residum

Residuum is a noun derived from the Latin residuum, meaning that which remains or a remainder. In English scholarly usage, residuum designates the portion of a substance or system that remains after a specified process, distinguishing it from the part that has been removed or transformed. The term is used across several disciplines, though it is less common in everyday language and often appears in older or more formal literature.

In chemistry and chemical engineering, residuum refers to the nonvolatile material left after distillation or evaporation. In petroleum refining, residuum or residual oil is the heavy fraction obtained after atmospheric or vacuum distillation; it typically requires further processing, such as upgrading, cracking, or coking, to convert it into lighter, saleable products. The broader concept of residue is more widely used in this context, but residuum remains prevalent in certain technical and historical texts.

In mathematics, residuum (sometimes treated as a variant spelling of residue) appears in older or more formal literature on complex analysis. It denotes the coefficient of (z − z0)⁻¹ in the Laurent series expansion of a function around a singularity z0. The residuum can be computed as the contour integral Res(f, z0) = (1/(2πi)) ∮ f(z)/(z − z0) dz. In contemporary standard terminology, the term residue is typically preferred for this concept, with residuum appearing mainly in historical or multilingual contexts.

Overall, residuum is a cross-disciplinary term tied to the general idea of what remains after an process or transformation. Its precise meaning depends on the field, and in many modern contexts, it coexists with the more common term residue or residue-like concepts.