Kuntjoro Adji Sidarto

A with-in host Dengue infection model with immune response

A model of viral infection of monocytes population by Dengue virus is formulated here. The model can capture phenomena that dengue virus is quickly cleared in approximately 7 days after the onset of the symptoms. The model takes into account the immune response. It is shown that the quantity of free virus is decreasing when the viral invasion rate is increasing. The basic reproduction ratio of model without immune response is reduced significantly by adding the immune response. Numerical simulations indicate that the growth of immune response and the invasion rate are very crucial in identification of the intensity of infection.

An Investigation on Gas Lift Performance Curve in an Oil-Producing Well

The main objective in oil production system using gas lift technique is to obtain the optimum gas injection rate which yields the maximum oil production rate. Relationship between gas injection rate and oil production rate is described by a continuous gas lift performance curve (GLPC). Obtaining the optimum gas injection rate is important because excessive gas injection will reduce production rate, and also increase the operation cost. In this paper, we discuss a mathematical model for gas lift technique and the characteristics of the GLPC for a production well, for which one phase (liquid) is flowing in the reservoir, and two phases (liquid and gas) in the tubing. It is shown that in certain physical condition the GLPC exists and is unique. Numerical computations indicate unimodal properties of the GLPC. It is also constructed here a numerical scheme based on genetic algorithm to compute the optimum oil production.

Optimization of Gas Injection Allocation in a Dual Gas Lift Well System

1. Abstract Optimization problem for oil production in a multi gas lift wells system is discussed. The main problem is to identify allocation of gas injection for each well to obtain maximum total oil production. The gas injection rate is constrained by a maximum limit. Oil production rate is a nonlinear function of gas injection rate, which is unknown explicitly. In existing approaches, the nonlinear function is estimated from empirical or numerical simulation data, by curve fltting using regression method, or estimated by piecewise linear function. We developed here, a mathematical model for gas lift well system, where the ∞uid ∞ow in reservoir and pipes consists of liquid and gas, so the conditions represent two phase ∞ow phenomena. Relationship between gas injection and oil production is given implicitly from the model. We have also developed a computation scheme to solve the optimization problem. Considering complexity of the problem, computation scheme is developed based on genetic algorithms. Our results show quite good estimation for optimum solution. The approach also gives better quality prediction over existing approach, since all computation results come from the model, not from regression or interpolation. 2. Keywords: Gas Lift, Gas Lift Performance Curve, Constrained Optimization, Genetic Algorithm.

Metabolic regulation and maximal reaction optimization in the central metabolism of a yeast cell

Regulation of fluxes in a metabolic system aims to enhance the production rates of biotechnologically important compounds. Regulation is held via modification the cellular activities of a metabolic system. In this study, we present a metabolic analysis of ethanol fermentation process of a yeast cell in terms of continuous culture scheme. The metabolic regulation is based on the kinetic formulation in combination with metabolic control analysis to indicate the key enzymes which can be modified to enhance ethanol production. The model is used to calculate the intracellular fluxes in the central metabolism of the yeast cell. Optimal control is then applied to the kinetic model to find the optimal regulation for the fermentation system. The sensitivity results show that there are external and internal control parameters which are adjusted in enhancing ethanol production. As an external control parameter, glucose supply should be chosen in appropriate way such that the optimal ethanol production can be achieve...

A new strategy of glucose supply in a microbial fermentation model

Strategy of glucose supply to achieve an optimal productivity of ethanol production of a yeast cell is one of the main features in a microbial fermentation process. Beside a known continuous glucose supply, in this study we consider a new supply strategy so called the on-off supply. An optimal control theory is applied to the fermentation system to find the optimal rate of glucose supply and time of supply. The optimization problem is solved numerically using Differential Evolutionary algorithm. We find two alternative solutions that we can choose to get the similar result: either long period process with low supply or short period process with high glucose supply.

