A tool having a pump-out unit, pumping unit, and NMR unit is disposed in a wellbore. On a pump-up cycle, after removing borehole fluids, a fluid is injected into a region of investigation. NMR measurements are made while fluid migrates into the region of investigation. On a production cycle, pressure is removed, allowing fluid to exit the formation while NMR measurements are made. A rate of fluid production is estimated using the time-dependent NMR measurements. Alternatively, the mass of a sample is measured. Fluid is injected into the sample and the mass of the injected sample is measured. Pressure is removed and the mass of the injected sample as the fluid migrates out of the sample is measured. The change in mass of the injected sample as the fluid migrates out of the sample is determined and a rate of fluid production is estimated using the determined change in mass.