AbstractFourstage singlewell pushpull (SWPP) tracer tests, including injection, chasing, resting, and pumping, were conducted in a fractured aquifer at Newark basin. An anomalous transport phenomenon observed in the SWPP tests is the linear decline of breakthrough curves (BTCs) at late time with slope of 1.8 in loglog plots. A timedependent fractional model is developed to interpret the anomalous transport behavior. This model considers a timedependent power law memory function and a timedependent fractional advectiondispersion operator. The fractional advectiondispersion equations (fADE) are solved in a radial coordinate system using the implicit Euler method. A semianalytical solution of the firstorder ratelimited mobileimmobile model (FORMIM) is derived for comparison. It is found that both the nonlocal transport in time and space can produce the longtailed BTC. A smaller timefractional or spacefractional index leads to a lower peak concentration and a larger latetime slope. The mass distribution of the fractionalinspace (FS) model exhibits power law decline at the leading plume edge. Early breakthrough during pumping is not observed because the mobile mass at the start of pumping is nonzero and more concentrated near the wellbore. The capacity ratio is an important factor that affects the peak concentration. A larger capacity ratio leads to greater peak concentration. A smaller timefractional index in the injection, chasing, or resting stage will move the BTC downward and the slope of the late time BTC is determined by the spacefractional index over all stages and the timefractional index in the pumping stage. The capability of the existing models to recover the BTC of the SWPP test is discussed and some guidelines for how to choose the appropriate model to interpret the SWPP test data are proposed.
