We simulate three types of forced‐gradient tracer tests (converging radial flow, unequal strength two well, and equal strength two well) and natural‐gradient tracer tests in multiple realizations of heterogeneous two‐dimensional aquifers with a hydraulic conductivity distribution characterized by a spherical variogram. We determine longitudinal dispersivities (α_L) by analysis of forced‐gradient test breakthrough curves at the pumped well and by spatial moment analysis of tracer concentrations during the natural‐gradient tests. Results show that among the forced‐gradient tests, a converging radial‐flow test tends to yield the smallest α_L, an equal strength two‐well test tends to yield the largest α_L, and an unequal strength two‐well test tends to yield an intermediate value. This finding is qualitatively explained by considering the aquifer area sampled by a particular test. A converging radial‐flow test samples a small area, and thus the tracer undergoes a low degree of spreading and mixing. An equal strength two‐well test samples a much larger area, so the tracer is spread and mixed to a greater degree. Results also suggest that if the distance between the tracer source well and the pumped well is short relative to the lengths over which velocity is correlated, then the α_L estimate can be highly dependent on local heterogeneities in the vicinity of the wells. Finally, results indicate that α_L estimated from forced‐gradient tracer tests can significantly underestimate the α_L needed to characterize solute dispersion under natural‐gradient flow. Only a two‐well tracer test with a large well separation in an aquifer with a low degree of heterogeneity can yield a value of α_L that characterizes natural‐gradient tracer spreading. This suggests that a two‐well test with a large well separation is the preferred forced‐gradient test for characterizing solute dispersion under natural‐gradient flow.