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Iftikhar Ali

Bio: Iftikhar Ali is an academic researcher from King Fahd University of Petroleum and Minerals. The author has contributed to research in topics: Control chart & Oil shale. The author has an hindex of 5, co-authored 19 publications receiving 70 citations.

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TL;DR: In this paper, a variational iteration method was used to find the power series solution of the Hilfer advection-diffusion PDE, which is easy to implement numerically and can be expressed in terms of Mittag-Leffler function.
Abstract: We propose a Hilfer advection–diffusion equation of order 0 α 1 and type 0 ≤ β ≤ 1 , and find the power series solution by using variational iteration method. Power series solutions are expressed in a form that is easy to implement numerically and in some particular cases, solutions are expressed in terms of Mittag-Leffler function. Absolute convergence of power series solutions is proved and the sensitivity of the solutions is discussed with respect to changes in the values of different parameters. For power law initial conditions it is shown that the Hilfer advection–diffusion PDE gives the same solutions as the Caputo and Riemann–Liouville advection–diffusion PDE. To leading order, the fractional solution compared to the non-fractional solution increases rapidly with α for α > 0.7 at a given time t ; but for α 0.7 this factor is weakly sensitive to α . We also show that the truncation errors, arising when using the partial sum as approximate solutions, decay exponentially fast with the number of terms n used. We find that for α 0.7 the number of terms needed is weakly sensitive to the accuracy level and to the fractional order, n ≈ 20 ; but for α > 0.7 the required number of terms increases rapidly with the accuracy level and also with the fractional order α .

16 citations

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TL;DR: In this paper, a Hilfer advection-diffusion equation of order $0 0.7$ at a given time $t$ was proposed, where the required number of terms increases rapidly with the accuracy level and also with the fractional order $\alpha$.
Abstract: We propose a Hilfer advection-diffusion equation of order $0 0.7$ at a given time $t$; but for $\alpha 0.7$ the required number of terms increases rapidly with the accuracy level and also with the fractional order $\alpha$.

15 citations

Posted Content
TL;DR: Pong et al. as discussed by the authors derived a nonlinear transport model for single phase gas flow in tight porous media, incorporating many important physical processes that occur in such porous systems: continuous flow, transition flow, slip flow, Knudsen diffusion, adsorption and desorption in to and out of the rock material, and a correction for high flow rates.
Abstract: Shale gas recovery has seen a major boom in recent years due to the increasing global energy demands; but the extraction technologies are very expensive. It is therefore important to develop realistic transport modelling and simulation methods, for porous rocks and porous media, that can compliment the field work. Here, a new nonlinear transport model for single phase gas flow in tight porous media is derived, incorporating many important physical processes that occur in such porous systems: continuous flow, transition flow, slip flow, Knudsen diffusion, adsorption and desorption in to and out of the rock material, and a correction for high flow rates (turbulence). This produces a nonlinear advection-diffusion type of partial differential equation (PDE) with pressure dependent model parameters and associated compressibility coefficients, and highly nonlinear apparent convective flux (velocity) and apparent diffusivity. An important application is to the determination of shale rock properties, such as porosity and permeability, by history matching of the the simulation results to data from pressure-pulse decay tests in a shale rock core sample [Pong K., Ho C., Liu J., Tai Y. Non-linear pressure distribution in uniform microchannels. ASME Fluids Eng. Div. (FED) Vol. 197, 51--56, (1994)]. The estimates of the rock porosity and the permeability from our model simulations are realistic of shale rocks, more realistic than obtained from previous models, and illustrates the potential of the modelling strategy presented here in producing accurate simulations of shale gas flow in tight reservoirs.

12 citations

Journal ArticleDOI
TL;DR: In this article, the authors have offered Hotelling T2 control chart base, which is used to continuously monitor two or more related characteristic independently, such as temperature and humidity, under ranked set schemes.
Abstract: Univariate control charts under ranked set schemes are used to continuously monitor two or more related characteristic independently. In this article we have offered Hotelling T2 control chart base...

