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Recent Submissions
Effects of Fluid and Reservoir Characteristics on Dimensionless Pressure and Derivative of a Horizontal Well in a Bounded Oil Reservoir with Simultaneous Single Edge and Bottom Water Drive
(American Journal of Engineering Research (AJER), 2021) Mutili Peter Mutisya, Adewole Stephen Ezizanami, Awuor Kennedy Otieno and Oyoo Daniel Okang’a
This study investigates the effects of fluid, wellbore and reservoir characteristics on dimensionless pressure and
dimensionless pressure derivatives at late time flow of a horizontal well in a bounded oil reservoir subjected to
a single edge and bottom water drive mechanisms. The properties considered in this paper include the
dimensionless well length, dimensionless reservoir width and dimensionless pay thickness. The main objective is
achieved by using the source and Green’s functions together with Newman product method. Spline functions for
interpolation in curve fitting was used to plot the graphs aided by MATLAB program. Results show that the
dimensionless pressure increases with decrease in dimensionless reservoir width and pay thickness. The
dimensionless pressure derivative potentially collapses to zero when the dimensionless pressure becomes
constant. Higher oil production is indicated by larger magnitudes of dimensionless pressure derivatives.
Information in this study will assist in designing and completion of horizontal wells in a bounded reservoir for
prolonged enhanced oil production.
Derivation of Black-Scholes-Merton Logistic Brownian Motion Di erential Equation with Jump Di usion Process
(JS Publication., 2019) Andanje Mulambula, D. B. Oduor and B. Kwach
Black- Scholes formed the foundation of option pricing. However, some of the assumptions like constant volatility and
interest among others are practically impossible to implement hence other option pricing models have been explored to
help come up with a much reliable way of predicting the price trends of options. Black-scholes assumed that the daily
logarithmic returns of individual stocks are normally distributed. This is not true in practical sense especially in short
term intervals because stock prices are able to reproduce the leptokurtic feature and to some extent the volatility smile .
To address the above problem the Jump-Di usion Model and the Kou Double-Exponential Jump-Di usion Model were
presented. But still they have not fully addressed the issue of reliable prediction because the observed implied volatility
surface is skewed and tends to atten out for longer maturities; The two models abilities to produce accurate results
are reduced. This paper ventures into a research that will involve Black-Scholes-Merton logistic-type option pricing with
jump di usion. The knowledge of logistic Brownian motion will be used to develop a logistic Brownian motion with jump
di usion model for price process.
MSC:
91GXX, 91G50, 62P05, 97M30.
Cost-benefit Analysis for a Containerized MBR System for Treatment of Fish Processing Wastewater for Industries in Kisumu, Kenya and Comparison to Wastewater Stabilization Ponds and Activated Sludge Process
(Boffin Access Limited, 2020-08-16) Jane Mburu, Ephraim Gukelberger, Paul Mwangi Robert Kinyua and Jan Hoinkis
The study aimed to calculate a cost benefit analysis for a containerized membrane
bioreactors (MBR) system with flow capacity of 10m3 per day, suitable for use by fish
industries within urban settlements such as Kisumu city in Kenya where land is scares and
expensive. Further a comparative cost analysis for a containerized MBR system, activated
sludge process (ASP) and wastewater stabilization ponds (WSP) treatment systems was
conducted relative to treatment volume to determine their economic viability. The cost
benefit analysis was calculated as the difference between total input and total output. The
total input was the sum of capital expenditure (CAPEX) and operation expenditure (OPEX)
while the total output was the cost per m3 of treated water generated and reused over the
course of the plant life. The comparative analysis was conducted using basic cost model
equations. The MBR system had a cost benefit of 13.1 €/m3d-1 which is approximately ≥
99% with an assumption that all treated water generated is reused on site. The cost per
m3 of treated water was estimated at 1.32€/m3d-1. The results obtained from the correlation
cost curves demonstrated that MBR systems with flow capacity of 10m3d-1 to 45m3d-1
are more economical in terms of CAPEX relative to ASP and WSP whose investment cost
is driven higher by cost of land. Correlation cost curves showed a high OPEX for MBR
systems attributed to high energy requirement. However, MBR systems encourage reuse
of the treated water thus becomes economical in the long run over the course of the plant
life. Containerized MBR systems were found to be more appropriate for use by industries
operating in the urban centers in Kisumu where land is expensive, relative to ASP and WSP
that require high capital cost for acquiring land and for construction.
Volatility Estimation Using European-Logistic Brownian Motion with Jump Di usion Process
(© JSPublication., 2020) Andanje Mulambula, D. B. Oduor, and B. O. Kwach
Volatility is the measure of how we are uncertain about the future of stock or asset prices. Black-Scholes model formed the
foundation of stock or asset pricing. However, some of its assumptions like constant volatility and interest among others
are practically impossible to implement hence other option pricing models have been explored to help come up with a
much reliable way of predicting the price trends of options. The measure of volatility and good forecasts of future volatility
are crucial for implementation, evaluation of asset and derivative pricing of asset. In particular, volatility has been used in
nancial markets in assessment of risk associated with short-term uctuations in nancial time-series. Constant volatility
is not true in practical sense especially in short term intervals because stock prices are able to reproduce the leptokurtic
feature and to some extent the volatility smile . To address the above problem the Jump-Di usion Model and the Kou
Double-Exponential Jump-Di usion Model were presented. But still they have not fully addressed the issue of reliable
prediction because the observed implied volatility surface is skewed and tends to atten out for longer maturities; the two
models abilities to produce accurate results are reduced. This study ventures into a research that will involve volatility
estimation using European logistic-type option pricing with jump di usion. The knowledge of logistic Brownian motion
will be used to develop a logistic Brownian motion with jump di usion model for price process.
MSC:
91GXX, 91G50, 62P05, 97M30.
A Mathematical Model for Pressure Distribution in a Bounded Oil Reservoir Subject to Single-Edged and Bottom Constant Pressure
(IOSR Journal of Mathematics (IOSR-JM), 2020-07) Mutili Peter Mutisya, Adewole Stephen Ezizanami, Awuor Kennedy Otieno and Oyoo Daniel Okang’a
Well test analysis of a horizontal well is complex and difficult to interpret. Most horizontal well mathematical
models assume that horizontal wells are perfectly horizontal and are parallel to the top and bottom boundaries
of the reservoir. As part of effort towards correct horizontal well test analysis, the purpose of this study is to
develop a mathematical model using source and Green’s functions for a horizontal well completed in an oil
reservoir at late time flow period, where the reservoir is bounded by an edge and bottom constant pressure
boundaries.
The purpose of the derivation is to understand the effects of well completion, well design and reservoir parameters
on pressure and pressure derivative behavior of the well at late flow time, when all these external boundaries are
presumed to have been felt. If the model is applied for well test analysis therefore information like reservoir
natural permeability distribution, actual external boundary types and even the well completion performance will
be decidable easily. Dimensionless variables were used to derive throughout the derivations.
Results of the derivation show that the dimensionless pressure and dimensionless pressure derivatives increase
with increase in dimensionless well length. This means that higher well productivity is achievable with extended
well length when the reservoir is surrounded partially by constant pressure boundaries. Furthermore, the models
show that higher directional permeabilities would also encourage higher well productivity at late flow time. The
dimensionless pressure derivative will, as a result of a constant dimensionless pressure, potentially collapse
gradually to zero at the moment the dimensionless pressure begins to exhibit a constant trend. Finally, the
dimensionless pressure and dimensionless pressure derivatives vary inversely with the reservoir dimensionless
width at late flow time.
