Sharif Digital Repository

An index for characterizing wettability of reservoir rocks is presented using slope analysis of spontaneous imbibition recovery data. The slope analysis is performed using the known exact analytical solution to infinite acting period of counter-current spontaneous imbibition. The proposed theoretically based wettability index offers some advantages over existing methods: (1) it is a better measure of the spontaneous imbibition potential of rock (because the magnitude is directly proportional to the imbibition rate); (2) there is no need for forced displacement data; (3) there is no need for waiting until the spontaneous imbibition process ceases completely; and (4) the data needed to run the... 

An index for characterizing wettability of reservoir rocks is presented using slope analysis of spontaneous imbibition recovery data. The slope analysis is performed using the known exact analytical solution to infinite acting period of counter-current spontaneous imbibition. The proposed theoretically based wettability index offers some advantages over existing methods: (1) it is a better measure of the spontaneous imbibition potential of rock (because the magnitude is directly proportional to the imbibition rate); (2) there is no need for forced displacement data; (3) there is no need for waiting until the spontaneous imbibition process ceases completely; and (4) the data needed to run the... 

It has been proven that tapering the piezoelectric beam through its length optimizes the power extracted from vibration based energy harvesting. This phenomenon has been investigated by some researchers using semianalytical, finite element and experimental methods. In this paper, an exact analytical solution is presented to calculate the power generated from vibration of exponentially tapered unimorph and bimorph with series and parallel connections. The mass normalized mode shapes of the exponentially tapered piezoelectric beam with tip mass are implemented to transfer the proposed electromechanical coupled equations into modal coordinates. The steady states harmonic solution results are... 

In naturally fractured reservoirs, modeling of mass transfer between matrix blocks and fractures is an important subject during gas injection or contaminant transport. This study focuses on developing an exact analytical solution to transient tracer transport problem along a discrete fracture in a porous rock matrix. Using Gauss-Legendre quadrature, an expression was obtained in the form of a double integral which is considered as the general transient solution. This solution has the ability to account the following phenomena: advective transport in fractures and molecular diffusion from the fracture to the matrix block. Certain assumptions are made which allow the problem to be formulated... 

The eccentricity between the circular fiber and its coating as well as the imperfection at the fiber-coating-matrix interfaces associated with certain composites can have a remarkable effect on the movement of a dislocation. For an in-depth understanding of such phenomena, the present work provides an exact analytical solution for the interaction between an eccentrically coated circular inhomogeneity embedded in an infinite elastic medium with imperfect interfaces and a screw dislocation. The dislocation may be located inside one of the regions: the core inhomogeneity, coating, or the matrix. The corresponding boundary value problem is solved by using conformal mapping and complex potential... 

An exact analytical solution for one-dimensional fluid flow through rock matrix block is presented. The nonlinearity induced from flow functions makes the governing equations describing this mechanism difficult to be analytically solved. In this paper, an analytical solution to the infiltration problems considering non-linear relative permeability functions is presented for finite depth, despite its profound and fundamental importance. Elimination of the nonlinear terms in the equation, as a complex and tedious task, is done by applying several successive mathematical manipulations including: Hopf-Cole transformation to obtain a diffusive type PDE; an exponential type transformation to get a... 

Particle capture at porous media in cross-flow microfiltration is studied to investigate permeability reduction as a function of membrane pore size and particle size distribution. A new model in pore scale and its pertinent mathematical expressions, which consider pore and particle size distribution, are provided. Permeability reduction of the membrane because of size exclusion during particulate suspension flow was predicted using the developed model. It is assumed that the size exclusion is the dominant mechanism of particle retention causes pore blocking and permeability reduction in the porous media.The exact analytical solution of the stochastic model for size exclusion is used to... 

Particle capture at porous media in cross-flow microfiltration is studied to investigate permeability reduction as a function of membrane pore size and particle size distribution. A new model in pore scale and its pertinent mathematical expressions, which consider pore and particle size distribution, are provided. Permeability reduction of the membrane because of size exclusion during particulate suspension flow was predicted using the developed model. It is assumed that the size exclusion is the dominant mechanism of particle retention causes pore blocking and permeability reduction in the porous media.The exact analytical solution of the stochastic model for size exclusion is used to... 

Rectangular plates on distributed elastic foundations are widely employed in footings and raft foundations of variety of structures. In particular, mounted columns and single footings may partially occupy the rectangular plate of any kind. This study deals with free vibration problem of thin rectangular plates on Winkler and Pasternak elastic foundation model which is distributed over a particular arbitrary area of the plate. Closed form solutions are developed through solving the governing differential equations of plates. Moreover, a novel mathematical approach is proposed to find the exact analytical solution of free vibration of plates with mixed or fully-clamped boundary conditions.... 

One of the main properties of today's distributed and parallel systems, such as mobile ad-hoc networks and grids, is their heterogeneity in the available resources. Further, many applications of such systems are subject to Time/Utility Function (TUF) time constraints for jobs, unavoidable variability in job characteristics and arrivals, and statistical assurance requirements on timeliness behaviors. In this paper, we propose an exact analytical solution for performance evaluation of dynamic policies used for routing of TUF-constrained Firm Real-Time (FRT) jobs among parallel single-processor queues with arbitrary processing rates and capacities. The analytical method can be used for the... 

The performance of an infinitely segmented magnetohydrodynamic generator is analyzed using the second law of thermodynamics entropy generation criterion. The exact analytical solution of the velocity and temperature fields are provided by applying the modified Hartmann flow model, taking into account the occurrence of the Hall effect in the considered generator. Contributions of heat transfer, fluid friction, and ohmic dissipation to the destruction of useful available work are found, and the nature of irreversibilities in the considered generator is determined. In addition, the electrical isotropic efficiency scheme is used to evaluate the generator performance. Finally, the implication of... 

The exponential growth in the semiconductor industry and hence the increase in chip complexity, has led to more power usage and power density in modern processors. On the other hand, most of today's embedded systems are battery-powered, so the power consumption is one of the most critical criteria in these systems. Dynamic Voltage and Frequency Scaling (DVFS) is known as one of the most effective energy-saving methods. In this paper, we propose the optimal DVFS profile to minimize the energy consumption of a battery-based system with uncertain task execution time under deadline constraints using the Calculus of Variations (CoV). The contribution of this work is to analytically calculate the... 

In Li-ion batteries the interface between the nano-size spherical core graphite and its surrounding solid electrolyte interphase (SEI) layer, just inside SEI is susceptible to damage. Thus, accurate determination of the associated elastic fields is one of the challenges in optimizing the lifetime and capacity of Li-ion batteries. The required precision is achieved by considering the core graphite which belongs to the crystal class D6h as homogeneous spherically isotropic and SEI layer as functionally graded (FG) isotropic material. Moreover, to account for the surface/interface effects appropriately the core-shell nano-structure subjected to the diffusion-induced time-dependent nonuniform... 

A new mathematical model was developed and an exact analytical solution without approximations of previous work was derived for the description of the kinetics and equilibrium characteristics of drug loading from a finite external solution onto ion-exchange microspheres. The influence of important parameters pertinent to material properties and loading conditions on the kinetics, efficiency, and equilibrium of drug loading was analyzed using the developed model and equations. The numerical results showed that the rate of drug loading increased with increasing initial drug concentration in the solution or with the relative volume of the external solution and the microsphere. The maximum...