Nonlinear pinch analysis targeting inspired by options valuation and Black-Scholes-Merton model

Abstract

A novel function-condition product (FCP) approach, where conditions are evaluated using Boolean logic, is proposed for pinch analysis targeting with two distinct advantages. First, a direct targeting formula with Boolean expressions coerced to numeric equivalents provides a superior alternative to a multi-step targeting algorithm with surplus/deficit resource loads cascaded across intervals. Second, the targeting formula allows direct calculation at any level to generate even a nonlinear grand composite curve (GCC) rather than a piecewise-linear GCC with constant slope segments within each interval. The FCP approach is initially developed for the valuation of financial derivatives (specifically, options), where the payoff and P&L (profit and loss) diagrams for option strategies at expiry are shown to be analogs of piecewise-linear GCCs. The pre-expiry P&L curves for options valued by the Nobel prize-winning Black-Scholes-Merton (BSM) model are then shown to be analogous to nonlinear GCCs. An FCP formula for targeting the minimum utilities in heat exchanger networks (HENs) and the optimum mass separating agent flowrates in mass exchanger networks (MENs) is finally derived based on formally demonstrating that each stream in a HEN / MEN is equivalent to a spread in an option strategy. To illustrate various aspects of the new methodology, examples of a crude oil option strategy (for a bull put spread, put ratio spread and butterfly spread), of HENs for both constant and variable specific heat capacity C_p, and of a reactive MEN with a general nonlinear equilibrium function are considered in detail.