The Chicontepec paleochannel contains an unconventional tight oil sandstone also characterized by natural fractures. Chicontepec ranks worldwide as a giant reservoir with volumes of original-oil-in-place (OOIP) ranging between 137,300 and 59,000 MMbbls. As of 2020 cumulative oil recovery was 340.38 MMbbls, which is a significant volume by normal standards. However, for Chicontepec this represents only 0.32 to 0.75% of the OOIP, truly an insignificant percent recovery. The fact that almost all the oil is being left in this unconventional reservoir provides the key motivation for the research developed in this thesis: Finding a practical economic means of increasing oil production rates and recovery from Chicontepec. Since nearly every available method in the oil and gas industry has been tried in the past in Chicontepec to increase oil recovery with limited success despite large investments, this thesis concentrated on developing novel but realistic models with a view to increase Chicontepec oil recovery. The following new methods were developed 1) A dual porosity petrophysical model for shaly sandstones that contain natural fractures. 2) A dual porosity well testing model for horizontal wells penetrating an unconventional naturally fractured reservoir. 3) A practical means of integrating the dual porosity petrophysical and well testing models. 4) A means of integrating actual available oil production data with the 3 items mentioned above. It is concluded that the novel methodology developed in this thesis has the potential to increase oil recovery from Chicontepec. This is significant as a mere 1% increase in oil recovery corresponds to 1,373MM or 590 MMbbls, depending on the OOIP used for the calculation. Any one of these two volumes is larger than the cumulative oil produced in Chicontepec up to the year 2020 (340.38 MMbbls). And based on results of this study the increase in percent recovery could be larger.