calculate mud pump efficiency made in china

Rig pump output, normally in volume per stroke, of mud pumps on the rig is  one of important figures that we really need to know because we will use pump out put figures to calculate many parameters such as bottom up strokes,  wash out depth, tracking drilling fluid, etc. In this post, you will learn how to calculate pump out put for triplex pump and duplex pump in bothOilfield and Metric Unit.

A properly serviced pulsation dampener is critical for your mud pumps’ efficiency, safety, and performance. Unfortunately, there aren’t many resources available to educate personnel on executing safe and effective servicing procedures. Please review the following steps with your personnel for safe pulsation dampener maintenance.

Find W series mud pump from pressure grouting pump manufacturer - Saigao gruop in China. The W series mud pump can be widely used in all kinds of works in oil field, which is su...

Find W series mud pump from pressure grouting pump manufacturer - Saigao gruop in China. The W series mud pump can be widely used in all kinds of works in oil field, which is su...

[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;

[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.

[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.

[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:

[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.

[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.

As the viscosity of oil continues to increase and wellbore conditions continue to become more complicated, the lifespan and pump efficiencies of electric submersible pumps and screw pumps commonly used in oilfields have declined, affecting the normal operation of equipment, and the economic benefits have deteriorated year by year. At present, the most commonly used pumps in the exploitation of heavy oil are submersible electric pumps. However, the efficiencies of electric submersible pumps with semi-open impellers are lower than 30% when transporting liquids with viscosities greater than 50 cp, and pump leakage is significant [1,2]. The labyrinth screw pump (or labyrinth pump) is a non-contact power pump and a new type of screw pump with a small flow, high head, and low specific speed. It is suitable for the transport of high-viscosity, high-gas-content, and particle-containing media.

Many scholars have been committed to studying pump theory based on the labyrinth spiral seal mechanism. The earliest scientist who developed the labyrinth screw pump was a Soviet scientist. The purpose of the research and development at that time was to solve the problem of conveying viscous media containing particles. In the labyrinth spiral seal, Golubiev [3] found that the structure of opening a single or multiple threads on the surface of the ring seal could increase the pressure of the sealing liquid in the thread grooves, thereby achieving the purpose of preventing liquid leakage. Bilgen [4] and Karow [5] used laminar and turbulent flow models to numerically analyze the spiral structure of the labyrinth and obtained the flow characteristics in the spiral cavity of the labyrinth under different conditions. Zhu [6] used the laminar flow model to analyze the flow in the labyrinth spiral and obtained the plane flow solution and the spatial flow solution of the oblique section in the honeycomb body. In addition, some researchers have also conducted theoretical analysis and experimental research on the labyrinth seal structure [7,8,9]. These analysis results all showed that the labyrinth spiral structure can produce a greater pumping pressure at high speeds. In terms of the pumping mechanism, Golubiev [10] believed that the pumping pressure of the labyrinth screw pump was caused by the strong turbulent friction of the fluid between the rotor and the stator acting on the threaded wall. Bilgen and Akgungo [4] regarded the fluid flow in the pump as the superposition of the drag flow of the rotor thread on the fluid and the pressure flow under the pressure difference between the two ends of the pump. In terms of structural design, many researchers used computational fluid dynamics (CFD) to numerically simulate trapezoidal, triangular, and rectangular labyrinth pumps, respectively, and analyzed the influence of the thread design parameters on the pumping capacity [11,12,13]. Ma [14] calculated and compared the performances of labyrinth pumps with different thread shapes and found that the rectangular labyrinth screw pump is more suitable for transporting highly viscous media and for multiphase flows.

In the transportation of viscous media, the performance of the labyrinth screw pump is positively correlated to the viscosity of the media, and thus, it can be used in the petrochemical, pharmaceutical, metallurgical, and electric power industries. However, the efficiencies of the currently known labyrinth pumps are very low, which has limited their development. Some scholars have studied the advantages of labyrinth pumps in conveying air-containing, high-viscosity, and other media, but there have been few studies on the structural optimization of labyrinth screw pumps [15,16].

