Introduction

Petroleum engineers have traditionally used downhole dynamometer cards Petroleum engineers have traditionally used downhole dynamometer cards to diagnose the operation of sucker rod pumps. Specific problems have characteristic cards. The analysis procedure typically compares the unknown card with a library of known cards.

At least one expert systems successfully diagnoses sucker rod pump problems. EXPROD uses a statistical pattern recognition scheme to problems. EXPROD uses a statistical pattern recognition scheme to obtain a diagnosis.

This paper gives a numerical pattern recognition scheme "NUPRO" that correctly diagnoses 100 unknown cards from a library of 37 known cards.

NUMERICAL PATTERN RECOGNITION SCHEME

The NUPRO procedure uses the following steps

  1. Obtain a library that includes both healthy and problem cards. The library should be as complete as possible. NUPRO can identify any problem in the library.

  2. Obtain the unknown card. The unknown card is usually calculated from a surface dynamometer card using a sucker rod simulator.

  3. Both force and position must be scaled in all cards. All cards need to be scaled the same way. The following gives excellent results. sprl = (prl - mprl)/(pprl - mprl) + 1. pprl = peak polished rod load. mprl = minimum polished rod load. sprp = (Prp - mprp)/(pprp - mprp) + 1. pprp = peak polished rod position. mprp = minimum polished rod position.

  4. Select n points in a consistent way from each card. This applies equally to the library of known cards and to the all unknown cards. Each point consists of two numbers. The result is n polished rod load numbers and n polished rod position numbers. There are several consistent ways to select the n points from the cards. The n points can be equally or unequally spaced.

  5. Create a 2n dimensional vector for each card. Do this by arranging the 2n numbers in some sequence. The same sequence must be used for all the cards. One way is have n position numbers followed by n force numbers. Another way is to alternate position and force numbers.

  6. Normalize all the card vectors. This makes the magnitude of each vector equal to one.

  7. Select one library card vector and dot it with the unknown card vector. One-by-one, each of the library card vectors must be dotted with the unknown card vector. If there are 37 library vectors, then there are 37 dot products.

  8. This is how NUPRO finds the library card that is closest to the unknown card. NUPRO diagnoses the unknown card by finding the largest dot product. The largest dot product is the best match.

  9. The library of cards should be complete. This is important because an incomplete library will eventually give an incorrect diagnosis.

RESULTS

NUPRO has been tested. The NUPRO test is a program with a 37-card library. An additional program with a 37-card library. An additional one hundred, significantly different problem cards were used to test NUPRO. Every one of the problem cards tested gave the expected solution. problem cards tested gave the expected solution.

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