No / The advection–dispersion equation (ADE) is one of the most widely used methods for estimating natural stream pollution at different locations and times. In this paper, variational iteration method (VIM) is utilized to obtain a semianalytical solution for 1D ADE in a temporally dependent solute dispersion within uniformsteady flow. Through a computational validation, the effect of different parameters such as uniform flow velocity and dispersion coefficient on the solute concentration values has been investigated. Results show that the change in velocity has a strong effect on fluid density variation. However, when the diffusion coefficient has been increased, the change in flow and velocity behaviors is negligible. To verify the proposed semianalytical solution, the results were compared to analytical solutions and errors were found to be <0.7% in all simulations.

Horizontal wells have been used to increase reservoir recovery, especially in unconventional reservoirs, and hydraulic fracturing has been applied to further extend the contact with the reservoir to increase the efficiency of development. In the past, many models, analytical or numerical, were developed to describe the flow behavior in horizontal wells with fractures. Source solution is one of the analytical/semi-analytical approaches. To solve fractured well problems, source methods were advanced from point sources to volumetric source, and pressure change inside fractures was considered in the volumetric source method. This study aims at developing a method that can predict horizontal well performance and the model can also be applied to horizontal wells with multiple fractures in complex natural fracture networks. The method solves the problem by superposing a series of slab sources under transient or pseudosteady-state flow conditions. The principle of the method comprises the calculation of semi-analytical response of a rectilinear reservoir with closed outer boundaries. A statistically assigned fracture network is used in the study to represent natural fractures based on the spacing between fractures and fracture geometry. The multiple dominating hydraulic fractures are then added to the natural fracture system to build the physical model of the problem. Each of the hydraulic fractures is connected to the horizontal wellbore, and the natural fractures are connected to the hydraulic fractures through the network description. Each fracture, natural or hydraulically induced, is treated as a series of slab sources. The analytical solution of superposed slab sources provides the base of the approach, and the overall flow from each fracture and the effect between the fractures are modeled by applying superposition principle to all of the fractures. It is assumed that hydraulic fractures are the main fractures that connect with the wellbore and the natural fractures are branching fractures which only connect with the main fractures. The fluid inside of the branch fractures flows into the main fractures, and the fluid of the main fracture from both the reservoir and the branch fractures flows to the wellbore. Predicting well performance in a complex fracture network system is extremely challenged. The statistical nature of natural fracture networks changes the flow characteristic from that of a single linear fracture. Simply using the single fracture model for individual fracture, and then adding the flow from each fracture for the network could introduce significant error. This study provides a semi-analytical approach to estimate well performance in a complex fracture network system.

Removal of CO2 directly from anthropogenic sources (capture) and its disposal in geological formations can take place for medium-term time periods (storage), or it can be permanent (sequestration), with the CO2 eventually becoming dissolved in the aqueous phase. The latter is the main subject of this dissertation. Carbon dioxide sequestration covers a wide range of strategies and alternatives. The main objective of CO2 sequestration alternatives is secure disposal of carbon in large amounts and for a lengthy time scale (typically 1000 years). Injection of CO2 into subsurface formations is generally considered as the main option for CO2 sequestration. Geological sequestration through injection covers a broad variety of target formations: disposal in depleted oil and gas reservoirs, trapping in oil reservoirs, replacing CH4 in coal bed methane recovery processes, trapping in deep aquifers, and salt cavern placement are the major CCS alternatives in geologic formations. In this thesis, hydrogeologic interaction between the injectant (CO2) and the host fluid (saline water) during injection is the main subject of the project. Because of the density and viscosity contrast of displacing and displaced fluids, the pattern of saturation progression is complicated. A set of semi-analytical solutions is developed for quick estimation of the position of isosats (contours of saturation) during primary injection in homogenous cases with simple geometry. All of the mathematical solutions are developed based on two assumptions; incompressible fluids and rocks and vertical equilibrium (capillary-gravity condition) for geometries with large aspect ratio (L >> H). First, a series of analytical solutions for primary drainage for a set of linear relative permeability functions is developed. The first analytical solution is based on the assumption of locally linearized Leverett-J functions, and by using the method of characteristics, a formulation for the isosats’ geometry is obtained. A semi-analytical solution is then proposed for calculation of the position of isosats with linearized relative permeability functions and arbitrary capillary-saturation correlation. The analytical solution is extended to incorporate a specific form of nonlinearity of the relative permeability function. Nonlinear relative permeability functions are also incorporated in another semi-analytical solution, and the positions of the isosats for any arbitrary Leverett-J function and relative permeability functions are developed. Sequential gas-saline injection is also modeled in that chapter. For approximate verification of the analytical solutions, a FEM numerical model is developed and the results of the analytical solutions are compared with the numerical solutions. These new analytical solutions provide powerful tools for prediction of saturation distribution during injection in vertical and horizontal wells, as well as for carrying out stochastic assessments (Monte Carlo simulations) and parametric weight assessment. The domain of applications of the new solutions go far beyond the limited question of CO2 sequestration: they can be used for injection of any less viscous fluid into a reservoir, whether the fluid is lighter or denser than the host fluid (gas injection, water-alternating gas injection, water injection into viscous oil reservoirs, solvent injection).