Roshan Sharma

Semi Discrete Scheme for the Solution of Flow in River Tinnelva

The Saint-Venant equation is a mathematical model which could be used to study water flow in an open channel, river etc. The Kurganov-Petrova (KP) method, which is a second order scheme, is used to solve the Saint-Venant equations with good stability. Water flow of a river between two hydropower stations in Norway has been simulated in this study using MATLAB and OpenModelica. The KP scheme has been used to discretize the Saint-Venant equations in spatial domain, yielding a collection of Ordinary Differential Equations (ODEs). These are then integrated with time using the variable steplength solvers in MATLAB: ode23t, ode23s, ode45, and fixed step-length solvers: The Euler method, the second and fourth order Runge Kutta method (RK2 and RK4). In OpenModelica built-in, variable step-length DASSL solver has been used. From the simulation, it was observed that all solvers produce more or less similar results. Volumetric flowrate calculation indicated numerical oscillation with variable step-length solvers in MATLAB. The results indicated that it is reasonable to match the order of the space and time discretization.

Nonlinear Model Predictive Control for Optimal Operation of Electric Submersible Pump Lifted Oil Field

In this work, optimal operation of an Electric Submersible Pump (ESP) lifted oil field is developed by using a Nonlinear Model Predictive Control (NMPC) framework. NMPC is used not only for setpoint tracking but also as an economic optimizer for maximizing profit. Optimal control problem is formulated as a general nonlinear programming (NLP) problem with process constraints. The scope of the NMPC framework is to operate the ESP of each oil well inside its designated operating window by minimizing the cost of the total power consumed by all the ESPs in the field and the cost of operating the separator. In other words, the speed of the ESPs and the production choke valves opening should be optimally chosen for maximizing the profit. At the same time, the capacity of the separator should not be exceeded. The simulation results show that the production choke valves are always 100% opened to maintain optimal fluid flow rate from the reservoir. With no constraints in the top side facility (separator capacity), it is optimal to run the ESP pumps in the upper right corner of the allowed operating window for the ESPs.

Mixed Integer Nonlinear Optimization for ESP Lifted Oil Field and Improved Operation through Production Valve Choking

The demand for the total production of oil from an Electric Submersible Pump (ESP) lifted oil field may vary with time. It may not always be economically profitable to use all of the available oil wells for varying production rates. Depending on the amount of oil to be produced from the oil field, some of the oil wells may have to be shut down. The number of oil wells to be used should be properly selected. Not only the number of oil wells should be known, but which wells to use should also be exactly identified. The operating speed of the ESP and the production choke valve opening of each selected oil well should be optimally chosen so that the profit from the oil field is maximized by keeping the operational expenses at the minimum. The oil well scheduling problem is formulated as a Mixed Integer Nonlinear Programming (MINLP) problem. The cost of the electrical power consumed by the pumps, the operational cost of separation process and the income from the oil production are considered for the MINLP formulation. In the first part of the paper, the production choke valves are always fully opened and the number of wells and their respective pump speeds are calculated for varying total production flow rates. However, in the second half of the paper, it is shown that the operation of the oil field can be improved in terms of power consumption through production valve choking.

Uncertainty and Sensitivity Analysis for a Model of an Electric Submersible Pump Lifted Oil Field

Dynamic and mechanistic models of an Electrical Submersible Pump (ESP) lifted oil field are frequently used for understanding the process dynamics and the interactions occurring between the oil wells under varying operating conditions. They are also used to calculate the total fluid produced from the oil field. In this article, uncertainty and sensitivity analysis of such a model is studied. If the model is used for control and optimization of an oil field, it is important to see if the output calculated using the mathematical model lies within a confidence interval under the presence of uncertainties. It is also important to understand which parameters have strong/weak influence on the model output. The uncertainty analysis is performed by using the Monte Carlo simulation method. Morris method of elementary effect is used for input factor screening. To quantify the effect of the input factors on the model output, a variance based method of sensitivity analysis is used.