If your question is related with the methods for determining the open and close porosity, the most simple method is a combination of density determination by picnometry and water absorption. If water solubility is expected, then other inert liquids are to be used. In this way we suppose that all the open pores are accesible to the liquid. If it not the case then other complementary methods like Mercury Porosimetry or BET could be employed.
If your question is related with definition of the porosity types, then you must to incorporate other important concept used in membranes: percolation. That is, what part of your porosity is percolating or no?
What is exactly the meaning of the term MIP are you using, molecular impringing polymer? What is your aim, to determine the pore characteristics of the matrix?
Thank you very much Carlos R. Gonzalez-Gonzalez. MIP is Mercury Intrusion Porosimeter
The aim is to give a detailed description of the pores, pore size distribution as well as pore connectivity of a porous Matrix in relation with the gas, moisture or Thermal diffusion through the matrix
In complement to Jaime´s answer, X-ray computed tomography can allow you to discriminate easily between closed and open porosity. Closed porosity will be selected as a set of individual pores whereas open porosity will be selected as a large continuous pore as long as the connection or opening to the edge happens within the scanned field of view.
Attached are 2 links to examples of closed porosity in concrete and of open porosity in PMMA.
Small angle scattering with contrast matching can also be used to quantify accessible vs closed porosity (and PSD). In SANS for example, mixtures of H2O and D2O are used for contrast matching.