**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 **

**Abstract **

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.

**Hassen**** A. Muttlak **

**Department
of Mathematical Sciences **

**King
Fahd University of Petroleum & Minerals **

**Abstract **

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 **

**Abstract **

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 **

**Abstract **

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
**

**and**

**Khalid**** Masood**

**Hafr**** Al-Baten ****Community College**

**Abstract**

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**

**Abstract**

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.