PRODUCTION CALCULATIONS

ERDC TN-DOER-I5

August 2000

of the slurry, and either a doppler or magnetic flow meter for measuring the flow velocity in the

pipe. Typically, the signals from these instruments are processed through a cross-point display unit

which consists of two pointers that indicate the optimum production based on the pointer positions

(slurry density and flow velocity).

For hopper dredges, the production is determined by measuring the average density of the load in

the hopper. This is accomplished by relating the draft of the hopper barge to the weight of material

in the hopper. The draft measurements are generally made by differential pressure transducers

located in the bottom of the hull of the vessel. The hopper volume at any time is determined by

water-level sensors mounted above the hopper. By knowing the weight of the dredged material in

the hopper and the hopper volume, the average density of the material in the hopper can be

calculated.

Real-time production data such as flow rate of dredged solids (kg/hr), and flow rate of dredged in

situ volumes (m3/hr) for in-line production meter systems, and total weight (kg) and total in situ

volume (m3) for hopper monitoring systems can be made available to dredging personnel by

processing the signals from the instruments through a data acquisition system linked to a personal

computer. These signals are input into computer codes which calculate the production of dredged

material.

PURPOSE: The data reduction equations used to calculate the production quantities associated

with pipeline and hopper dredges contain variables that introduce error into the final production

calculation. These variables include not only the measurements made by the instrumentation, but

also those associated with the dredging environment such as the density of the water and dredged

sediments. The error due to one variable may be insignificant, but the propagation of the error

through a data reduction equation with multiple variables may result in excessive uncertainty or

error in the final result. This technical note will present an analytical method for determining the

influence of each variable in the production equation on the total error resulting from the production

calculation. Equations defining both solids and in situ volumetric production will be introduced.

A mathematical method for determining the percent error or uncertainty of production calculations

using these equations will be discussed and applied to example dredging problems.

PRODUCTION CALCULATIONS: The in-line production meter system provides production

data in the form of solids flow rate or volumetric flow rate, with solids flow rate referring to only

the flow rate of solids (weight per unit time) in the pipe, and volumetric flow rate referring to the

volume of in situ material flowing through the pipe (volume per unit time). The equation for the

in situ volumetric flow rate is defined by:

a f a Af

ρ - ρw

VOL t = s

(1)

ρi - ρw

where

ρi

= the in situ dredged sediment density

ρs

= the slurry density measured by the nuclear density probe