Molecular-level decisions are increasingly recognized as an integral part of process design. Finding the optimal process performance requires the integrated optimization of process and solvent chemical structure, leading to a challenging mixed-integer nonlinear programming (MINLP) problem. The formulation of such problems when using a group contribution version of the statistical associating fluid theory, SAFT-γ Mie, to predict the physical properties of the relevant mixtures reliably over process conditions is presented. To solve the challenging MINLP, a novel hierarchical methodology for integrated process and solvent design (hierarchical optimization) is presented. Reduced models of the process units are developed and used to generate a set of initial guesses for the MINLP solution. The methodology is applied to the design of a physical absorption process to separate carbon dioxide from methane, using a broad selection of ethers as the molecular design space. The solvents with best process performance are found to be poly(oxymethylene)dimethylethers.