Applications and optimization of response surface methodologies in high-pressure, high-temperature gauges

Abstract

High-Pressure, High-Temperature (HPHT) pressure gauges are commonly used in oil wells for pressure transient analysis. Mathematical models are used to relate input perturbation (e.g., flow rate transients) with output responses (e.g., pressure transients), and subsequently, solve an inverse problem that infers reservoir parameters. The indispensable use of pressure data in well testing motivates continued improvement in the accuracy (quality), sampling rate (quantity), and autonomy (lifetime) of pressure gauges.

This body of work presents improvements in three areas of high-pressure, high-temperature quartz memory gauge technology: calibration accuracy, multi-tool signal alignment, and tool autonomy estimation. The discussion introduces the response surface methodology used to calibrate gauges, develops accuracy and autonomy estimates based on controlled tests, and where applicable, relies on field gauge drill stem test data to validate accuracy predictions. Specific contributions of this work include:

- Application of the unpaired sample t-test, a first in quartz sensor calibration, which resulted in reduction of uncertainty in gauge metrology by a factor of 2.25, and an improvement in absolute and relative tool accuracies of 33% and 56%, accordingly. Greater accuracy yields more reliable data and a more sensitive characterization of well parameters.

- Post-processing of measurements from 2+ tools using a dynamic time warp algorithm that mitigates gauge clock drifts. Where manual alignment methods account only for linear shifts, the dynamic algorithm elastically corrects nonlinear misalignments accumulated throughout a job with an accuracy that is limited only by the clock's time resolution.

- Empirical modeling of tool autonomy based on gauge selection, battery pack, sampling mode, and average well temperature. A first of its kind, the model distills autonomy into two independent parameters, each a function of the same two orthogonal factors: battery power capacity and gauge current consumption as functions of sampling mode and well temperature -- a premise that, for 3+ gauge and battery models, reduces the design of future autonomy experiments by at least a factor of 1.5.