mud pump design calculation made in china

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).

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.

(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.

Mud Pump Valve & Seat are made of premium alloy steel through one-piece forging and carburizing treatment processes, thereby ensuring high intensity. In addition, the precise calculation is performed and CNC machining is conducted for the dimensional matching of the valve seat and valve body working angles to enhance the service life of the valve body and valve seat. Our valve products are able to work smoothly in normal mining and digging conditions for over 400 hours.

With advancements in offshore oil drilling, deepwater drilling technology has been developing consistently, which has promoted the development of conductor jetting, dynamic killing, well logging while-drilling and pressure while-drilling techniques [1]. However, the exploration and development of deepwater resources still suffer from many challenges, which mainly span following three aspects [3–8]. First, if a riser is adopted during operation, riser length must grow with increasing water depth, yielding a heavy and cumbersome structure, especially for the upper riser, which must bear a larger tension. Second, difficulties arise during advancing in the horizontal section; when drilling in the horizontal section, it is difficult for the drilling fluid to carry the rocks. Moreover, the borehole friction increases rapidly, resulting in extra weight constraints. Third, owing to the narrow pore-fraction pressure window, a precise control of wellbore pressure is required for formations with severe leakage, reservoir pressure failure, and high sulfur content. Therefore, focusing on a series of challenges in deepwater drilling, a subsea closed-cycle riserless drilling method with pump + gas combined lift is proposed in this study, providing the theoretical foundation and design basis for efficient, economical, and safe subsea drilling applications.

In this work, the advantages of closed-cycle riserless drilling method using a pump + gas combined lift are analyzed and its multiphase flow drilling model is proposed. By solving the model, the influence of drilling fluid displacement, gas injection displacement, gas injection site and seawater depth on drilling hydraulic parameters can be obtained. The optimization hydraulic parameters design method of closed-cycle riserless drilling method with a subsea pump + gas combined lift is proposed.

In 2001, a Norwegian company called AGR developed a riserless mud recovery (RMR) drilling technology based on its cutting transportation system (CTS). The principle of this technology is to pump mud subsea to the drilling platform by leveraging the mud suction module at the wellhead, subsea mud lifting pump, as well as mud return pipeline, thereby forming a closed-cycle of drilling fluid. The practice costs and risks are significantly lower than that of methods using risers [9]. First, RMR was merely adopted for shoal-water oil-and-gas exploitation, which is mainly targeted to solve the drilling challenges concerning complex subsea conditions and shallow risks and ensures a smooth borehole drilling operation on the surface layer. In 2003, the first commercial RMR application was performed in the Caspian Sea. As the technology developed, the closed-cycle riserless drilling system has been advancing from shallow sea to deep sea applications. The issues restricting the application of deepwater closed-cycle drilling methods with risers mainly stem from the lifting capacity of mud lifting pump and strength of mud return pipeline. Therefore, AGR, together with Shell, BP America, and DEMO2000, formed an industrial project team to develop the so-called deepwater RMR system, and successfully conducted a field test in the South China Sea (Malaysia) at a depth of 1,419 m in September 2008. The test has proved the feasibility of this technology in deepwater drilling applications and its advantages for drilling in the South China Sea, such as safe drilling in strata with shallow risk, overcoming the mud logging restrictions, extending the setting depth of surface casing, etc. In 2008, the RMR drilling system has been adopted for a drilling operation with self-elevating platform for the first time, which achieved favorable results. The deepwater RMR system is illustrated in Figure 1.

Compared with the conventional riserless mud lifting systems, this system has introduced an innovative gas lifting process by adopting a gas + pump combined lifting scheme. This design can effectively decrease the subsea pump working power, enhance the lifting head, reduce the cost and difficulty of construction, improve the reliability of lifting systems, and enable the application of closed-cycle riserless drilling in offshore applications with higher depth. The gas + pump combined lifting system is illustrated in Figure 2.

Major advantages of this novel subsea closed-cycle riserless drilling method with a subsea pump + gas combined lift in deepwater drilling are as follows:

(1) Riserless drilling: Conventional offshore drilling adopts risers to isolate seawater inside the drilling fluid system. The dual-channel drill pipeline exposed to seawater replaces the cumbersome riser system and its components, thereby reducing the amount of drilling fluid and number of drilling pumps required, as well as the bearing capacity and space requirements for drilling rig deck. Moreover, it can reduce the quantity of casing, optimize the structure along well depth, and obtain a wellbore with a single diameter.

