Nodding Donkey Oil Pump

Dominik Mugele –
Vania Sousa –


Nowadays a bigger part of the fuel we use is derived of fossil combustible, which consists in oil, natural gas and mineral coal. The extraction of such combustibles is made both offshore and onshore, depending on where are the reservoirs located, producing thousands of barrels of combustible a day. Especially in the onshore extraction, many techniques of elevation of fluids are used; most oil wells, at the early stages of their life, flow naturally to the surface. These are called flowing wells. The basic prerequisite to ensure flowing production is that the pressure at well bottom be sufficient to overcome the sum of pressure losses occurring along the flow path to the surface. When this criterion is not met it is necessary to use mechanical process that supplement the pressure of gases in the reservoir, this is, artificially increase the internal pressure of gases. The techniques of artificial lift aims to maximize the volume of oil to be extracted and of those available on market the most popular is certainly the one made with nodding donkeys. This project was based on a nodding donkey that makes the extraction by the means of rods, which is a basic mechanism where a downhole pump is used to increase the pressure in the well in order to override flowing pressure losses. This type of artificial lift uses a positive displacement plunger pump and a surface driving unit that converts the rotary movement of the motor to alternating motion needed to drive the pump. The rod string connects the surface pumping unit to the downhole pump and the third basic element is the pump itself, which, from the earliest times, worked on the positive displacement principle and consisted of a stationary cylinder and a moving plunger. This whole system has stood the test of the time and is still a reliable alternative for the majority of artificial lift installations.


The purposes of this project are to model and simulate a nodding donkey unit (surface equipment) working during the well pump, calculate the reaction forces on the rod and simulate/calculate the required torque of the engine.


The first step was to find a suitable model to base our project on. There are several geometrical arrangements of the component parts and the one we have chosen was the Mark II geometrical arrangement, especially because:

  • the equalizer bearing is located on the beam very close to the horsehead and this unique  characteristic improves performance over the other geometries
  • the rotary counterweights are placed on a separate counterbalance arm and is phased by an angle t (usually about 24 degrees). This feature ensures a more uniform net torque variation over the complete pumping cycle.

We must point out that in order to make the simulation simpler we have chosen to model only the surface mechanism, so all downhole equipment was not designed.

Geometry chosen it was now time to pick a commercial model to get the inspiration for designs so we have picked up the Lufkin 640 pumping unit.

To start to model, the main structure was projected in order to accommodate all the other components. Each component was individually designed and then constrained to the main structure.

The walking beam and the head were attached to the main structure by the means of a revolute joint. The cranks and counterweights placed and attached to the structure by rotational spindles that would rotate as the motor sent its motion through a small pulley to the belt and arriving at the bigger pulley, which would move the counterweights this way making all the system work, moving the rod up and down.

Just for information, the picture below shows what happens on the plunger and ball valves downhole in more detail:

Simulations and analysis of results

This 1DOF-model is driven by a velocity driver that acts on the joint at the pinion shaft, as the engine itself is not modelled. These kind of pumps were used for different kind of depths at diverse pumping speeds. So, it was decided here to use an average value of n = 15 strokes per minute which requires as well for the velocity driver a turning speed of φ = 15 turns per minute.

The continuous driven pinion shaft leads to a deformed velocity of the rod movement because of the pinion axis being in a backward position which creates an upstroke that occurs in approximately 195° of crank rotation. The rod velocity is shown in the following picture.

The maximum velocity for the upstroke is lower, about 1.5 m/s, than for the down stroke, about 1.8 m/s. This unconformity is desired. It supports the lifting movement as there is now less physical work necessary .

Forces acting on the model were those acting on the rod. Friction within the mechanism is neglected here. In the literature often all those rod forces were combined to a so called “polished rod load” which contains:

  • The weight of the rod string
  • A buoyant force that reduces the rod weight
  • Mechanical and fluid friction forces along the rod string
  • Dynamic forces occurring at the string
  • The fluid load on the pump plunger

In the model the rod weight and the weight reducing buoyant force were combined to an typical mass value of about m_rod = 3000kg. The fluid load is estimated to be about m_fluid = 6000kg.

Friction forces depend on the moving direction of the rod and consists mainly of the friction between rod and fluid and between the fluid and the wall (the latter only during the rising stroke). Therefore two different friction parameters have been used in the simulation.

In general it is a hard or even impossible problem to obtain the friction parameters of a working pump. They depend on several aspects as the fluid composition and the pump equipment condition which were quite variable. So in this case they were chosen to achieve average maximum and minimum values of the polished rod loads. These in total on the rod acting forces were depicted in the following picture.

The according to amount minimum forces lie around 26 kN the maximum is at about 90 kN. In the diagram the value is always negative because the forces were acting downwards all the time. They reach their largest amount during the upstroke when the weight acting on the rod is increased due to the fluid’s mass and velocity and the friction acts downwards as well. During the down stroke the weight is reduced and friction forces reduce the total forces even more as it is acting against the down movement.

With the simulation it is possible as well to determine the required momentum auf the driving engine. The driving engine is connected to the pinion shaft via a belt drive. The pinion momentum can be transferred to the engine’s momentum using the radiuses of the pulleys. The result is shown in picture:

During the upstroke the momentum reaches its highest amount of about 5000 Nm. For the down stroke a lower momentum of about 3000 Nm is required to maintain the velocity.

A video of the simulation can be found following the link below:

Nodding Donkey Pump Simulation


The aims of the project have been achieved. During the process a working model has been developed and reaction forces on the rod within their realistic boundaries have been simulated. Additionally the required momentum at the engine to maintain the pump’s velocity has been obtained.

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