how to measure mud pump efficiency quotation

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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.

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Mud pump liner selection in today"s drilling operations seldom (at best) considers electrical implications. Perhaps, with more available useful information about the relationships between mud pump liner size and operational effects on the electrical system, certain potential problems can be avoided. The intent of this paper is to develop those relationships and show how they affect an electrical system on example SCR rigs.Introduction

There, seems to be little consideration for the relationships between liner size and demand on a rig"s engine/generator set(s). Yet, consideration for this relationship can prove to be very helpful to drillers and operators in efficiency of a rig"s electrical system. In order to develop the relationships and help drillers and operators understand the importance of each, relationships between liner size, pump speed, pump pressure, and electrical power will be developed. Only basic physical laws will be used to develop the relationships; and, once developed, the relationships are readily applied to realistic examples utilizing a mud pump manufacturer"s pump data. Finally, conclusions will be drawn from the examples.DEVELOPMENT OF RELATIONSHIPS BASIC RELATIONSHIPS

where HHP= Hydraulic horsepower, GPM = Mud pump volumetric flow rate in gallons per minute, and PST Mud pump output pressure in pounds peer square inch.

Hydraulic horsepower is reflected to the mud pump motor via a multiplier for mechanical efficiency. it follows that motor horsepower is then represented by

The Hex Pump is an axial piston mud pump with six vertical pistons driven by two AC motors via a gear and a specially profiled cam. In contrast to crankshaft-driven triplex pumps, the Hex pump delivers a nearly pulsation free flow. Consequently, there is no need for pulsation dampeners on either the suction or discharge side when running this pump. Other major advantages are compactness (reduced weight and footprint) and no need for replacing liner sizes to achieve high pressure or flow. The Hex 240 version with 4 1/2" liners has a rated capacity of 2540 HP, a maximum rated pressure of 7500 PSI and a maximum flow capacity of 1034 GPM.

The Hex Pump has substantially less weight than a comparable Triplex pump, and this results in increased variable deck load capacity on drilling units. The potential cost savings related to increased variable deck load capacity both on new builds and on existing rigs will be discussed in this paper. Also, the potential steel weight reduction in the substructure on drilling units will be discussed.

The Hex Pump creates a clean standpipe pressure with much lower pressure fluctuation levels than triplex pumps. Due to this, there are no need for pulsation dampeners when running the Hex Pump. This additionally leads to much better and cleaner MWD-signals for the directional driller. As a consequence, this will contribute to faster and more accurate drilling in long and complicated directional wells.

The design and development of the Hex Pump is described in SPE paper 79831, ref /1/; "Development and Performance Testing of the Hex Mud Pump", but for the understanding of this paper it is important to understand the functionality of the Hex Pump design. Some of the main items are therefore repeated in this paper. SPE paper 92507, ref. /2/, "Operational experience with use of a Hex Pump on a land rig" focuses on the improved MWD-measurements related to use of Hex Pump compared to triplex pumps. Some of the main items discussed there will also be repeated in this paper.

Electronic Pump Stroke Counters are a vital part to any drilling rig operation. When a mud pump is in operation, the driller must know how much mud is flowing down hole in order to keep the operation running at peak efficiency. Pump stroke counters assist the driller by measuring the mud pump’s strokes per minute and total strokes. So, how does a pump stroke counter tally the mud pump’s strokes

Electronic Pump Stroke Counters are a vital part to any drilling rig operation. When a mud pump is in operation, the driller must know how much mud is flowing down hole in order to keep the operation running at peak efficiency. Pump stroke counters assist the driller by measuring the mud pump’s strokes per minute and total strokes. So, how does a pump stroke counter tally the mud pump’s strokes, and why it is important? In order to understand that, you’ll need to know some basic information about mud pumps.

Knowing how a mud pump functions is important in understanding the role a pump stroke counter plays in rig operations. Mud pumps act as the heart of the drilling rig, similar to how our heart works. Just as our heart circulates blood throughout our bodies, a mud pump circulates essential drilling mud down the hole and back up to the surface. Mud tanks house drilling mud, and a mud pump draws the fluid from the mud pump. A piston draws mud in on the backstroke through the open intake valve and pushes mud through the discharge valve and sends it towards the rig. By circulating fluid, the mud pump ensures that the drill bit is cool and lubricated and that cuttings are flushed from the hole. The two main kinds of pumps used are duplex and triplex pumps, where the duplex pump has two pistons and the triplex pump has three. Whether the rig is using a duplex or triplex pump, it is important to know how many strokes per second the pistons are moving. The driller monitors strokes per minute to determine how much costly, yet essential, mud is being pumped into the system with the use of a mud pump stroke counter system. Now, that you know about mud pumps, you’ll need to know what’s in a stroke counter system.

Stroke Counter — The stroke counter stainless steel box is mounted on the driller’s console and is either square or rectangular in shape, depending on the number of pumps it is monitoring. Stroke counters will show strokes per minute and total strokes, and when a particular mud pump is operating the strokes/minute and total strokes will be displayed. Power is supplied by a 3.6 volt lithium battery, and the counter contains a crystal-controlled real time clock with 100 parts per million accuracy or better. Each counter is mounted to the console with 1/4” stainless steel hex head bolts, lock washers and nuts.

