The power and pump cylinders are connected by rods, so the number of operational cycles ($n_c$) of both cylinders are equal. Thus, the volumetric flow of the hydraulic pump ($Q_B$) for the configurations using the single rod ($Q_{Bs}$) can be described by Eq. 4.$$\begin{array}{}\text{(3)}& Q_{Bs}=785.\left(2.d_p^2-<!--\; -\; -->d_{ph}^2\right).L.n_c.{\mathrm{\eta <!--\; ?\; -->}}_{vol}\end{array}$$

Source:

where,

The force of the power cylinder $F_{AP}$ required to deliver the production fluid depends on the column pressure $P_C$ exerted on the area of the pump cylinder (upward cycle $A_{B1}$ or downward cycle $A_{B2}$. The SLP pump cycle occurs when the power actuator force is greater than the resistance of the pump actuator $D_E$. Fig. 4 illustrate the force in the pump module with single pump actuator.

Fig. 4 - Forces in the SLP¹ pump module, where the red color indicates the pressure of the hydraulic pump and the blue color the pressure of the production column for the upwards and downwards movements.

In the downward movement, the area $A_{B2}$ is subjected to the static column pressure of the fluid $P_C$. Thus, using Eq. 4, the column pressure force $\left(F_{PC(SL{P}^1)}\right)$ can be defined in the downward cycle exerted on the double-acting pump $D_E$ of the SLP¹. Similarly, the column pressure force in the upward cycle exerted on the double-acting pump (DE ), replacing the area $A_{B2}$ by $A_{B1}$.

source

where,

In addition to analyzing the forces developed between the hydraulic pump pressure and the available areas of the power actuator $A_P$, the emergence of other induced pressures should be noted. Such pressures could according to [13] originate from the resistance to the flow of the fluid in the pipe, in the return filter or any other resistance hindering the fluid from exiting the cylinder, which may be greater than the pressure supplied to the cylinder, thus causing possible stoppages. During the pumping process the production fluid moves from the production zone up to the surface (Fig. 5). In addition to the force exerted by the production column, the load losses caused by the friction of the liquid flow in the delivery pipe and the localized losses related to the singularities in the pipe installation project must be considered.

 

Fig. 5 - SLP - installation, delivery and detail of pump module.

Considering the preliminary flow in the delivery pipe/production column and neglecting the localized losses due to the minimal use of singularities, the manometric head of the SLP ($H_{man}$) and the loss of load ($h_f$) can be estimated using Eq. 5 and Eq. 6.

source

where,

AbbreviationExpansion

The hydraulic power module of the SLP (Fig. 6) consists of a submersible electric motor (M), hydraulic pump (B), filters (suction and return) (F), pressure relief valve ($L_S$), reservoir (T), 4/2-way directional (control) valves, 4/3-way directional (control) valve - negative open center (CAN), sequence valves ($L_{p1}$ and $L_{p2}$ ) and the suction, pressure and return lines.

Fig. 6 - Hydraulic scheme of SLP¹ simulated in Automation Studio™.

In order to raise the production fluid to the surface, the working pressure of the hydraulic pump (PB ) must act on the piston of the power actuator (AAP ), resulting in the forward movement of the power actuator (FAP ). According to [14], Eq. 7 and Eq. 8 determine the force of the power actuator developed for the down and up cycles of the SLP¹, respectively.

source

where,

AbbreviationExpansion

$P_T$- tank pressure, Pa;
$F_{a(A_P)}$- power actuator friction force, N;
$A_{P1}$- area of power actuator subjected to hydraulic pump pressure, m².