(2) Closed-cycle system: When a subsea pump + gas combined lift is used, drilling fluid is pumped to the well bottom through the inner pipe of the drilling pipeline; then, it impacts the rock stratum via jet from the drill bit. The fluid, carrying rock debris cut by the drilling bit, is then lifted to the subsea mud pipeline along the annular channel formed between the wellbore and drilling pipe. Exploiting the drilling fluid return pipeline, rock debris are carried to the drilling platform via the subsea pump + gas combined lift. Closed-cycle serves as the basis for the implementation of deepwater drilling technology with pressure control. Via precise control of bottom hole pressure and drilling fluid flow, this technique can address the narrow safety density window issue in deepwater drilling, while reducing down-time and well control risks.

(3) High cutting carrying efficiency: In conventional offshore drilling applications, the drilling fluid is pumped in via drill pipe and returned through the borehole annulus and riser annulus after carrying the cuttings. By leveraging the subsea pump + gas combined lift, carried drilling fluid cuttings return to the wellhead via the drilling fluid return pipeline. The drilling fluid is not required to be transported at high velocities for carrying cuttings to the wellhead, which reduces the scouring of the borehole wall, which is greatly applicable to wells with large displacement and horizontal wells.

(4) Enlarging the working water depth of third- and fourth-generation drilling rigs: deepwater and ultra-deepwater operations mandate significant load-bearing requirements on drilling rigs and deck space. Hence, for conventional offshore drilling, fifth-, sixth- or seventh-generation drilling rigs are required. The novel closed-cycle riserless drilling method using a subsea pump + gas lift alleviates the load-bearing capacity and space requirements on the drilling rig deck. Consequently, third- and fourth-generation drilling rigs can be adopted for such drilling operations, which reduces the daily running costs of drilling rigs and increases their working water depth.

This technology aims to optimize the hydraulic parameters in deepwater drilling. The hydraulic parameter accuracy directly affects the safety and efficiency of drilling. Significant discrepancies exist between the novel closed-cycle riserless drilling with a subsea pump + gas combined lift and conventional deepwater drilling applications, which are mainly observed in the calculation of gas-liquid-solid three-phase flow in the upper return pipeline, wellbore pressure, and cutting carrying efficiency when subsea pump is online. The wellbore multiphase flow model states the fundamental theory for calculating the hydraulic parameters of the novel closed-cycle riserless drilling with a subsea pump + gas combined lift.

The foremost multiphase flow simulation of the well kick adopts homogeneous flow models. Leblanc and Leuis (1968) established the first multiphase flow model of a well kick suitable for gas overflow [10]. This model assumes that the overflowing gas exists as a continuous column inside the wellbore; then, performs simple calculations regarding the pressure change in the annulus during overflow without considering the mutual slippage between gas and liquid phases. Similarly, based on the concept of homogeneous flow, Horberock and Stanbery (1981) calculated the average value of gas-liquid characteristic parameters [11]; then, they established the continuity and momentum conservation equations of the homogeneous fluid in vertical pipeline. Subsequently, they simulated the pressure change in the wellbore. Santos (1982) established a relatively comprehensive multiphase flow model of deepwater kick by assuming a bubbly status in the wellbore during overflow [12]. In their model, they introduced the void fraction concept, as well as the effects of gas-liquid slippage and friction pressure losses in two-phase flows. Nickens (1987) considered the velocity slippage between different phases as well as the friction pressure loss of single and multiple flows. By numerically solving the dynamic equations of mass conservation for gas and liquid phases simultaneously, a comprehensive multiphase flow model in the wellbore has been established [13]. However, many factors, such as temperature variation, gas dissolution, etc., were not considered in this model. Adopting the established model, the effects of wellbore shape and hydraulic parameters of drilling assembly on the borehole pressure distribution were investigated. Moreover, many scholars, such as White and Walton (1990), Van Slyke and Huang (1990), Szczepanski et al. (1998), Nunes et al. (2002), and Velmurugan et al. (2016), applied the classic model of gas-liquid two-phase flow during well kick to analyze the multiphase flow pattern in the wellbore under different working conditions, namely, varying mud types [14, 15], overflowing gas composition, and deepwater drilling [16–18]. Sun et al. (2017, 2022) integrated the hydrate phase balance equilibrium and phase transition rate models with the multiphase flow model of deepwater well kick [19, 20]. Based on their analysis, they discovered that during well kick, the phase transition of hydrate would lead to concealment in the early stage and burstiness in the later stage. Fu et al. (2020, 2022) revealed that the hydrate formation makes drilling fluid exhibit the shear-thinning at low shear rate condition and the shear-thickening at high shear rate condition. The corresponding rheological model of drilling fluid is developed incorporating hydrate concentration, shear rate and additive concentration, which has an important contribution to improvement of the multiphase flow [21–23].