The optimization of a pump structure often depends on data samples collected through experimental design methods and uses various methods, such as Kriging or artificial neural network models, to construct the approximate functional relationship between the optimization parameters and the optimization objective. OPTIMUS, Tosca, and other platforms are used to estimate the functional relationships between the input parameters and output parameters through optimization models and algorithms, and the optimal control parameter combination can be obtained. However, in the process of hydraulic optimization, the optimization is still carried out with the help of design experience, and the optimization results are often not ideal. In contrast to the above optimization models, the essence of the response surface methodology is to replace the model with data. The response surface approach can estimate the variations of the entire design space based on the sample points obtained by the experimental design and graphically express the functional relationship between the input and output. The response surface provides estimated values for the output parameters, and the output function value can be obtained only through the response surface, without the need to perform operations on the original model. Therefore, using the response surface model to optimize the structure of the pump can reduce the calculation time considerably.

Zhang [17] selected a fluoroplastic two-phase-flow centrifugal pump as the research object, adopted the response surface optimization model, and optimized the structure of the pump with the main geometric parameters of the impeller as the optimization parameters to improve the efficiency of the pump and reduce the wear rate. Gao [18] determined the optimization parameters according to the degree of influence of the structural parameters on the objective function and selected the efficiency, shaft power, and head of the pump as the optimization objectives. A response surface optimization model between the structural parameters and the objective function was constructed, and the interactions between the structural parameters were examined.

The structure of the labyrinth screw pump is extremely complex, and the rotor and stator have different structural parameters. Furthermore, the fluid domain involves the handling of dynamic and static interfaces. As a result, the relationship between the objective function and the optimization parameters is difficult to express explicitly, and some optimization parameters are not continuous (the number of stator and rotor screw threads should be rounded according to actual engineering needs). Therefore, the traditional gradient optimization method is not suitable for this study. In response to these problems, we used response surface optimization technology to optimize the structure of the labyrinth pump. Selecting the fluid area of the main part of the rectangular labyrinth screw pump as the research object, the goal was to improve the efficiency and head of the pump and find the best combination of structural parameters.

Section 2 introduces the geometry and operation parameters of the labyrinth screw pump. Section 3 of this article presents the setup and experimental verification of the numerical simulation method. Section 4 describes the process of structural optimization. Section 5 discusses the influence of the internal flow and the oil viscosity on the performance of the labyrinth pump and analyzes the optimization results of the labyrinth pump. This article applies the neural network response surface optimization model to the labyrinth pump, which provides a certain theoretical reference for the design of the labyrinth pump.

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The mud pump piston is a key part for providing mud circulation, but its sealing performance often fails under complex working conditions, which shorten its service life. Inspired by the ring segment structure of earthworms, the bionic striped structure on surfaces of the mud pump piston (BW-160) was designed and machined, and the sealing performances of the bionic striped piston and the standard piston were tested on a sealing performance testing bench. It was found the bionic striped structure efficiently enhanced the sealing performance of the mud pump piston, while the stripe depth and the angle between the stripes and lateral of the piston both significantly affected the sealing performance. The structure with a stripe depth of 2 mm and angle of 90° showed the best sealing performance, which was 90.79% higher than the standard piston. The sealing mechanism showed the striped structure increased the breadth and area of contact sealing between the piston and the cylinder liner. Meanwhile, the striped structure significantly intercepted the early leaked liquid and led to the refluxing rotation of the leaked liquid at the striped structure, reducing the leakage rate.

Mud pumps are key facilities to compress low-pressure mud into high-pressure mud and are widely used in industrial manufacture, geological exploration, and energy power owing to their generality [1–4]. Mud pumps are the most important power machinery of the hydraulic pond-digging set during reclamation [5] and are major facilities to transport dense mud during river dredging [6]. During oil drilling, mud pumps are the core of the drilling liquid circulation system and the drilling facilities, as they transport the drilling wash fluids (e.g., mud and water) downhole to wash the drills and discharge the drilling liquids [7–9]. The key part of a mud pump that ensures mud circulation is the piston [10, 11]. However, the sealing of the piston will fail very easily under complex and harsh working conditions, and consequently, the abrasive mud easily enters the kinematic pair of the cylinder liner, abrading the piston surfaces and reducing its service life and drilling efficiency. Thus, it is necessary to improve the contact sealing performance of the mud pump piston.