The frictional forces and dynamic behaviour within hydraulic cylinders are not well documented; this is in part because there are a considerable number of factors that are difficult to estimate. The dominant contribution to friction undoubtedly comes from the seal assembly, including the wiper or scraper rings. Also friction depends greatly on the type of seal, surface finishes and operating circumstances, besides there is significant variability associated with temperature and wear and tear effects to further confuse the problem [14]. Studies such as those of [15]–[16][17] and [18] present models to estimate the friction in hydraulic cylinders. Other authors, such as [19], [20] and [21] used load correction coefficients ($\eta$) to compensate for friction losses, approximately 10% to 20% of the theoretical force.

The pressure required in the up and down cycles of the SLP hydraulic pump can be determined as they are directly related to the area on which the column pressure acts. However, the power actuator force ($F_{AP}$) is proportional to the force induced by the column pressure ($F_{PC}$) acting on the pump cylinder. In this work the power actuator force ($F_{AP}$) is considered to be the corrected force required to lift the production or the corrected design force. This force must be adjusted in order to compensate for the friction losses of the drive of the power actuator itself, as well as of the pump actuator and the fluid flow in the pipes. According to [22], the power actuator force, hydraulic pump pressure, and electric motor power can be determined by Eq. 9, Eq. 10 and Eq. 11, respectively.

source

where,

AbbreviationExpansion

SECTION III. Optimization Algorithms

The optimization task is carried out using different optimizers including the particle swarm optimization (PSO), genetic algorithm (GA) and harmony search algorithm (HS).

For a new pumping system design one must look for the parameters that allow the system to operate with higher productivity and lower energy losses. Thus, the need for approximate solutions arises.

Metaheuristic algorithms are well-known approximate methods for solving and optimizing problems. Here we adopt metaheuristic optimization algorithms to determine a set of best solutions that maximize the design criteria of the SLP. In this work we use the four optimization algorithms described as follows.

The PSO algorithm is a population-based stochastic optimization technique that presents similarities to the evolutionary computational techniques, such as Genetic Algorithms [23]. PSO is a popular optimization method that is widely used in various applications, and it is simple and is able to obtain optimal results. However, it may become trapped in the local optimal point, especially in high dimensional problems [24].

As stated by [25], the PSO algorithm begins by randomly generating a swarm of particles that fly through a problem space, and each particle represents a candidate solution to the optimization problem. The suboptimal value of each particle can be derived from a user-defined fitness function that is linked to the objective function (cost function). In the iteration, each particle moves toward the ideal location, with the speed updated according to the best position achieved (the best improved particle) and the best overall position obtained from any swarm particle so far (best overall).

According to [26], the working steps of the PSO method for solving a objective function optimization can be described as:

1-Initializes a population (matrix) of particles with random positions and velocities in the dimensions of the problem space. The decision variables in PSO are counted by the dimension of each particle;
2-Compute the fitness value of each particle through an objective function;
3-For each particle, if the current particle fitness value is better than its previous value, the current best fitness value is set as the new ${\text{P}}_{best}$ .
4-Choose the particle with the best fitness value (${\text{P}}_{best}$ ) of all the particles as the ${\text{G}}_{best}$ ;
5-Update particle velocity and position according to Eq. (12), Eq. (13) [25], [27];
6-Repeat as of 2 until the maximum number of iterations is reached.

source

where $v_{id}^t$ is the velocity of the particle, $x_{id}^t$ is the position of the particle, $p_{id}^t$ is position of the best particle in the current iteration, ptgd is the best position of the particle globally, $\omega$ is the coefficient of inertia, $c_1$ is the cognitive constant and $c_2$ is the social constant, $r_1$ and $r_2$ are numbers that lie in the range of 0 to 1 that avoid trapping in minimum local minima and to allow the divergence of a small percentage of particles to a wider exploration of the search space.

GA is a metaheuristic inspired by the process of natural selection. Essentially, natural selection acts as a type of optimization process that is based on conceptually simple operations of competition, reproduction, and mutation [28]. A genetic algorithm (GA) uses strings of binary coding, 0 and 1, to encode whatever informationis needed to define a distinct solution to a problem. This solution may then be tested to produce a fitness value [29]. A Genetic Algorithm is typically represented by the following pseudocode.
 

