mud pump stroke sensor made in china

1.The pumping sensor can be fixed to the mud pump head by the bracket, or the appropriate part of the turntable, and the closest distance between the position of the sensing surface of the measured object and the end surface of the sensor is within 30 mm. (According to the influence of the use environment, the rated working distance is generally taken. 80%), plus the working voltage, when the end of the inductive sports sensor is close, the indicator light is on; when away from the sensor, the indicator is off.

2.The turntable speed sensor can be fixed to the appropriate part of the drive shaft of the turntable with the bracket. It should be convenient to install and repair. The model of the drill is selected. A piece of iron with a length and width of 30mm is welded on the shaft of the drive shaft or the airbag clutch. The position of the end face should be close to the end face of the sensor. Adjust the fixing nut of the sensor so that the distance between the iron sensor is within the effective range of the working distance.

The RIGCHINA Pump Stroke Counter/Rate Meter displays both the total number of strokes and the strokes per minute for 3 mud pumps up to 1,024 strokes per minute for each pump. Push buttons conveniently located on the front of the instrument make it easy for the operator to reset each pump count

The SK-8Y2X series alloy film sensor consists of an ion-beam sputtering alloy film sensor and a signal modulation circuit and is applicable to detection of fluid pressure, differential pressure or liquid level. The Sensor is made using the modern film equipment and etching technique. The sensor has unique technique and excellent performance and can stably run in severe environment. The liquid medium pressure/differential pressure acts on the corrosion resistant stainless steel elastic film to deform the film, as shown in the strain schematic diagram. An alloy film strain resistance comprising Wheatstone bridge has been made on the film. Film deformation changes the geometry and value of the resistance, and the bridge outputs corresponding electrical signals. The electronic circuit amplifies the bridge output signals and converts them into standard 4~20mA current signals for output.

The Magneto® Pump Stroke Sensor is the latest new product from ASD Holdings (Advanced Sensor Design). ASD has successfully introduced unique products for the Oil & Gas Industry for over a decade. In this newest creation we find that the Magneto® Pump Stroke Sensor has been patented by Advanced Sensor Design. It is the world’s first pump stroke sensor that is mounted to the outside housing of the rig pump. It is mounted and stays in place by the use of a heavy duty magnet. The Magneto PSS is completely capable of detecting and counting Oil Rig “mud pump piston strokes” without having to make or be in contact with the pistons.

It is no longer a requirement to open the covers of the Oil Rig mud pumps to install a C-clamp style micro switch with a metal whisker. (Note picture below labeled C-clamp style micro switch) No longer is it necessary to bore a hole through the pump housing in order to get a proximity switch close enough to a piston to count actual strokes. (Note picture below labeled Cable going through pump housing) The Magneto® Pump Stroke Sensor is simple to install and easy to monitor!

The magnetic base of the Magneto® PSS makes it totally different than anything available in the marketplace today relative to its form and fit. However, that is not its only outstanding feature. Advanced Sensor Design is using “State of the Art” electronic circuitry that has the ability to give the end user (Oil Rig Mud Pump Operator) an On/Off switch type electrical output. Just like what the conventional mud pump sensors emit today. The obvious benefit to the oil rig is that No Special accommodations to their Data Acquisition Systems are required.

Our pump stroke counter systems (CPS101 Series) measure the stroke rate and number of strokes on mud pumps. The oilfield pump stroke system is user-friendly and reliable and is configurable to measure up to three mud pumps at once. Our digital pump stroke counter systems are manufactured here in the U.S. by Crown Oilfield Instrumentation, and Crown’s Pump Stroke Counter provides easy monitoring of strokes per minute on multiple mud pumps. Each mud pumps’s stroke rate can be selected individually and the display is updated regularly for accurate monitoring. LCD displays indicate both pumps strokes per minute and the total number of strokes. Located at the bottom of the panel, push buttons provide easy operation and reseting of each pump. When you need to accurately monitor and maintain the amount of mud being pumped, you can trust Crown’s oilfield stroke counters.

[0003] A kick can be defined as a well control problem in which the pressure found within the drilled formation is greater than the mud or fluid hydrostatic pressure acting on the borehole or face of the formation. This formation pressure causes fluids to flow from the formation into the well bore. In almost all drilling operations, the operator attempts to maintain a hydrostatic pressure greater than the formation pressure and thus prevent kicks. On occasion, however, and for various reasons, the formation pressure exceeds the mud pressure and a kick will occur. Kicks have become even more common due to the present trend of increasing drilling rates by using lighter drilling mud.

[0006] FLOW RATE CHANGE - An increase in the flow-out or flow rate leaving the well while pumping at a constant rate is one of the primary kick indicators. The increased flow rate is interpreted to mean that the formation is forcing formation fluids into the well bore. A decrease in the flow rate exiting from the well while pumping at a constant rate is an indicator of lost circulation.

[0007] FLOWING WELL WITH PUMPS OFF - When the rig pumps are not moving the mud, a continued flow-out from the well indicates that a kick is in progress. An exception to this indicator is when the mud in the drill pipe is considerably heavier than that in the annulus, as in the case of a slug.

[0008] PIT VOLUME CHANGE - If the volume of fluid in the pits is not changed as a result of surface controlled actions, an increase in pit volume indicates that a kick is occurring. The fluids entering the well bore as a result of the kick displace an equal volume of mud at the flow line and result in a pit gain. A decrease in pit volume under these conditions indicates lost circulation.

[0012] Presently, flow-in measurement is based on the number of strokes per minute of triplex mud pumps (see Fig. 1). The flow race obtained from the pump strokes is then corrected by a volumetric pump efficiency. This pump efficiency can fluctuate between 80% to 95% accounting for inaccuracies of plus or minus seven and one half percent in the flow-in measurement.

[0014] Using the pump strokes and the paddle measurement for flow-in and flow-out respectively, the best accuracy for the differential flow over the entire fluid flow range cannot be much better than about twenty-five percent, or three hundred (GPM) in twelve hundred GPM. This is more than ten times the required accuracy, rendering prior methods of differential flow rate measurement inadequate for desired kick detection.