Because the novel closed-cycle riserless drilling method with a subsea pump + gas combined lift is still in its initial stage globally, current research on the multiphase flow pattern in wellbore is mainly based on the working conditions of deepwater drilling applications with risers. The multiphase flow patterns in wellbore that are affected by multiple factors, such as subsea pump and gas injection, are rarely reported. Hence, the existing theoretical model is difficult to apply in most cases.

When using the novel deepwater closed-cycle riserless drilling with a subsea pump + gas combined lift, gas lifting module enters wellbore through the mud return pipeline and changes the flow patterns of drilling fluid from liquid-solid two-phase flow to complex three-phase flow comprising gas, liquid, and solid. The selection process of pump + gas combined lifting parameters is constrained by various restrictions, such as borehole cleanliness, mud pump capacity, formation stability, rated power of lifting pump, etc. The following requirements should be fulfilled:

The drilling fluid return pipeline is divided into two sections, namely, sections a and b. Along the drilling fluid return pipeline, the section from the subsea lifting pump to the intersection of gas injection pipeline and drilling fluid return pipeline is named section a of the return pipeline (as shown in Figure 2). Accordingly, the section from subsea lifting pump to the intersection of the gas injection pipeline and drilling fluid return pipeline to the drilling ship is named section b of return pipeline. The multiphase flow equations of sections a and b are established. No gas phase exists in section a of drilling fluid return pipeline. By considering only the liquid and cutting phases, the multiphase flow equations in section a of drilling fluid return pipeline are stated as follows:

To solve control equations of multiphase flow, it is necessary to combine the calculation equations of gas phase volume fraction, drilling fluid rheology, distribution coefficient, and drift velocity[19].

The temperature and pressure of drilling fluid inside the return pipeline on sea surface are measured using thermometer and pressure gauges at the wellhead. The displacement of drilling fluid is calculated based on the mud pump readings. The air injection displacement is measured according to the gas flowmeter, and the cutting displacement is calculated based on the mechanical drilling speed.

With the same pumping parameters, the drilling fluid displacement varies from 5 L/s to 40 L/s with 5 L/s increments. The multiphase flow model for the closed-cycle riserless drilling is used during the analysis, and the influence of subsea pump displacement on the multiphase flow in the return pipeline is examined, as demonstrated in Figure 3. The simulation results indicate that in the section mudline, the pressure along depth inside the return pipeline increases with increasing drilling fluid displacement values; moreover, in the section below mudline, the pressure along depth inside the return pipeline decreases with increasing drilling fluid displacement. This is because the subsea pump is located at the mudline level. In the section above the mudline, increasing the liquid phase displacement will result in higher subsea pump discharge pressure and larger fluid kinetic energy in the pipeline. Hence, the pressure inside the pipe increases. In the section below mudline, as the fluid in the pipeline is not affected by the subsea pump, the well bottom pressure decreases with an increasing drilling fluid displacement, decreasing the pressure inside the pipeline.