1- Initialize the first generation with a population of N randomly-generated individuals;

2- Evaluate the fitness (objective function) for each individual of the current generation;

3- Until the fitness of the fittest individuals is not high enough:

1- Create the next generation using M

2-Pair N-M members from the previous population, produce offspring (crossover) and insert them into the new generation;

3-Select R members of the new generation and randomly invert a bit in each (mutation);

4-Update fitness;

4-Current fittest individual from the current generation is the best solution.

According to [30] and [31], HS is a metaheuristic optimization method that has the advantages of not requiring an initial value and can be considered to have discontinuous functions as well as continuous functions because it does not require differential gradients. It does not require an initial value setting for the variables, and it is free from divergence and may escape local optimal. A comprehensive explanation of this algorithm can be found in [32]. A pseudocode for the Harmony Search Algorithm can be summarized as follows:

1- Define an objective function to be optimized;

2- Initialize an array of real numbers (harmonics);

3- Define the pitch adjusting rate, pitch limits and bandwidth;

4- Define the harmony memory accepting rate, Repeat for a number of iterations:

1-Generate new harmonics using the best harmonics (solutions);

2- Adjust pitch to find new harmonics;

3- Choose an existing harmonic randomly if harmony memory accepting rate is reached, or

4- Adjust the pitch randomly within limits if pitch adjusting rate is reached;

5- Otherwise, randomly generate new harmonics;

6- If harmonics are better, accept the new solutions

5-Current best harmonics are the best solutions.

SECTION IV. Computational Simulation

According to [33], the Automation Studio™ environment is an design and simulation solution covering project/machine technologies including hydraulics, pneumatics, electrical, controls, human machine interface (HMI), and communications.

Pandhare and Metkar [34] presented a review paper that gave details of some of the design techniques which can be used on the Automation Studio™ for automatic hydraulic machines.

He et al. [35] used the Automation Studio™ in the hydraulic drive system to analyze pressure, acceleration and flow-load parameters of the two cylinders. The results of the parameter tests presented similarities with the results of the simulation. Thus the model could be simplified and the parameters adjusted from simulations of the system.

In this work, the Automation Studio™ is used to perform test scenarios, in order to better understand the behaviour of the proposed system and to evaluate the set of design parameters determined by optimization. To minimize the complexity of the simulated model, friction and temperature variation were not considered in the Automation Studio™ software.

SECTION V. Optimizing the Design of the SLP

SLP design requires optimzing parameters in the search space as described in Table 1. In order to minimize the energy consumption of the SLP, the optimal parameter set of displacement of cylinders ($L$), diameter of the delivery pipe (${\text{d}}_b$), piston diameter of the power and pumping cylinders (${\text{d}}_b$), the rod diameters of the cylinders (${\text{d}}_{ph}$) and rod safety coefficient ($S$) must be minimized. In contrast, the volumetric flow (${\text{Q}}_{SLP}$) and manometric head (${\text{H}}_{man}$) must be maximized. To achieve such criteria, in this paper we define the single objective function (${\text{f}}_o$) in Eq. 14 to be optimized.

source

TABLE 1 - Parameters Chosen for the Search Space - SLP¹

SECTION VI. SLP⁰ Prototype

A conceptual prototype of the SLP⁰ was developed as for the initial operational tests in order to validate the operational parameters, as well as to observe if there were any practical difficulties that were not possible to identify during the SLP design phase. The tests with the prototype were able to evaluate the operation of the actuator and to validate the control system that during the project design was based on the pressure of the system, which was initially done by mechanical systems. In the first phase, hydrostatic and hydrodynamic tests were not performed. The SLP⁰ components are shown in Fig. 7 and Fig. 8.

Fig. 7 - Assembly of the power set.

Fig. 8 - Fitting the hydraulic pipes into a housing and detail of hydraulic filter and piping.