[0015] Electromagnetic flow meters have also been used but have drawbacks. They do not work in oil based muds (conductivity too low). They require complete modification of the return line. In offshore rigs where modification of the return line is difficult and space is limited, there is usually no way to install them. They require expensive maintenance to sustain their accuracy.

[0019] Further, U.S. Patent No. 4,754,641 to Orban et al., while providing improved results relative to the other methods for measuring fluid flow in return lines, still suffers from inaccuracies due to the requirement of a velocity probe which is inherently inaccurate in measuring mud flow in a drilling rig return line due to the wide range of elements in the mud. Thus, even with this advance, the art does not provide a method for sufficiently accurately determining a volumetric fluid flow rate such that a kick or lost circulation determination can be made in real time on a drilling rig.

[0024] In accord with the objects of the invention, improved methods and systems are disclosed for use in a return line system of a drilling rig to aid in accurately determining a volumetric flow rate of mud in the return line without the aid of a direct velocity measurement means. The system invention broadly comprises: a non-intrusive level sensor located in or in proximity to the return line for sensing the height or level of the mud flowing in the return line and providing a signal indicative thereof; and a processor responsive to the level sensor signals for determining, in conjunction with knowledge of the return line configuration and mud parameters, the flow-out rate of the mud. Where the level sensor is acoustic, the system also includes a multiple of correction sensors for determining the temperature gradient in the return line and for investigating the presence of gas in the return line, and for providing signals indicative thereof to the processor which is responsive thereto. A more complete system also includes calibration means for calibrating the flow-out rate with the flow-in rate, and means responsive to the calibration means for determining an undesirable condition such as a kick or fluid loss. Where the system is to be used on a rig which is subject to movement (e.g. a floating rig), angle and position sensors are also employed.

[0025] In accord with other objects of the invention, the level sensor is installed in a chimney which extends from the flow line and which is in close enough proximity to the bell nipple (e.g. less than 10 feet away) such that the mud level is high and the friction between the mud which is in supercritical flow and the flow line is kept small. Where the level sensor utilized is an ultrasonic pulse echo transceiver, the correction sensors include a plurality of temperature sensors at different height locations (e.g. near the mud, at the junction of the return line and a chimney in which the transceiver is mounted, and near the transceiver), to provide information regarding the temperature gradient in the return line, as well as a calibration target which acts to sense a change in sound velocity due to the presence of gas in the return line. Data from the temperature sensors and calibration target help provide a determination of the speed of sound in the air (or air/gas) above the mud such that the echo time measured by the ultrasonic transceiver can be properly correlated to a distance between the transceiver and the mud surface. By knowing the shape and size of the return line, the slope of the return line, the height of the fluid in the return line, and a mud parameter such as the viscosity/density ratio, an accurate flow-out determination can be made without the use of a direct velocity sensor. Where the slope of the return line is changing (as determined by the angle sensor) due to movement of the rig, the flow-out results can be corrected to compensate for the motion. The flow-out determinations are calibrated against the flow-in measurements which are made by detecting mud pump strokes (the positive displacement per pump stroke being known).

[0027] FIG. 1 is a schematic view of a drilling fluid or "mud" circulation system for a floating or fixed drilling rig where a flow measuring system embodying the invention may be used;

[0028] FIG. 2a is a cross-sectional view of a return line system of the invention illustrating the fitting of an ultrasonic sensor system into an opening in the return line and schematically illustrating connection of the sensor system to a computer and associated instrumentation;

[0035] FIGS. 7a and 7b are logs of the flow-in of mud-displacing cement into a well-bore as measured from a cement truck, and the volumetric flow-out therefrom as measured by the system of the invention, respectively.

[0036] The volumetric flow sensor system, generally designated S, and associated computer 14, embodying the invention are illustrated in Figs. 1-3. The flow measuring system includes an ultrasonic level sensor S, and a processing means or digital computer 14, as best illustrated in Fig. 2a.

[0037] Referring to Fig. 1, a floating or fixed drilling rig mud circulation system is schematically illustrated, and it will be appreciated that the invention may be used with a bottom supported offshore drilling rig or a land drilling rig, as well as with a floating rig. As discussed above, flow rate into the well may be derived by counting the strokes per minute of mud pumps 16 or by direct measurement with a flow meter. After the "mud" or drilling fluid travels down the drill string 18, it moves up the annulus 20 between the casing 22 and the drill string 18 to the bell nipple 24. A return line 26 communicates with the bell nipple 24, as best shown in Figs. 1 and 2a, to return the mud to the mud pits 28. The flow-out measuring sensor system S according to the invention is disposed in the return line 26 in relative close proximity to the bell nipple 24; preferably within ten feet thereof.

[0038] The sensor system S in cooperation with a computer 14, which by way of example only includes a disk memory 28, a RAM memory 30, a CPU 32, and a ROM memory 34 (see Fig. 2a), is provided to accurately measure in real time the flow Q through return line 26. The volumetric flow Q is simply the product of the cross-sectional area A of fluid flowing at a given location in the line and the average velocity of the fluid moving at that location. However, because a determination of velocity is not made with a velocity probe, as most velocity probes are either intrusive or cannot handle the wide range of mud rheology, cuttings, gas, etc., the determination is made in the following manner,

[0039] In a simple return line geometry such as that seen in Fig. 2a, the velocity of mud in the annulus 20 is typically between one-half and one ft/sec, whereas the velocity of the mud in the return line 26 is typically between five and ten ft/sec. The acceleration of the mud is due to gravity and the slope of the return line, with the slope being great enough (e.g. typically greater than .5 degrees) to overcome the retarding effects of friction between the fluid and the pipe wall. In fact, most return lines have a slope of between two and twenty degrees. Under these conditions, a "critical flow" is established in the bell nipple, with the mud having a depth Hc and velocity Vc as seen in Fig. 2b. As the flow accelerates down the return line, the mud is in supercritical flow, and the velocity increases and the mud depth decreases, as is seen in Fig. 2b. This condition continues until the friction loss increases enough to offset the gravitational forces causing the acceleration. However, most return lines are too short for this equilibrium to be reached.

