Keywords

1 Introduction

The screw pump is a pump in which the head of the pumped liquid is achieved by displacing the liquid by the screw rotors (one or more) rotating inside the stator of the appropriate shape. By the nature of the impact of the working elements, screw pumps are categorized as volumetric pumps. The world oil and gas industry has developed and offers in the market of oilfield equipment a wide range of screw submersible pumps. The peculiarity of these units is that they have the ability to regulate the rotation speed of the drive rod string by changing the gear ratio in the reducers. In existing designs, regulation of mechanical type is applied at the expense of installation of changeable pulleys of belt gears [1,2,3,4]. In this case, the overall dimensions and labor intensity of installation works during the transition of the well to another mode of operation significantly increase.

In order to increase and accelerate oil production a large number of wells are equipped with high-performance submersible oil pumps in Russia, for which new technologies of pump manufacturing have been created, their design, operation and repair technologies have been perfected. Despite all the advantages of the installations, namely high reliability, corrosion resistance, satisfactory wear resistance, simple design, there are such drawbacks as instability and impossibility of operation in the range of low flows up to 35 m3/day, low efficiency, performance control occurs with loss of either the pressure characteristics or the drop of efficiency, disruption of supply at high gas content [5,6,7,8]. Equipping wells with screw pump installations and their incorrect selection, often leads to exceeding the maximum allowable underbalance in the reservoir.

The purpose of the work is to improve the technical and economic performance of the surface drive design by changing the method and extending the regulation range.

2 Materials and Methods

The most common surface drive of a screw pump is the V-belt drive. The use of this type of screw pump drive does not allow full control of the pump flow. The interchangeable set of pulleys is limited by their small number (on average 4 pcs), which allows using the pump only in 4 operating modes.

Analysis of technical information [9,10,11,12,13,14] allowed us to determine that the most promising technical solution for severe operating conditions, is the use of reducing insert 2 (Fig. 1). The use of this type of drive will reduce the labor intensity of regulating the screw pump delivery, reduce the metal intensity of the construction as a whole, as well as expand the regulation range.

Fig. 1
figure 1

Surface drive screw pump with reducing insert: 1—motor; 2—reducing insert; 3—gearbox; 4—spinner's wheel; 5—connector; 6—adapter; 7—seal; 8—sealing unit; 9—seal; 10—pump drive shaft; 11—bottom case; 12—top case; 13—driving pulley; 14—driven pulley; 15—coupling; 16—coupling; 17—insert mounting node; 18—cover; 19—motor mounting node; 20—screw

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The proposed surface drive of the submersible pump unit is equipped with a reducing insert 2, kinematically connected with the reducer 3 and made as a two-stage gear mechanism, including the leading, middle and driven gears of different diameters, consistently meshed with each other, and the middle wheel shaft is made with two connection ends, and the intermediate gear shaft is provided with one connection end, derived respectively from the module and reducer bodies, which in the output places of the connection ends are connected with the drive shaft. This makes it possible to connect the motor 1 to either of the connection ends of the gearbox shafts, which are connected to the leading or intermediate gearbox shaft. The leading, middle and slave wheels of the module are designed with successively increasing in unequal proportions diameters. This design allows different gear ratios, larger than one, from the driving wheel to the middle wheel, from the middle wheel to the driven wheel, and from the driving wheel to the driven wheel. As a result, the drive of one complete set allows one to obtain fourteen values of drive transmission ratios, and consequently as many combinations of pressures and screw pump feeds.

The tasks of research are: (i) selection of gear ratios of the drive; (ii) design calculation of the reducing insert; (iii) computer simulation of the drive; (iv) study of the strength characteristics of the body of the reducing insert.

Let us consider technical characteristics of drive of pump 12PX52 (see Table 1) for kinematic calculations. The drive includes the main reducer, to the input shaft of which the rotation from the asynchronous electric motor is transferred by means of the V-belt drive. The drive is regulated by installing interchangeable pulleys.

Table 1 Main characteristics of the 12PX52 pump drive
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The kinematic diagram of the proposed version of the drive is shown in Fig. 2. To save the technical characteristics of the drive set, the problem of determining such a transfer ratio of drive, at which the output shaft of the drive would rotate at a speed of 203, 243, 304 and 348 rpm with an error of not more than 5% [15]. Transmission ratios must comply with the standard series of Russian GOST 2185–2006.

Let us designate gears K1–K7 (Fig. 2). Let us designate the motor *D, where * is a number of connecting end of the drive shaft, on which the electric motor is installed. The nomial speed of the electric motor nM = 1000 rpm.