In general, the supply flow for traditional hydraulic speed control has two basic forms: where the valve control or a fixed displacement pump is driven by a variable speed motor whose engine speed determines the flow [36]–[37][38][39].

The dynamic response of the valve control system is fast, but the efficiency is low [40], [41], the efficiency of the pump control system is high, but the dynamic response of the system is slow [42], [43].

The SLP⁰ volumetric production flow is controlled by the rotations of the hydraulic pump motor using a frequency inverter, increasing and decreasing the hydraulic oil flow and consequently the hydraulic actuator stroke frequency. Table 2 shows the parameters used for the construction of the SLP⁰.

Table. 2 - Operational Simulation Characteristics Used for the SLP⁰ Prototype

SECTION VII. SLP¹ Experimental Test Bench

In order to validate the working design of the SLP, referring to the volume produced, a similar hydraulic system was prepared on an experimental test bench using rigid and flexible pipes, fittings and 1/2”-inch check valves. The system was set up on the Hydraulic and Pneumatic Laboratory - LHP experimental test bench at the Federal Institute of Education, Science and Technology of Ceará - IFCE. Fig. 9, shows that, unlike the final design of the SLP, using only mechanical components this system uses inductive sensors such as limit switches and solenoid valves to control the power cylinder. The use of electrical components was necessary due to the reduced number of flexible hoses available at the LHP/IFCE, however we did not considered this would affect the objective of the tests. The test consists of pumping VG 46 hydraulic oil from the test bench reservoir to an external reservoir with a capacity of 5 liters. In order to minimize localized load losses, 1/4” to 1/2” adapters were used in the pump connections of the hydraulic cylinder for the SLP¹ tests. The pressure tests of the hydraulic system, varied from 5 to 50 bar.

Fig. 9 - Simulation of the SLP¹ on the hydraulic experimental test bench at the LHP/IFCE.

In order to obtain greater reliability in the results, an average of ten runs for each pressure level was used. Table 3 shows the parameters used and specifications of the components of the LHP/IFCE.

Table. 3 - SLP¹ - Parameters Used and Specifications of the Components Tested on the LHP/IFCE Bench

SECTION VIII. Results

The operational curves of the numerical simulation of the power and pump modules and the experimental SLP⁰ and SLP¹ test curves in a controlled environment will be presented here. The choice for the SLP⁰ and SLP¹ tests is because their configurations are less complex, with lower manufacturing costs, as well as the latter being the double-acting pump chosen to develop a fully operational prototype.

A. Parameters Optimization

In this work, we use the optimization framework PyGMO (the Python Parallel Global Multiobjective Optimizer) that provides two PSO implementations, namely PSO and GPSO (Generative PSO), a simple GA (SGA) and a improved HS (IHS). Except for the number of generations and population size, for our purpose the standard parameters of the algorithms provided by PyGMO implementations applies.

Here we present the average of the results of the PSO algorithm for 15 particles and maximum of 20 optimizations per particle and using the search space determined according to Table 1. The simulation presents 300 iterations; however, according to Fig. 10 and Fig. 11, the sub-optimal values converge with a smaller number of iterations. Table 4 shows the best objective values obtained in the simulation of the PSO algorithm (in bold) and the best objective values obtained in the simulation the GPSO, SGA and IHS algorithms. Table 4 also shows the mean ($\stackrel{¯<!--\; ¯\; -->}{x}$) and small standard deviations ($\mathrm{\sigma <!--\; s\; -->}$) between the four optimization algorithms revealing they can find a very similar set of pump parameters.

Table. 4 SLP Design Parameters Obtained for the Best Objective Values Estimated With the Optimization Algorithms (PSO, GPSO, SGA and IHS)

Fig. 10 Evolution of the optimized parameters ${\text{Q}}_{SLP}$ , ${\text{d}}_t$ and ${\text{H}}_{man}$ using PSO.