[0040] The inventors have found that in a typical return line with mud in supercritical flow, an increase of flow typically translates into an increase in mud depth (level) according to a substantially linear relationship for flow rates above about two hundred gallons per minute (200 GPM). Put another way, and as seen in Fig. 4 which shows the relationship between flow rate, mud level, and velocity in a return line, mud velocity is almost constant above 200 GPM, and an increase in flow rate directly translates into an increase in mud depth. Thus, for any given return line configuration with typical flow rates, the measured height of the mud in the return line may be calibrated to a flow race with reasonable accuracy. By way of example, the measurements indicated in Figure 4, which relate level to flow, were made three feet from the bell nipple in a return line of twelve inch diameter and five degree slope, and a mud with a density of twelve PPG and viscosity of ten cp. For return lines of different diameter or slope, mud of a different viscosity/density ratio, and a measurement location of different distance from the bell nipple, the curves of Figure 4 would assume different values.

[0041] As stated above, a review of Fig. 4 indicates that the GPM flow-out can be determined directly from the mud level without a determination of velocity. Thus, for the stated return line geometry and mud properties, a measured mud depth (or level) of 2.4 inches is equivalent to a mud flow-out of 300 GPM, while a measured mud depth of 4.8 inches is equivalent to a mud flow-out of 900 GPM. With a slope of 2.4"/600 GPM, in order to achieve a desired accuracy of the order of 25 GPM, a measurement of mud depth must be accurate to at least 0.1 inch.

[0042] Given the fact that flow rate can be measured directly from mud level if the return line geometry and mud makeup are known, means and methods for making the level measurement must be set forth. One preferred means for accomplishing the mud level measurement is seen in Fig. 2a where a sensor system mounts on the return line 26 and sits in an eight inch diameter hole cut into the return line. Sensor system S includes a chimney section 40 of six inch diameter in which the mud level sensor is mounted, and an inflatable seal 41 which fits around the chimney and inside pipe flanges 43 welded to the cut in the return line 26. For mechanical stability and alignment purposes, a support 45 is provided around chimney 40. Turnbuckles 46 connect the support to clamp 48 which grips the return line 26. This permits alignment of the sensor system S relative to the return line such that the sonic beam produced by a transceiver 50 (as discussed below) is substantially normal to the mud. In this arrangement, sonic beam reflections can be received and sensed by the transceiver 50.

[0043] Sensor system S may be provided in any top entry opening in return line 26, although it is preferable that the system be employed within ten feet of the bell nipple. Sensor system S achieves access to the interior of return line 26 without the need for line 26 being disconnected from an existing rig hookup to bell nipple 24.

[0044] The sensor system S includes a mud depth or level sensor for measuring the distance between the sensor and the mud surface. The sensor preferably includes an ultrasonic transmitter-receiver ("transceiver") 50 which both transmits and detects ultrasonic waves. Because a transceiver cannot detect a wave immediately after it has transmitted one (i.e. the transceiver has "dead time"), the transceiver 50 is preferably mounted in a housing or chimney 40 which removes the transceiver from the mud surface and causes the return signal to be received after the dead time. Mounting the transceiver 50 in the chimney 40 also protects it from mud splashing. Even so, a water sprayer 79 which receives water from water source 58 is preferably provided to clean the transceiver 50 and the other sensors located in or about chimney 40.

[0045] To convert the echo return time into a distance requires knowledge of the velocity of sound in the medium through which the sound pulse travels, as distance is equal to the product of time and velocity. Parameters affecting the velocity of sound include the temperature and the composition of the medium through which the sound travels. As the composition and the temperature of the "air" above the mud in the return line can change over time, additional sensors are utilized to monitor these parameters. For temperature, preferably three sensors 29a, 29b, and 29c are utilized to measure the heat gradient present between the mud surface and the transceiver 50. Thus, the first sensor 29a is placed on adjustable pole 52 and located near the mud. A second sensor 29b is located at the junction of the return line 26 and the chimney 40, while the third sensor 29c is located close to the transceiver 50. The sensors used are preferably AD590 solid state devices available from Analog Devices which produce exactly 1 microamp per degree Kelvin and are accurate enough to be calibrated electrically.

[0046] A manner for compensating the determined echo time for temperature gradients and changes therein is found in U.S. Patent #4,754,641 and will not be further discussed herein. It should suffice to note that all temperature determinations are fed via signal conditioners 57 and A/D converter 59 to the computer or processor means 14 which utilizes the temperature and echo time information in providing a distance, and hence a return line mud height determination. It should also be noted that similar techniques can be used with fewer or greater numbers of temperature sensors to provide more or less accuracy, and it is not the intent hereof to be limited to exactly three temperature sensors.

[0047] In taking into account the composition of the medium through which the sound is travelling, it is not necessary to determine the actual composition. Rather, it is only necessary to have a reference from which relative changes can be calculated. In particular, the provision of a reference target 51 on adjustable pole 52 at a known distance from the transceiver 50 permits a determination of the time it takes for the ultrasonic waves to travel a fixed distance at the temperatures provided by the temperature sensors 29a and 29b in whatever medium is present (e.g. air, gas, or air/gas mixture). Thus, by first sensing the reference echo time from transceiver 50 to target 51 and back to transceiver 50, and then sensing the echo time from transceiver 50 to the mud surface and back to the transceiver 50, the reference echo time can be used in conjunction with the temperature information to determine the distance between the transceiver 50 and the mud surface in an extremely accurate manner.

where Vs is the sonic velocity, Ta, Tm, and Tt are respectively the absolute temperature, the mean temperature of the mud path and the mean temperature of the target path, K is the effect of the gas composition on the sonic velocity, Lm is the distance from the transceiver 50 to the mud surface in the return line, Lt is the distance from the transceiver to the target, and △Tm and △Tt are the mud echo and target echo times respectively.

which indicates that with the reference target, the distance to the mud surface is derived from measurable (△Tm, △Tt, Tm, Tt) or known (Lt) parameters and is not dependent on the composition effect K of the gas. It should be noted that Tm and Tt as provided represent the mean of the gradient over distances Lm and Lt respectively, and that more complex representations more specifically accounting for temperature gradients would suggest themselves to those skilled in the arts.

