The closed-loop liquid-liquid fluid phase equilibria of aqueous solutions of poly(ethylene glycol) (PEG) binary mixtures are studied using the statistical associating fluid theory for potentials of variable range (SAFT-VR). A molecular model of the mixture is developed which takes into account the delicate balance between the water-water, water-PEG, and PEG-PEG hydrogen-bonding interactions as well as the usual repulsive and attractive/dispersive contributions. A fully transferable intermolecular potential model is proposed which allows one to study any aqueous PEG system with the molecular weight of the polymer as sole input. An excellent predictive description of the liquid-liquid phase behavior of these systems is achieved; mixtures involving shorter polymers are used to determine the binary (unlike) interaction parameters, and we are then able to predict the phase behavior of mixtures of larger molecular weight in good agreement with experimental data. The high-pressure (GPa) phase behavior of the liquid-liquid phase equilibria in these systems is also studied. The region of closed-loop immiscibility is seen to become less extensive with an initial increase in pressure. For intermediate molecular weights (2000 less than or similar to MW less than or similar to 100 000 g/mol) of the polymer the liquid phase becomes homogeneous when the pressure is increased beyond a high enough threshold, and at even higher pressures a second region of liquid-liquid separation is observed. In the case of high molecular weight polymers (MW greater than or similar to 100 000 g/mol) the fluid phase behavior is characterized by an hourglass-shaped region of immiscibility with liquid-liquid separation persisting for all pressures considered. The dome-shaped regions of liquid-liquid immiscibility predicted for aqueous solutions of PEG of intermediate molecular weight (2000 less than or similar to MW less than or similar to 75 000 g/mol) are reminiscent of the pressure-temperature denaturation boundaries found in protein systems which are thought to be governed by a corresponding increase in water solubility into the hydrophobic core.