Oilfield primary separator units are subject to nonlinear fluid dynamic and mechanical constraints. Their design represents a challenging and important problem. In this paper we present separator design problems for which the lowest cost, optimal, solution is found using sequential quadratic programming techniques. The optimization models utilize existing separator design theories and relationships. They consist of a declarative set of equations and inequalities that is independent of the solution method and hence it is easy to make modifications and the assumptions are clear. The models are outlined and discussed in the context of horizontal separators. The efficiency and effectiveness of the suggested systematic design method are exemplified by two illustrative design cases.