This paper proposes a theoretical approach aimed at evaluation of fluid compression factor, activity, and cohesion energy at near-critical and overcritical temperatures, for the fluid molar volumes ranging from 40% of the critical value. Such data are necessary in the theoretical description of sorption processes, developed in our previous papers. The approach is based on separate analysis of fluid entropy and cohesion energy. A theoretical model is used, which makes possible to derive a formula for the athermal compression factor of hard sphere fluids. It involves using a correction for the fluid accentric factor. Also applicability of other expressions is discussed. In turn, the mathematical model for the fluid cohesion energy was obtained by high accuracy approximation of universal compression factor data, with critical point conditions being taken into account. It is recommended to complete the compression data with empirical orthobaric compression factors. The coefficients of the model are expressed as functions of the fluid accentric factor. As the result, a state equation applicable for fluids of accentric factor less than 0.45 and reduced molar volume larger than 0.5 is proposed. For methane and carbon dioxide, the equations of better accuracy are proposed, with coefficients adjusted individually by nonlinear optimization. They are applicable for the reduced volume ranging from 0.4.