BASIC SEPARATION THEORY
Because of their number and complexity, the mathematical formulas used in calculating the
pressure points in Figure A-3 will not be presented. The operator will read and record only
those values which are measured by instruments and will not be required to perform any of the
mathematical calculations involved in completing a circuit balance. However, the following
discussion will give an indication as to the procedures involved in determining these values.
To calculate a circuit balance for Stage N in Figure A-3, pressures P and P and temperature
T are recorded. Then, knowing P and T and a constant previously determined in a test loop,
it is possible to calculate the flow W (N - 1). Since the "A" barrel of the compressor has
essentially a constant suction volume in the normal operating range, the interstage flow is
proportional to the compressor "A" suction pressure and temperature. Next, it is known that
the flow in a cascade must operate at a steady state condition to prevent an accumulation of
deficiency of inventory in any one section. It may therefore be assumed that the flow
downward to a stage is equal to the flow upward from the same stage. (This assumption is
not valid for all stages in a cascade but for practical applications the error is negligible.) From
this assumption, W is equal to W (N - 1). With P , W , and pressure drop data obtained in
the test loop, P can be calculated.
In a test loop, data is taken on converters of different sizes and types to determine pressure
variations with different amounts of flow and cut. If W is found in the same manner as W
(N - 1), it is then possible with the test loop data to calculate P . Also, with the converter data,
and knowing W , P , and W (W = W + W ), P and subsequently, P are found.
Again using pressure drop data, P can be calculated from W and P . With P , P is calculated
by knowing the "B" pressure ratio of the compressor.
From the calculated values obtained from a circuit balance, it is possible to make further
calculations which indicate the operational and productive characteristics of the cascade. For
example, P , P , and the flows through a converter must be known before the actual
permeability of the barrier can be calculated. Also, these values make it possible to accurately
predict horsepower requirements under varying conditions of flow and pressure. Another
important application of the circuit balance is in the determination of inventory in the cascade
where pressures and temperatures not otherwise measured are required.