Mathematical analysis of the effect of the constant temperature assumption in the leak test of PTB Testing Instructions, Volume 25

Abstract

<p class="Abstract">"PTB Testing Instructions, Volume 25: Gas meters – Test rigs with critical nozzles" (PTB 25) includes a detailed description of a test to evaluate the tightness of the rig (leak test). The mathematical modeling of this test assumes that temperature remains constant, and it is established a maximum allowable change of 0.1 K during the test. PTB 25 defines a maximum value of the leak flow rate as criteria for approval of the test.</p><p class="Abstract">In this work, the effect of the assumption of constant temperature over the leak test result was analyzed. Different processes in which the real leak flow rate was zero and there was a change in the temperature of the system equal to the maximum permissible (according to PTB 25) were simulated, and the leak flow rate calculated by PTB 25’s model was determined. The assumption of constant temperature does not simplifies drastically the mathematical model. It is concluded that PTB 25’s maximum allowable temperature change is too high for most practical situations, leading to errors that exceeds the maximum allowable leakage rate. The factors “test time” and “enclosed volume” have a high effect over the magnitude of the error given by PTB 25’s leak flow rate model.</p>