[0050] Although knowing the actual composition of the medium through which the sound pulses travel is not necessary in practicing the present invention, it has been found that the method and apparatus of the present invention can be used effectively to detect the presence of methane gas (CH₄) in the mud return line and to calculate an approximate volumetric fraction of methane. Specifically, since the speed of sound in "air" (nitrogen/oxygen mixture) is approximately 332 m/sec at 0°C while the speed of sound in methane is approximately 430 m/sec., a large change in the speed of sound measurement derived from the target signal may properly be interpreted to indicate the introduction of methane into the return line since methane is by far the most abundant gas encountered during a drilling operation.

[0053] In order to obtain both target and mud echo information, the target 51 should be located in the return line such that the echoes received from the target do not interfere with the echoes received from the mud surface. In return lines of different diameters, the location might need to be different to avoid the second echo of the target. The placement of the target 51 on the adjustable pole 52 permits such adjustment and ensures that the target can be located at a location of more than half the distance from the transceiver to the mud surface. Alternatively, if desired, the sensing of the target and mud echoes can be time multiplexed. Also, if desired, automatic adjustment of transceiver transmission frequency in order to obtain the largest echo signals available can be provided by having microprocessor 61 which controls sensor 50 conduct a search for the best frequency.

[0054] Once the distance between the transceiver 50 and the mud surface (and the distance between the transceiver and the pipe or sediment surface of an "empty" pipe which may be determined by using the sensor system or through a knowledge of the pipe diameter etc.) is determined by the computer 14, a direct determination of flow rate may be obtained from a look-up table representing the mud height to flow rate relationship for the particular return line and mud parameters. Such a look-up table is generated either by accumulating experimental data or according to the following theoretical analysis.

[0055] Flow rate (Q) may be defined as the mathematical product of fluid velocity (V) and the cross-sectional flow area of the mud (A); i.e. Q = VA. The cross-sectional flow area of the mud is simply a function of the mud level and the geometry of return line. Complicating factors such as the presence of sediment 87 (as seen in Fig. 3) may also be taken into account, such as discussed in U.S. Patent #4,754,641. The sediment level may be determined in the absence of flowing mud. It is assumed that the sediment is simply stationary material which is taking up some of the cross-sectional area of the return line. While the resulting geometry of the fluid flow is not a simple one, it is nevertheless within the knowledge of those skilled in the art to solve for the cross-sectional flow area.

[0056] A determination of average fluid velocity (V) is not as straight-forward as the determination of cross-sectional area, particularly because the determination is not a direct one (i.e. no velocity sensors are used). With a simple return line geometry and no friction, the velocity of the mud would be a direct result of the vertical fall of the liquid surface; the energy of which would be converted from potential to kinetic energy. In particular, such a system could be described according to the following relationships:

where Vc is the critical velocity, g is the acceleration due to gravity, Ac is the critical cross-sectional area of the mud in the return line close to the junction of the return line with the bell nipple (i.e. the critical area), and b is the surface width of the fluid. For a given mud flow rate Q and geometry which relates Ac and b, the critical velocity Vc, the critical area Ac, and the critical depth hc become known. As a result, tables can be generated which relate various flow rates Q and resulting values of Vc, Ac and hc.

[0058] While relationships (5) - (10) assume the absence of friction up to the critical point, it will be appreciated that friction does play a role in the velocity of the mud in the return line, and accounting for friction is necessary. The following conservation of energy equation makes such an account:

where f is a friction factor, H is the height of the fluid surface at the location of the level sensor, L is the distance from the bell nipple to the level sensor, Z is equal to the product of L and the sine of the slope angle ϑ of the return line,(i.e. Z = L sin ϑ) and D is the hydraulic diameter which is equal to 4A/wetted perimeter. The slope angle ϑ of the return line is either predetermined, or is measured with an angle sensor 12. Angle sensor 12 is preferably a pendulum sensor, with the pendulum acting to change the resistance of a potentiometer. The pendulum sensor 12 is particularly important with respect to rigs which are subject to movement as will be discussed hereinafter.

[0059] With the provided continuity (6) and critical flow (10) equations and with the provided energy equation (11), the velocity V at the location of the level sensor can be determined as long as the friction factor f can be found. The friction factor f can be determined according to the Reynold"s number Re pursuant to well known equations. The Reynold"s number, in turn, is dependent on the velocity, hydraulic diameter, density and viscosity of the flowing fluid according to Re = VDρ/µ. The density and viscosity are typically monitored on the job site and are available. Account, however, should be taken if the viscosity or density changes significantly over time. By keeping the location of the level sensor near the bell nipple, a crude estimate of friction is sufficient, as the inventors have determined that within approximately ten feet of the bell nipple, the friction losses of the returning fluid are small and that a crude estimate yields reasonable results. In fact, Re and f are considered to be constant and equal to their critical values throughout the length of the return line (although the critical values may change over time if the flow or mud parameters change). This is a reasonable approximation for as the velocity increases, the depth decreases, tending to keep Re constant. A typical friction loss of about twenty percent yields a velocity reduction of about ten percent, and an error of ten percent in analyzing the friction losses would result in a tolerable change of velocity of only one percent. Regardless of how the friction loss determination is originally estimated, calibration of flow-out corrects for any inaccuracies as is hereinafter described. In sum, then, equations (5) - (11) are solved at the outset of a job for the fixed values of the pipe size D, distance between the sensor system S and the bell nipple L, return line slope ϑ, mud viscosity µ, and mud density ρ, to establish the height (h) to flow (Q) look-up table appropriate for the job.