Solving inverse problem for Markov chain model of customer lifetime value using flower pollination algorithm

Customer Lifetime Value is an important and useful concept in marketing. One of its benefits is to help a company for budgeting marketing expenditure for customer acquisition and customer retention. Many mathematical models have been introduced to calculate CLV considering the customer retention/migration classification scheme. A fairly new class of these models which will be described in this paper uses Markov Chain Models (MCM). This class of models has the major advantage for its flexibility to be modified to several different cases/classification schemes. In this model, the probabilities of customer retention and acquisition play an important role. From Pfeifer and Carraway, 2000, the final formula of CLV obtained from MCM usually contains nonlinear form of the transition probability matrix. This nonlinearity makes the inverse problem of CLV difficult to solve. This paper aims to solve this inverse problem, yielding the approximate transition probabilities for the customers, by applying metaheuristic ...

A robust method for determining the optimum horizontal well direction and length for a petroleum field development using genetic algorithm

Locating a horizontal well to maximize a gas field production requires not only a right direction but also horizontal segment length. This is due to the longest segment does not necessarily give the maximum gas production, and each direction has its own optimum segment length. Currently, this problem is solved through a trial and error method. This method requires significant efforts and time to find the best location in order to provide a good reservoir model. In this study, a new construction of an optimization problem for optimizing gas production is proposed. Genetic Algorithm is applied to avoid the trial and error procedure. A set of two consecutive objective functions is constructed, i.e., one which is based on the quality of basic reservoir rock properties resulted from summing of all the grids of objective function values in a chosen direction, and the second one which is derived from a curve fitting cubic spline function of the cumulative gas production at a plateau time period with respect to t...

Computing Complex Roots of Systems of Nonlinear Equations Using Spiral Optimization Algorithm with Clustering

Finding complex roots of a system of nonlinear equations is not an easy numerical computation problem. A method of locating and finding all real and complex roots of systems of nonlinear equations in a single run is proposed here. The method that was first proposed for finding all real roots of systems of nonlinear equations is now slightly modified and adapted so that it can be used also for finding complex roots of the corresponding system. The root finding problem is transformed to optimization problem and then a spiral optimization algorithm of Tamura and Yasuda is used to solve the optimization problem. In order to locate the position of the roots, we proposed a certain clustering technique. Several test problems have been examined. This combination of technique enables ones to locate and find all real and complex roots within a bounded domain in all test cases.

Solving a fuzzy initial value problem of a harmonic oscillator model

Modeling in systems biology is often faced with challenges in terms of measurement uncertainty. This is possibly either due to limitations of available data, environmental or demographic changes. One of typical behavior that commonly appears in the systems biology is a periodic behavior. Since uncertainties would get involved into the systems, the change of solution behavior of the periodic system should be taken into account. To get insight into this issue, in this work a simple mathematical model describing periodic behavior, i.e. a harmonic oscillator model, is considered by assuming its initial value has uncertainty in terms of fuzzy number. The system is known as Fuzzy Initial Value Problems. Some methods to determine the solutions are discussed. First, solutions are examined using two types of fuzzy differentials, namely Hukuhara Differential (HD) and Generalized Hukuhara Differential (GHD). Application of fuzzy arithmetic leads that each type of HD and GHD are formed into α-cut deterministic system...

Particle Swarm Optimization for Calculating Pressure on Water Distribution Systems

Flow assurance, aimed to ensure the availability of water flow rate and the sufficiency of pressure on each customer, is one of objectives that should be achieved by water supplying companies. An essential step before dealing with it is to predict pressure distribution on each node. Using the analogy of Kirchoff’s Law for the electrical current to the flow of water in pipelines, a non-linear equation system involving fluid dynamics modeling is constructed and used for determining pressure distribution. It is obvious that the system is not a simple one since it contains many non-linear equations expressing the complexity of the network. In this study, we implement Particle Swarm Optimization (PSO) to solve the system by transforming a root-finding task into an optimization problem. Finally, we present a case study using Hanoi network along with a result compared with EPANET, Firefly Algorithm (FA), and a combination of Genetic Algorithm (GA) and Newton’s method.