Impact of Geo-mechanical Properties on the Fracture Treatment of Utica Shale

Unconventional gas reservoirs become one of the most important energy sources in United States and all over the world. The Appalachian basin has very organic rich shale formations; it contains Marcellus and Utica shale formations with billions of cubic feet of natural gas as reserve. The development in hydraulic fracturing technology with horizontal drilling for thousands of lateral feet increase the recoverable gas from the shale formations and challenges the researchers to understand the fracturing mechanism and to study the relation between operation parameters and formation properties with the fracturing treatment outcome.;The main objective of this thesis was to study the impact of formation geo-mechanical properties such as horizontal stress level, Young\u27s modulus and Poison\u27s ratio on the fracturing treatment outcome and also on the complex fracture growth. More precisely, the impact of these properties on the growth of discrete fracture network (DFN). A single horizontal well model was built using commercial software to simulate the fracturing treatment. This model built based on Utica shale properties obtained from different sources.;In this thesis, we investigated the impact of horizontal stress level, Young\u27s modulus, Poison\u27s ratio and the leak-off coefficient. The results showed that the horizontal stress level plays a significant role in controlling the fracture orientation and growth, also affects the stimulated reservoir volume (SRV). The Young\u27s modulus and the Leak-off coefficient also impact the fracture and the discrete fracture network. It has been determined that the formations with high Young\u27s modulus generated high SRV. The Poison\u27s ratio had negligible impact on the fracturing treatment outcome

Solution of Nonlinear Partial Differential Equations by New Laplace Variational Iteration Method

Nonlinear equations are of great importance to our contemporary world. Nonlinear phenomena have important applications in applied mathematics, physics, and issues related to engineering. Despite the importance of obtaining the exact solution of nonlinear partial differential equations in physics and applied mathematics, there is still the daunting problem of finding new methods to discover new exact or approximate solutions. The purpose of this chapter is to impart a safe strategy for solving some linear and nonlinear partial differential equations in applied science and physics fields, by combining Laplace transform and the modified variational iteration method (VIM). This method is founded on the variational iteration method, Laplace transforms and convolution integral, such that, we put in an alternative Laplace correction functional and express the integral as a convolution. Some examples in physical engineering are provided to illustrate the simplicity and reliability of this method. The solutions of these examples are contingent only on the initial conditions

Analytical Solution for Telegraph Equation by Modified of Sumudu Transform "Elzaki Transform"

In this work modified of Sumudu transform [10,11,12] which is called Elzaki transform method ( new integral transform) is considered to solve general linear telegraph equation, this method is a powerful tool for solving differential equations and integral equations [1, 2, 3, 4, 5]. Using modified of Sumudu transform or Elzaki transform, it is possible to find the exact solution of telegraph equation. This method is more efficient and easier to handle as compare to the Sumudu transform method and variational iteration method. To illustrate the ability of the method some examples are provided.   Keywords: modified of Sumudu transform- Elzaki transform - Telegraph equation - Partial Derivative

Solution of Linear and Nonlinear Partial Differential Equations Using Mixture of Elzaki Transform and the Projected Differential Transform Method

The aim of this study is to solve some linear and nonlinear partial differential equations using the new integral transform "Elzaki transform" and projected differential transform method. The nonlinear terms can be handled by using of projected differential transform method; this method is more efficient and easy to handle such partial differential equations in comparison to other methods. The results show the efficiency and validation of this method. Keywords: Elzaki transform, projected differential transform method, nonlinear partial differential equations

Solution of Telegraph Equation by Modified of Double Sumudu Transform "Elzaki Transform"

In this paper, we apply modified version of double Sumudu transform which is called double Elzaki transform to solve the general linear telegraph equation. The applicability of this new transform is demonstrated using some functions, which arise in the solution of general linear telegraph equation. Keywords: Double Elzaki Transform, modified of double Sumudu transforms, Double Laplace transform, Telegraph Equation

Synthesis, identification and anticonvulsant activity of dehydrozingerone

The present study aimed to synthesize and characterize dehydrozingerone as well as to investigate its anticonvulsant activity in experimental animals.  A simple method was used to synthesize dehydrozingerone using vanillin and acetone. The synthesized drug dehydrozingerone was characterized using thin layer chromatography (TLC), high performance liquid chromatography (HPLC), infrared spectroscopy (IR) and physicochemical tests.The synthesized product was  tested for its potential anticonvulsant activity using maximum electroshock (MES) induced seizure models in rats. The synthesized dehydrozingerone showed TLC profile, FT IR spectra and HPLC chromatogram similar to the authentic sample. The physicochemical characters (colour, taste, flavour, solubility and melting point) were also similar to what was found in the literature. All these results indicated that the produced product was dehydrozingerone. A dose dependent anticonvulsant activity was produced by dehydrozingerone. Eighty percent anti-MES activity was presented by 100 mg/kg.  The findings indicated that dehydrozingerone represents a bioactive molecule possessing anticonvulsant activity. In addition, it is an easily synthesized compound from cheap starting materials. In conclusion dehydrozingerone may find its place as antiepileptic agent if further clinical studies will be conducted

Homotopy Perturbation and Elzaki Transform for Solving Nonlinear Partial Differential Equations

In this work, we present a reliable combination of homotopy perturbation method and Elzaki transform to investigate some nonlinear partial differential equations. The nonlinear terms can be handled by the use of homotopy perturbation method. The proposed homotopy perturbation method is applied to the reformulated first and second order initial value problem which leads the solution in terms of transformed variables, and the series solution is obtained by making use of the inverse transformation. The results show the efficiency of this method. Keywords: Homotopy perturbation methods, Elzaki transform nonlinear partial differential equations

A New Homotopy Perturbation Method for Solving Systems of Nonlinear Equations of Emden-Fowler Type

In this work, we apply the new homotopy perturbation method (NHPM) to get accurate results for solving systems of nonlinear equations of Emden–Fowler type, we indicate that our method (NHPM) is equivalent  to the variational iteration method (VIM) with a specific convex. Four examples  are given  to illustrate our proposed methods. The method is easy to carry out and gives very accurate solutions for solving linear and nonlinear differential equations

On existence and uniqueness of generalized solutions for a mixed-type differential equation.

In this paper, we study a boundary value problem for a mixed–type differential equation. The existence and uniqueness of generalized solution is proved. The proof is based on an energy inequality and the density of the range of the operator generated by this problem