Thormod E. Johansen

Water Enhancement Using Nanoparticles in Water Alternating Gas (WAG) Micromodel Experiments

Nanotechnology has found widespread application in a diverse range of industries. Researchers are now investigating whether nanotechnology can be applied to enhance oil recovery (EOR). The goal of enhanced oil recovery is to manipulate the fluid-fluid properties (interfacial tension, viscosity), and fluid-rock properties (contact angle, relative permeability) between the injected fluid and the residual oil phase to improve pore scale recovery efficiency. Adding nanoparticles to the injected water has been shown to improve oil recovery. In this study, nanoparticles were added to the water phase of water alternating gas (WAG) and injected into waterflood residual oil in two dimensional glass micromodels to study the effect of the nanoparticles qualitatively at low pressures. Silicon oxide (SiO2) and aluminum oxide (Al2O3) nanoparticles, at different concentrations, were dispersed in the brine and injected as the water phase in WAG followed by air as the gas phase. Response Surface Methodology (RSM) was used to investigate the effect of the factors and interactions between the factors on oil recovery. The results from the micromodel studies indicate that adding a small amount of nanoparticles to the brine can enhance residual oil recovery.

Global Triangular Structure in Four-Component Conservation Laws

This paper demonstrates that the mathematical structure of one-dimensional flows in which four components partition between two phases is governed by the geometry of equilibrium tie lines. We define global triangular structure, and we prove that models of four-component flow exhibit global triangular structure if and only if tie lines meet at one edge of a quaternary phase diagram, or if tie lines lie in planes. For such systems, shock and rarefaction surfaces coincide, and the analysis of wave structures is straightforward. We show also that when equilibrium K-values are independent of composition, the requirements for triangular structure are satisfied, though exampies are given for other triangular systems with variable K-values. An example solution is given for a four-component system with constant K-values. We report a solution for five-component flow with constant K-values to demonstrate that the simplifications that arise from triangular structure can be used to advantage in the construction of solutions to multicomponent Riemann problems.

An Integrated Horizontal- and Vertical-Flow Simulation With Application to Wax Precipitation

This research explored a few opportunities of improving the simulations available to reservoir engineers in the oil and gas industry. Three very specific simulation models were used in this thesis. Firstly, improvements were made to an inflow model for a horizontal well by making it possible to run the model for different fluids easily. Secondly, a vertical flow model was developed by combining a well-known, multi-phase flow correlation with a multi-phase temperature model. A novel approach was developed to solve these two models in sequence. Thirdly, this thesis scoped out the application of two different wax crystallization models. It was the first time that these wax models were tested using a flow simulator. The results obtained from all three simulation models were in par with theory and expectations. It was concluded that these models together would be a very useful tool for both the industry and for further research work.

A new streamline model for near-well flow validated with radial flow experiments

Streamline simulation is a powerful tool that can be used for full field forecasting, history matching, flood optimization, and displacement visualization. This paper presents the development and the application of a new semi-analytical streamline simulation method in the near-wellbore region in polar/cylindrical coordinate systems. The main objective of this paper is to study the effects of the permeability heterogeneity and well completion details in the near-wellbore region. These effects dictate the streamline geometries, which in turn influence well productivity. Previous streamline applications used a constant flow rate for each stream tube. In this paper, streamline simulation is performed under the assumption of constant pressure boundaries, which is a novel and non-trivial extension of streamline simulation. Solutions are constructed by treating each stream tube as a flow unit by invoking analytical solutions for such geometries. In addition, visualization experiments are conducted to investigate the effect of the heterogeneity. Two-dimensional waterflooding visualization experiments in radial porous media are performed with constant pressure boundaries. The streamline simulator is applied to history match the relative permeabilities using these experiments, thereby validating the new near-well streamline method.

A New Coupled Axial-Radial Productivity Model for Horizontal Wells with Application to High Order Numerical Modeling

For long, highly productive wells, frictional pressure loss cannot be ignored. The axial flow along the well trajectory in the near-well region must therefore also be considered. A new, fully analytical model for coupled radial well inflow and axial reservoir flow has been developed. The new model will be briefly reviewed and solutions to steady state flow summarized. A discussion on the usage of the new model in simulation of horizontal wells together with its numerical performance compared to standard finite difference methods will be presented. The new analytical model has been used in the formulation of a numerical scheme for simulation of coupled well inflow and near-well reservoir flow. The analytical model results in a linear pressure distribution in the axial direction and a logarithmic pressure distribution in the radial direction in each near-well reservoir segment. Therefore, the pressure distribution is piecewise linear/logarithmic, contrary to existing piecewise constant distribution resulting from a standard finite difference method. Calculation examples are presented applying both the new method and the standard finite difference method to determine the pressure profiles and flow rates in both the wellbore and the near-well reservoir. Numerical results show that the new method represents a substantial improvement compared to a standard finite difference method, requiring fewer segments to achieve the same accuracy. The new method is more accurate especially near the heel, where accuracy is most important. This numerical scheme has also been proved to be higher order accurate in space discretization than a standard finite difference scheme. Since the axial flow rate is built into the new model analytically, the need for local grid refinements around the well is reduced.