Micro Limit Switch — The micro switch is connected to a c clamp near the mud pump piston. The micro switch stainless steel rod (sometimes called a whisker) sticks out in the piston housing near the piston. As the piston passes the rod, it moves the rod and the switch sends an electronic signal back to the counter. The counter increases by one each time the piston moves the rod, counting the mud pump’s strokes. The switch’s signal is then transmitted to the stroke counter. These micro switches are built to stand up to demanding outdoor conditions. They can withstand shock, equipment vibration, extreme temperatures, water and dust.

Cable and Junction Box – A cable is connected to the back of the pump stroke counter and then to the junction box. From the junction box, the cables travel to the limit switches.

Pump Stroke Counters are like a blood pressure machine. Each time our heart pumps, a blood pressure machine reads our systolic and diastolic blood pressure by way of our pulse. A mud pump stroke counter functions in much the same way. Just as a blood pressure machine detects our pulse so too does a limit switch rod detect the movement of the piston. When the stainless steel rod is moved, the micro limit switch detects the movement. The signal is sensed as a contact closure, and it is transmitted to the stroke counter where the contact closure is converted to a logic pulse. The pulse feeds two separate circuits. The total strokes circuit reads and displays the closures one at a time, totaling them up to reveal the total strokes in the LED window. The second pulse is sent along a separate circuit which is a rate circuit. This rate circuit will average the closures against the real time clock. The result is displayed as the total strokes per minute.

Pump stroke counters are essential to drilling rig operations because they measure the efficiency of mud pumps. Knowing strokes per minute and total strokes of the pistons helps the driller to determine if the correct amount of mud is going down hole. Having this information aids in running a drilling rig at peak efficiency, assists in extending drill bit life, and avoids costly overuse of drilling rig mud. Unsure which pump stroke counter is right for your application? Give our friendly, knowledgeable staff a call or email. We’ll keep you turning right.

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The fluid end of a duplex or triplex pump offers hundreds of opportunities for error. The results of an error in such a high-pressure system can mean (1) expensive downtime on the pump and maybe the entire rig, (2) expensive repair-replacement, and (3) possible injury or death of a crewman or a company man. Under the laws of nature, pump pistons and liners will wear, and there will be some corrosion and metallurgical imperfections, but the majority of pump failures are manmade. Theoretically, thorough training and retraining should avoid most mud pump problems. Realistically, a critical failure analysis during repair will be necessary to determine how to correct the failure. Telltale signs of trouble are distortion of piston rods, frayed piston polymer, discoloration, odor, hard-to-remove piston, rod cracks, pitting, total fracture, valve seat wear, and unsuitable external appearance.

GDEP is the original creator of the drilling pump and continues to set the standard for durable, high-quality drilling pumps that can withstand the world’s toughest drilling environments. Starting with our PZ7 and rounding out with the market"s most popular pump, the PZ1600, our PZ Series of pumps are the perfect choice for today"s high-pressure drilling applications.

The piston is one of the parts that most easily become worn out and experience failure in mud pumps for well drilling. By imitating the body surface morphology of the dung beetle, this paper proposed a new type (BW-160) of mud pump piston that had a dimpled shape in the regular layout on the piston leather cup surface and carried out a performance test on the self-built test rig. Firstly, the influence of different dimple diameters on the service life of the piston was analyzed. Secondly, the analysis of the influence of the dimple central included angle on the service life of the piston under the same dimple area density was obtained. Thirdly, the wear of the new type of piston under the same wear time was analyzed. The experimental results indicated that the service life of the piston with dimples on the surface was longer than that of L-Standard pistons, and the maximum increase in the value of service life was 92.06%. Finally, the Workbench module of the software ANSYS was used to discuss the wear-resisting mechanism of the new type of piston.

The mud pump is the “heart” of the drilling system [1]. It has been found that about 80% of mud pump failures are caused by piston wear. Wear is the primary cause of mud pump piston failure, and improving the wear-resisting performance of the piston-cylinder friction pair has become the key factor to improve the service life of piston.

Most of the researchers mainly improve the service life of piston through structural design, shape selection, and material usage [1, 2]. However, the structure of mud pump piston has been essentially fixed. The service life of piston is improved by increasing piston parts and changing the structures of the pistons. However, the methods have many disadvantages, for example, complicating the entire structure, making piston installation and change difficult, increasing production and processing costs, and so on. All piston leather cup lips use rubber materials, and the material of the root part of the piston leather cup is nylon or fabric; many factors restrict piston service life by changing piston materials [3]. Improving the component wear resistance through surface texturing has been extensively applied in engineering. Under multiple lubricating conditions, Etsion has studied the wear performance of the laser surface texturing of end face seal and reciprocating automotive components [4–6]. Ren et al. have researched the surface functional structure from the biomimetic perspective for many years and pointed out that a nonsmooth surface structure could improve the wear resistance property of a friction pair [7, 8]. Our group has investigated the service life and wear resistance of the striped mud pump piston, and the optimal structure parameters of the bionic strip piston have improved piston service life by 81.5% [9]. Wu et al. have exploited an internal combustion engine piston skirt with a dimpled surface, and the bionic piston has showed a 90% decrease in the average wear mass loss in contrast with the standard piston [10]. Gao et al. have developed bionic drills using bionic nonsmooth theory. Compared with the ordinary drills, the bionic drills have showed a 44% increase in drilling rate and a 74% improvement in service life [11]. The present researches indicate that microstructures, like superficial dimples and stripes, contribute to constituting dynamic pressure to improve the surface load-carrying capacity and the wear resistance of the friction pair [12–21].