Effect of drilling fluid displacement on gas volume fraction inside the return pipeline is calculated and demonstrated in Figure 5. As the gas migrates from the gas injection point at a depth of 400 m, the gas volume fraction decreases with increasing drilling fluid displacement. When the drilling fluid displacement is 5 L/s, 10 L/s, 15 L/s, 20 L/s, 25 L/s, 30 L/s, 35 L/s, and 40 L/s, the gas volume fraction returning to the wellhead is 0.913, 0.846, 0.787, 0.737, 0.692, 0.653, 0.617, and 0.586, respectively. Lowering the subsea pump displacement will result in a larger sectional gas volume fraction in the pipeline, which significantly increases effects of gas injection on cutting migration. As shown in Figure 6, during the upward migration of gas along the pipeline, the flow velocity first increases slowly and then rapidly owing to the gas volume expansion. The gas velocity in gas injection section increases gradually with an increasing drilling fluid displacement. The effects of a fluid displacement lower than 15 L/s are more significant compared with those of other setpoints.

The drilling fluid displacement is closely associated with pump lifting power. As illustrated in Figure 7, the results of calculating the drilling fluid displacement effect on pump lifting power indicate that a higher drilling fluid displacement results in a higher subsea pump working power, which exhibits a nonlinear relationship. During the actual riserless drilling process, considering the power configuration of drilling platform or drilling ship, the subsea pumps should be selected to combine the effects of sites and amount of gas injection. Moreover, to optimize cutting carrying efficiency, a minimum drilling fluid displacement is obtained for selecting the corresponding pump power, which serves as a theoretical basis for selecting the proper subsea pumps.

The most prominent characteristic of novel riserless drilling is the combination of gas injection and subsea pump lift processes. The variations in the gas injection displacement has great impact on the pressure and volume fraction in the pipeline as well as the subsea pump power. By setting the gas injection displacement to 60 m3/h, 80 m3/h, 100 m3/h, 120 m3/h, 140 m3/h, 160 m3/h, 180 m3/h, and 240 m3/h, the effect of gas injection displacement on the multiphase flow in wellbore can be calculated.

As shown in Figure 8, the pressure along depth inside the return pipeline decreases with increasing gas injection displacement values above the mudline level. In the section below the mudline, the gas injection displacement has no effect on pressure in the pipeline is shown. Therefore, in this study, only pressure simulation results in the section above mudline are considered. Affected by gas injection displacement, the discharge pressure of the subsea pump fluctuates greatly. When the gas injection displacement changes from 60 m3/h to 240 m3/h, the pump discharge pressure decreases from 17.288 to 5.527 MPa. A higher gas injection displacement results in smaller pressure losses in the return pipeline and a higher pressure in the pipeline with the same depth.

Gas injection displacement is crucial for ensuring the efficient migration of cuttings and enhance the pumping capacity. Figure 9 demonstrates the effect of varying gas injection displacement using an injection site at 400 m on the gas volume fraction in the return pipeline. A larger gas injection displacement results in a higher gas proportion and fluid kinetic energy throughout the section inside the pipeline; therefore, cuttings can be carried to the wellhead more easily. From the calculation procedure depicted in Figure 10, the gas flow velocity increases with increasing gas injection displacement; its cutting carrying capacity is enhanced significantly as well. When the gas injection displacement elevates from 60 m3/h to 240 m3/h, the gas flow velocity at the wellhead increases from 0.8182 m/s to 3.273 m/s.

The effect of gas injection displacement on pump power is analyzed, which can greatly decrease the load-bearing capacity of pump. By increasing gas injection displacement, the subsea lifting pump power decreases (see Figure 11). Especially in the case of low gas injection displacement, its effect on pump power is more significant. As gas injection displacement elevates from 60 m3/h to 120 m3/h, the pump power decreases by 8.28 kW. In the case of high gas injection displacement, as gas injection displacement increases from 180 m3/h to 240 m3/h, the pump power decreases by 6.01 kW. Therefore, the subsea pump and gas lifting equipment cannot be operated at a high operation efficiency simply by constantly increasing the gas injection displacement. Consequently, in the design stage, the lifting capacity of subsea pump and optimal gas injection displacement should be thoroughly considered.

Gas injection displacement and sites are the key parameters of gas lifting. Properly selecting the gas injection sites significantly affects the subsea pump power requirements. The interaction between the depth of gas injection sites and pump lifting power is calculated as shown in Figure 12. Keeping the gas injection displacement constant, as the depth of gas injection sites increases, the subsea pump power requirement is reduced with a decreasing slope. As the gas injection site depth changes from 100 to 400 m, the pump power decreases from 57.255 to 49.14 kW, an 8.115 kW reduction. As the gas injection site depth changes from 400 to 700 m, the pump power is reduced by 2.903 kW. A deeper gas injection site results in higher requirements for the air compressor on the platform. Based on the conditions of this example, the recommended depth of gas injection site is 400 m.