[0060] Turning to Figure 5, the method for determining the flow rate in the return line, which utilizes calibration is seen. At 100 the echo times for the reference target and for the mud surface are measured, along with the temperature gradient in the return line and chimney as measured by the temperature sensors. Also, as will be discussed hereinafter, the flow into the well is measured. In a preferred embodiment, the angle of the return line, and the density and viscosity of the mud are further measured. At 104, the echo times and temperature gradient are used to find the fluid flow height H. Also, at 104 the mud viscosity and density are used in conjunction with parameters stored at 200 such as the return line geometry (e.g. diameter), the horizontal distance from the bell nipple to the measurement location (L), the return line slope (ϑ), the gravitational constant (g), and any other relevant parameters which are constant for the given system, to provide a determination of the velocity of the mud in the return line at the measurement location in accord with equations (4) through (11) above. From the fluid flow height, the cross-sectional area of the mud in the return line at the measurement location is determined at 104. If available, additional information such as sediment level (box 107) may be provided to the processor which determines at 104 the cross-sectional area of the mud.

[0061] At 110, a determination of the flow-out (Q) of the mud from the wellbore is obtained from a transform (i.e. look-up table such as is represented by Fig. 4 for the provided return line and mud parameters) which relates the flow height to flow-out. Alternatively, the flow-out (Q) is found as the product of the determined cross-sectional area (A) of the mud and the mud velocity (V) at the measurement location. The flow-out (Q) determination at 110, however, is preferably viewed as a theoretical flow-out, such that through a calibration, an absolute flow-out determination (which is only absolute relative to the accuracy of the flow-in pump measurements) can be made. Thus, at start-up a single or multi-point calibration lasting only several minutes is preferably performed, and provides a calibration between the actual flow-out and the "estimated" theoretical flow out. The calibration accounts for non-linearity, errors in estimating friction, and other systematic errors which may be present such as changes in geometry, mud properties, sensor calibration, etc. Then, during drilling, when the theoretical flow-out determination is made at 110, the flow-out determination is corrected at 112 by the calibration constant calculated at start up.

[0062] The corrected flow-out determination is subjected to a trend analysis where the flow-out determination of 112 is compared at 118 continuously to the flow-in measurement measured by the positive displacement mud pump strokes at step 100 to determine whether there is any difference between the two. Where there is a difference, that difference is monitored at 119 over time to determine whether the difference is relatively constant over time. If the difference is relatively constant (i.e. steady or slowly changing) it is assumed that the flow-in or flow-out calibration has drifted and an average calibration coefficient (over a period of about an hour) is determined at 120 and fed back to the calibration correction step 112; i.e. autocalibration. If the difference between flow-out and flow-in (ΔQ) is not relatively constant, a determination is made at 122 as to whether the rate of change is greater than or equal to 10 GPM/Min over a four minute time scan. If the rate of change is less than 10GPM/Min (as seen in Fig. 6a) noise or measurement drift is assumed, and the situation is accommodated via autocalibration. If the rate of change is greater than 10 GPM/Min a warning is given, and if it lasts for four minutes, as seen in Fig. 6b, an alarm is sounded by gauge 62 (of Fig. 2) and an influx (kick) or an outflux (fluid loss) situation is declared at 125. Regardless, the flow-out, and delta flow determinations are preferably recorded at recorder 60 (of Fig. 2) in a log format over time.

[0063] If the rig is a "floater" as opposed to being bottom supported, the instantaneous flow rates vary with the heave of the vessel. For that reason, an average flow rate must be determined over a heave cycle for an accurate determination of flow-out. Accordingly, a heave position detector (not shown) which is standard equipment on floaters is used to find the heave cycle to which the rig is subjected, and the instantaneous flow-out rate determined at 110 (utilizing the appropriate look-up chart for the angle ϑ of the return line sensed by angle sensor 112) is averaged at 114 over that cycle. The average flow-out is then subjected to the trend analysis 118 where it is compared to the flow-in. The delta flow is then monitored at 119 to determine whether the delta flow is changing. If not, autocalibration is conducted at 120 in order to provide a calibration constant which can be used to correct the average flow-out determination of 114. Additional detail regarding averaging for floating rigs may be had with reference to U.S. Patent #4,754,641.

[0064] Testing the system and method inventions during a cementing operation where the flow-in was carefully measured independently by the cement truck pumps (not by the rig mud pumps), it was determined that the system and method inventions provide an excellent determination of flow-out. As seen in Figs. 7a and 7b, during a period of slightly over an hour, the measured flow-out (Fig. 7b) tracked the known flow-in (Fig. 7a) accurately. In fact, the total volume of cement and mud that was used during the hour as measured by the cement truck was two hundred seven barrels, while the measured (via integration) displaced out-flow was two hundred one barrels; a very acceptable difference of only three percent.

[0065] There have been described and illustrated herein systems and methods for measuring the volumetric flow of a fluid in a return line. While particular embodiments have been illustrated and described, it is not an intention that the invention be limited thereto, as it is intended that the invention be as broad in scope as the art will allow. For example, while a system was described as having three temperature sensors, and a reference target for "sensing" a change in medium above the mud, it will be appreciated by those skilled in the art that the sensors and reference target are employed for compensating the transceiver echo time for a changed speed of sound, and that other correction means could be utilized. Also, while the system was described as using an ultrasonic transceiver, equivalents of the same, including separate transmitters and receivers, could easily be utilized. In fact, if desired, the ultrasonic transceiver as well as the temperature sensors and reference target may all be replaced by an optic or radar system which could accurately sense the height of the mud in the return line. Further, while the sensor system is preferably located within ten feet of the bell nipple in order to minimize the effect of friction, it will be appreciated that it is still possible to locate the sensor system beyond that distance if account is taken of friction in accord with the technical discussion provided herein with reference to Reynold"s numbers etc., or if account is taken of friction through calibration. Therefore, it will be apparent to those skilled in the art that yet other changes and modifications may be made to the invention as described without departing from the scope and spirit of the invention as so claimed.

