MINIMUM TIME FOR MAXIMUM ALLOWABLE SEDIMENT ACCUMULATION

IN A RESERVOIR FOR FLOOD CONTROL

M.K.A. Abdulrahman, A.T. Mudi and A.A. Nurudeen

Department of Mathematics & Statistics, Kaduna Polytechnic, P. M. B. 2021, Tudun Wada,

Kaduna, Nigeria

Abstract

Mathematical modelling has remained a cost-effective way to diagnose and analyse

systems with varying degree of complexities. This approach to reservoir network

modelling will provide a sustainable avenue in reservoir design, location,

management and flood control. A set of a nonlinear system of ODE was developed to

study the inflow and outflow of water from the reservoir in the network where runoff

in each sub-catchment remain the major input into the model. Further analysis of

the system of ODEgoverning this system gave more insight into reservoir operation

for multipurpose use. An optimal control problem formulated to determine the

minimum time for maximum allowable sediment accumulation. The failure of LQR

to be a reasonable estimate of the optimal height of water in the reservoir led to the

use of the tracked-LQR. The height obtained is used to estimate the current sediment

height which determines the current useful life of the reservoir. The current

information about the state of the reservoir is a tool that allows managers to control

inflow into the reservoir to maintain the design useful life of the reservoir.

Keywords: ODE; Sediment, Useful Life; LQR; Tracked LQR; NOH