During deepwater drilling, as seawater depth increases, the requirements regarding drilling equipment and engineering risks will increase as well. The subsea pumping power variations with respect to different seawater depths are calculated as illustrated in Figure 13. The calculation results exhibit that as seawater depth increases, the subsea pump lifting power increases almost linearly. The subsea pump power requirements increase with an increasing depth, during which the effect of gas lifting increases as well. Based on the conditions of this example, subsea pump power increases by 4.97 kW for every additional 100 m in seawater depth.

The novel deepwater closed-cycle riserless drilling method with a subsea pump + gas combined lift aims to address the marine environment pollution and poor wall protection issues caused by open-cycle drilling operation, while avoiding the high costs and risks associated with drilling operations that use risers. In a conventional closed-cycle riserless drilling system, the return of mud is only powered by the subsea lifting pump. Therefore, the flow rate and cutting carrying effect of mud return can be solely controlled by adjusting the lifting pump. For the novel deepwater closed-cycle riserless drilling method with a subsea pump + gas combined lift, the interaction between process parameters of gas lift and flow pattern of mud return, as well as the coupling between each process parameter during pump + gas combined lifting, should be considered to achieve efficient cutting carrying.

In a fixed deepwater drilling block, given the drilling depth, seawater depth, and other drilling parameters, the minimum return velocity of cutting carrying and its corresponding subsea pump rated power with gas lifting can be calculated. By designing orthogonal experiments, the subsea pump power can be simulated and calculated, which can fulfill the cutting carrying requirements with respect to different gas injection depths of gas injection pipeline, gas injection displacements, and drilling fluid displacements. The minimum subsea pump power is selected to optimize and maximize the cutting carrying efficiency by gas injection. In the block with large seawater depth, it might be preferred to first increase gas injection displacement and then increase the depth of gas injection sites. Consequently, the subsea pump load can be decreased as much as possible; in other words, a high-efficiency deepwater drilling process with a low-power subsea pump can be achieved.

The multiphase flow model of the deepwater closed-cycle riserless drilling with a subsea pump + gas combined lift has been proposed to analyze the effects of drilling fluid displacement, gas injection displacement, gas injection site, and seawater depth on the multiphase flow in the novel closed-cycle riserless drilling wellbore. Subsequently, the following conclusions are obtained:

(2) With increasing gas injection displacement, it is easier to carry the cuttings and return them to the wellhead, which reduces the subsea lifting pump power requirement.

JW Overall structure design and numerical simulation. JS: Multiphase flow model of closed-cycle riserless drilling biulding. WX: Advantages of the novel subsea closed-cycle riserless drilling method using a pump + gas combined lift in deep-sea drilling analysis. HC: Mesh generation and solution of multiphase flow model. CW: Effect of gas injection site on the subsea pump lifting power analysis and language check. YY: Effect of seawater depth on the subsea pump lifting power analysis. RQ: Optimization of hydraulic parameters analysis.

1. Peter A. Deepwater Drilling: Well Planning, Design, Engineering, Operations, and Technology Application. Houston, Texas: Gulf Professional Publishing (2019).

2. Yang X, Sun J, Zhang Z, Xu L, Wang C, Liu Z, et al. Design and Application of Drilling System Digital Prototype for deepwater Drilling Platform. IOP Conf Ser Mater Sci Eng (2020) 964:012027. doi:10.1088/1757-899x/964/1/012027

9. Li X, Zhang J, Tang X, Mao G, Wang P. Study on Wellbore Temperature of Riserless Mud Recovery System by CFD Approach and Numerical Calculation. Petroleum (2020) 6(2):163–9. doi:10.1016/j.petlm.2019.06.006

14. White DB, Walton IC. A Computer Model for Kicks in Water- and Oil-Based Muds. In: IADC/SPE Drilling Conference; February 1990; Houston, Texas (1990). SPE-19975.

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.