In nature, insects have developed the excellent wear-resistant property in the span of billions of years. For instance, the partial body surface of the dung beetle shows an irregularly dimpled textured surface with the excellent wear-resistant property that is conducive to its living environment [7, 8, 22]. The dung beetle, which is constantly active in the soil, shows a body surface dimple structure that offers superior drag reduction. These dimples effectively reduce the contact area between the body surface and the soil. Moreover, the friction force is reduced. Therefore, the dung beetle with the nonsmooth structure provides the inspiration to design the bionic mud pump piston. This paper proposed a new type of piston with dimpled morphology on its surface and conducted a comparative and experimental study of different surface dimpled shapes, thus opening up a new potential to improve the service life of the mud pump piston.

A closed-loop circulatory system was used in the test rig, which was built according to the national standard with specific test requirements. The test rig consisted of triplex single-acting mud pump, mud tank, in-and-out pipeline, reducer valve, flow meter, pressure gauge, and its principle, as shown in Figure 1. Both the pressure and working stroke of the BW-160 mud pump are smaller than those of the large-scale mud pump, but their operating principles, structures, and working processes are identical. Therefore, the test selected a relatively small BW-160 triplex single-acting mud pump piston as a research object, and the test results and conclusion were applicable to large-scale mud pump pistons. The cylinder diameter, working stroke, reciprocating motion velocity of piston, maximum flow quantity, and working pressure of the BW-160 triplex single-acting mud pump were 70 mm, 70 mm, 130 times/min, 160 L/min, and 0.8–1.2 MPa, respectively.

The mud pump used in the test consisted of water, bentonite (meeting the API standard), and quartz sand with a diameter of 0.3–0.5 mm according to actual working conditions. The specific gravity of the prepared mud was 1.306, and its sediment concentration was 2.13%. Whether mud leakage existed at the venthole in the tail of the cylinder liner of the mud pump was taken as the standard of piston failure. Observation was made every other half an hour during the test process. It was judged that the piston in the cylinder failed when mud leaked continuously; its service life was recorded, and then it was replaced with the new test piston and cylinder liner. The BW-160 mud pump is a triplex single-acting mud pump. The wear test of three pistons could be simultaneously conducted.

The mud pump piston used in the test consisted of a steel core, leather cup, pressing plate, and clamp spring. The leather cup consisted of the lip part of polyurethane rubber and the root part of nylon; the outer diameter on the front end of the piston was 73 mm, and the outer diameter of the piston tail was 70 mm, as shown in Figure 2. We proceeded in two parts during the design of the dimpled layout pattern because the piston leather cup consisted of two parts whose materials were different. The dimples at the lip part of the leather cup adopted an isosceles triangle layout pattern, and the dimples at the root part were arranged at the central part of its axial length, as shown in Figure 3(a). Dimple diameter (D, D′), distance (L), depth (h), and central included angle (α) are shown in Figure 3. The dimples on the piston surface were processed by the CNC machining center. Since then, the residual debris inside the dimples was cleaned.

Schematic of dimpled piston: (a) dimpled layout of piston, (b) dimpled array form diagram, (c) cross section view of the piston leather cup, and (d) original picture of dimpled piston.

The test program was divided into three contrast groups. The dimple depth in the test was 2.5 mm. Table 1 shows the comparison between the service life of dimpled piston with different diameters L-D1, L-D2, and L-D3 and that of the L-Standard piston. In Table 1, a comparison between the L-D4 piston with dimples at the leather cup root and the L-D2 piston is shown to study the influence of dimples at the leather cup root on the piston service life. Table 2 gives the influence of the dimple central included angle on piston service life when the dimple area density was the same by taking the L-D2 area density as a criterion. Table 3 displays a comparison of the wear patterns of pistons with different dimple diameters and L-Standard pistons under the same wear time. This object of the group test is to analyze the dimple wear pattern at the leather cup root under the existence of dimples at the roots of all leather cups.

Table 1 shows that average service lives of L-Standard, L-D1, L-D2, and L-D3 were 54.67 h, 57.17 h, 76.83 h, and 87.83 h, respectively. Therefore, the mud pump pistons with dimples provide longer service life than the L-Standard piston. As the dimple diameter increases, the piston service life was improved, and the largest percentage increase of the service life was 60.65%. The service life of the L-D4 piston was about 81.17 h, which increased by 7.94% compared with that of the L-D2 piston, indicating that the piston with dimples at the leather cup root could improve piston service life.

