Residual solvent content in the precursor fibers from polyacrylonitrile (PAN) is one of the key parameters that severely affects the mechanical properties of resultant carbon fibers to a large extent. Although its significance is well-known, the influence of precursor tow size (i.e., number of filaments) on the kinetics of solvent removal is not yet reported. In order to develop the relationship for better PAN precursor spinning line design, a computational model using MATLAB is presented. The model uses a finite difference method (FDM) approach using Fick’s second law of diffusion for dynamically determining the residual solvent content in fibers after passing through various units. It is assumed that the multifilament tow takes the shape of a cylindrical geometry, considering hexagonal closed packing (HCP). The models were simulated for 1K, 2K, and 3 K precursor fiber tows passing a typical wet-spinning line. The model data values are also verified with consistent data recorded from Gas Chromatography-Mass Spectrometry (GC/MS) equipment. According to the data presented, solvent removal efficiency significantly reduces as tow size increases, while the washing unit operation is the most influential on extraction due to longer retention times. While significant size reduction occurs in the stretching unit but its influence on solvent reduction is not comparable with the washing unit. This paper presents a theoretical and reliable methodology for optimizing spinning plant parameters, selecting appropriate units, and developing higher-quality PAN precursors for high-performance carbon fiber applications.