Effects of free convection and friction on heat-pulse flowmeter measurement

Abstract

► A well-designed system was set up to test performance of heat-pulse flowmeter. ► Measurement error at low flow velocities resulted primarily from free convection. ► Turbulence causes a loss of accuracy and precision at high flow velocities. ► An empirical formula was developed for calibrating measured velocities. ► Improved characterization of the vertical profile of hydraulic conductivity. Heat-pulse flowmeter can be used to measure low flow velocities in a borehole; however, bias in the results due to measurement error is often encountered. A carefully designed water circulation system was established in the laboratory to evaluate the accuracy and precision of flow velocity measured by heat-pulse flowmeter in various conditions. Test results indicated that the coefficient of variation for repeated measurements, ranging from 0.4% to 5.8%, tends to increase with flow velocity. The measurement error increases from 4.6% to 94.4% as the average flow velocity decreases from 1.37 cm/s to 0.18 cm/s. We found that the error resulted primarily from free convection and frictional loss. Free convection plays an important role in heat transport at low flow velocities. Frictional effect varies with the position of measurement and geometric shape of the inlet and flow-through cell of the flowmeter. Based on the laboratory test data, a calibration equation for the measured flow velocity was derived by the least-squares regression analysis. When the flowmeter is used with a diverter, the range of measured flow velocity can be extended, but the measurement error and the coefficient of variation due to friction increase significantly. At higher velocities under turbulent flow conditions, the measurement error is greater than 100%. Our laboratory experimental results suggested that, to avoid a large error, the heat-pulse flowmeter measurement is better conducted in laminar flow and the effect of free convection should be eliminated at any flow velocities. Field measurement of the vertical flow velocity using the heat-pulse flowmeter was tested in a monitoring well. The calibration of measured velocities not only improved the contrast in hydraulic conductivity between permeable and less permeable layers, but also corrected the inconsistency between the pumping rate and the measured flow rate. We identified two highly permeable sections where the horizontal hydraulic conductivity is 3.7–6.4 times of the equivalent hydraulic conductivity obtained from the pumping test. The field test results indicated that, with a proper calibration, the flowmeter measurement is capable of characterizing the vertical distribution of preferential flow or hydraulic conductivity.