There have been many attempts to use mathematical method in order to characterize shale gas/oil reservoirs with multi-transverse hydraulic fractures horizontal well. Many authors have tried to come up with a suitable and practical mathematical model. To analyze the production data of a shale reservoir correctly, an understanding and choosing the proper mathematical model is required. Therefore, three models (the homogeneous linear flow model, the transient linear dual porosity model, and the fully transient linear triple porosity model) will be studied and compared to provide correct interpretation guidelines for these models. The analytical solutions and interpretation guidelines are developed in this work to interpret the production data of shale reservoirs effectively. Verification and derivation of asymptotic and associated equations from the Laplace space for dual porosity and triple porosity models are performed in order to generate analysis equations. Theories and practical applications of the three models (the homogeneous linear flow model, the dual porosity model, and the triple porosity model) are presented. A simplified triple porosity model with practical analytical solutions is proposed in order to reduce its complexity. This research provides the interpretation guidelines with various analysis equations for different flow periods or different physical properties. From theoretical and field examples of interpretation, the possible errors are presented. Finally, the three models are compared in a production analysis with the assumption of infinite conductivity of hydraulic fractures.

Extremely small pore size, low porosity, and ultra-low permeability are among the characteristics of shale rocks. In tight shale reservoirs, the nano-confinement effects that include large gas-oil capillary pressure and critical property shifts could alter the phase behaviors, thereby affecting the oil or gas production. In this research, two in-house simulation models, i.e., a compositionally extended black-oil model and a fully composition model are developed to examine the nano-pore confinement effects on convective and diffusive multicomponent multiphase fluid transport. Meanwhile, the effect of nano-confinement and rock intrinsic properties (porosity and tortuosity factor) on predicting effective diffusion coefficient are investigated. First, a previously developed compositionally extended black-oil simulation approach is modified, and extended, to include the effect of large gas-oil capillary pressure for modeling first contact miscible (FCM), and immiscible gas injection. The simulation methodology is applied to gas flooding in both high and very low permeability reservoirs. For a high permeability conventional reservoir, simulations use a five-spot pattern with different reservoir pressures to mimic both FCM and immiscible displacements. For a tight oil-rich reservoir, primary depletion and huff-n-puff gas injection are simulated including the effect of large gas-oil capillary pressure in flow and in flash calculation on recovery estimations. A dynamic gas-oil relative permeability correlation that accounts for the compositional changes owing to the produced gas injection is introduced and applied to correct for changes in interfacial tension (IFT), and its effect on oil recovery is examined. The results show that the simple modified black-oil approach can model well both immiscible and miscible floods, as long as the minimum miscibility pressure (MMP) is matched. It provides a fast and robust alternative for large-scale reservoir simulation with the purpose of flaring/venting reduction through reinjecting the produced gas into the reservoir for EOR. Molecular diffusion plays an important role in oil and gas migration in tight shale formations. However, there are insufficient reference data in the literature to specify the diffusion coefficients within porous media. Another objective of this research is to estimate the diffusion coefficients of shale gas, shale condensate, and shale oil at reservoir conditions with CO2 injection for EOR/EGR. The large nano-confinement effects including large gas-oil capillary pressure and critical property shifts could alter the phase behaviors. This study estimates the diffusivities of shale fluids in nanometer-scale shale rock from two perspectives: 1) examining the shift of diffusivity caused by nanopore confinement effects from phase change (phase composition and fluid property) perspective, and 2) calculating the effective diffusion coefficient in porous media by incorporating rock intrinsic properties (porosity and tortuosity factor). The tortuosity is obtained by using tortuosity-porosity relations as well as the measured tortuosity of shale from 3D imaging techniques. The results indicated that nano-confinement effects could affect the diffusion coefficient through altering the phase properties, such as phase compositions and densities. Compared to bulk phase diffusivity, the effective diffusion coefficient in porous shale rock is reduced by 102 to 104 times as porosity decreases from 0.1 to 0.03. Finally, a fully compositional model is developed, which enables us to process multi-component multi-phase fluid flow in shale nano-porous media. The validation results for primary depletion, water injection, and gas injection show a good match with the results of a commercial software (CMG, GEM). The nano-confinement effects (capillary pressure effect and critical property shifts) are incorporated in the flash calculation and flow equations, and their effects on Bakken oil production and Marcellus shale gas production are examined. The results show that including oil-gas capillary pressure effect could increase the oil production but decrease the gas production. Inclusion of critical property shift could increase the oil production but decrease the gas production very slightly. The effect of molecular diffusion on Bakken oil and Marcellus shale gas production are also examined. The effect of diffusion coefficient calculated by using Sigmund correlation is negligible on the production from both Bakken oil and Marcellus shale gas huff-n-puff. Noticeable increase in oil and gas production happens only after the diffusion coefficient is multiplied by 10 or 100 times. / Doctor of Philosophy / Shale reservoir is one type of unconventional reservoir and it has extremely small pore size, low porosity, and ultra-low permeability. In tight shale reservoirs, the pore size is in nanometer scale and the oil-gas capillary pressure reaches hundreds of psi. In addition, the critical properties (such as critical pressure and critical temperature) of hydrocarbon components will be altered in those nano-sized pores. In this research, two in-house reservoir simulation models, i.e., a compositionally extended black-oil model and a fully composition model are developed to examine the nano-pore confinement effects on convective and diffusive multicomponent multiphase fluid transport. The large nano-confinement effects (large gas-oil capillary pressure and critical property shifts) on oil or gas production behaviors will be investigated. Meanwhile, the nano-confinement effects and rock intrinsic properties (porosity and tortuosity factor) on predicting effective diffusion coefficient are also studied.