skill in the art of oil and gas well drilling operations. Furthermore, in certain embodiments the fluid rheology information may be presented on the display 270 of the control system 260 in graphical fashion, such as is depicted by the graph 300 of FIG. 3. In other embodiments, the fluid rheology information may be presented numerically on the display 270, whereas in at least some embodiments the information may be presented on the display 270 in both numerical and graphical fashion, or in any other suitable manner known in the art. FIG. 4 schematically depicts one embodiment of another exemplary system 200 that may be used for measuring the properties of a drilling fluid. As shown in FIG. 4, the system 200 is configured similarly to the system 200 of FIG.1A, wherein however the capillary rheometer 234 includes only a single capillary tube 245 having a tube length 245L and an inside radius 245r. While the single capillary tube 245 is depicted in FIG. 4 as being substantially straight and substantially vertically oriented, it should be understood by one of ordinary skill after a complete reading of the present disclosure that the length 245L of the tube 245 may be increased as required for a given application in similar fashion to the capillary tubes 245, 246, and/or 247 shown in FIG. 1B, e.g., by including extension loops and/or coiled configurations. In the illustrative embodiment depicted in FIG. 4, the intermediate pressure sensors 224b and 224c of the system 200 shown in FIG. 1A are not present in the system 200 of FIG. 4, and only the bottom inlet pressure sensor 224a and top outlet pressure sensor 224d are positioned at the respective inlet and outlet ends of the single capillary tube 245. In this configuration, and as with the systems 200 shown in FIGS. 1A-1C, the capillary rheometer 234 is arranged such that the fluid flow 201 therethrough is in a substantially vertically upward direction, although as previously noted, other rheometer orientations may also be used. The system 200 of FIG. 4 may also include a plurality of pumps 204a-c, each of which may be driven by a respective drive motor 210a-c. Additionally, a fluid analyzer system 262 may be positioned in the pump discharge line 208, and a fluid discharge device 225 (for maintaining the capillary rheometer 234 substantially full of fluid) or a choke valve 226 (for inducing a back pressure on the capillary rheometer 234), or both a fluid discharge device 225 and a choke valve 226, may also be positioned in the fluid line 207 that is coupled to the top pressure sensor 224d. However, it should be understood that in at least some exemplary embodiments, the top outlet pressure sensor 224d may also be eliminated from the system 200 of FIG. 4, in which case the fluid discharge device 225 may be positioned at the top end 234t of the capillary rheometer 234 (and the single capillary tube 245) in similar fashion to the system 200 depicted in FIG. 1C. As shown in FIG. 4, the pumps 204a-c may be arranged in parallel together with corresponding control valves 211a-c, and the external control system 260 may be operatively coupled to the drive motors 210a-c of the pumps 204a-c as well as to the respective control valves 211a-c. During operation of the system 200 of FIG. 4, the control system 260 may then be used to control the pumps 204a-c and control valves 211a-c such that only a single one of the pumps 204a-c delivers the fluid flow 201 to the capillary rheometer 234 at any given time. In some embodiments, each of the plurality of pumps 204a-c may be sized and/or configured differently so that each pump is capable of delivering different ranges of fluid flow rates to the capillary rheometer 234, i.e., the single capillary tube 245. In this way, the various flow rates delivered by the pumps 204a-c through the single capillary tube 245 and the corresponding pressure differentials as measured between the pressure sensors 224a and 224d for each flow rate may be used to determine fluid shear stresses and corresponding strain rates in similar fashion to the methodology described with respect to equations (1) through (19) above. Depending upon the range, accuracy, and control with which a given pump may be capable of delivering the requisite spectrum of fluid flow rates to the capillary rheometer 234 so as to generate the data points needed to determine the rheological properties of the fluid, the system 200 may be operated using only a single pump, such as the pump 204a, thereby eliminating the need to rely upon the use of a plurality pumps in the manner illustrated in FIG. 4. Accordingly, the present disclosure describes various methods and systems that may be used to measure the properties of a fluid, such as a drilling fluid, or drilling mud, and the like. Furthermore, arranging a plurality of capillary tubes of different sizes (e.g., different tube lengths and/or tube radii) in series permits a plurality of data points to be obtained on a fluid flowing through an illustrative system at various flow rates, thus enabling a substantially continuous real-time evaluation of the rheology of the fluid. Moreover, substantially continuous real-time evaluation of fluid rheology may also be accomplished by arranging one or more pumps to deliver a wide range of fluid flow rates a system that includes only a single capillary tube, and obtaining a plurality of data points on the fluid at the various flow rates. The particular embodiments disclosed above are illustrative only, as the invention may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. For example, the method steps set forth above may be performed in a different order. Furthermore, no limitations are intended to the details of construction or design herein shown. It is therefore evident that the particular embodiments disclosed above may be altered or modified and all such variations are considered within the scope and spirit of the invention.

