a b s t r a c tSome shale gas and oil wells undergo month-long shut-in times after multi-stage hydraulic fracturing well stimulation. Field data indicate that in some wells, such shut-in episodes surprisingly increase the gas and oil flow rate. In this paper, we report a numerical simulation study that supports such observations and provides a potentially viable underlying imbibition and drainage mechanism. In the simulation, the shale reservoir is represented by a triple-porosity fracture-matrix model, where the fracture forms a continuum of interconnected network created during the well stimulation while the organic and inorganic matrices are embedded in the fracture continuum. The effect of matrix wettability, capillary pressure, relative permeability, and osmotic pressure, that is, chemical potential characteristics are included in the model.The simulation results indicate that the early lower flow rates are the result of obstructed fracture network due to high water saturation. This means that the injected fracturing fluid fills such fractures and blocks early gas or oil flow. Allowing time for the gravity drainage and imbibition of injected fluid in the fracture-matrix network is the key to improving the hydrocarbon flow rate during the shut-in period.

Some shale gas and oil wells undergo month-long shut-in times after multi-stage hydraulic fracturing well stimulation. Field data indicate that in some wells, such shut-in episodes surprisingly increase the gas and oil flow rate. In this paper, we report a numerical simulation study that supports such observations and provides a potentially viable underlying imbibition and drainage mechanism. In the simulation, the shale reservoir is represented by a triple-porosity fracture-matrix model, where the fracture forms a continuum of interconnected network created during the well simulation while the organic and non-organic matrices are embedded in the fracture continuum. The effect of matrix wettability, capillary pressure, relative permeability, and osmotic pressure, that is, chemical potential characteristics are included in the model.The simulation results indicate that the early lower flow rates are the result of obstructed fracture network due to high water saturation. This means that the injected fracturing fluid fills such fractures and blocks early gas or oil flow. Allowing time for the gravity drainage and imbibition of injected fluid in the fracture-matrix network is the key to improving the hydrocarbon flow rate during the shut-in period.

Horizontal wells are used in unconventional oil and gas reservoirs to increase production by creating large drainage surface areas and contact volumes. Production is further improved by applying hydraulic fracture stimulation in horizontal wells. Hydraulic fracturing increases well productivity via the large drainage surface of the fracture and by rejuvenating existing natural fractures as well as creating new fractures in the vicinity of the wellbore. The affected reservoir volume is known as the stimulated reservoir volume (SRV) which includes a complex flow network that creates different flow regimes.We will present several short and long pressure transient tests conducted in vertical and horizontal wells, to determine critical formation properties of the low-permeability, dual-porosity Middle Bakken and Three Forks reservoirs. Pressure transient test data were obtained via permanent downhole pressure gauges. The bilinear and linear flow regimes of the pressure buildup tests are the focus of the analyses. For this, we have presented an analytical solution using numerical inverse Laplace transform as well as closed-form approximate solutions.Flow rate transient analysis of long-duration production data were also conducted to compare with the results of the pressure transient analyses. All tests indicated that the field measured permeability is several orders of magnitude greater than permeability measured on core plugs. This indicates the presence of a network of interconnected fractures and microfractures in the stimulated near-well regions without which no significant production would result. The details of the well tests and analyses will be presented for engineering applications.

Pressure and rate transient analyses are reliable methods to estimate effective formation permeability of unconventional reservoirs. The results of such analyses are used to validate or fine-tune the numerical simulation models both for the primary and enhanced oil and gas recovery methods. Pressure-rate transient test applications in unconventional reservoirs are somewhat different from similar tests in conventional reservoirs because of the extremely tight nature of target formations and the use of horizontal wells as an integral part of well completion and reservoir stimulation. Accordingly, this paper presents theory, mathematical formulation, and application of the numerical and analytical well testing solutions to characterize unconventional reservoirs. The mathematical models pertain to the single-porosity and dual-porosity concepts. In the latter we focused on the issues surrounding the unsteady state (USS) and pseudo steady state (PSS) flow. The models studied in this paper were a 1-D analytical model and a hybrid 3-D numerical model that combines the USS and PSS dual-porosity formulations; a trilinear analytical model and a MINC (Multiple Interacting Continua) numerical model. The 3-D numerical model was compared with the trilinear analytical and MINC numerical models. In unconventional reservoirs the dual-porosity environment emanates from the auxiliary effect of multi-stage hydraulic fracturing for which the unsteady-state mathematical solutions are more appropriate. The benefits of such solutions are supported by field results, which we will present and discuss. Furthermore, the results of pressure-transient and rate-transient analyses of two oil wells in an unconventional reservoir were presented.

In this thesis, I present a new method to model heterogeneity and flow channeling in petroleum reservoirs-specially reservoirs containing interconnected microfractures. The method is applicable both to conventional and unconventional reservoirs where the interconnected microfractures form the major flow path. The flow equations, which could include flow contributions from matrix blocks of various size, permeability and porosities, are solved by the Laplace transform analytical solutions and finite-difference numerical solutions. The accuracy of flow from and into nano-Darcy matrix blocks is of great interest to those dealing with unconventional reservoirs. Thus, matrix flow equations are solved using both pseudosteady-state (PSS) and unsteady-state (USS) formulations.The matrix blocks can be of different size and properties within the representative elementary volume (REV) in the analytical solutions and within each control volume (CV) in the numerical solutions.While the analytical solutions were developed for slightly compressible linear systems, the numerical solutions are general and can be used for non-linear multi-phase, multi-component flow problems.The mathematical solutions were used to analyze the long-term performance of a gas well and two oil wells in two separate unconventional reservoirs. Finally, the formulations were used to assess enhanced oil recovery potential from a typical nano-Darcy matrix block. It is concluded that matrix contribution to flow is very slow in a typical low-permeability unconventional reservoir and much of the enhanced production is from the fluids contained in the microfractures than in the matrix.In addition to field applications, the mathematical formulations and solution methods are presented in a transparent fashion to allow easy utilization of the techniques for reservoir and engineering applications. iv TABLE OF CONTENTS ABSTRACT