As reported, nonsmooth surface structures can improve the mechanical sealing performance, while structures with radial labyrinth-like or honeycomb-like surfaces can effectively enhance the performance of gap sealing [12–14]. The use of nonsmooth structures into the cylinder liner friction pair of the engine piston can effectively prolong the service life and improve work efficiency of the cylinder liner [15–17]. The application of nonsmooth grooved structures into the plunger can improve the performance of the sealing parts [18, 19]. The nonsmooth structures and sizes considerably affect the sealing performance [20]. Machining a groove-shaped multilevel structure on the magnetic pole would intercept the magnetic fluid step-by-step and slow down the passing velocity, thus generating the sealing effect [21–23]. Sealed structures with two levels or above have also been confirmed to protect the sealing parts from hard damage [24]. The sealing performance of the high-pressure centrifugal pump can be improved by adding groove structures onto the joint mouth circumference [25]. The convex, pitted, and grooved structures of dung beetles, lizards, and shells are responsible for the high wear-resistance, resistance reduction, and sealing performance [26–28]. Earthworms are endowed by wavy nonsmooth surface structures with high resistance reduction and wear-resistance ability [29]. The movement of earthworms in the living environment is very similar to the working mode of the mud pump piston. The groove-shaped bionic piston was designed, and the effects of groove breadth and groove spacing on the endurance and wear-resistance of the piston were investigated [30]. Thus, in this study, based on the nonsmooth surface of earthworms, we designed and processed a nonsmooth striped structure on the surface of the mud pump piston and tested the sealing performance and mechanism. This study offers a novel method for prolonging the service life of the mud pump piston from the perspective of piston sealing performance.

The BW-160 mud pump with long-range flow and pressure, small volume, low weight, and long-service life was used here. The dimensions and parameters of its piston are shown in Figure 1.

A mud pump piston sealing performance test bench was designed and built (Figure 3). This bench mainly consisted of a compaction part and a dynamic detection part. The compaction part was mainly functioned to exert pressure, which was recorded by a pressure gauge, to the piston sealed cavity. This part was designed based on a vertical compaction method: after the tested piston and the sealing liquid were installed, the compaction piston was pushed to the cavity by revolving the handle. Moreover, the dynamic detection part monitored the real-time sealing situation and was designed based on the pressure difference method for quantifying the sealing performance. This part was compacted in advance to the initial pressure P0 (0.1 MPa). After compaction, the driving motor was opened, and the tested piston was pushed to drive the testing mud to reciprocate slowly. After 1 hour of running, the pressure P on the gauge was read, and the pressure difference was calculated as , which was used to measure the sealing performance of the piston.

To more actually simulate the working conditions of the mud pump, we prepared a mud mixture of water, bentonite (in accordance with API Spec 13A: viscometer dial reading at 600 r/min ≥ 30, yield point/plastic viscosity radio ≤ 3, filtrate volume ≤ 15.0 ml, and residue of diameter greater than 75 μm (mass fraction) ≤ 4.0%), and quartz sand (diameter 0.3–0.5 mm) under complete stirring, and its density was 1.306 g/cm³ and contained 2.13% sand.

The test index was the percentage of sealing performance improvement β calculated aswhere and are the pressure differences after the runs with the standard and the bionic pistons, respectively ().

Figure 4 shows the effects of stripe depth and angle on the sealing performance of mud pump pistons. Clearly, the stripe depth should be never too shallow or deep, while a larger angle would increase the sealing performance more (Figure 4).

