Heavy-oil mobility in reservoir rocks can be improved, using nanotechnology, by reducing the viscosity of the oil and improving the rock wettability to a water-wet condition. Previous pilot studies in Colombian heavy oil fields reported that nanoparticles dispersed in an oleic carrier fluid (diesel) increased oil production rates between 120–150% higher than before the interventions. However, to optimally deploy a massive nanofluid intervention campaign in heavy oil fields, it is valuable to implement simulation tools that can help to understand the role of operational parameters, to design the operations and to monitor the performance. The simulator must account for nanoparticle transport, transfer, and retention dynamics, as well as their impact on viscosity reduction and wettability restoration. In this paper, we developed and solved, numerically, a 3D mathematical model describing the multiphase flow and interaction of the nanoparticles with oil, brine, and rock surface, leading to viscosity reduction and wettability restoration. The model is based on a multiphase pseudo-compositional formulation, coupled with mass balance equations, of nanoparticles dispersed in water, nanoparticles dispersed in oil, and nanoparticles retained on the rock surface. We simulated a pilot test study of a nanofluid stimulation done in a Colombian heavy oil field. The injection, soaking, and production stages were simulated using a 3D single-well formulation of the mathematical model. The comparison of simulation results with the pilot test results shows that the model reproduced the field observations before and after the stimulation. Simulations showed that viscosity reduction during the post-stimulation period is strongly related to the detachment rate of nanoparticles. Simulation indicates that the recovery mechanism of the nanofluid stimulation is initially governed by viscosity reduction and wettability alteration. At latter times, wettability alteration is the main recovery mechanism. The nanoparticles transferred to the residual water promote the wettability alteration to a water wet condition. The model can be used to design field deployments of nanofluid interventions in heavy oil reservoirs.