S2 Table:The stress and strain values of pump valve components under different seating velocity for the optimized spring stiffness and valve body quality. (DOCX)

The influence of spring stiffness and valve quality on the motion behaviors of reciprocating plunger pump discharge valves was investigated by fluid structure interaction (FSI) simulation and experimental analysis. The mathematical model of the discharge valve motion of a 2000-fracturing pump was developed and the discrete differential equations were solved according to FSI and results obtained by ANDINA software. Results indicate that spring stiffness influences the maximum lift, the opening resistance and shut-off lag angle, as well as the fluid velocity of the clearance, the impact stress and the volume efficiency of the pump valve in relation to the valve quality. An optimal spring stiffness parameter of 14.6 N/mm was obtained, and the volumetric efficiency of the pumping valve increased by 4‰ in comparison to results obtained with the original spring stiffness of 10.09N/mm. The experimental results indicated that the mathematical model and FSI method could provide an effective approach for the subsequent improvement of valve reliability, volumetric efficiency and lifespan.

Reciprocating pumps have been widely applied in the petrochemical, gas and general industry fields. Reciprocating pump operation is closely related to the efficiency and reliability of the suction and discharge valves. The valve is a key component of a reciprocating pump, which directly influences the performance and lifespan of the reciprocating pump. It has been proved that poor valve motion is the primary cause of valve failure and high flow resistance [1, 2]. Two factors greatly influence the valve motion and the subsequent fatigue and impact stress which acts upon the valve: valve quality and spring stiffness. The valve quality refers to the quality of the valve body testing by electronic balance. Therefore, a reasonably quality of pump valve and spring stiffness does not only extend the service life of a 2000-fracturing plunger pump, but also improves pump volumetric efficiency. Thus, the parameters optimization of valve quality and spring stiffness has a significant impact on the kinematics analysis of a reciprocating pump valve.

Many previous works have been conducted to investigate the valve dynamics of reciprocating pumps. Some studies have given greater focus to numerical simulations of valve motions. In 1968, U. Adolph determined the second order nonlinear differential equation of valve movement; however, this equation is only suitable to describe valve motion after the opening of the valve, rather than addressing the opening and closing processes of the valve [3–5]. The effects of the structure of the reciprocating compressor valve on established life and movement laws have been previously addressed by Xiao, who optimized valve structure from the spring and valve disc cone angle [6]. Movement of the valve when exposed to unsteady flow was studied by L. Boswirth, whose results indicate that a theoretical model alone cannot accurately describe the actual working condition because of fluctuations in gas pressure, mutation of the internal structural shape and changes in flow [7, 8]. Simulation analyses of valve motion indicate that springs and the Westphal phenomenon both influence the volumetric efficiency of the reciprocating pump. Moreover, a great spring stiffness can easily cause impact damage to the valve body and seat [9, 10]. Dynamic modeling of the flow process inside pressure regulating and shut-off valves was investigated by B.K. Saha, et al. using a computational fluid dynamic approach [11]. This method was able to predict spool movement and the final spool position when the spool position deviates from equilibrium; higher friction coefficients between the valve body and the spool were determined to be associated with quicker spool stability. Wang, et al. conducted an experimental investigation of valve impact velocity and the inclining motion of reciprocating compressors [12]. Results indicate that the inclining motion is negligible in the process of valve opening, while severe inclining motion was observed while the discharge valve was closing. When the pressure ratio exceeds 2.55, the inclining angle becomes uncertain due to the short time span encompassed by the discharge process. Furthermore, this experimental study provides a useful method for both valve testing and the optimization of valve reliability. Choi, et al. previously discussed the dynamic behavior of the valve system in a linear compressor based on fluid-structure interaction [13]. Numerical analysis indicated that the discharge valve opened when the piston compressed approximately 85% of the full stroke volume under the conditions of conical spring pre-load of 32N. As the pre-load was increased, the timing of the discharge valve opening was observed to be independent of the pre-load, though the discharge valve closure accelerated. An optimal pre-load of 48N was determined for the conical compression spring in order to achieve pump efficiency and reasonable impact stress. Wang and Liu have conducted some studies regarding the influence of spring stiffness on the performance of pump valves [14, 15], which indicate that spring stiffness has a significant influence on the motion characteristics of a reciprocating pump. A proper spring with optimized stiffness should be selected in order to achieve a balance between the pressure loss and leakage; previous literature indicates that a large spring stiffness results in increasing valve losses, whereas a small spring stiffness cannot efficiently seal the cylinder from the discharge chamber [16]. However, there is very little research which investigates the movement law of reciprocating plunger pump discharge valves from the perspective of optimized design of spring stiffness through FSI and experimental verification.

In this study, FSI and experimental analysis are conducted to study the motion law of discharge valves in order to improve the volume efficiency and stability of the reciprocating plunger pump through the optimized design of the spring stiffness and valve quality parameters.

The working principle of a plunger pump fluid end depends on a changing medium volume of sealed pump chambers achieved by the reciprocating movement of the plunger, thus realizing the suction and discharge operation of the pump valve. The valve itself consists primarily of spring, valve body, rubber sealing gasket and valve seat, as shown in Fig 1. This analysis primarily investigates the discharge valve motion of the plunger pump.

The structural diagram of the reciprocating pump discharge valve is depicted in Fig 2. According to fluid mechanics and the structure of the valve [17, 18], the continuous flow of valve clearance is given as follows:

Under discharge pressure conditions, the volumetric efficiency of plunger pumps is a volume ratio between the practical excretion liquid volume and the pump stroke volume in a discharge stroke.

Under the actual working conditions of the plunger pumper, the compressed of the liquid is relatively smaller and inevitable, and ignoring the seal leakage between the plunger and the cylinder. So the quantity of reflux, which is caused by the closure lag of the suction and discharge valve, is the main factors of the volume loss. Moreover, reducing the closing lag angle of suction and discharge valve can effectively improve the volumetric efficiency of pumps. Finally, the optimization design of the volumetric efficiency becomes the optimization of the lag angle.

When the hydraulic end of the fracturing pump operates under normal working conditions, a significant nonlinear response of valve motion may occur due to the combined effects of the high-speed impact of the flow field and the spring force, resulting in damage to the pump valve. FSI analysis of valve motion will determine the appropriate structure for optimized spring stiffness and valve quality. A model of the hydraulic end of the pump valve was developed by inputting valve motion as a nonlinear fluid-structure interaction system. Next, the structural and fluid models were established using computation solid and fluid dynamics. Meanwhile, the grid changes of the fluid-structure interaction interface were documented by the Arbitrary Lagrange-Euler (ALE) method, which is able to successfully simulate actual experimental conditions.

