The time-dependent ensemble average of the first-order longitudinal second spatial moment, ⟨S11'R⟩, of nonergodic plumes of a sorbing solute in linear equilibrium and the effective longitudinal dispersivity, γ11'R, were evaluated for the line sources of different lengths normal or parallel to the uniform mean velocity, ¿, in two- and three-dimensional physically and chemically heterogeneous and statistically isotropic media. Physical and chemical heterogeneity is described with a random hydraulic conductivity field K(x) and a random retardation factor field R(x), respectively. The retardation factor is defined as 1 + Kd(x), where Kd(x) is the distribution coefficient. The fields K(x) and Kd(x) are assumed to be lognormally distributed and correlated. Three correlation models between Y = log K and W = log Kd are considered: the perfectly positive correlation (model A), the perfectly negative correlation (model B), and no correlation (model C). The values of Z11'R, which is defined as ⟨ S11'R⟩ minus its initial value, and γ11' R for all three correlation models increase as the length of a line source l increases. As l→ ∞, Z11'R or γ11'R approach their respective ergodic limits X11'R or α11'R. The asymptotic longitudinal dispersion due to the physical and chemical heterogeneity is Fickian for a line source normal to ¿ and non-Fickian for a line source parallel to ¿. The positive correlation between Y and W reduces Z11'R and γ11'R, the negative correlation enhances Z11'R and γ11'R, and no correlation slightly enhances Z11'R and γ11'R, in comparison with nonreactive Z11' and γ11'. The larger the value of the mean retardation factor, the large its effect on Z11'R and γ11'R. The three-dimensional Z11'R and γ11'R are slightly larger than their respective two-dimensional counterparts.