Figure 4 illustrates the surface wear patterns of pistons with different dimple diameters in the service life test. Figures 4(a) and 4(a′) show wear patterns on the surface of the L-Standard piston. This figure shows that intensive scratches existed in parallel arrangement on the piston leather cup surface, enabling high-pressure mud to move along the scratches from one end of the piston to the other easily, which accelerated the abrasive wear failure with the abrasive particles of the piston. Figures 4(b), 4(b′), 4(c), 4(c′), 4(d), and 4(d′) show the wear patterns of the leather cup surfaces of L-D1, L-D2, and L-D3 pistons, respectively. Figures 4(b), 4(b′), 4(c), 4(c′), 4(d), and 4(d′) show that the scratches on the leather cup surface became shallower and sparser and the surface wear patterns improved more obviously as the dimple diameter increased. If the piston leather cup surface strength was not affected to an extent as the dimple diameter increased, the reduced wear zone near the dimple would become greater and greater, indicating that the existence of dimples changed the lubricating status of the leather cup surface, their influence on nearby dimpled parts was more obvious, and they played active roles in improving the service life of the piston.

Surface wear patterns of pistons with different dimple diameters in the service life test: (a) L-Standard piston, (b) L-D1 piston, (c) L-D2 piston, and (d) L-D3 piston. (a′, b′, c′, d′) are partial enlarged pictures of (a, b, c, d).

Figure 5 displays the wear patterns of the leather cup root parts of the L-D4 and L-D2 test pistons. The wear patterns of the nylon root parts of the L-D4 pistons are fewer than those of the L-D2 pistons, as shown in Figure 5. When the leather cup squeezed out high-pressure mud as driven by the piston steel core, it experienced radial squeezing while experiencing axial wear. Therefore, the area with the most serious wear was the piston leather cup root part, and the friction force at the leather cup root was much greater than that at the other areas. The rapid wear at the root decreased the piston load-carrying capacity and then affected the service life of piston. The dimples at the piston leather cup root could reduce the wear of the piston leather cup root and improve the service life of piston.

Wear patterns of the piston leather cup root with and without dimples: (a) comparison chart of root wear of the L-D4 and L-D2 pistons, (b) partial enlarged diagram of root wear of the L-D4 piston, and (c) partial enlarged diagram of root wear of the L-D2 piston.

Table 2 indicates that the average service life of the L-S1 piston was 105.00 h, which is about twice that of the L-S2 piston (59.50 h) and was obviously improved in comparison with that of the L-D2 piston (76.83 h), indicating that, under the same dimple area density, the smaller the dimple central included angle was, that is, the closer the circumferential arrangement of dimples was, the longer the service life of the piston would be, and the increase of the maximum value of service life was 92.06%.

Figure 6 shows the surface wear patterns of the L-S1 and L-S2 test pistons. In Figures 6(a) and 6(a′), the scratches on the piston leather cup surface became sparse and shallow in the dimpled area. Figures 6(b) and 6(b′) show that the wear was slight in the area close to the dimples. The farther the scratches were from the dimpled area, the denser and deeper the scratches would be. The L-S1 piston had a small dimple central included angle, which was arranged more closely on the piston surface. The lubricating effects of oil storage in each row of dimples were overlaid very well, which was equivalent to amplifying the effect of each row of dimples in Figure 6(b), making the wear on the whole piston leather cup surface slight, preventing the entry of high-pressure mud into the frictional interface, and lengthening the service life of piston.

Wear patterns of pistons with different dimple central included angles under the same area density: (a) L-S1 piston and (b) L-S2 piston. (a′, b′) were partial enlarged pictures of (a, b).

Before all pistons have not failure, T1, T2, T3, and L-Standard experienced equal-time wear. This test set the wear time at 30 h. The piston leather cup mass was W0 before the test. After the test, the mass of the piston leather cup was W1. During the test, the wear loss of the piston leather cup was W = W0 − W1. The wear mass percentage of the test piston leather cup was calculated as φ = W/W0. The test results are shown in Table 3.

Table 3 shows that the average wear mass percentages of the L-Standard, T1, T2, and T3 pistons were 6.98%, 6.59%, 4.22%, and 3.83%, respectively. The wear mass percentages of the dimpled pistons were basically lower than those of the L-Standard piston and decreased as the dimple diameter increased. Figure 7 shows the wear patterns of the piston leather cup. The wear rules displayed in Figure 7 were similar to those displayed in Figure 4. The only difference was that the wear in Figure 7 was slighter than that in Figure 4. Based on the wear under the same time, the existence of dimples reduced the piston wear.

