There should be good agreement between log porosity and core porosity. Contrary to this some times it happens that to regress log porosity with log permeability is inconclusive/strange. Same could be happen when try to regress core permeability with core porosity. In the absence of any correlation we can use the nearby formation information (existing wells from the same formations). Last but not least it is always required to correct core perm to the log the log scale bcoz of the change of environment (from small scale to big scale) as well as insitu conditions.
There should be good agreement between log porosity and core porosity. Contrary to this some times it happens that to regress log porosity with log permeability is inconclusive/strange. Same could be happen when try to regress core permeability with core porosity. In the absence of any correlation we can use the nearby formation information (existing wells from the same formations). Last but not least it is always required to correct core perm to the log the log scale bcoz of the change of environment (from small scale to big scale) as well as insitu conditions.
Core porosity and core permeability are the baseline. Use multipliers and different zones/rock classes to relate core porosity to log porosity. As for peambility, log log plot between core porosity and core permeability should give a good agreement with different zones/classes in mind as well. Then relate log porosity to core permeability.
Finally, once you have a well test, use the well test permeability as the base and multipliers to the core permeability since most of the times the core misses the high permeability sections (Like fractures, friable sand, bugs..etc) which can not be tested (during making plugs to test it). .
It is always better to establish porosity permeability relation ships based on facies/rock types. Different rock types will have different poro-perm relation ships. Defining the pore size distributions from log derived porosity permeability and core derived porosity permeability data and comparing at that level the distributions and making the relation ships at that level would provide realistic poro-perm relation ships. The best way of calibration would be from testing methods
Actually, I didn't get a porosity-permeability correlation because I had only Neutron Porosity, which represents the total porosity. Then, I got more data including Density Porosity that refers to effective porosity. Therefore, the correlation between log and core porosity is somehow better than the case in the question before.