The structural field model of the discharge valve body was established by using ANDINA commercial software in conjunction with the fluid-structure interaction analysis; the interaction between the valve body and the fluid was achieved by selecting the FSI pattern for analysis. The valve body is represented by a simplified plane model, because the actual reciprocating pump valve body is discoid and conical in shape. The fluid field of valve motion is divided into three zones, which is convenient for the meshing and coupling analysis of the fluid-solid interface (Fig 4). According to the literature [19], in order to reduce the level of complexity of the solution of a 3D problem in axisymmetric structure, it can translate the 3D problem to a 2D problem by setting correction factors. The plunger chamber, valve body, and discharge chamber are all symmetric geometric cylinders, allowing the fluid-structure interaction model to be simplified into a 2D plane model.

According to the working principles of the hydraulic end of the plunger pump, the plunger displacement is a sinusoidal function which varies with time; therefore the entire displacement of the moving wall is a sinusoidal function which varies with time, and is defined by time function 2, depicted in Fig 6(B). During the operation of the reciprocating pump, a pressure of 40 MPa is always present in the discharge line; therefore, the outlet of the fluid field represents the pressure boundary condition of 40 MPa, which is defined by time function 1. In addition, the other boundary conditions of the fluid field was defined as a no-slip wall boundary. The relationship between fluid flow, velocity, sectional area and pressure difference can be expressed as follow:

Where Q is flow; μ is flow coefficient; A is cross sectional area; ∆P is the pre and post pressure difference of the pump valve; ρ is the fluid density.

Under the promotion of the plunger, the internal pressure of the liquid in the pump chamber gradually increases, and then the liquid discharges when the discharge valve opens. The variable displacement of flow field at the inlet results in the changes of the pre-and post pressure difference of the pump valve. And other parameters of Eq 9 are constant, so the discharge flows of a plunger pump continuous change.

Fig 8 presents a flowchart of the finite element simulation procedure for the ANDINA iterative solution to the valve motion analysis, as described in Eq (6). First, the structure and flow model determined by the valve body dynamic analysis were established under the FSI pattern in the ANDINA software. Next, the boundary conditions were defined by the actual operating conditions of the pump valve. Then, the initial 2D mesh was introduced into the fluid and structure field domain, as shown in Fig 7. Mesh size of the valve clearance fluid field has great influence over the motion of the valve body, while the number of grid cells depends upon the valve body lift. The ALE method was employed for dynamic analysis of the mesh [20, 21]. According to this method, grid points in the fluid were continuously updating depending on the movement of the free fluid surface and the fluid-solid interface. “C” calculates the valve body displacement after calculating the various forces acting on the valve. During the calculation, the function dynamically interacts with the ANDINA FSI solver before communicating the current valve position to the solver. The mesh of the geometry needed to modify during operation of the reciprocating plunger movement was then automatically generated in the ANDINA FSI, and the flow is again analyzed for the new geometry. This cycle of calculation continues until the valve body comes to a full stop.

A 3DS-7/12.5 triplex plunger pump was employed for experiment (S1 Fig). It was driven by power plant (including a variable frequency motor and torque speed sensors, etc.) in order to pump the water medium into the piping system (S2 Fig), which would then flow back to the water tank, thus forming a closed system. The plunger displacement sensor is installed in the power end of the plunger and the discharge valve displacement sensor is installed in the valve body of the discharge valve (S3 Fig). In this process, data from various sensors was automatically collected via a data acquisition card (Altai Beijing science and Technology Co., Ltd.USB2821) (S4 Fig); data was then saved and displayed in the computer (S5 Fig), which was shown in Fig 9.

1) Torque speed sensor; 2) angular displacement sensor; 3) inhalation flow sensor; 4) temperature sensor; 5) pressure sensor; 6) displacement sensor; 7) vibration sensor; 8) discharge pressure sensor; 9) discharge flow sensor; 10) temperature sensor.

The used experimental devices mainly consisted of three parts: machinery equipment, electrical equipment and a data acquisition system. The machinery equipment was composed of a 3DS-7/12.5triplex plunger pump, a Y250M-6 motor with a frequency converter, a fluid reservoir, as well as discharge and suction piping lines and valves. The electrical equipment comprises a torque and speed sensor, split differential voltage linear displacement sensor (made in Shenzhen Si Ming Wei Testing Equipment Co., Ltd.), a pump body vibration sensor, a flow sensor (made in Tianjin Si Mite Precision Instrument Co., Ltd.), and a switch control cabinet. The data acquisition system included a data acquisition card (made at Beijing Altai Science and Technology Development Co., Ltd.), as well as transmission cables and a computer.

Fig 10 depicts the data acquisition system diagram. All signals collected by sensors were inputted to the data acquisition card, and the motor speed was adjusted by a system control signal. Calibration of sensors (S1 Table) and collection frequency were determined before data collection. According to the highest frequency of pump valve motion, the collection frequency should meet the accuracy of the valve displacement (900Hz).during the discharge valve motion cycle, requiring more than 100 collected data points (S1 Text).

Flow field analysis of valve motion does not only obtain the erosion position and eddy current situation, but also has the potential to improve the hydraulic end structure of the reciprocating pump. The clearance between the valve and the valve seat changes with time, therefore, the liquid velocity analysis for valve clearance significantly impacts structural and kinematics optimization (S1 Movie). Greater sprint stiffness correlates to smaller flow areas of valve clearance. According to the law of continuous flow mass conservation, the velocity of the fluid which flows through the valve clearance is larger under identical plunger speed conditions, as shown in Fig 13(A). Higher fluid velocities tend not only to form vortices, which result in energy loss, but often the flow speed is so great as to induce gasket seal leakage and the deformation of erosion rubber; the rubber damage is particularly significant when the fluid medium is intermixed with hard particles. This is also consistent with more than 80% of observed valve failures caused by rubber erosion in oil fields. As shown in Fig 13(B), variations in valve quality have particular impact upon valve motion; however, the effect is small in comparison to the effects induced by the spring stiffness parameter.