During the operation of the mud pump piston, the outside surface of the piston leather cup comes in contact with the inner wall of the cylinder liner and simultaneously moves to push the mud. The lip part of the piston leather cup mainly participated in the piston wear and exerted a sealing effect, while the piston root part mainly exerted centralizing and transitional effects. In the mud discharge stroke, the lip part of the piston experienced a “centripetal effect,” and a gap was generated between the lip part and the cylinder liner. The greater the contact pressure between the lip part and cylinder liner of the piston was, the smaller the gap was, and the entry of high-pressure mud into the contact surface between the piston and cylinder liner was more difficult. The piston root easily experienced squeezing under high pressure, and the smaller the equivalent stress caused by the piston root was, the more difficult the squeezing to occur. Hence, the contact pressure at the lip part of the piston and the equivalent stress at the root were analyzed, and they would provide a theoretical basis for the piston wear-resisting mechanism. The ANSYS Workbench module was used to perform a comparative analysis between the contact pressure at the lip part and the equivalent stress at the root of the three kinds of pistons (i.e., L-Standard piston, L-S1 piston, and L-D1 piston). The service life of the L-S1 piston exhibited the best improvement effect, whereas that of the L-D1 piston demonstrated the worst improvement effect. The piston adopted a 1 mm hexahedral grid, and the grid nodes and elements are as shown in Table 4.

We could obtain the contact pressure nephograms of the three pistons by analyzing the contact pressure of the lip parts of the L-Standard piston and two dimpled pistons, as shown in Figure 8.

The contact pressure nephograms of the three pistons indicate that the dimpled structure on the piston surface changed the distribution state of contact pressure. Three nodes were selected at the same position of each piston to obtain the contact pressure values. The node positions are shown in Figure 8(c), and the average pressure value of three nodes was the pressure value at the lip part of this piston. The contact pressure value of the L-Standard piston was 0.6027 MPa and that of the L-D1 and L-S1 pistons was 0.6840 MPa and 1.0994 MPa, respectively. Compared with the L-Standard piston, the contact pressure at the lip part of the L-S1 piston increased, the gap between the piston and cylinder liner became small, which could effectively prevent abrasive particles from participating in the wear and resulting in piston failure, and there was greater improvement in the service life of piston. The contact pressure of the L-D1 piston did not increase too much, and the degree of improvement of the piston service life was not obvious.

An equivalent stress analysis of the root parts of the L-Standard piston and two dimpled pistons was conducted to obtain the equivalent stress nephograms of the three pistons, as shown in Figure 9.

The equivalent stress nephograms of the three pistons show that the root of the L-Standard piston bore great stress and was easily squeezed, which accelerated piston wear and reduced piston service life. The dimpled structure could reduce the equivalent stress at the piston root and lengthen piston service life. Three nodes were selected in the same root positions of the three pistons. Their positions are as shown in Figure 9(c). The average value of the equivalent stresses of the three nodes was the equivalent stress value at the root of this piston. The equivalent stress value of the L-Standard piston was 0.1093 MPa, that of the L-D1 piston was 0.1066 MPa, and that of the L-S1 piston was 0.0922 MPa. The dimpled structure of the L-S1 piston could reduce the equivalent stress at the root and reduce the occurrence of root squeezing wear. The equivalent stress value of L-D1 did not decrease too much, and the degree of improvement of the piston service life was not obvious.

The lubricating oil on the mud pump piston surface could reduce the wear of piston and cylinder liner and improve the service life of pistons with the reciprocating movement. The lubricating oil would eventually run off and lose lubricating effect, which would result in piston wear. The finite element fluid dynamics software CFX was used to establish the fluid domain model of the dimpled and L-Standard pistons and analyze the lubricating state on the piston surface. The piston surface streamlines are shown in Figure 10. This figure shows that the lubricating fluid did not experience truncation or backflow phenomenon when passing the surface of the L-Standard piston. When the lubricating fluid flowed through the surface of the dimpled piston, it presented a noncontinuous process. Its flow velocity at the dimpled structure slowed down obviously because it was blocked by the dimpled structure.

Figure 11 shows the piston cross section streamline. This figure shows that the existence of dimples changed the distribution status of the lubricating flow fields on the contact surface between the piston and cylinder liner. The lubricating oil entered the dimpled structure in a large quantity, and the flow velocity slowed down. The dimpled structure on the piston surface enlarged the storage space of the lubricating oil and made it difficult for the lubricating oil inside the dimpled structure to be taken away by the cylinder liner to improve the lubricating conditions of the friction pair interface, reduce the frictional resistance between the piston and cylinder liner, reduce wear, and improve the piston service life.

When the piston moved in the cylinder liner, a small quantity of solid particles in mud entered gap of piston and cylinder liner and participated in abrasion. The dimpled structure on the piston surface could store some abrasive particles (as shown in Figure 6(a′)) during the piston wear process to prevent these particles from scratching the piston and cylinder liner and generating gullies, thus avoiding secondary damage to the piston and cylinder liner and improving the piston service life.

This paper presented a dimpled-shape mud pump piston; that is, the piston leather cup surface had a dimpled array morphology in regular arrangement. The experimental results can provide the basic data for design engineering of the mud pump piston with a long service life. The comparative analyses of service life and wear patterns for dimpled mud pump pistons and L-Standard pistons were conducted. The main results and conclusions were summarized as follows:(1)The service life of the mud pump piston with dimpled morphology on the surface improved in comparison with that of the L-Standard piston, and the service life increase percentages were from 4.57% to 92.06%.(2)The piston service life would increase with the dimple diameter under the same dimpled arrangement pattern, and the maximum increase in the value of service life was 60.65%.(3)The service life of the piston with dimples increased by 7.94% in comparison with that with none.(4)Under the same dimpled arrangement patterns and area densities, the tighter and closer the dimples were arranged on the piston surface, the longer the service life of piston was, and the maximum increase in the value of service life was 92.06%.(5)Under the same wear time, the wear of the dimpled piston slightly decreased in comparison with that of the L-Standard piston, and the minimum value of wear mass percentage was 3.83%.(6)The dimpled shape could not only change the stress state of the piston structure, improve piston wear resistance, and reduce root squeezing, but also increase oil storage space, improve lubricating conditions, and enable the accommodation of some abrasive particles. Furthermore, the dimpled shape was the key factor for the service life improvement of the mud pump piston.