To determine the number of teeth of the drive gears, we accept the following sequences of inclusion of gears to achieve the required speeds of the output shaft:

  1. (i)

    \(1{\text{D}} \to {\text{K}}1{\text{K}}2 \to {\text{K}}6{\text{K}}7 \to 243{\text{ rpm}};\)

  2. (ii)

    \(2{\text{D}} \to {\text{K}}2{\text{K}}3 \to {\text{K}}4{\text{K}}5 \to {\text{K}}6{\text{K}}7 \to 203{\text{ rpm}};\)

  3. (iii)

    \(3{\text{D}} \to {\text{K}}6{\text{K}}7 \to 348{\text{ rpm}};\)

  4. (iv)

    \(4{\text{D}} \to {\text{K}}4{\text{K}}5 \to {\text{K}}6{\text{K}}7 \to 304{\text{ rpm}}.\)

Fig. 2
figure 2

Kinematic diagram of the drive

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To solve the problem, we made a MathCAD program (Fig. 3), in which we solve the system of inequalities, including the equations of kinematic balance of the drive for options 1 − 4 with the requirement of achieving no more than 2% deviation from the set frequency of rotation of the output shaft.

According to the results of the calculation (see Fig. 3), we conclude that the accuracy of the kinematic calculation of the drive gears is satisfactory.

Let us consider other variants of switching on the motor and drive gears, using the obtained gear ratios:

  1. (v)

    \(1D \to K1K2K3 \to K4K5 \to K6K7 \to 140\,{\text{rpm}};\)

  2. (vi)

    \(1D \to K1K2K3 \to K6K7 \to 156\,{\text{rpm}};\)

  3. (vii)

    \(2D \to K2K3 \to K6K7 \to 218\,{\text{rpm}};\)

  4. (viii)

    \(1D \to K1K2 \to K4K5 \to K6K7 \to 223\,{\text{rpm}}.\)

The indicated drive switching variants were obtained when using the insert as a reducer. The design of the reduction insert in the surface drive of a screw pump allows it to be used both as a reducer and as a multiplier.

The remaining variants of actuator switching are calculated using the insert as a multiplier - shafts (v) and (vi) are used for installation of the electric motor, respectively, shafts (i) and (ii) are used for connection with the reducer.

  1. (ix)

    \(6D \to K3K2K1 \to K4K5 \to K6K7 \to 700 \,{\text{rpm}};\)

  2. (x)

    \(6D \to K3K2K1 \to K6K7 \to 784\, {\text{rpm}};\)

  3. (xi)

    \(6D \to K3K2 \to K4K5 \to K6K7 \to 500 \,{\text{rpm}};\)

  4. (xii)

    \(6D \to K3K2 \to K6K7 \to 560\, {\text{rpm}};\)

  5. (xiii)

    \(5D \to K2K1 \to K6K7 \to 490\, {\text{rpm}};\)

  6. (xiv)

    \(5D \to K2K1 \to K4K5 \to K6K7 \to 438\, {\text{rpm}}.\)

Fig. 3
figure 3

Calculation of drive gear ratios in MathCAD

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Let us determine the values of relative theoretical flow per one revolution of the pump screw (Table 2). On average, there is 0.261 m3/day of pump flow per screw revolution.

Table 2 Results of kinematic calculation of the drive
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Let us determine the efficiency of the reduction insert µe:

$$ \mu_e = \mu_c \mu_b \mu_g , $$
(1)

where µc is the coupling efficiency, µb is the bearing pair efficiency, µg is the efficiency of gearing

$$ \mu_e = 0.98 \cdot 0.97^2 \cdot 0.99^3 = 0.931. $$

Then we determine the rotational speed of each shaft of the reduction insert and the reducer:

$$ \begin{gathered} n_1 = n_M = 1000\, {\text{rpm}};n_2 = \frac{n_1 }{u} = \frac{1000}{{1.4}} = 714\, {\text{rpm}};{ }n_3 = n_4 = \frac{n_2 }{u} = \frac{714}{{1.6}} = 446\, {\text{rpm}};{ } \hfill \\ n_5 = \frac{n_3 }{u} = \frac{446}{{1.12}} = 398 \,{\text{rpm}};{ }n_6 = \frac{n_4 }{u} = \frac{398}{{2.8}} = 142\,{\text{rpm}}{.} \hfill \\ \end{gathered} $$

Let us find the power transmitted by each drive shaft:

$$ P_i = P_M^{\prime} \eta_1 \eta_2 \eta_3 \ldots \eta_n , $$
(2)

where P’M is the motor power; P’M = 22 kW; η1,…,ηn is the efficiency of mechanisms and devices preceding the i-th shaft.