Fig. 11 Evolution of the optimized parameters ${\text{d}}_b$ , ${\text{d}}_p$ and ${\text{d}}_{ph}$ using PSO.

The results obtained from the best values with the evolutionary optimization PSO, SGA and IHS metaheuristic algorithm have standard deviation indices less than 1.3. Therefore they are presented as one of the solutions of the optimization of the SLP parameters.

B. SLP⁰ Tests

The simulation using the Automation Studio™ environment and tests with the $SL{P}^0$ prototype showed that the system worked as planned and even the power and pump cylinders of the apparatus showed a regular movement, varying proportionally with the speed of the motor. Moreover, as the speed of the electric motor and hydraulic pump increased, the measured speed of the power and pump cylinders approached the theoretical one, probably due to the decrease of the electric motor slippage and the increase in the pump volume efficiency. Control of the speed using the frequency inverter was also without any problems, and the number of pump cycles could be varied accordingly. Fig. 12 shows the measurements taken and the theoretical velocity. In the tests, the SLP⁰ showed a volumetric displacement of 2730 ml of oil per cycle and the maximum average speed of the actuator was 0.1 m/s.

Fig. 12 SLP⁰ - Speed of hydraulic power cylinder and the hydraulic pump.

C. SLP¹ Experimental Test Bench

The system performed as expected with the production of the fluid in both directions of the pump cylinder. The results demonstrated that with an increase of hydraulic pump pressure, the SLP production presented a linear growth. However, due to the configuration used in the tests pressures below 5 bar and above 40 bar were not possible. At pressures below 5 bar the feed force developed by the power cylinder was less than the force required to move the pump cylinder due to friction. While for the pressures above 40 bar the higher pump speed caused induced pressures in the chambers opposing the pump movements, this occurred as it was not possible to increase the diameter of the pump connections of the hydraulic cylinder. Induced pressures acting on the areas available in the chambers opposing the pump cylinder movement generate forces contrary to the feed force of the power cylinder. Thus, the force obtained by the hydraulic pump pressure was not sufficient to move the power/pump assembly.

The graph in Fig. 13 shows that in the 5 to 15 bar range the curve shows a moderate growth of the SLP¹ production, since the cycle time varies from about 5.7 to 4.1 seconds. At pressures between 20 and 40 bar the cycle time varies from 3.1 to 2.4 seconds, which is equivalent to a 25% increase in the pumping speed. At pressures above 40 bar and with the evidence of flow and pressure induced in the pump cylinder, the cycle time presents an abnormal growth of up to 12 seconds, caused by intermittent movements of the power/pump assembly and consequently a reduction in production.

Fig. 13 - SLP¹ operating curve in the experimental test bench.

Using Eq. 2 with pressures of 5 to 40 bar, the production values of the SLP¹ prototype were 2.02 to 4.83 liters per minute. The system tested on the experimental test bench showed an average error of 3.27% and 1% between the calculated production (estimated) and simulated production in the Automation Studio™ environment, respectively. The graph in Fig. 13 shows that the estimated cycle time between the calculated and simulated in the Automation Studio™ has similar curves and presents an approximate error of 5.43%.

D. SLP¹ Numerical Simulation

The diameter of the well is a relevant and limiting factor for the design and construction of the SLP whose diameter must be less than that of the well. Thus, the dimensions of SLP were established according to results obtained from the PSO algorithm and commercial values presented in Table 5.

Table 5. Parameters Used in the Simulation of the SLP¹ Prototype

Ranges of operational parameters were also adopted, and are presented in Table 6.

