A one-dimensional dynamic partial differential equation (PDE) agglomeration model is derived based on the continuous Safronov agglomeration equation. A regularized PDE agglomeration model, represented by a set of convection-reaction-diffusion PDEs, can be solved within a standard adaptive-mesh implicit numerical framework that does not require additional quadrature assumptions to evaluate the aggregation integral. The PDE agglomeration model is solved numerically using a general Newton's-method-based implicit Galerkin finite-element algorithm. The applied algorithm uses an automatic Gear-type time step and nonuniform adaptive-mesh strategies, which aids solution convergence. A numerical solution of the model for an agglomeration degree of 99.9% closely matches an asymptotic analytic solution of the original Safronov equation, which confirms the accuracy of the numerical procedure used. It is also shown that the number density function predicted by the new PDE agglomeration model satisfactorily agrees with the analytic solution of the Smoluchowski agglomeration equation. For small particle sizes and first and zeroth full moments, the two models give similar solutions. However, for larger particle sizes and the second full moment, the difference between the two models increases with increasing degree of agglomeration. Industrially important gibbsite agglomeration is used as a case study to demonstrate the application of the new numerical approach for agglomeration modeling.