The 2,200-hp mud pump for offshore applications is a single-acting reciprocating triplex mud pump designed for high fluid flow rates, even at low operating speeds, and with a long stroke design. These features reduce the number of load reversals in critical components and increase the life of fluid end parts.

The pump’s critical components are strategically placed to make maintenance and inspection far easier and safer. The two-piece, quick-release piston rod lets you remove the piston without disturbing the liner, minimizing downtime when you’re replacing fluid parts.

Researchers have shown that mud pulse telemetry technologies have gained exploration and drilling application advantages by providing cost-effective real-time data transmission in closed-loop drilling operations. Given the inherited mud pulse operation difficulties, there have been numerous communication channel efforts to improve data rate speed and transmission distance in LWD operations. As discussed in “MPT systems signal impairments”, mud pulse signal pulse transmissions are subjected to mud pump noise signals, signal attenuation and dispersion, downhole random (electrical) noises, signal echoes and reflections, drillstring rock formation and gas effects, that demand complex surface signal detection and extraction processes. A number of enhanced signal processing techniques and methods to signal coding and decoding, data compression, noise cancellation and channel equalization have led to improved MPT performance in tests and field applications. This section discusses signal-processing techniques to minimize or eliminate signal impairments on mud pulse telemetry system.

At early stages of mud pulse telemetry applications, matched filter demonstrated the ability to detect mud pulse signals in the presence of simulated or real noise. Matched filter method eliminated the mud noise effects by calculating the self-correlation coefficients of received signal mixed with noise (Marsh et al. 1988). Sharp cutoff low-pass filter was proposed to remove mud pump high frequencies and improve surface signal detection. However, matched filter method was appropriate only for limited single frequency signal modulated by frequency-shift keying (FSK) with low transmission efficiency and could not work for frequency band signals modulated by phase shift keying (PSK) (Shen et al. 2013a).

In processing noise-contaminated mud pulse signals, longer vanishing moments are used, but takes longer time for wavelet transform. The main wavelet transform method challenges include effective selection of wavelet base, scale parameters and vanishing moment; the key determinants of signal correlation coefficients used to evaluate similarities between original and processed signals. Chen et al. (2010) researched on wavelet transform and de-noising technique to obtain mud pulse signals waveform shaping and signal extraction based on the pulse-code information processing to restore pulse signal and improve SNR. Simulated discrete wavelet transform showed effective de-noise technique, downhole signal was recovered and decoded with low error rate. Namuq et al. (2013) studied mud pulse signal detection and characterization technique of non-stationary continuous pressure pulses generated by the mud siren based on the continuous Morlet wavelet transformation. In this method, generated non-stationary sinusoidal pressure pulses with varying amplitudes and frequencies used ASK and FSK modulation schemes. Simulated wavelet technique showed appropriate results for dynamic signal characteristics analysis.

As discussed in “MPT mud pump noises”, the often overlap of the mud pulses frequency spectra with the mud pump noise frequency components adds complexity to mud pulse signal detection and extraction. Real-time monitoring requirement and the non-stationary frequency characteristics made the utilization of traditional noise filtering techniques very difficult (Brandon et al. 1999). The MPT operations practical problem contains spurious frequency peaks or outliers that the standard filter design cannot effectively eliminate without the possibility of destroying some data. Therefore, to separate noise components from signal components, new filtering algorithms are compulsory.

Early development Brandon et al. (1999) proposed adaptive compensation method that use non-linear digital gain and signal averaging in the reference channel to eliminate the noise components in the primary channel. In this method, synthesized mud pulse signal and mud pump noise were generated and tested to examine the real-time digital adaptive compensation applicability. However, the method was not successfully applied due to complex noise signals where the power and the phases of the pump noises are not the same.