Then we determine the torques on the drive shafts:

$$ T_i = 9550\frac{P_i }{{n_i }} , $$
(3)

where Pi is the power transmitted by the shaft; ni is the number of revolutions of the shaft.

The data obtained are present in Table 3.

Table 3 Design parameters of drive shafts
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The three-dimensional parametric model of the reducing insert is made using CAD KOMPAS-3D [16,17,18,19,20].

The shafts are taken unified to ensure the possibility of installation (the connecting ends of the shafts must be identical). In this case, it is sufficient to calculate the most heavily loaded shaft, namely the slow-speed shaft [20,21,22].

Using the torque and the number of revolutions of the shaft (Table 3), we determine its geometric parameters and build 3D models of all the shafts of the reduction insert.

3 Results and Discussion

To calculate the main parameters of the gears: number of teeth, module, gear width, center distance, pitch diameter, we used the capabilities of CAD software KOMPAS-3D. Calculating formulae, we perform in the document “Fragment” in the parametric mode. It is most appropriate to use the Main (user) section for this purpose. This section does not directly control the graphic image. Therefore, we can freely draw ratios, formulae, equations, etc. in this section. We must use the KOMPAS-3D syntax. Similar to MS Excel, the program allows for automatic recalculation in accordance with the created calculation model when data changes are made. In addition, if some data are constants, we can use a table of variables where we enter the parameters for the first and second step in sequence, linking the subsequent formula with the previous one so that if one of the parameters changes, recalculation will be performed automatically. We use well-known formulae for gear design [23, 24]. Automated calculation and data for the construction of a 3D model of the reduction insert gears allows us to obtain a family of three-dimensional models of gear inserts for the changed design conditions. After creating 3D models of shafts and gears, we design the reduction insert housing and bearing covers. In the result of assembling all the parts, a ready 3D model of the reducer insert is obtained, with the help of which the study of strength characteristics of its parts becomes possible.

Based on the obtained data (Table 2), a comparative graph is plotted (Fig. 4). It can be seen that the range of flow rates when using a modular insert is much wider than when using a V-belt drive. This will allow one to cover the maximum range of well flow rates using a screw pump. The accuracy of adjustment to the required screw pump capacity in order to provide the required well flow rate will also be higher.

Fig. 4
figure 4

Dependences of screw pump delivery on drive output shaft speed: 1—with gear box; 2—with V-belt transmission

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The strength characteristics of the reducing insert body were investigated by the finite element method in SolidWorks Simulation CAD. To carry out the calculations, it is necessary to apply external loads acting on the housing:

  1. (i)

    perceived on the cylindrical surfaces of the housing at the bearing locations (radial load);

  2. (ii)

    through the mass of the electric motor;

  3. (iii)

    taken up by the own mass of the reducing insert.

The magnitude of the radial load applied to each of the bearing seating surfaces is equal to the reaction forces acting on the shafts of the reducing insert during their operation.

In addition to the loads, the model included the following constraints: locking against displacements in all directions of the bolt hole surfaces, simulating bolt joints.

The results of the study of the reduction insert housing are presented in the form of equivalent stresses (Fig. 5) and the yield stress safety factor (Fig. 6).

Fig. 5
figure 5

Calculation results present equivalent stress diagram

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Fig. 6
figure 6

Calculation results present yield stress safety factor diagram

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As it can be seen, the equivalent stresses are evenly distributed over the hull area. The maximum value of stresses is 109 MPa. The minimum yield strength coefficient of the material is 2.59. For cast iron castings, the hull has sufficient strength and will withstand acting loads.

4 Conclusions

In the result of the conducted research, the design of a surface drive of a screw pump with the use of a reduction insert is proposed. The kinematic diagram of the unit is built, the drive gear ratios are selected and the kinematic calculation is performed. Based on the obtained data, a comparative diagram of the two drives by the regulation range was built, where the advantage of the improved drive is clearly shown. A 3D model of the reduction insert was built in KOMPAS-3D CAD, taking into account the recommendations for designing reducers. The reducing insert housing was analyzed for strength and stresses in the SolidWorks Simulation software environment, as a result of which it was revealed that it has an adequate safety margin.

Thus, an improved surface drive of a screw downhole pump was designed. The range of delivery control using this type of drive is much wider than that of the original drive. It will allow adjusting the pump more accurately to the flow rate of the well, and get optimal performance with increasing the service life of the pump by removing excessive load from it.

The proposed screw pump drive design has greater possibilities caused by the following possible sources of economic efficiency:

  1. (i)

    decrease in metal consumption and overall dimensions of the offered drive design;

  2. (ii)

    decrease in labor input of installation works on installation and adjustment of the drive;

  3. (iii)

    increase of service life of the pump due to more accurate adjustment for optimum speed.