A new method for tieline calculations in binary fluid systems

We describe a method to determine tielines for a mixture with a given volume V_t and a given mole fraction x_t at fixed temperature, which is based on the orientation of the tangent plane to the Helmholtz free energy surface. The method works equally well for gas-liquid separation as for liquid-liquid separation. The method is based on a rotation in coordinate space followed by a rotation in function space which establishes the correct direction and the end points of the tieline. The mathematics is described and the general outline of a computer program to implement the method is given. This is followed by an application to a special form of the van der Waals equation, which describes the influence of chain-molecules as proposed by Tompa. The example given shows a three phase separation and the influence of the chain-length thereupon.