SOCIETY OF PETROLEUM ENGINEERS

Mid-Continent Section, Tulsa, Oklahoma

Abstracts courtesy of Ken Saveth, ksaveth@juno.com

In-situ PC Pump Testing - Jose Luis Arrellano: University of Tulsa Artificial Lift Projects (TUALP)

The purpose of this presentation is to compare in-situ pump performance between progressing cavity, electric submersible, & beam pumps. A new term is also introduced in determining the pump displacement. This term is called the "slippage term".

Oak Resources, Inc.; a Tulsa, OK. based company provided eight (8) wells for testing in Carter County, OK during the summer of 1996. Progressing Cavity Pumps (PCP), Electric Submersible Pumps (ESP), & Beam Pumps are all used in this field. On the Progressing Cavity Pump side,

eight (8) PCPs were tested using existing production facilities & a power profiler to obtain the power consumption from each well. A computer program was developed to predict the volumetric & mechanical efficiencies of the different methods of lift.

The typical well configuration is as follows:

Casing = 7" with a 5 1/2" liner

Tubing = 2 7/8"

Q_oil = 8 BPD

API Oil = 33°

Water Cut = 98%

Working Fluid Level = 1118 ft.

Well Head Pressure = 50 psi

BHT = 105 F

A BMI 3060 Power Profiler was used to obtain the power consumption & power factor on each well. This allowed for comparison of overall efficiency between the different artificial lift systems. The liquid flow rate & fluid levels were measured with existing field equipment; a positive displacement flow meter & digital acoustic fluid level machine.

In order to conduct the simulation of the progressing cavity pump, the pump discharge & pump displacement were needed. To obtain the pump discharge, the weight of the fluid column, the frictional losses, & the pressure drop (considering the rotation of rods) are required. To obtain the pump displacement, the theoretical pump displacement & the pump slippage are required.

In order to simulate the pressure discharge when the rod string is rotated, the following conditions were assumed:

Coaxial Pipes

Single Rod

Constant Production

Incompressible Fluid

Viscosity Constant in Radial Direction

With these assumptions, the continuity equation can be considered with the following boundary conditions & equation:

w = 0 at r = R_t

w = w ₁ at r = R₀

V = 0 at r = R_t

0 =

Governing equations in the radial, angular, & axial directions were also considered. Using the continuity equation & the boundary conditions, an additional pressure is obtained.

Pump displacement from a theoretical standpoint, is a function of the pump’s geometry & rotational speed as well as the fluid properties, the pressure drop across the pump, & the slippage. This slippage reduces the theoretical pump displacement & depends on such factors as (1) pressure drop across the pump, (2) fluid properties, & (3) compression fit. It is safe to assume that whatever the compression fit is between the rotor & stator, there will still be some slippage of the production as the rotor turns. It is proposed that this is in the form of a "thin slit". The flow through this "thin slit" is what we have termed the slippage factor.

In order to model this slippage factor, we took a look at the theory of flow in the annular area between two (2) circular tubes. The Hagen-Poiseuille Law relates the volumetric flow rate to the pressure drop forces causing reverse flow. Using this law, an equation relating the flow rate in narrow slits was expressed.

Q_s =

Considering a curved thin slit, the following expression can be used:

Q_s =

Setting all the geometric parameters equal to 1, yields the following:

Q_s =

p /6 can be replaced with an adjustable parameter that accounts for the pump geometry. With these in mind, the pump capacity is given as the theoretical pump displacement - slippage. The following equation applies:

Pump Displacement = D x 4e x P_s x RPM -

A computer program was written to determine the volumetric & mechanical efficiencies of the three AL methods used in this test. The results of this program are shown in the following table:

The resulting volumetric efficiency comparison between PCPs, ESPs, & Beam Units are 73.26%, 67.45%, & 73.34% respectively. The mechanical efficiency comparison between the same systems are 47.6%, 29.45%, & 17.8% respectively. Several other wells were also evaluated with similar results.

In summary, a computer program was developed to predict the volumetric & mechanical efficiencies using field data. The effect of pump speed was considered in order to predict the pump discharge pressure. In addition, a "slippage term" was introduced to predict the pump displacement. It was found from this study, that the volumetric efficiency of the Progressing Cavity Pumps are often higher then Electric Submersible Pumps & Beam Units & definitely more mechanically efficient. In this particular field in Carter County, OK, a considerable cost savings have been achieved with the PCPs being used.

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