Valve quality has little effect on the shut-off lag angle, due to the smaller effect of gravity when compared to the spring force. However, increasing valve quality correlates to greater opening resistances, as shown in Fig 14. Therefore, there is an optimal parameter value of valve quality in order to obtain better valve motion performance. The optimized valve quality is 2.3Kg, which produces a volume efficiency increase of 0.04d when compared to the original valve quality. Therefore, the impact of pump valve quality on volume efficiency may be negligible, but valve quality is closely related to the stable operation of the pump valve.

The optimized spring stiffness was obtained by investigating the influence of various stiffness values on shut-off lag angle and the opening resistance of the valve, as shown in Fig 15. As the spring stiffness increases, the opening resistance gradually increases and the shut-off lag angle is gradually reduced. Therefore, the intersection between the two variables provides the optimal spring stiffness for a 2000-fracturing pump valve: 14.6N/mm. The volume efficiency of the pump valve increased by 4‰, as compared to the volume efficiency achieved with the original spring stiffness of 10.09N/mm.

Dynamics analysis of the discharge valve motion demonstrated that impact contact occurred during the reciprocating movement between the valve body and the valve seat, and that impact contact was the primary cause of damage to the valve assembly. Therefore, contact analysis of valve assembly was conducted for various pump valve spring stiffness values. Valve assemblies include the valve body, a sealing gasket and the valve seat; the material of the valve body and seat is 20CrMnTi, while the sealing gasket is made of polyurethane rubber. The boundary conditions and constrains of valve impact contact analysis are shown in Fig 5(B). According to the actual operating conditions of the hydraulic end of the plunger pump, the seating velocity of the valve body with various spring stiffness values is 1m/s, 0.6m/s,0.5m/s and 0.4m/s. The maximum stress-strain curve of different pump valve seating velocities is shown in Fig 16, based on ABQUS finite element analysis (S6 Fig). Results indicate that the impact contact stress and strain of the valve body and valve seat increase with an increase in seating velocity; however, the increased amplitude is small, and far less significant that the yield stress of the material. Therefore, variation in the pump valve seating velocity has relatively small influence on the service life of the valve assembly. However, the fluid-solid interaction and impact contact analysis of the hydraulic end of the pump demonstrate that greater spring stiffness of the valve produces higher liquid velocities of valve clearance, and subsequently greater impact contact stress and strain of the valve assembly. Finally, the excessive liquid velocity of the valve clearance caused erosion and washout damage to the sealing gasket.

The reciprocating plunger pump is mainly used in the fracturing process in oil exploration. Therefore, the volumetric efficiency of the pump valve is closely related to the working performance of the fracturing pump. Moreover, the opening lag angle of the discharge valve increased with the increase of the opening resistance, which influenced the instantaneous erosion rate of the valve clearance fluid, accelerating the erosion failure of the valve components. And the shut-off lag angle was the main parameter, which influenced the volume efficiency of the pump valve (Eq 8). Figs ​Figs1414 and ​and1515 are the curves that the opening resistance and shut-off lag angle varies with different spring stiffness and valve body quality. It indicated that the two variables intersections of the pump valve opening resistance and shut-off lag angle are the optimized spring stiffness and valve body quality values. And further, the maximum stress and strain values of valve components (as shown in Fig 16) are in the range of the allowable safety when the maximum seating velocity of the valve body is 1m/s for the optimized spring stiffness and valve body parameters (S2 Table). Therefore, the optimization design can’t result in the impact and fatigue failure of valve components.

Under the conditions of the same valve quality and motor speed, when the spring stiffness of the pump valve is greater, the opening time of the pump valve is relatively delayed while the closing time is relatively early; additionally, the valve opening resistance increases, while the closing lag time decreases. Moreover, larger spring stiffness results in smaller valve lifts. At a fixed spring stiffness and motor speed, results indicate that lower valve quality results in large valve lifts, but little effect on opening and closing lag times, as shown in Fig 17. By comparing the experimental results of valve motion with the computer simulation results, the mathematical model and simulation calculation methods have been verified.

Theoretical exploration and physical experiments were conducted to investigate the effect spring stiffness and valve quality on the opening resistance, shut-off lag angle and fluid velocity of valve clearance of valve motion for a 2000-fracturing pump under operating conditions. The kinematic behaviors of valve motion for a 2000-fracturing pump were compared and analyzed with regard to spring stiffness and valve quality on the discharge side of the pump. The following conclusions were drawn based on the obtained theoretical and experimental results:A mathematical model was successfully established to describe the discharge valve motion of a 2000-fracturing pump; discrete solutions to differential equations were achieved via FSI simulation of ANDINA software.

FSI simulation results indicated that spring stiffness and valve quality have significant impacts on the nonlinear motion of the valve body of a 2000-fracturing pump. In comparison to the valve quality, spring stiffness demonstrated a greater impact on maximum lift, opening resistance, shut-off lag angle, the fluid velocity of clearance and the volume efficiency of the pump valve. The optimized spring stiffness was identified as 14.6N/mm; the volumetric efficiency of the pumping valve increased by 4‰ compared to results obtained with the original spring stiffness of 10.09N/mm.

Pump valve seating velocity has a relatively small impact on the service life of the valve assembly for various spring stiffnesses. However, greater spring stiffness results in greater flow velocity of valve clearance, which has obvious influence on erosion of the pump valve.

The experimental results indicated that the mathematical model and FSI simulation results correctly interpreted the effects of spring stiffness and valve quality on the valve lift and closing lag time of the 2000-fracturing pump.

S2 TableThe stress and strain values of pump valve components under different seating velocity for the optimized spring stiffness and valve body quality.

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15. Liu YH, Lei JQ, Shi JQ. The effects of spring stiffness on the performances of oil fracturing pump. Journal of Oil and Gas Technology. 2010; 32(2): 385–87.

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