Naturally fractured reservoirs are abundant in the earth’s crust and host a substantial percentage of oil reserves globally. The main mechanism of oil recovery during waterflooding of these types of reservoirs is through spontaneous imbibition of water into the matrix and simultaneous counter-current flow of oil out of the matrix. Understanding the predominate recovery mechanism enhances reserves estimates, accurate simulation forecasts and overall sound development plans. Dual-porosity and dual-permeability simulations are used in the industry to simulate waterfloods in naturally fractured reservoirs. One of the key parameters in these simulations is the matrix-fracture transfer term, which is not well understood and modeled, especially in mixed-wet reservoirs. The same transfer term is used for primary, secondary and tertiary recovery processes, though it should change depending on the mechanisms of oil recovery. The key mechanism during primary recovery is depressurization, not spontaneous imbibition. The main goal of this research is to develop an accurate representation of the matrix-fracture transfer term in waterflooding for dual-porosity simulators. The analytical and semi-analytical solutions for 1D counter-current imbibition were studied for defining the exact solution in fractured porous media. Fine-grid, single-porosity numerical solutions were developed that are consistent with the 1D analytical solutions, in conjunction with coarse-grid single-porosity conceptual models. Both single-porosity models are used as reference against dual-porosity conceptual models to address the built-in matrix-fracture transfer terms through recovery of the matrix element. The error in simulation was defined as the difference in recoveries between the fine-grid single-porosity solution and the dual-porosity solutions. A detailed investigation of both rock and fluid inputs affecting transfer terms in dual-porosity was made in an effort to match the transient solution obtained from fine-grid single-porosity models. The inclusion of transient effect in dual-porosity requires optimizing the following inputs which are shape factor, capillary exponent and oil relative permeability exponent. Two main processes were proposed for optimization. Firstly, an accuracy-based Latin Hyper Cube sampling method was utilized that converged to the solution quickly. Secondly, utilizing a machine learning algorithm (specifically an Artificial Neural Net model) that predicts recovery accuracy based on the aforementioned chosen inputs. The machine learning model needed many iterations to converge to a solution

This research utilizes the imbibition experiments and X-ray tomography results for modeling fluid flow in naturally fractured reservoirs. Conventional dual porosity simulation requires large number of runs to quantify transfer function parameters for history matching purposes. In this study empirical transfer functions (ETF) are derived from imbibition experiments and this allows reduction in the uncertainness in modeling of transfer of fluids from the matrix to the fracture. The application of the ETF approach is applied in two phases. In the first phase, imbibition experiments are numerically solved using the diffusivity equation with different boundary conditions. Usually only the oil recovery in imbibition experiments is matched. But with the advent of X-ray CT, the spatial variation of the saturation can also be computed. The matching of this variation can lead to accurate reservoir characterization. In the second phase, the imbibition derived empirical transfer functions are used in developing a dual porosity reservoir simulator. The results from this study are compared with published results. The study reveals the impact of uncertainty in the transfer function parameters on the flow performance and reduces the computations to obtain transfer function required for dual porosity simulation.

This thesis presents procedures to properly simulate naturally fractured reservoirs using dual-porosity models. The main objectives of this work are to: (1) determine if the spontaneous imbibition can be simulated using a two phase CMG simulator and validate it with laboratory experiments in the literature; (2) study the effect of countercurrent imbibition in field scale applications; and (3) develop procedures for using the dual-porosity to simulate fluid displacement in a naturally fractured reservoir. Reservoir simulation techniques, analytical solutions and numerical simulation for a two phase single and dual-porosity are used to achieve our objectives. Analysis of a single matrix block with an injector and a producer well connected by a single fracture is analyzed and compared with both two phase single and dual-porosity models. Procedures for obtaining reliable results when modeling a naturally fractured reservoir with a two phase dual-porosity model are presented and analyzed.

Streamline-Simulation emphasizes the unique features of streamline technology that in many ways complement conventional finite-difference simulation. It fills gaps in the mathematical foundations.

This book deals exclusively with naturally fractured reservoirs and includes many subjects usually treated in separate volumes. A highly practical edition, Naturally Fractured Reservoirs is written for students, reservoir geologists, log analysts and petroleum engineers.

The current streamline formulation is limited to single-porosity systems and is then not suitable for application to naturally fractured reservoirs. Describing the fluid transport in naturally fractured reservoirs has been recognized as a main challenge for simulation engineers due to the complicated physics involved. In this work, we generalized the streamline-based simulation to describe the fluid transport in naturally fractured reservoirs. We implemented three types of transfer function: the conventional transfer function (CTF), the diffusion transfer function (DTF), and the empirical transfer function (ETF). We showed that these transfer functions can be implemented easily in the current single-porosity streamline codes. These transfer functions have been added as a source term to the transport equation that describes the saturation evolution along the streamlines. We solved this equation numerically for all types of transfer functions. The numerical solution of the continuity equation with DTF and ETF requires discretizing a convolution term. We derived an analytical solution to the saturation equation with ETF in terms of streamline TOF to validate the numerical solution. We obtain an excellent match between the numerical and the analytical solution. The final stage of our study was to validate our work by comparing our dual-porosity streamline simulator (DPSS) to the commercial dual-porosity simulator, ECLIPSE. The dual-porosity ECLIPSE uses the CTF to describe the interaction between the matrix-blocks and the fracture system. The dual-porosity streamline simulator with CTF showed an excellent match with the dual-porosity ECLIPSE. On the other hand, dual-porosity streamline simulation with DTF and ETF showed a lower recovery than the recovery obtained from the dual-porosity ECLIPSE and the DPSS with CTF. This difference in oil recovery is not due to our formulation, but is related to the theoretical basis on which CTF, DTF, and ETF were derived in the literature. It was beyond the scope of this study to investigate the relative accuracy of each transfer function. We demonstrate that the DPSS is computationally efficient and ideal for large-scale field application. Also, we showed that the DPSS minimizes numerical smearing and grid orientation effects compared to the dual-porosity ECLIPSE.