Claims

WHAT IS CLAIMED: 1. A system (200) for measuring fluid properties, the system (200) comprising: a capillary rheometer (234) comprising a plurality of capillary tubes that are arranged for series flow of a fluid therethrough, wherein each of said plurality of capillary tubes has a different inside tube radius; and

a pump (204) that is adapted to pump said fluid through said capillary rheometer (234) at a plurality of different flow rates. 2. The system (200) of claim 1, wherein each of said plurality of capillary tubes has a different tube length. 3. The system (200) of claim 1, wherein an outlet end (234t) of said capillary rheometer (234) is positioned at a height level (234h) above an inlet end (234b) of said capillary rheometer (234). 4. The system (200) of claim 1, wherein said capillary rheometer (234) comprises a pressure sensor positioned between each of said plurality of capillary tubes. 5. The system (200) of claim 4, further comprising an inlet pressure sensor (224a) positioned at an inlet end (234b) of said capillary rheometer (234). 6. The system (200) of claim 5, further comprising an outlet pressure sensor (224d) positioned at an outlet end (234t) of said capillary rheometer (234). 7. The system (200) of claim 1, wherein said plurality of capillary tubes comprises a first capillary tube (245) having a first inlet and a first outlet and a second capillary tube (246) having a second inlet and a second outlet, said first outlet being positioned at a first height level (245h) above said first inlet, said second outlet being positioned at a second height level (246h) above said second inlet, and said first outlet being positioned proximate said second inlet.

8. The system (200) of claim 7, wherein said first capillary tube (245) has a first inside radius (245r) and said second capillary tube (246) has a second inside radius (246r) that is greater than said first inside radius (245r). 9. The system (200) of claim 7, wherein said first capillary tube (245) has a first tube length (245L) and said second capillary tube (246) has a second tube length (246L) that is greater than said first tube length (245L). 10. The system (200) of claim 7, further comprising a pressure sensor (224b) that is adapted to sense a pressure in said capillary rheometer (234) at said first outlet and said second inlet. 11. The system (200) of claim 1, wherein said pump (204) is a one of a progressive cavity pump, a peristaltic pump, and a piston pump. 12. The system (200) of claim 1, further comprising a flow discharge device (225) positioned proximate an outlet end (234t) of said capillary rheometer (234), said flow discharge device (225) being adapted to maintain said capillary rheometer (234) substantially completely full of fluid. 13. The system (200) of claim 1, further comprising a choke valve (226) that is adapted to create a back-pressure on said capillary rheometer (234). 14. The system (200) of claim 12, further comprising an outlet pressure sensor (224d) positioned at an outlet end (234t) of said capillary rheometer (234), wherein said flow discharge device (225) is positioned downstream of said outlet pressure sensor (224d). 15. The system (200) of claim 1, further comprising a fluid analysis device (262) that is adapted to measure at least one of a temperature and a pH of a fluid flowing through said system (200).

16. A capillary rheometer (234) for determining the rheology of a fluid, the capillary rheometer (234) comprising:

a first capillary tube (245) having a first inside radius (245r);

a second capillary tube (247) having a second inside radius (247r) that is different than said first inside radius (245r), wherein said second capillary tube (247) is arranged in series flow with said first capillary tube (245) such that a fluid flowing through said capillary rheometer (234) sequentially exits an outlet end of said first capillary tube (245) and enters an inlet end of said second capillary tube (247); and

