Methods of Peusner's network of thermodynamics enable the symmetric or hybrid transformation of classic Kedem-Katchalsky (K-K) equations into a network form. In the case of binary non-electrolyte solutions (homogenous and non-homogenous ones), two symmetric and two hybrid forms of the K-K equations may be obtained, containing relatively symmetric ( or or hybrid ( or Peusner's coefficients. In the following paper, the network form of the K-K equations was obtained, containing the Peusner's coefficients and creating matrix of the second row of the Peusner's coefficients The equations were used to study transport of aqueous glucose solutions through a Nephrophan membrane oriented horizontally as well as configurations A and B of a membrane system. The configuration A involves a solution with a higher concentration placed under the membrane, whereas a solution with a lower concentration is placed above the membrane. In the configuration B, the solutions are swapped with places. Dependences of the Peusner's coefficients and for non-homogenous ( and homogenous ( solutions upon the average concentration of glucose in the membrane ( were calculated. The transport properties of membrane are characterized by coefficients determined experimentally: the coefficient of reflection (), hydraulic permeability (, and solution permeability () for aqueous glucose or ethanol solutions. The calculations show that values of coefficients , and depend non-linearly on both the membrane and the configuration of the membrane system. The values of the coefficients are different from the values of the coefficients and Moreover, the coefficients and do not depend on the configuration of the membrane system. It was shown that there is a threshold value of concentration above which relations and depend on the configuration of the membrane system.