12 citations

Journal ArticleDOI
TL;DR: Pong et al. as discussed by the authors developed a nonlinear transport model for single-phase gas flow in tight porous media, which incorporates many important physical processes that occur in such porous systems: continuous flow, transition flow, slip flow, Knudsen diffusion, adsorption and desorption into and out of the rock material.
Abstract: A nonlinear transport model for single-phase gas flow in tight porous media is developed. The model incorporates many important physical processes that occur in such porous systems: continuous flow, transition flow, slip flow, Knudsen diffusion, adsorption and desorption into and out of the rock material, and a correction for high flow rates. This produces a nonlinear advection–diffusion type of partial differential equation with pressure-dependent model parameters and associated compressibility coefficients, and highly nonlinear apparent convective flux (velocity) and apparent diffusivity. A key finding is that all model parameters should be kept pressure dependent for the best results. An application is to the determination of rock properties, such as porosity and permeability, by history matching of the simulation results to data from pressure-pulse decay tests in a rock core sample (Pong et al. in ASME Fluids Eng Div 197:51–56, 1994).

9 citations


Cited by
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TL;DR: This review article aims to present some short summaries written by distinguished researchers in the field of fractional calculus that will guide young researchers and help newcomers to see some of the main real-world applications and gain an understanding of this powerful mathematical tool.

922 citations

Journal ArticleDOI
01 Jan 1895-Nature
TL;DR: In this paper, it was shown that it is possible under certain suppositions to have a number of spectral rays with a very restricted number of degrees of freedom, and that the vibrations under these circumstances would not be quite homogeneous, but if the electron oscillates about any one position sufficiently long to perform a few thousand oscillations, we should hardly notice the want of homogeneity.
Abstract: THE difficulty of reconciling line spectra with the kinetic theory of gases, has been referred to by Prof. Fitzgerald (NATURE, January 3, p. 221). The following considerations show that it is possible under certain suppositions to have a number of spectral rays with a very restricted number of degrees of freedom. Most of us, I believe, now accept a definite atomic charge of electricity, and if each charge is imagined to be capable of moving along the surface of an atom, it would represent two degrees of freedom. If a molecule is capable of sending out a homogeneous vibration, it means that there must be a definite position of equilibrium of the “electron.” If there are several such positions, the vibrations may take place in several periods. Any one molecule may perform for a certain time a simple periodic oscillation about one position of equilibrium, and owing to some impact the electron may be knocked over into a new position. The vibrations under these circumstances would not be quite homogeneous, but if the electron oscillates about any one position sufficiently long to perform a few thousand oscillations, we should hardly notice the want of homogeneity. Each electron at a given time would only send out vibrations which in our instruments would appear as homogeneous. Each molecule could thus successively give rise to a number of spectral rays, and at any one time the electron in the different molecules would, by the laws of probability, be distributed over all possible positions of equilibrium, so that we should always see all the vibrations which any one molecule of the gas is capable of sending out. The probability of an electron oscillating about one of its positions of equilibrium need not be the same in all cases. Hence a line may be weak not because the vibration has a smaller amplitude, but because fewer molecules give rise to it. The fact that the vibrations of a gas are not quite homogeneous, is borne out by experiment. If impacts become more frequent by increased pressure, we should expect from the above views that the time during which an electron performs a certain oscillation is shortened; hence the line should widen, which is the case. I have spoken, for the sake of simplicity, as if an electron vibrating about one position of equilibrium could only do so in one period. If the forces called into play, by a displacement, depend on the direction of the displacement, there would be two possible frequencies. If the surface is nearly symmetrical, we should have double lines.

463 citations

01 Feb 2009
TL;DR: A long history of bounding the ratio for and, various origins of this topic are clarified, several developed courses are followed, different results are compared, useful methods are summarized, new advances are presented, some related problems are pointed out, and related references are collected as mentioned in this paper.
Abstract: By looking back at the long history of bounding the ratio for and , various origins of this topic are clarified, several developed courses are followed, different results are compared, useful methods are summarized, new advances are presented, some related problems are pointed out, and related references are collected.

174 citations

Journal ArticleDOI
TL;DR: In this paper, a review of the shale gas transport process during shale gas production is presented, and the corresponding multi-scale simulation models that describe the gas multiscale transport mechanisms and accurately predict the amount of shale production are explained.

137 citations