Modeling semi-steady state near-well flow performance for horizontal wells in anisotropic reservoirs

This paper presents a novel methodology to model semi-steady state horizontal well flow performance in an anisotropic reservoir taking into account flow in the near-well region for an arbitrary well trajectory. It is based on an analytical productivity model describing coupled axial reservoir flow and radial well inflow. In order to apply this model in an anisotropic reservoir, the permeability field relative to the radial direction perpendicular to the well trajectory and the axial direction along the well trajectory must first be determined. A classical space transformation is used in concert with rotational transforms to obtain a virtual isotropic model. The transformation preserves the volumes and pressures. It is not a novel concept, but different from previous approaches in the sense that it is only applied in the near-well domain to formulate an equally isotropic media. As a result, the use of this virtual isotropic model requires the Dietz shape factor for an ellipse, transformed from the original cylindrical near-well domain. The Dietz shape factors are determined numerically in this research. The semi-steady state well/near-well model is implemented in a numerical simulator incorporating formation anisotropy and wellbore hydraulics. The specific productivity index along the well trajectory is generated using the virtual configuration. Numerical results for different anisotropy ratios and also incorporating frictional losses in the well are presented. Furthermore, the well/near-well model is applied in coupling with streamline reservoir model for a water flooding case. This appears to be the first coupling of a well hydraulics model and a streamline simulator. It presents the application of the well/near-well model in integrated reservoir simulation in an efficient and accurate manner. The results demonstrate that the coupling approach with a streamline reservoir model and the well/near-well is of great potential for advanced well simulation efficiently.

Analytical coupled axial-radial semi-steady state productivity model for horizontal wells in anisotropic medium

The classical productivity models are solutions to one-dimensional radial flow equations for vertical wells at different flow conditions. A new, fully analytical model for coupled radial well inflow and axial reservoir flow has been developed under the assumption of semi-steady state flow, i.e. the axial flow and the well inflow are solved simultaneously in closed form expressions. This coupled axial-radial flow model results in a quadratic pressure profile in the axial direction and a quadratic-logarithmic pressure profile in the radial direction. The new productivity equations are formulated by using either external pressure or average reservoir pressure in addition to flowing wellbore pressure. For the special case where axial flow or radial flow is zero, it is shown that the formulas coincide with the classical formulas for radial and linear flow, respectively. The new productivity model is also developed for an anisotropic medium by implementing a space transformation in the near-well region. The anisotropic productivity model highlights the flow in the near-well region and provides flexibility in choosing configuration of near-well simulation grid blocks. An algorithm for the simulation of the near-well flow and horizontal well productivity is presented.

Four-component Gas/Oil Displacement with Constant Pressure Boundaries

This paper presents the analytical solution of four-component gas/oil displacements under constant pressure boundary conditions. All the previous studies in gas/oil displacement problems have been accomplished under the assumption of constant flux boundaries. In practice however, gas flooding projects are often conducted with constant injection pressure and constant producing well pressure. In this work, a novel generation of Buckley-Leverett’s classic fractional flow theory is applied to solve the problem of four-component gas/oil displacements under constant pressure boundaries. Conservation of mass in a one-dimensional, dispersion-free medium, for a four-component gas/oil displacement system leads to a set of partial differential equations. The solution of the corresponding initial value problem under constant flux boundary conditions consists of rarefaction waves, shock waves and constant states connecting the injection state to the production state. In incompressible systems with constant pressure boundaries, the total volumetric flux is a function of time and hence, the classical Buckley-Leverett theory is not valid. However, the saturation wave structure obtained from the constant flux boundary condition problem can be used in the solution of the associated problem with constant pressure boundaries by determining the flux analytically as a function of time. The solution for a four-component gas/oil displacement case study is presented. The determination of time dependent volumetric flux from the solution of the constant flux problem is demonstrated. Results are also obtained using a numerical approach and are compared to the analytical results. This indicates that the analytical solution is indistinguishable from the numerical solution as the number of grid blocks in the numerical method approaches infinity. However, a very fine grid is needed for an acceptable solution. Key Words: Gas injection, constant flux boundary condition, constant pressure boundary condition.