Developing a Two-Dimensional Semi-Analytical Solution on a Plan View for a Consecutive Divergent Tracer Test Considering Regional Groundwater Flow

Abstract

Multiple successive tracer tests are often conducted to obtain reliable breakthrough curve results under regional groundwater flow, especially when the accuracy is crucial. In such cases, the period of rest between the end of the first divergent tracer test and the initiation of the second divergent tracer test allows the tracer from the first test to travel along with the background regional flow, thereby influencing the distribution of residual tracer concentration. This residual tracer could potentially interfere with breakthrough curve results from the tracer injection in the second tracer test. Additionally, the conventional analytical solution used for the divergent tracer test considers only radial flow; regional flow and consecutive tracer tests are ignored. Consequently, interpreting the behaviour of the tracer in consecutive divergent tracer tests under regional flow conditions is challenging using conventional measures because of background regional concentration. This study proposes a new semi-analytical solution, considering the effects of divergent radial and regional flows in consecutive tracer tests, addressing a critical gap in the conventional analytical solutions that, despite their practical necessity, have not been previously developed. The proposed semi-analytical solution was subjected to parameter studies under various scenarios. In our case studies, the conventional analytical solution based on a single tracer test can be safely used for parameter estimation only in cases where the injected mass for the subsequent tracer test is approximately six-fold that of the first tracer test or if the drift time is longer than 10 days.