This work focuses on the study of ink seepage and spreading into paper to ease the deciphering of digitized ancient documents and therefore make them legible and researchable. A three-dimensional model is proposed for the simulation of ink seepage into paper at the fiber level. The model takes into account a finite volume of ink and describes the system state through gravity, cohesion and adhesion force interactions. At the mesoscopic scale, the writing paper is modeled using a discretized fiber structure generated using a numerical deposition procedure. A modified Monte Carlo method is introduced for the simulation of the ink dynamics. Finally a multiphase lattice Boltzmann method is suggested to fine-tune the mesoscopic variational model parameters and it is shown that the ink seepage behaviors predicted by the proposed model can resemble those predicted by a method relying on first principles.