We simulate transient behavior of viscous- and capillary-dominated water invasion at mixed-wet conditions directly in scanningelectron- microscope (SEM) images of Bentheim sandstone by treating the pore spaces as cross sections of straight tubes. Initial conditions are established by drainage and wettability alteration. Constant rate or differential pressure is imposed along the tube bundle. The phase pressures vary with positions along the tube length but remain unique in each cross section, consistent with 1D core-scale models. This leads to a nonlinear system of equations that are solved for the interface positions as a function of time. The cross-sectional fluid configurations are computed accurately at any capillary pressure and wetting condition by a semianalytical model that is based on free-energy minimization. The fluid conductances are estimated by newly derived explicit expressions that are shown to be in agreement with numerical computations performed directly on the cross-sectional fluid configurations. An SEM image of Bentheim sandstone is taken as input to the developed model for simulating the evolution of saturation profiles during waterfloods for different flow rates and several mixed-wet conditions, which are established with various initial water saturations and contact angles. It is demonstrated that the simulated saturation profiles depend strongly on initial water saturation at mixedwet conditions. The saturation profiles exhibit increasingly gradual behavior in time as the contact angle, defined on the oil-wet solid surfaces, increases or the initial water saturation decreases. Front menisci associated with positive capillary pressures promote oil displacement by water, whereas for large and negative capillary pressures at small flow rates, oil displaces water because the associated front menisci retract. This results in the development of pronounced gradual saturation fronts at mixed-wet conditions. The waterfloods simulated at conditions established with a large initial water saturation and small contact angle on the oil-wet solid surfaces exhibit sharp Buckley-Leverett saturation profiles for high flow rates because the capillary pressure is small and less important. The shape of the saturation profiles is interpreted on the basis of the simulated capillary pressure curves and the corresponding fluid configurations occurring in the rock image.