Mathematical relationship between the densities and the corresponding volumes of mixtures of liquid-solid slurries and clear fluid blends, such as drilling muds and completion fluids. Assumptions are: (1) masses and volumes of components are additive and (2) material is neither generated nor lost from the system. As a simple example, below are the two material-balance equations for a three-component mixture of oil (o), water (w) and solids (s), where V = volume percent, D = specific density and MW = mixture weight. (This could represent a simple, weighted oil-base mud formulation. )

MW = DsVs + DoVo + DwVw
100% = Vs + Vo + Vw.

By solving these equations simultaneously, an unknown parameter can be found if other parameters are known or can be estimated accurately. Material-balance equations are used to derive formulations of muds, to calculate the amount of barite needed to weight-up a mud, to determine the amount of water needed to dilute a mud, and to find the volume of two or more muds to mix together to achieve a new mud weight and volume. Material balance is also the basis for calculating solids content of muds based on mud testing data.