Correction of metabolic parameters and unit process performance data. Part I. derivation of equations

Abstract

Abstract An understanding of the dynamics of oxygen consumption by the culture animal is needed to properly design and operate an aeration system. In commercial production systems, oxygen consumption rates are typically determined under flowing water conditions. A simple mass balance on a flow-through system results in the following equation in terms of mg oxygen/(kg fish h): Oxygen Consumption = - flow mass of fish ( C t i n - C t ) + rearing volume mass of fish dC dt The formula commonly used to estimate oxygen consumption is biased because it only considers the first term. The error in the oxygen consumption rate depends primarily on the rate of change of oxygen within the rearing unit ( d C / d t ) and is larger when the oxygen consumption rate has a significant variation with time. This same lag response can also bias other metabolic rates (carbon dioxide, ammonia, solids) and the computation of performance and efficiencies of unit processes such as biofilters and solids removal processes. While a number of approaches have been developed to correct oxygen consumption rates for the impact of this hydraulic lag, their accuracy has never been evaluated in any comprehensive manner and in many cases, their derivation is entirely lacking. To better understand their assumptions and limitations, the derivation of these correction approaches (and several new methods) have been clearly and comprehensively developed in this article. Without this background information, it is difficult to understand the differences between the approaches and their potential limitations. In companion paper, the accuracy of the correction equations and analysis assumptions will be evaluated.