The standard piston and the bionic piston were numerically simulated using the academic version of ANSYS® Workbench V17.0. Hexahedral mesh generation method was used to divide the grid, and the size of grids was set as 2.5 mm. The piston grid division is shown in Figure 8, and the grid nodes and elements are shown in Table 3. The piston cup was made of rubber, which was a hyperelastic material. A two-parameter Mooney–Rivlin model was selected, with C10 = 2.5 MPa, C01 = 0.625 MPa, D1 = 0.3 MPa−1, and density = 1120 kg/m3 [32, 33]. The loads and contact conditions related to the piston of the mud pump were set. The surface pressure of the piston cup was set as 1.5 MPa, and the displacement of the piston along the axial direction was set as 30 mm. The two end faces of the cylinder liner were set as “fixed support,” and the piston and cylinder liner were under the frictional interfacial contact, with the friction coefficient of 0.2.

To better validate the sealing mechanism of the bionic striped pistons, a piston’s performance testing platform was independently built and the sealed contact of the pistons was observed. A transparent toughened glass cylinder liner was designed and machined. The inner diameter and the assembly dimensions of the cylinder liner were set according to the standard BW-160 mud pump cylinder liners. The sealing contact surfaces of the pistons were observed and recorded using a video recorder camera.

Figure 14 shows the surface contact of the standard piston and the bionic piston. Clearly, in the contact areas between the standard piston and the cylinder liner, only the narrow zone at the lip mouth contacted, as the contact width was only 4.06 mm. On the contrary, the contact areas between the bionic piston and the cylinder liner were all very wide, as the contact width was about 18.36 mm, and the sealed area was largely enlarged (892.8 mm2 vs. 4037.6 mm2) according to the contact areas calculated, which were favorable for improving the sealing performance.

(1)The bionic striped structure significantly enhanced the sealing performance of the mud pump pistons. The stripe depth and the angle between the stripes and the piston were two important factors affecting the sealing performance of the BW-160 mud pump pistons. The sealing performance was enhanced the most when the stripe depth was 2 mm and the angle was 90°.(2)The bionic striped structure can effectively enhance the contact pressure at the piston lips, enlarge the mutual extrusion between the piston and the cylinder liner, reduce the damage to the piston and cylinder liner caused by the repeated movement of sands, and alleviate the abrasion of abrasive grains between the piston and the cylinder liner, thereby largely improving the sealing performance.(3)The bionic striped structure significantly intercepted the leaked liquid, reduced the leakage rate of pistons, and effectively stored the leaked liquid, thereby reducing leakage and improving the sealing performance.(4)The bionic striped structure led to deformation of the piston, enlarged the width and area of the sealed contact, the stored lubricating oils, and formed uniform oil films after repeated movement, which improved the lubrication conditions and the sealing performance.

The bionic striped structure can improve the sealing performance and prolong the service life of pistons. We would study the pump resistance in order to investigate whether the bionic striped structure could decrease the wear of the piston surface.

When two (or more) pumps are arranged in serial their resulting pump performance curve is obtained by adding theirheads at the same flow rate as indicated in the figure below.

Centrifugal pumps in series are used to overcome larger system head loss than one pump can handle alone. for two identical pumps in series the head will be twice the head of a single pump at the same flow rate - as indicated with point 2.

With a constant flowrate the combined head moves from 1 to 2 - BUTin practice the combined head and flow rate moves along the system curve to point 3. point 3 is where the system operates with both pumps running

When two or more pumps are arranged in parallel their resulting performance curve is obtained by adding the pumps flow rates at the same head as indicated in the figure below.

Centrifugal pumps in parallel are used to overcome larger volume flows than one pump can handle alone. for two identical pumps in parallel and the head kept constant - the flow rate doubles compared to a single pump as indicated with point 2

Note! In practice the combined head and volume flow moves along the system curve as indicated from 1 to 3. point 3 is where the system operates with both pumps running

In practice, if one of the pumps in parallel or series stops, the operation point moves along the system resistance curve from point 3 to point 1 - the head and flow rate are decreased.