Table 6. Operational Simulation Characteristics Used for the SLP¹ Prototype

In order for the SLP to function properly, the minimum cycle time of the hydraulic cylinders must be observed. This is limited by the maximum forward and back rate of the hydraulic power cylinder that is dictated by the flow rate of the hydraulic pump. Fig. 14 shows that for a given SLP volumetric flow, between 5 m³/d and 40 m³/d, the number of pump cycles reduces with an increase of the diameter of the hydraulic pump cylinder; however on maintaining cylinder diameter constant at 73.98 mm (value estimated by the PSO), the number of cycles must increase to increase production. Consequently, keeping the diameter of the pump cylinder constant, the volumetric flow of the SLP and the cycle time are inversely proportional. The average error € between the number of cycles per minute calculated (${\text{n}}_{cSL{P}^1}$) and simulated in the Automation Studio™ program (${\text{n}}_{cAS}$) is 1.25%. Table 7 shows the results obtained.

Table 7. Number Cycles Per Minute of the Pumping Cylinder Calculated and Simulated in the Automation Studio™ (${\text{n}}_{cAS}$)

Table 8. Power Submersible Motor Calculated (Pot ${}_{SL{P}^1}$) and Simulated in the Automation Studio™ (Pot ${}_{AS}$)

Fig 14. SLP¹ - Number of cycles per minute for the diameter of the pump piston in the 60 to 80 mm range and simulated with Automation Studio™ (${\text{n}}_{cAS}$) with pump diameter = 73.98 mm (dashed line).

The power of the submersible motor, responsible for the activation of the hydraulic pump, is greater when there is an increase in the volumetric flow of the SLP or manometric head of the fluid. When compared to other methods of artificial lift, the SLP requires submersible motors with lower power at greater depths due to the fact that the hydraulic systems present yield gains and consum power of the system in relation to the weight and size of the components. Considering the variation of the manometric head and the power of the electric motor relative to the working pressure of the hydraulic pump, the SLP volumetric flow curves present a linear behavior, as can be seen in Fig. 15.

Fig 15. SLP¹ - Load loss for diameter of 63.50 mm (dashed line).

Fig 16. SLP¹ - Submersible power motor for a cylinder piston diameter of the pump = 73.98 mm and simulation with Automation Studio™ for Hman = 807.91 m (dashed line).

Also for the maximum stipulated geometric head (${\text{h}}_{geo}=800.00$ m), with the diameter of the delivery pipe of 63.50 mm (2 1/2”) and volumetric flow (${\text{Q}}_{SLP}$) of 39.37 m3/d), the maximum power is approximately 4.33 kW for manometric head (${\text{H}}_{man}$) of ˜807.91 m. The average error between the Power of the submersible motor calculated (Pot${}_{mot}$ ) and simulated in the Automation Studio™ (Pot${}_{mot}$ -AS) is 8.12%. Table 9 shows the results obtained.

Table 9 - Reynolds Number Calculated (Re) and Simulated in the Automation Studio™ (Re ${}_{AS}$)

Fig. 17 shows that the Reynolds number (Re) in all volumetric flow ranges is less than 2000. Thus, the flow of the fluid in the delivery pipe of the SLP has a laminar flow, even if its diameter is less than 63.50 mm. However, the diameters in this range should not be adopted, since they present high losses of load. Considering the delivery pipe diameter adopted in this study (63.50 mm), Fig. 17 shows that it is possible to use lower commercial diameters, since the SLP can be considered a high pressure pump with low volumetric flow, however, causing low speed flows inside the pipes. Using the diameter of 63.50 mm for the delivery pipe (dashed line), the Reynolds coefficient (calculated) is observed to be between 13.66 and 107.48. The average error between the Reynolds number calculated ((Re) and simulated in the Automation Studio™ (Re${}_{AS}$ ) is 0.43%. Table 9 shows the results obtained.

Figure 17 - SLP¹ - Reynolds number (Re) for delivery pipe diameter 50 to 75 mm range and simulated with Automation Studio™ (Re${}_{AS}$) with pump diameter = 63.5 mm (dashed line).

