6 th Annual Sucker Rod Pumping Workshop Wyndham Hotel, Dallas, Texas September 14 17, 2010 Modified Everitt-Jennings (MEJ) Method and the Gibbs Method: Downhole Card Comparison Victoria Ehimeakhe, Ph. D. Weatherford
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 onedimensional 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. 2010 Sucker Rod Pumping Workshop 2
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. 2010 Sucker Rod Pumping Workshop 3
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. 2010 Sucker Rod Pumping Workshop 4
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 (H H ) is given by: where Q is the production rate, F g is the specific fluid gravity, F l is the fluid level. The damping factor is then given by the following equation: where g is the gravity constant, H PR 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. 2010 Sucker Rod Pumping Workshop 5
stroke and damping factor 2010 Sucker Rod Pumping Workshop 6
Full Well Gibbs : 87.24 MEJ : 86.19 Gibbs : 6097 MEJ : 6146 stroke : 2 damping factor : 1 2010 Sucker Rod Pumping Workshop 7
Fluid Pound Well Gibbs : 138.98 MEJ : 138.56 Gibbs : 3852 MEJ : 3984 stroke : 3 damping factor : 4 2010 Sucker Rod Pumping Workshop 8
Fluid Pound Well Gibbs : 98.05 MEJ : 97.90 Gibbs : 2098 MEJ : 2286 stroke : 2 damping factor : 4 2010 Sucker Rod Pumping Workshop 9
Fluid Pound Well Gibbs : 34.97 MEJ : 34.92 Gibbs : 1172 MEJ : 1209 stroke : 3 damping factor : 4 2010 Sucker Rod Pumping Workshop 10
Gas Compression Gibbs : 100.27 MEJ : 100.01 Gibbs : 2796 MEJ : 2883 stroke : 2 damping factor : 6 2010 Sucker Rod Pumping Workshop 11
Gas Compression Gibbs : 83.99 MEJ : 83.74 Gibbs : 2966 MEJ : 3272 stroke : 2 damping factor : 7 2010 Sucker Rod Pumping Workshop 12
Viscous Fluids Gibbs : 97.22 MEJ : 96.92 Gibbs : 4994 MEJ : 4992 stroke : 2 damping factor : 3 2010 Sucker Rod Pumping Workshop 13
Viscous Fluids Gibbs : 58.1 MEJ : 58.4 Gibbs : 2724 MEJ : 2726 stroke : 2 damping factor : 1 2010 Sucker Rod Pumping Workshop 14
Worn Pump Gibbs : 42.03 MEJ : 42.19 Gibbs : 5049 MEJ : 4918 stroke : 2 damping factor : 2 2010 Sucker Rod Pumping Workshop 15
Slanted Card Gibbs : 101.87 MEJ : 101.90 Gibbs : 1136 MEJ : 1148 stroke : 2 damping factor : 1 2010 Sucker Rod Pumping Workshop 16
Tagging Bottom Gibbs : 86.44 MEJ : 86.03 Gibbs: 5696 MEJ : 5798 stroke : 1 damping factor : 1 2010 Sucker Rod Pumping Workshop 17
Unexplained Card Shape Gibbs : 118.75 MEJ : 117.48 Gibbs : 4724 MEJ : 4878 stroke : 3 damping factor : 4 2010 Sucker Rod Pumping Workshop 18
Unexplained Card Shape Gibbs : 114.84 MEJ : 115.05 Gibbs: 14809 MEJ : 14490 stroke : 2 damping factor : 1 2010 Sucker Rod Pumping Workshop 19
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. 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. 2010 Sucker Rod Pumping Workshop 21
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. 2010 Sucker Rod Pumping Workshop 22
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