modified everitt-jennings (mej) method and the gibbs method: … · 2012. 11. 20. · sept. 14 -...

6th Annual Sucker Rod Pumping Workshop

Wyndham Hotel, Dallas, TexasSeptember 14 – 17, 2010

Modified Everitt-Jennings (MEJ) Method and the Gibbs Method:

Downhole Card ComparisonVictoria Ehimeakhe, Ph. D.Weatherford

Sept. 14 - 17, 2010 2010 Sucker Rod Pumping Workshop 2

Introduction

• The most accurate method to control a beam pumping well is based on fillage calculated from the downhole card.

• Downhole data can be directly measured by a downhole dynamometer or can be calculated by solving the one-dimensional damped wave equation.

• For years no significant innovations in solving the wave equation have been implemented, leaving the Gibbs method as the most prevalently used method in the industry.

• Over the past two years, Weatherford has implemented the Everitt-Jennings method for solving the wave equation. A paper was presented with details during the SWPSC 2010, entitled “Comparative Study Of Downhole Cards Using Modified Everitt-Jennings Method And Gibbs Method”.

Solving the Wave Equation• The irreversible energy losses which occur along the rod string

because of elasticity, take the form of stress waves traveling down the rod string at the speed of sound.

• The one dimensional damped waved equation models the propagation of stress waves in an ideal slender bar.

• The wave equation reads as follows:

• The modified Everitt-Jennings (MEJ) method uses finite differences to solve the wave equation at M steps down the rod string.

• The modified Everitt-Jennings method also utilizes an iteration on the net stroke and damping factor approach, which includes a fluid level calculation.


Advantages of using MEJ• The use of finite differences to solve the wave equation involves

dividing the rod string into a finite number of nodes.• The number of nodes can be picked by the user.• This guarantees that the position, load and stress can be

calculated at each level down the taper.• The MEJ computes the minimum number of nodes necessary for

the computation to be stable insuring a successful calculation each time.

• The use of the iteration on the damping factor allows the user to be assured that the proper damping factor is picked for each stroke, without manual intervention.

• This step is crucial when managing moderate to large groups of wells.


Iteration on the net stroke and damping factor

• In the Everitt-Jennings method, the hydraulic horsepower represents the useful work expended to lift the given amount of liquid from the dynamic fluid level to the surface.

• The hydraulic horsepower (HH) is given by:where Q is the production rate,

Fg is the specific fluid gravity, Fl is the fluid level.

• The damping factor is then given by the following equation:

where g is the gravity constant, HPR is the polished rod horsepower,τ is the period of the stroke,ρ is the taper density,A is the taper cross sectional area,L is the taper length,S is the net stroke length.


Iteration on the net stroke and damping factor


Full WellNet stroke:

Gibbs : 87.24

MEJ : 86.19

Load range:

Gibbs : 6097

MEJ : 6146

Iteration on the net stroke : 2

Iteration on the damping factor : 1


Fluid Pound WellNet stroke:

Gibbs : 138.98

MEJ : 138.56

Load range:

Gibbs : 3852

MEJ : 3984





Gibbs : 98.05

MEJ : 97.90

Load range:

Gibbs : 2098

MEJ : 2286





Gibbs : 34.97

MEJ : 34.92

Load range:

Gibbs : 1172

MEJ : 1209




Gas CompressionNet stroke:

Gibbs : 100.27

MEJ : 100.01

Load range:

Gibbs : 2796

MEJ : 2883




Gas CompressionNet stroke:

Gibbs : 83.99

MEJ : 83.74

Load range:

Gibbs : 2966

MEJ : 3272




Viscous FluidsNet stroke:

Gibbs : 97.22

MEJ : 96.92

Load range:

Gibbs : 4994

MEJ : 4992




Viscous FluidsNet stroke:

Gibbs : 58.1

MEJ : 58.4

Load range:

Gibbs : 2724

MEJ : 2726




Worn PumpNet stroke:

Gibbs : 42.03

MEJ : 42.19

Load range:

Gibbs : 5049

MEJ : 4918




Slanted CardNet stroke:

Gibbs : 101.87

MEJ : 101.90

Load range:

Gibbs : 1136

MEJ : 1148




Tagging BottomNet stroke:

Gibbs : 86.44

MEJ : 86.03

Load range:

Gibbs: 5696

MEJ : 5798




Unexplained Card ShapeNet stroke:

Gibbs : 118.75

MEJ : 117.48

Load range:

Gibbs : 4724

MEJ : 4878




Unexplained Card ShapeNet stroke:

Gibbs : 114.84

MEJ : 115.05

Load range:

Gibbs: 14809

MEJ : 14490




Comparison with updated Gibbs damping factor

• For the above well, the results from the MEJ are compared first to results from the Gibbs method without human intervention, and second to results from the Gibbs method after the damping factor was manually modified until the desired results were produced.

• As seen above, the Gibbs downhole card without manual intervention displayed a loop, which is removed after intervention.

• The MEJ card iterated to the correct damping factor. Sept. 14 - 17, 2010 2010 Sucker Rod Pumping Workshop 20

Statistics: 1000 wells


•A sample of 1000 wells was selected at random from different locations.• These wells represent almost every downhole conditions possible - rod type, well depth, fluid viscosity, etc.• The net stroke values using the results from the MEJ and the Gibbs method were recorded and compared.• From the above graph, in 81% of the cards studied, the difference in the net stroke values is less than 2 inches, while in 89% of the cards studied, the difference in the net stroke values is less than 3 inches.

Conclusions• When applied to field data as well as laboratory data, results

from the modified Everitt-Jennings proved similar for the most part to the results from the Gibbs method by yielding cards having the same shape, similar load ranges and similar net strokes.

• In some cases, the results from the modified Everitt-Jennings method were superior to that of the Gibbs method – providing smoother data with less noise and a better approximation of the damping factor.

• Using the modified Everitt-Jennings algorithm improves well analysis and optimization through more accurate determination of the downhole conditions, as well as a more realistic determination of the volume of fluid produced on each stroke. This is due to more accurate net downhole stroke values and damping factor approximation.



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modified everitt-jennings (mej) method and the gibbs method: … · 2012. 11. 20. · sept. 14 -...

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