The force of the power cylinder depends on the diameter of the pump cylinder piston and the pressure exerted by the production column. The forward force of the power cylinder exhibits a linear and proportional growth with the geometric height, as shown in Fig. 18. Using a manometric head (${\text{H}}_{man}$) of 807.91 m and the same diameters of the power and pump cylinder pistons according to Table 5, Fig. 18 shows that to raise the fluid (${\text{H}}_{man}$) to 800 m a force of approximately 33,566.61 N is needed. The average error between the force forward of the power cylinder calculated (${\text{F}}_a$) and simulated in the Automation Studio™ (${\text{F}}_{aAS}$ ) is 9.7%.

Fig 18. - SLP¹ - Forward force of the power cylinder with ${\text{d}}_{p2}=73.98$ mm and ${\text{d}}_{b2}=89.05$ mm and simulated with Automation Studio™ - $H_{man}=807.91$ m (dashed line).

The pressure data of the hydraulic pump and the number of cycles shown can be changed according to the operating characteristics of the SLP. Considering the parameters obtained by the PSO Algorithm and also the operating conditions in which only the forces of the pumping process are considered. Fig. 19 shows the intersection point of operation for SLP¹ is approximately 40 m³/d (daily production) and a total manometric head of approximately 2400 m for hydraulic pump pressure at 7.9 Mpa, power cylinder diameter equal to 89.05 mm and 8.03 cycles per minute.

Fig 19. - SLP¹ operating curve estimate and and operating range for ${\text{Q}}_{SL{P}^1}=39.37{\text{m}}^3$

However, to have an ideal daily production of 39.37 m3/d, the pumping piston diameter (${\text{d}}_b$) should be approximately 74 mm and the manometric height should be 807.91 m.

SECTION IX. Conclusion

The pumping device proposed here shows evidences of being efficient in terms of load pressure loss, because unlike some proposals using hydraulic systems, where the force unit is on the surface, the insertion of the force unit here is coupled with the pump unit in the well. Thus there is a significant reduction of load pressure losses of the hydraulic oil and a greater use of the power of the motor-pump assembly, in addition to reducing the lengths of pipe used.

The design and shape of the SLP are coherent with fewer and faster maintenance operations. Although it has operational principles similar to mechanical pumping with rods, it does not need a rod column, and does not require heavy machinery on the surface.

Although this work describes the SLP obtaining petroleum from the subsoil, the proposed pumping system can be used to produce fluids with petroleum-like densities, such as obtaining water from underground aquifers. However, it must be constructed with corrosion-resistant steel and sealing elastomers, in accordance with the requirements that allow the system to operate with durability and safety.

The SLP⁰ and SLP¹ experiments show the importance to delimit the range of operation within which the SLP must operate, since the pipes and hydraulic components must be suitable for the flow of hydraulic oil and the production fluid in order to avoid high pressures of the pump hydraulics, high hydraulic oil temperatures and induced contrary pressures and flow.

The projections based on the analytical analyzes presented by the SLP¹, as well as the initial tests with the SLP⁰ and SLP¹ prototypes indicate that the SLP apparatus may be an option for an artificial lift system in reservoirs with great depths. In a future work we intend to finalize the prototype, insert it in a production environment similar to a real one and validate the operational parameters presented in the curves obtained from this work.

The computational simulation using Automation Studio™ software allowed us to identify and correct induced pressure in the directional valve control lines, analyze the dynamics of the proposed pumping system, and simulate various operating conditions such as volumetric displacement change, elevation height, and fluids, among others. The comparison of the results obtained with the analytical method, experiments at the Hydraulic and Pneumatic Laboratory (LHP) and simulated in Automation Studio™, presented an average error of 3.27% for analytical method and at the Hydraulic and Pneumatic Laboratory (LHP) and simulated in Automation Studio™ and test in Hydraulic and Pneumatic Laboratory (LHP) of 8.67%. The calculated and simulated Automation Studio™ values of the parameters (QSLP¹ , nc , tc , Pmot , Pb , Re e and Fa ) presented an overall accuracy of 95.48%.