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An incredibly useful engineering calculation for sucker rod pumps is theoretical pump displacement. This is important information for sizing pumping equipment. And if we know the theoretical barrels per day (BPD) a particular sucker rod pump installation can lift, we can use this information to diagnose problems. One simple procedure is to compare the theoretical capacity with the actual production using a simple
bucket test.
The calculation is very simple; multiply the "K" factor for the particular sucker rod pump (from the table below) by the pumping unit stroke length in inches by the pumping unit speed in strokes per minute (SPM). Measure the stroke length in inches at the polished rod / polished rod liner and time the speed with a watch (SPM refers to a complete cycle or revolution of the pumping unit crank).
The formula is expressed as: P = K x S x SPM
Where P is lifted BPD, K is the pump constant (or "K" factor), S is the stroke length in inches, and SPM is the strokes per minute with one stroke taken as a full rotation of the pumping unit crank.
Note: For metal plunger pumps, a slip factor must be used to correct for volumetric inefficiency. For deep wells, rod stretch becomes an issue in the calculation. However, for shallow wells, especially with soft-packed plungers, this simplified calculation is remarkably accurate.
Example: A shallow stripper well equipped with a 1-1/2 inch insert pump has an old Jensen D-4 pumping unit with a stroke length of 18 inches, and is pumping at 12 strokes per minute. Look up the "K" factor for the 1-1/2 inch insert pump - .262. Multiply .262 times 18 times 12 and find you can lift a maximum of 56.6 barrels per day of total fluid (.262 x 18 x 12 = 56.6 BPD).
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