a first pressure sensor (224b, 224c) positioned between said first and second capillary tubes (245, 247), said first pressure sensor (224b, 224c) being adapted to measure a pressure of said fluid flowing through said capillary rheometer (234). 17. The capillary rheometer (234) of claim 16, wherein said outlet end of said first capillary tube (245) is at a greater height level than an inlet end of said first capillary tube (245) and an outlet end of said second capillary tube (247) is at a greater height level than said inlet ends of said first and second capillary tubes (245, 247). 18. The capillary rheometer (234) of claim 16, wherein said first pressure sensor (224b) is coupled to said outlet end of said first capillary tube (245), said first pressure sensor (224b) being adapted to measure a pressure of a fluid flowing through said capillary rheometer (234) as said fluid exits said outlet end. 19. The capillary rheometer (234) of claim 16, wherein said first pressure sensor (224c) is coupled to said inlet end of said second capillary tube, said first pressure sensor (224c) being adapted to measure a pressure of a fluid flowing through said capillary rheometer (234) as said fluid enters said inlet end. 20. The capillary rheometer (234) of claim 16, wherein said first inside radius (245r) is less than said second inside radius (247r).

21. The capillary rheometer (234) of claim 16, wherein said first capillary tube (245) has a first tube length (245L) and said second capillary tube (247) has a second tube length (247L) that is greater than said first tube length (245L). 22. The capillary rheometer (234) of claim 16, further comprising a third capillary tube (246) having a third inside radius (246r) that is different from said first and second inside radii (245r, 247r), wherein said third capillary tube (246) is positioned between and arranged in series flow with said first and second capillary tubes (245, 247) such that a fluid flowing through said capillary rheometer (234) sequentially exits said outlet end of said first capillary tube (245), thereafter enters an inlet end of said third capillary tube (246), exits an outlet end of said third capillary tube (246), and enters said inlet end of said second capillary tube (247). 23. The capillary rheometer (234) of claim 22, wherein said third inside radius (246r) is greater than said first inside radius (245r) and less than said second inside radius (247r). 24. The capillary rheometer (234) of claim 23, wherein said first capillary tube (245) has a first length (245L), said second capillary tube (247) has a second tube length (247L) that is greater than said first tube length (245L), and said third capillary tube (246) has a third tube length (246L) that is greater than said first and second tube lengths (245L, 247L). 25. The capillary rheometer (234) of claim 22, further comprising a second pressure sensor (224c), wherein said first pressure sensor (224b) is coupled to said outlet end of said first capillary tube (245) and to said inlet end of said third capillary tube (246) and said second pressure sensor (224c) is coupled to said outlet end of said third capillary tube (246) and to said inlet end of said second capillary tube (247). 26. The capillary rheometer (234) of claim 25, wherein said first pressure sensor (224b) is adapted to measure a pressure of a fluid flowing through said capillary rheometer (234) as said fluid exits said outlet end of said first capillary tube (245) and said second pressure sensor (224c) is adapted to measure a pressure of said fluid as said fluid exits said outlet end of said third capillary tube (246).

27. The capillary rheometer (234) of claim 25, further comprising an inlet pressure sensor (224a) coupled to an inlet end of said first capillary tube (245), said inlet pressure sensor (224a) being adapted to measure a pressure of a fluid flow entering said capillary rheometer (234). 28. The capillary rheometer (234) of claim 25, further comprising an outlet pressure sensor (224d) coupled to an outlet end of said second capillary tube (247), said outlet pressure sensor (224d) being adapted to measure a pressure of a fluid flow exiting said capillary rheometer (234). 29. The capillary rheometer (234) of claim 25, further comprising a flow discharge device (225) coupled to an outlet end (234t) of said capillary rheometer (234), said flow discharge device (225) being adapted to maintain said capillary rheometer (234) substantially completely full of fluid. 30. A method of determining the rheology of a fluid, the method comprising:

operatively coupling a pump (204) to a capillary rheometer (234) comprising a plurality of capillary tubes, wherein said plurality of capillary tubes are arranged for series flow and each of said plurality of capillary tubes has a different inside radius; controlling operation of said pump (204) so as to pump a fluid through said capillary rheometer (234) at a series of pre-determined flow rates;

determining a pressure differential of said fluid flowing through said capillary rheometer (234) across each of said plurality of capillary tubes for each of said series of pre- determined flow rates; and

determining the rheology of said fluid for each of said pre-determined flow rates and each of said determined pressure differentials across each of said plurality of capillary tubes. 31. The method of claim 30, wherein each of said pre-determined flow rates corresponds to a different strain rate imparted to said fluid flowing through each of said plurality of capillary tubes and each of said determined pressure differentials corresponds to a different shear stress imparted to said fluid flowing through each of said plurality of capillary tubes/