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 striped structure was designed and processed on the contact surface between the piston cup and the cylinder liner. The striped structure was 5 mm away from the outermost part of the lip, which ensured the lip could contact effectively with the cylinder liner. Based on the structural dimensions of the piston cup, we designed a 2-stripe structure, and the very little stripe space affected the service life of the piston [30]. Thus, the stripe space of our bionic piston was set at 5 mm. According to the machining technology, two parameters of stripe depth h and the angle between the stripes and lateral of the piston α were selected (Figure 2).

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 orthogonal experimental design method was used to study the effect of factors and the best combination of factor levels [31]. Stripe depth h and angle α were selected as the factors and were both set at three levels in the sealing performance tests (Table 1).

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 ().

The sealing performance tests showed the striped structures all effectively enhanced the contact sealing between the piston and the cylinder liner. In particular, the increase of sealing performance relative to the standard piston minimized to 21.05% in the bionic striped piston with a stripe depth of 3 mm and angle of 45° and maximized to 90.79% in the bionic striped piston with the stripe depth of 2 mm and angle of 90°. Range analysis showed the sealing performance of pistons was affected by the stripe depth h and angle α, and these two parameters (h and α) have the same effect on the sealing performance.

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).

Sealing validity tests were conducted to validate the sealing performance of the bionic striped pistons. It was observed whether the sealing liquid would leak at the tail of the cylinder liner, and the time of leakage was recorded. The standard piston and the most effective bionic piston were selected to compare their sealing performances.

Both the standard piston and the bionic striped piston leaked, which occurred after 84 and 249 minutes of operation, respectively (Figure 5). Figure 6 shows the pressures of the two pistons during testing. Clearly, the sealing pressure of the standard piston declined rapidly before the leakage, but that of the bionic piston decreased very slowly. After the leakage, the reading on the pressure gauge in the standard piston declined to 0 MPa within very short time, but that of the bionic piston decreased much more slowly.

The beginning time of leakage was inconsistent between the standard and bionic pistons (84 minutes vs. 249 minutes). In order to compare the leakage of these two pistons, the leaked liquid was collected when the piston started to leak. The volume of the leaked liquid was measured using a graduated cylinder every 5 minutes from the 84th minute and 249th minute, respectively (both considered as 0 minute), for 20 minutes. Figure 7 shows the leaked amounts of the standard piston and the bionic piston. Clearly, after the leakage and failure, the leaking speed and amount of the bionic piston were both smaller than those of the standard piston.

The piston lips and the cylinder liner were under interference contact, and their mutual extrusion was responsible for the lip sealing. Thus, a larger pressure between the piston lips and the cylinder liner reflects a higher lip sealing effect.

The bionic striped piston with the highest sealing performance (h = 2 mm, α = 90°) was selected for the sealing mechanism analysis and named as the bionic piston. The 3D point cloud data of standard piston were acquired by using a three-dimensional laser scanning system (UNIscan, Creaform Inc., Canada). Then, the standard piston model was established by the reverse engineering technique. The striped structure of the bionic piston was modeled on basis of the standard piston.4.1.1. Contact Pressure of Piston Surface

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.

Figure 9 shows the pressure clouds of the standard piston and the bionic piston. Since the simulation model was completely symmetrical and the pressures at the same position of each piston were almost the same, three nodes were selected at the lip edge of each piston for pressure measurement, and the average of three measurements was used as the lip edge pressure of each piston. The mutual extrusion between piston and cylinder liner happened at the lip, and thereby the larger of the lip pressure was, the better the sealing performance was. The lip pressure of the standard piston was smaller than that of the bionic piston (2.7371 ± 0.016 MPa vs. 3.0846 ± 0.0382 MPa), indicating the striped structure enhanced the mutual extrusion between the bionic piston and the cylinder liner and thereby improved the sealing performance between the lips and the cylinder liner. As a result, sand could not easily enter the piston-cylinder liner frictional interface, which reduced the reciprocated movement of sand and thereby avoided damage to the piston and the cylinder liner.

Figure 10 shows the surface pressures from the lip mouth to the root in the standard piston and the bionic piston. The surface pressure of the bionic piston surpasses that of the standard piston, and the pressure at the edge of each striped structure changes suddenly: the pressures at the striped structure of the bionic piston are far larger than at other parts. These results suggest the contact pressure between the edges of the striped structures and the cylinder liner is larger, and the four edges of the two striped structures are equivalent to a four-grade sealed lip mouth formed between the piston and the cylinder liner, which generates a multilevel sealing effect and thereby largely enhances the sealing effect of the piston.

