FORMATION DAMAGE MECHANISMS AND NUMERICAL SIMULATION OF PERMEABILITY IMPAIRMENT IN HORIZONTAL WELLS

Puzzling circumstance associated with formation damage near wellbore occur frequently, resulting in permeability impairments and increased pressure losses. Potential damage phenomenon usually starts from drilling to completion via production and such mechanisms have been fully considered. Most of the existing tasks to mitigate the near oil wellbore damages involve use of empirical models, conducting experiments, frequent shut down of wells for proper well tests and pressure maintenance are highly expensive and time consuming. Permeability impairments have been simulated by modifying Darcy’s equation to optimize reservoir pressure for improved near wellbore in horizontal wells. The model, transient linear partial differential equation (TLPDE) for impaired permeability is developed and numerically resolved using finite difference method. The model was implemented by writing codes in MATLAB language and the solution obtained was validated using synthetic/ field data. The results obtained for TLPDE model indicated pressure depletion over time. This was also shown for every values of coefficient of anisotropy until 400 days when the anisotropy became insignificant approaching isotropy condition, suggesting permeability impairment. Numerical simulation proved to be effective in simulating near oil wellbore damages. This paper describes the detailed mechanisms of formation damage and provided a numerical approach to model impaired permeability in horizontal wells. This approach allowed us to study the impact of various damage mechanisms related to drilling, completion conditions and significant improvement of near oil wellbore for well performance.

Semiclassical Approach to the Nonlocal Kinetic Model of Metal Vapor Active Media

A semiclassical approach based on the WKB–Maslov method is developed for the kinetic ionization equation in dense plasma with approximations characteristic of metal vapor active media excited by a contracted discharge. We develop the technique for constructing the leading term of the semiclassical asymptotics of the Cauchy problem solution for the kinetic equation under the supposition of weak diffusion. In terms of the approach developed, the local cubic nonlinear term in the original kinetic equation is considered in a nonlocal form. This allows one to transform the nonlinear nonlocal kinetic equation to an associated linear partial differential equation with a given accuracy of the asymptotic parameter using the dynamical system of moments of the desired solution of the equation. The Cauchy problem solution for the nonlinear nonlocal kinetic equation can be obtained from the solution of the associated linear partial differential equation and some algebraic equations for the coefficients of the linear equation. Within the developed approach, the plasma relaxation in metal vapor active media is studied with asymptotic solutions expressed in terms of higher transcendental functions. The qualitative analysis of such the solutions is given.

Modified Representations for the Close Evaluation Problem

When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor resolution when evaluated closed to (but not on) the boundary. To address this challenge, we provide modified representations of the problem’s solution. Similar to Gauss’s law used to modify Laplace’s double-layer potential, we use modified representations of Laplace’s single-layer potential and Helmholtz layer potentials that avoid the close evaluation problem. Some techniques have been developed in the context of the representation formula or using interpolation techniques. We provide alternative modified representations of the layer potentials directly (or when only one density is at stake). Several numerical examples illustrate the efficiency of the technique in two and three dimensions.

Approximation of Subsurface Seepage using 2- Dimensional Boussineq Equation

Groundwater is the main source of fresh water available for human beings. The surface water groundwater interaction affects the quantity and quality of groundwater. Hence the study of surfacewater-groundwater interaction is the emerging topic in this new era. In this paper, the analytical approximation of water table fluctuation in the aquifer is presented. The aquifer is subjected to the recharge and withdrawal activity through multiple basins and wells in the domain. The time dependent multiple recharge is considered. The flow is approximated by a non linear partial differential equation called Boussineq equation. The solution of Boussineq equation is developed using Finite Fourier cosine transform. Response of the solution to using numerical examples has been tested. Effect of aquifer parameters on the fluctuation of water table formation mainly water mound and cone of depression due to recharge and withdrawal are presented. The effect of permeability of aquifer base on the water table is also discussed.

Two-Dimensional Mathematical Model of Carbon Dioxide (CO2) Transport in Concrete Carbonation Proses

A new two-dimensional mathematical model was developed to describe the transport phenomena of carbon dioxide in concrete structures. By treating transport phenomena as a concrete carbonation process, a two-dimensional linear partial differential equation was derived based on the principle of mass balance and convective-dispersive Equation. It was found the analytical solution by the separation of variables method combined with some substitution approaches. The numerical results are presented to illustrate the practical application of this model.

New Exact Solutions of Date Jimbo Kashiwara Miwa Equation Using Lie Symmetry Groups

In this article, new exact solutions of 2 + 1 -dimensional Date Jimbo Kashiwara Miwa (DJKM) equation are constructed by applying the Lie symmetry method. By considering similarity variables obtained through Lie symmetry generators, considered 2 + 1 -dimensional DJKM equation is transformed into a linear partial differential equation with reduction of one independent variable. Afterwards by using Lie symmetry generators of this linear PDE, different invariant solutions involving exponential and logarithmic functions are explored which lead to the new exact solutions of the DJKM equation. Graphical representations of the obtained solutions are also presented to show the significance of the current work.

A solution of linear and non-linear partial differential equation of fractional order

We know that the solution of partial differential equations by analytical method is better than the solution by approximate or series solution method. In this paper, we discuss the solution of linear and non-linear fractional partial differential equations involving derivatives with respect to time or space variables by converting them into the partial differential equations of integer order. Also we develop an analytical formulation to solve such fractional partial differential equations. Moreover, we discuss the method to solve the fractional partial differential equations in space as well as time variables simultaneously with the help of some examples