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TRAINING MANUAL FOR DAU ENGINEERS

METROLOGY

Introduction
Metrology is the science of measurements. In Well Testing, we acquire data at the surface and downhole using mechanical and electrical transducers. The performance of these transducers or gauges is paramount to producing accurate and reliable data and depends on many parameters. The purpose of this training page is to describe theparameters that affect pressure transducers and to familiarize yourself with the technical terms usually employed by the manufacturers to depict a pressure gauge. The last part of this training page looks at the calibration process used on pressure gauges.

Objectives
Upon completion of this training page, you should be able to complete the following tasks:
• Understand the metrological termsthat define a pressure gauge.
• Know how the characteristics of gauges can affect the pressure response.
• Differentiate between gauges based on their individual characteristics.
• Select the appropriate gauge for a specific purpose.
• Understand the purpose of a gauge calibration.
• Depict the calibration procedure.

Principles
This topic describes the typical parameters used tocharacterize a pressure gauge and depicts the purpose of the calibration process. Typical pressure measurement parameters can be split into the following main classes:
• Static Parameters
• Dynamic Parameters

Static Parameters
These parameters describe the transducer performance in static conditions. Under this classification, we can define the following:
• Accuracy
• Resolution
• Stability
•Sensitivity

Accuracy
It is the difference between a measured value and the true value obtained from a reference standard like a high precision dead weight tester (DWT). Accuracy should not only include the accuracy of the sensor but also include errors due to electronics (e.g., clock frequency changes with temperature). Accuracy is normally expressed as a ± value. This means the actualpressure can be more (+) or less (-) than the measured pressure (or temperature). The manufacturers generally refer to the static accuracy as the algebraic sum of all the errors influencing pressure measurement. The following are these errors:
• Mean quadratic deviation (MQD) also called fitting error
To translate the sensor output (volt, hertz) into pressure, a polynomial function is used:

wherePc is the computed pressure; G, H, I and J are coefficients (function of temperature and computed during the calibration); and s is the sensor output (volt, hertz)
The MQD expresses the difference between the actual pressure applied (Pa) to the transducer and the computed pressure (Pc) given by the sensor at the (n) pressure and temperature points measured during the calibration. It can bewritten as the following equation:


MQD measures the quality of the mathematical fit of the sensor response at one constant temperature. It is a function of the transducer linearity (i.e., the closeness of a calibration curve to a specified straight line) and of the calibration procedure (i.e., coefficient grid and polynomial function used). Figure 1 is a graphical representation of the MQD.Figure 1

• Hysteresis
This is defined as the maximum discrepancy of the transducer output signal between increasing and decreasing pressure excursions as shown in Figure 2.

Figure 2
To substantially reduce hysteresis, the pressure element should be pressurized somewhat higher than the highest anticipated well pressure and released several times before the gauge is run into a well.

•Repeatability
This is defined as the maximum pressure difference between two consecutive measurements done in the same direction (either up or down) as shown in Figure 3. Input values and operating conditions are the same for both measurements and the full range is traversed.


Figure 3

• dP/dT
This represents the temperature sensitivity of the pressure sensor. A gauge with a dP/dT of...