Modeling high-resolution down-hole pressure transducer to achieve semi-distributed measurement in oil an d gas production wells
Keywords:Quality factor, piezoelectric transducer, pressure, temperature, quartz resonator, loss mechanism.
A full 3D computer model is developed to evaluate the performance impact of intrinsic loss and various geometrical features in high-resolution pressure transducer. The intrinsic loss is modeled as viscosity factors, which allows for a more efficient computer model. In this paper, the developed model is applied to yield an insight in the evolution of high-resolution down-hole pressure transducer, from Hewlett-Packard\texttrademark\, to Quartzdyne\texttrademark. As the quality factor is related to the inverse of the resolution, the transducing element optimization process to achieve the highest quality factor possible is investigated, considering the impact of crystal quality and geometrical features, such as: thickness, diameter and convexity (plano-convex and bi-convex). Temperature-dependent elastic constants are used to improve the model accuracy in modeling temperature effects on the vibrating resonator-type transducer. Boundary load conditions are used to simulate hydrostatic pressure. The simulations to extract the frequency shift are carried out in the range of $14\,psi$ ($96.5\,kPa$) to $20000\,psi$ ($137.89\,MPa$) and $0\,^oC$ to $200\,^oC$ for pressure and temperature, respectively, as such ranges are typically found in oil and gas wells. A discrepancy in the published temperature dependence has been found. A miniaturization path to achieve semi-distributed measurement in oil and gas production wells is presented.