Direct Inversion of Measured Hydraulic and Electric

Transport Properties into a Geometrical Rock Model


Gabor Korvin


Earth Sciences Department

King Fahd University of Petroleum & Minerals 





The prediction of the interior structure of sedimentary rocks from measured bulk physical data is an inverse problem with a huge number of unknowns, which can be solved only approximately using the Least Mean Squares Error, the Maximum Entropy or the Tikhonov Regularization methods. However, as has been shown by the success of the Cole-Cole model of the Induced Potential in rocks, or the Thomeer model of Mercury Injection,  there are cases when an equivalent rock model with a few degrees of freedom can very well describe the behavior of a complex geologic system. 


In this research we have shown that:


(a) The theory of Nabil Akbar (1994) provides an equivalent rock model which is able to reproduce the measured hydraulic and electric transport properties,

(b) The model has only three parameters (average radius r, average distance between nearest pores d, average throat radius d)

(c) These three parameters can be directly determined from the measured porosity f, hydraulic permeability k and cementation exponent m. of the rock, using simple analytic expressions.


The derivation of these formulae is based on effective medium theory (Yonezawa & Cohen, 1983) and on Perez-Rozales' (1982) non-standard theory of electric conduction in rocks.


Examples will be presented for the direct inversion of carbonate rock measurements. The mathematically derived rock model will be shown to well agree with the structure seen in thin sections under the microscope.




Quality Control Charts using Ranked Set Sampling


Hassen A. Muttlak

Department of Mathematical Sciences

King Fahd University of Petroleum & Minerals 



       Different quality control charts for the sample mean are developed using ranked set sampling (RSS) and median ranked set sampling (MRSS). These new charts are compared to the usual control charts based on simple random sampling (SRS) data. The charts based on RSS and MRSS are shown to have smaller average run length (ARL) than the classical chart especially if the process starts to get out of control. The MRSS is compared with RSS and SRS data, it turns out that MRSS dominates all other methods in terms of the ARL if the process starts to get out of control. Real data are collected using the SRS, RSS and MRSS. These data sets are used to construct the corresponding control charts.  These charts are compared to usual SRS chart. It turns out that the newly developed charts are more efficient in estimating the population mean and the process is more stable. Through this study we are assuming that the underlying distribution is normal. A check of the normality for our data set indicated that the normality assumption is reasonable. 


Key Words: Average run length, lower confidence limit, median ranked set sampling, simple random sampling and upper confidence limit.



Defect detection on unpainted car body


M. T. Mustafa


Department of Mathematical Sciences

King Fahd University of Petroleum & Minerals 



            The talk presents results of an industrial project from automobile industry. The purpose is to develop a  fast defect detection method which is accurate enough in detection of defects as well as is well-suited for online inspection process.

            During the manufacturing process, car bodies can have small defects, for instance ripples or bumps. Such defects being very small in depth are not visible until cars are painted. However, it is expensive to repair the defects at this stage. A model is developed to detect ripples or bumps on unpainted car body by analyzing the scanned images, of unpainted car body, using smoothing splines .



Numerical Simulation in Reservoir Engineering:

An Overview


A. S. Harouaka and H. Menouar


CPM/Research Institute

King Fahd University of Petroleum & Minerals 




Reservoir simulation has been recently defined as the art, science and engineering of the modeling of flow in petroleum reservoirs by solving relevant equations using modern computers.


Specifically, we seek the solution to a system of highly nonlinear partial differential equations (PDE), describing a single or multiphase fluid flow in one two or three dimensions. The procedure most commonly used and accepted is to approximate the PDE by finite difference.


The discretisation process leads to a matrix A whose entries are mainly zeros. This matrix can be extremely large for reservoir engineering problems of a practical size. The solution technique needed to solve the matrix A is by far the most important part of any reservoir simulator and for large simulation problems, iterative solutions techniques have been preferred to direct ones.


The main objectives of this discussion are: 1) Present a brief description of a reservoir simulator; 2) show the different models currently being used and 3) describe how reservoir simulators are considered the primary tools for reservoir management.


An Inverse Problem in the Presence

of a mixed Boundary


F.D. Zaman


Department of Mathematical Sciences

King Fahd University of Petroleum & Minerals 


Khalid Masood

Hafr Al-Baten Community College








The inverse problems involving parameter identification have attracted considerable attention during recent years. The problem has been studies by various authors in seismic and acoustic context. These studies focus on the physical boundary of the medium satisfying one kind of boundary condition. We consider a model in which identification of an inhomogeinity is sought in the presence of mixed boundary conditions: the boundary consisting of two parts with different impedance coefficients. The Wiener-Hopf method provides with the solution of the mixed boundary value problem (direct scattering problem), while the inverse problem of the determination of inhomogeneity is reduced to the Fredholm integral equation of the first kind. The procedure can be applied to recover acoustic speed variation in an ocean due to a pollutant with non-homogeneous seabed seabed  or in the atmosphere in the presence of mixed conditions at the ground.



Optimal control of deteriorating production

inventory systems under various settings


L. Tadj M. Bounkhel Y. Benhadid R. Hedjar


King Saud University




We present in this paper various models to control the production rate of dynamic production inventory systems with deteriorating items. Among the models discussed are the model with inventory and production targets, the model with stock-dependent demand, the continuous review and periodic review models, and the predictive control model. We also propose some open problems.