Jianhui et al. (2007) researched the use of two-step filtering algorithms to eliminate mud pulse signal direct current (DC) noise components and attenuate the high frequency noises. In the study, the low-pass finite impulse response (FIR) filter design was used as the DC estimator to get a zero mean signal from the received pressure waveforms while the band-pass filter was used to eliminate out-of-band mud pump frequency components. This method used center-of-gravity technique to obtain mud pulse positions of downhole signal modulated by pulse positioning modulation (PPM) scheme. Later Zhao et al. (2009) used the average filtering algorithm to decay DC noise components and a windowed limited impulse response (FIR) algorithm deployed to filter high frequency noise. Yuan and Gong (2011) studied the use of directional difference filter and band-pass filter methods to remove noise on the continuous mud pulse differential binary phase shift keying (DBPSK) modulated downhole signal. In this technique, the directional difference filter was used to eliminate mud pump and reflection noise signals in time domain while band-pass filter isolated out-of-band noise frequencies in frequency domain.

Other researchers implemented adaptive FIR digital filter using least mean square (LMS) evaluation criterion to realize the filter performances to eliminate random noise frequencies and reconstruct mud pulse signals. This technique was adopted to reduce mud pump noise and improve surface received telemetry signal detection and reliability. However, the quality of reconstructed signal depends on the signal distortion factor, which relates to the filter step-size factor. Reasonably, chosen filter step-size factor reduces the signal distortion quality. Li and Reckmann (2009) research used the reference signal fundamental frequencies and simulated mud pump harmonic frequencies passed through the LMS filter design to adaptively track pump noises. This method reduced the pump noise signals by subtracting the pump noise approximation from the received telemetry signal. Shen et al. (2013a) studied the impacts of filter step-size on signal-to-noise ratio (SNR) distortions. The study used the LMS control algorithm to adjust the adaptive filter weight coefficients on mud pulse signal modulated by differential phase shift keying (DPSK). In this technique, the same filter step-size factor numerical calculations showed that the distortion factor of reconstructed mud pressure QPSK signal is smaller than that of the mud pressure DPSK signal.

Study on electromagnetic LWD receiver’s ability to extract weak signals from large amounts of well site noise using the adaptive LMS iterative algorithm was done by (Liu 2016). Though the method is complex and not straightforward to implement, successive LMS adaptive iterations produced the LMS filter output that converges to an acceptable harmonic pump noise approximation. Researchers’ experimental and simulated results show that the modified LMS algorithm has faster convergence speed, smaller steady state and lower excess mean square error. Studies have shown that adaptive FIR LMS noise cancellation algorithm is a feasible effective technique to recover useful surface-decoded signal with reasonable information quantity and low error rate.

Different techniques which utilize two pressure sensors have been proposed to reduce or eliminate mud pump noises and recover downhole telemetry signals. During mud pressure signal generation, activated pulsar provides an uplink signal at the downhole location and the at least two sensor measurements are used to estimate the mud channel transfer function (Reckmann 2008). The telemetry signal and the first signal (pressure signal or flow rate signal) are used to activate the pulsar and provide an uplink signal at the downhole location; second signal received at the surface detectors is processed to estimate the telemetry signal; a third signal responsive to the uplink signal at a location near the downhole location is measured (Brackel 2016; Brooks 2015; Reckmann 2008, 2014). The filtering process uses the time delay between first and third signals to estimate the two signal cross-correlation (Reckmann 2014). In this method, the derived filter estimates the transfer function of the communication channel between the pressure sensor locations proximate to the mud pump noise source signals. The digital pump stroke is used to generate pump noise signal source at a sampling rate that is less than the selected receiver signal (Brackel 2016). This technique is complex as it is difficult to estimate accurately the phase difference required to give quantifiable time delay between the pump sensor and pressure sensor signals.

As mud pulse frequencies coincide with pump noise frequency in the MPT 1–20 Hz frequency operations, applications of narrow-band filter cannot effectively eliminate pump noises. Shao et al. (2017) proposed continuous mud pulse signal extraction method using dual sensor differential signal algorithm; the signal was modulated by the binary frequency-shift keying (BFSK). Based on opposite propagation direction between the downhole mud pulses and pump noises, analysis of signal convolution and Fourier transform theory signal processing methods can cancel pump noise signals using Eqs. 3 and 4. The extracted mud pulse telemetry signal in frequency domain is given by Eqs. 3 and 4 and its inverse Fourier transformation by Eq. 4. The method is feasible to solve the problem of signal extraction from pump noise,

These researches provide a novel mud pulse signal detection and extraction techniques submerged into mud pump noise, attenuation, reflections, and other noise signals as it moves through the drilling mud.

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