The piston surface flow field was numerically simulated using the CFX module of the software ANSYS® Workbench V17.0. The side of the lips was set as fluid inlet, and the other side as fluid outlet, as shown in Figure 11. The inlet and outlet were set as opening models, and the external pressure difference between them was 0 Pa. The moving direction of the piston was opposite to the fluid flow direction. The fluid region was divided into grids of 0.2 mm, while the striped structures were refined to grade 2.

Figures 12 and 13 show the surface streamline clouds and sectional streamline clouds of the two pistons at the early stage of leakage when the fluid entered the interface. Clearly, compared with the standard piston, when the surface-leaked liquid from the bionic piston passed the striped structure, the streamlines were sparse and significantly decreased in number, and the flow velocity declined more. The flow velocity decreased from 0.9348 m/s to 0.7555 m/s in the bionic piston and from 0.9346 m/s to 0.9262 m/s in the standard piston. It shows that, after the blockage by the striped structures, the striped structure more significantly intercepted the leaked liquid and could reduce the leakage rate of the piston, thereby enhancing the sealing effect.

Figure 13 shows the section leakage streamline of the standard piston and the bionic piston. Clearly, compared with the standard piston, when the leaked liquid of the bionic piston flowed through the striped structures, the streamlines would reflux and reverse inside the striped structures, indicating the striped structures can efficiently store the leaked liquid and slow down the leakage.

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.

Figure 15 shows the oil film left after the piston running. The oil film width of the bionic piston was far larger than that of the standard piston (20.48 mm vs. 2.28 mm). The striped structure of the bionic piston could store the lubricating oils, and uniform oil films were formed after its repeated movement, which reduced the friction between the piston and the cylinder liner, so that the seal failure of the piston would not happen due to excessive abrasion.

(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.

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Multiplex piston pumps are positive-displacement reciprocating pumps that are configured with two or more plungers, and are often used in both drilling and well service operations. The most common multiplex pump may be equipped with three pistons (triplex pumps), and are discussed more herein. However, pumps with more or less than three pistons may be used for different applications. For example, quintuplex pumps are available and may generate less flow noise. In some low-cost applications, duplex pumps are also used. In a typical drilling rig configuration, multiplex piston pumps may be installed and operated simultaneously.

Multiplex pumps used in well service activities generally are capable of handling a wide range of fluid types, including corrosive fluids, abrasive fluids and slurries containing relatively large particulates.

When multiplex pumps are used, it is common practice to count the number of strokes to determine the volume of the fluid being pumped. The number of strokes a piston or plunger in a pump completes in a unit of time may be referred to as the stroke speed (typically measured in “strokes per minute” (SPM)). Generally, as the stroke speed increases, the flow rate of fluid being pumped by a triplex pump is also increased.

Rig operators may refer to the size (pump capacity) and the number of strokes to determine the pumped volume, represented in Equation A, below. The pumped volume may be estimated by multiplying the number of strokes by the fluid displaced during one stroke. The number of strokes may be obtained by the number of turns performed by the pump crankshaft multiplied by the number of pistons (plungers) of the pump.

The capacity is the theoretical displacement of one piston during its full stroke. The capacity may be calculated as 2 times the radius (R) of the rotational path of a crankpin pivot point around the crankshaft times the area (A) of the piston cross section. The flow rate is the pumped volume per unit of time, represented by Equation B, below.

As an example, a triplex pump having three pistons of 5-gallon capacity, and rotation speed of 40 RPM (revolution per minute) may have the following flow rate:

Known methods of estimating pumped volume and flow rate are estimates and/or theoretical calculations. However, the fluid volume discharged by each stroke of a multiplex pump is commonly lower that the theoretical capacity due to multiples effect such leakage, valve closing delay, and fluid compressibility.

This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter

In one aspect, embodiments of the present disclosure relate to methods that include determining a rotational position of a crankshaft in a multiplex pump from one or more sensors disposed on the crankshaft, determining a position of each of a plurality of pistons along a corresponding pump bore in relation to a total stroke length of each piston and a connecting rod length, calculating an individual theoretical displaced volume of fluid for each of a plurality of chambers in the multiplex pump based on the rotational position of the crankshaft, and summing the individual theoretical displaced volumes to determine a total theoretical pumped volume by the multiplex pump.

In another aspect, embodiments of the present disclosure relate to methods that include providing a multiplex pumping system having multiple multiplex pumps for pumping fluid downhole in a drilling operation, and calculating a volumetric efficiency of a first multiplex pump while the multiplex pumping system pumps fluid downhole, wherein the volumetric efficiency is calculated from a suction flow rate into the first multiplex pump and a theoretical discharge volume pumped out of the first multiplex pump.

In another aspect, embodiments of the present disclosure relate to systems that include a fluid source, multiple multiplex pumps, each multiplex pump having a crankshaft, at least one position sensor disposed on the crankshaft, multiple chambers, each chamber having an inlet in fluid communication with the fluid source via an inlet flowline and an outlet, multiple pistons, each piston slidingly engaged within the chamber, and multiple connecting rods, each connecting rod extending from one of the pistons to the crankshaft, a motor connected to the crankshaft, and a calibration tank selectively in fluid communication with the inlet of one of the multiplex pumps at a time.

