# Material Balance

January 14, 2006                                                                                                                                                                                                  ISSUE #169

A material balance is a set of equations that express the flows of materials. The mathematics is all based on the simple premise that what comes in must equal what comes out. Variables are easily changed in order to gauge the impact on a system. Material balance is key to analyzing, and understanding, the flow of material in a processing plant.

The concept of Brix is vital in a material balance done for fruit and vegetable processing facilities. Brix is much like a percentage, denoting the amount of sugar dissolved in water. It is measured in degrees, using an instrument called a refractometer. The equation for Brix is as follows: Bx = (Ds x 100)/(Ds + w), where Ds is the weight of dissolved solids and w is weight of water.

Note that suspended (or, insoluble) solids, which are almost always present, do not enter into the equation.

The beauty of Brix is that it holds constant as a flow of material is divided. That is, if a flow at 7° Bx is pumped into a screw press, the press liquor will have 7° Bx. Furthermore, if a drop of water is squeezed from the press cake, then it, too, will measure 7° Bx.

For example, if orange peel with 11° Bx and 9% suspended solids is fed into a screw press, both the press liquor and press cake will measure 11° Bx. (Naturally, the amount of suspended solids will be higher in the press cake than in the press liquor.)

Another important characteristic of dissolved sugar is that if flows of different Brix are mixed, diffusion occurs until a balance is achieved. Thus, if a pound of 50° Bx citrus molasses is added to two pounds of orange peel with 80 percent moisture and 11° Bx, the result will be three pounds of material with a moisture content of 70% and 25° Bx. When this material is pressed, the cake moisture content will be significantly lower than if the straight orange peel were pressed. This is simply because of the greater dissolved solids content in the water contained in the press cake.

Vincent has available a large number of material balances. These reflect single and double pressing, counter-flow diffusion, recirculation of press liquor, addition of oil house water, and many other options. These are transmitted by e-mail, in Excel.

The Excel spreadsheets contain a large number of simultaneous equations. Thus, Excel must be set on "reiterate" in order to find the common mathematical solution. Excel will freeze up if an illogical number is entered in error, so work must be saved frequently. In the event that a spreadsheet freezes, it must be closed without saving it.