Hysteresis model with parameters derived from calibration

Hysteresis loop

hys·ter·e·sis

 Hysteresis pronunciation [ his-tuh-ree-sis]/ˌhɪstəˈriːsəs/
Noun: Physics
The phenomenon in which the value of a physical property lags behind changes in the effect causing it, as for instance when magnetic induction lags behind the magnetizing force.
Gauge with shaft encoder
Fig. 1—Measuring hysteresis
Origin: late 19th century: from Greek husterēsis 'shortcoming, deficiency', from husterein 'be behind', from husteros 'late'.
Alternate derivation: The term, Hysteresis, is derived from ὑστέρησις, an ancient Greek word meaning "deficiency" or "lagging behind". It was coined by Sir James Alfred Ewing. Using only increasing pressures to calibrate a pressure gauge can only be accurate if the rate of calibration exactly matches the pressure changes occurring in the well. In fact during a drawdown, due to hysteresis, the predicted pressures will be worse than using a straight line calibration. By careful sampling of the gauge’s response during the calibration, we can move around inside the hysteresis loop as a function of the pressure change history. More details on Bourdon Tubes and Hysteresis.
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