In yet another aspect, embodiments of the present disclosure relate to systems that include multiple triplex pumps fluidly connected to a fluid source via inlet flowlines, a Coriolis meter disposed along a first inlet flowline, and at least one secondary flowline fluidly connecting a portion of the first inlet flowline upstream the Coriolis meter to one or more different inlet flowlines.

FIG. 3 shows a graph of the theoretical discharge rates of individual pistons in a triplex pump and the collective theoretical flow rate of the triplex pump.

FIG. 4 shows a graph of parameters during a calibration process for determining volumetric efficiency of a triplex pump according to embodiments of the present disclosure.

FIG. 5 shows a graph of the potential operating range of a triplex pump during a calibration process according to embodiments of the present disclosure.

FIG. 6A shows a graph of volumetric efficiency determined from the calibration process of a triplex pump according to embodiments of the present disclosure.

FIG. 6C shows a triplex efficiency curve corresponding to a given fluid compressibility Cfl_calin Graph A that can be normalized for an ideal fluid, and after obtaining corrected efficiency for each point i, Graph B may be generated to show the efficiency performance of the multiplex pump for the ideal fluid.

FIG. 7C shows multiplex pump behavior when the valves do not close instantaneously at the end of the suction stoke and the effect of closing delay for the discharge valves.

FIG. 7E graphically shows the relationship between multiplex pump efficiency and the potential operating range of the multiplex pump during calibration.

FIG. 7G includes a graph, Graph “D,” showing a multiplex pump affected by valve closing delay but no leakage, and a graph, Graph “E,” showing a piston pump affected by leak-rate and no effect of valve closing delay.

FIG. 7H shows data from a calibration normalized for an incompressible fluid in Graph B and plotted in a graph, Graph F, versus pump cycle time (period) in place of speed.

FIG. 9 shows a graph of the relationship between the fluid level over time for a calibration process to determine apparent viscosity according to embodiments of the present disclosure.

FIG. 10 shows a graph of the relationship between fluid level over time for a pumping process to determine apparent viscosity according to embodiments of the present disclosure.

FIG. 11 is a graph showing the relationship between the change in the fluid levels in the fluid source and calibration tank at different pump speeds and different valve positions.

FIG. 12C shows a graph of mechanical efficiency as a function of pump speed and discharge pressure according to embodiments of the present disclosure.

Embodiments of the present disclosure relate generally to accurate flow rate measurements of fluid being pumped downhole based on rotation speed and crankshaft instantaneous position in a triplex pump (or other multiplex pump) taking in account the pump efficiency. Some embodiments relate to methods that include determining the pump efficiency during normal operations, such as drilling a new portion of a well. Some embodiments relate to methods that include determining the contribution of different elements affecting the overall pump efficiency. Some embodiments relate to methods that include continuously verifying if the data from the last accepted calibration is still applicable with adequate results.

Embodiments of the present disclosure relate to multiplex pumps, including pumps having two or more pistons, such as duplex pumps, triplex pumps, quadraplex pumps, quintuplex pumps and others. However, because triplex pumps may be relatively more common in the field, discussion of multiplex pumps used in accordance with embodiments of the present disclosure may be simplified by referring to a triplex pump as an example of a multiplex pump. Thus, embodiments discussed herein referring to a triplex pump may also apply to multiplex pumps having more or less than three pistons.

The volumetric efficiency of a triplex pump may be obtained by calibrating the triplex pump at location and during drilling, such that calibration may be done without incurring non-productive time (“NPT”). The calibration may be performed at different flow rates and discharge pressure.

NPT refers to time when drilling operations do not occur, for example, where pumping drilling fluid downhole is paused for some reason. For example, NPT may include time from when a drill bit is pulled out of a wellbore to when it is run back to same depth to resume drilling, time required to nipple up and nipple down a BOP stack, pressure test of BOP, tripping of drill string, slip and cut time, and casing run times. Operations such as make up or laid down BHA, logging, fishing, jarring, wait on crew and equipment may also be part of NPT.

According to embodiments of the present disclosure, calibration methods for determining a triplex efficiency without incurring non-productive time (NPT) may include determining and comparing tank levels of fluid to be pumped through a triplex pump. Further, calibration methods may include outputting fluid at a discharge pressure similar to or within the range of the pressure of fluid being discharged during a flow rate measurement period.

Embodiments of the present disclosure also include flow measurement systems. A flow measurement system may include a fluid source, such as a mud tank, a calibration tank, and at least one triplex pump connected to the fluid source and the calibration tank. Each triplex pump may include a crankshaft, three chambers, three pistons slidingly engaged within each chamber, and connecting rods extending from each of the pistons to the crankshaft. A motor may be connected to the crankshaft to rotate the crankshaft at a rotational speed.

FIGS. 1A and 1B show examples of different configurations of a system according to embodiments of the present disclosure. The system 100 includes a fluid source 110, which is shown as being a mud tank. However, other fluid sources may