36 32. The method of claim 30, further comprising using said determined rheology of said fluid to establish a fluid rheology curve for said fluid. 33. The method of claim 32, further comprising determining a plastic viscosity of said fluid from said fluid rheology curve. 34. The method of claim 32, further comprising determining a yield point of said fluid from said fluid rheology curve. 35. The method of claim 30, wherein determining said rheology of said fluid comprises calibrating the Hagen-Poiseuille equation to account for non-Newtonian and non- laminar fluid effects and determining fluid strain rate and fluid shear stress using said calibrated Hagen-Poiseuille equation. 36. The method of claim 35, wherein said calibrated Hagen-Poiseuille equation has the form:

wherein μ is viscosity, ΔΡ is a pressure differential across a respective capillary tube, R is a radius of said respective capillary tube, L is a length of said respective capillary tube, Q is a flow rate of said fluid flowing through said capillary rheometer (234), and C_{l 5} al, a2, a3, and a4 are coefficients determined from applying a regression analysis to a set of data points obtained when at least one fluid having a known rheological behavior is pumped through said capillary rheometer (234).

37. The method of claim 35, wherein said calibrated Hagen-Poiseuille equation has the form:

wherein μ is viscosity, ΔΡ is a pressure differential across a respective capillary tube, R is a radius of said respective capillary tube, T is a temperature of said fluid flowing through said capillary rheometer (234), F_r is a flow regime correlation term, L is a length of said respective capillary tube, Q is a flow rate of said fluid flowing through said capillary rheometer (234), and are coefficients determined from applying a regression analysis

to a set of data points obtained when at least one fluid having a known rheological behavior is pumped through said capillary rheometer (234). 38. The method of claim 30, wherein said series of pre-determined flow rates comprises at least three pre-determined flow rates. 39. The method of claim 30, further comprising, prior to pumping said fluid through said capillary rheometer (234) at said series of pre-determined flow rates:

operating said pump (204) so as to substantially completely fill said capillary rheometer (234) with said fluid;

after substantially completely filling said capillary rheometer (234) with said fluid, shutting off said pump (204) and allowing said fluid to come to static pressure condition;

after allowing said fluid to come to said static pressure condition, determining a static non-flowing pressure differential across each of said plurality of capillary tubes; and

using said determined static non-flowing pressure differentials to determine a specific weight of said fluid. 40. The method of claim 39, wherein determining said rheology of said fluid further comprises using said determined specific weight of said fluid. 41. The method of claim 30, wherein each of said plurality of capillary tubes has a different tube length. 42. The method of claim 30, further comprising positioning an inlet pressure sensor (224a) at an inlet of said capillary rheometer (234) and positioning an intermediate pressure sensor (224b, 224c) between each of said plurality capillary tubes. 43. The method of claim 42, wherein determining said pressure differential of said fluid flowing through said capillary rheometer (234) across each of said plurality of capillary tubes comprises obtaining a pressure signal from said inlet pressure sensor (224a) and each of said intermediate pressure sensors (224b, 224c). 44. The method of claim 30, wherein controlling said operation of said pump (204) comprises operatively coupling an external control system (260) to at least said pump (204) and said capillary rheometer (234) and controlling said pump (204) with said control system (260) based on said series of pre-determined flow rates. 45. The method of claim 30, wherein said plurality of capillary tubes comprises at least a first and second capillary tube (245, 246/247), a first radius (245r) of said first capillary tube (245) being less than a second radius (246r/247r) of said second capillary tube (246/247) and a first tube length (245L) of said first capillary tube (245) being less than a second tube length (246L/247L) of said second capillary tube (246/247). 46. The method of claim 45, further comprising arranging said plurality of capillary tubes of said capillary rheometer (234) so that a height level of an outlet of said first capillary tube (245) is positioned above a height level of an inlet of said first capillary tube (246) and height level of an outlet of said second capillary tube (246/247) is positioned above a height level of an inlet of said second capillary tube (246/247) and above said height level of said outlet of said first capillary tube (245). 47. The method of claim 30, wherein said fluid is a drilling fluid. 48. The method of claim 30, further comprising determining at least one of a temperature and a pH of said fluid flowing through said capillary rheometer (234).