A new method for detecting, identifying, and estimating gross errors in steady state processes is described in this paper. The generalized likelihood ratio method is based on the likelihood ratio statistical test and provides a general framework for identifying any type of gross error that can be modeled. The procedure is illustrated with gross errors caused by measurement biases and leaks. One significant advantage of the method is that the identification of gross errors is not confounded by departure from steady state conditions, which may now be accounted for by "leaks." Also proposed is a new strategy for identifying multiple gross errors using serial compensation of gross errors, which may be applied to all types of gross errors including leaks and biases and which requires less computing time than the existing strategies.

LINEAR RECONCILIATION PROBLEMProcess data reconciliation and rectification and their relationship to process performance monitoring functions have been the subject of many recent publications. [See, for instance, Mah (1981) for a review of these publications.] In this note we shall confine our attention to process data reconciliation subject to linear constraints, and more specifically, to the problem of detecting and identifying the presence of one or more gross errors in the process data.Generally speaking, process measurements are corrupted by two types of errors: Random errors which are commonly assumed to be independently and normally distributed with zero mean, and gross errors which are caused by non-random events such as instrument biases, malfunctioning measuring devices, incomplete or inaccurate process models. Let y be an (n X 1) vector of measured variables, b be a (p X l ) vector of unknown parameters, D be an (n x p) matrix of known constants, for which rank (D) = p 5 n , and E be an (n X 1) vector of errors distributed normally with a zero mean vector and a known variance-covariance matrix Q. Then in the absence of gross errors, the basic model isand the general linear reconciliation problem is the least-squares estimation of b subject to the linear constraintswhere A is a (q X p) matrix of known constants and c is a (q X 1)vector of known constants. The linear reconciliation problem formulated above is a generalization of the reconciliation problems treated by previous investigators. Thus, the reconciliation of flow and inventory data reported by Mah et al. (1976) is a special case in which y is the vector of measured flow rates (v in their paper), D is an identity matrix, b is the vector of true flow rates s(p), A is the incidence matrix (A), p = n and c = 0. Nogita (1972) treated essentially the same problem but considered only the diagonal terms (variances) of the covariance matrix in his minimization. Almasy and Sztano (1975) also studied this problem but they allowed c to be non-zero.On the other hand, the reactor data reconciliation problem reported by Madron et al. (1977) contains no constraints (Eq. 2) on b which corresponds to the vector of extents of chemical reactions (x). For that problem y is the measured vector of increases in the numbers of moles of species (n+), D is their (1 X I) matrix (AT) of stoichiometric coefficients, n = I = number of reactive species, 1 = number of independent chemical reactions, and Q is denoted by F_ in their paper. Madron et al. (1977) actually considered an rsubvector of n+ (denoted by n : in their paper) corresponding to the r d I species for which measurements were made. A similar problem was studied by Murthy (1973Murthy ( ,1974.

A novel distillation scheme which makes use of secondary reflux and vaporization to enhance thermal efficiency is presented. Low operating temperatures, close boiling mixture, and tight product specifications appear to favor this scheme over the conventional distillation. Computer simulation indicates a potential utility reduction of 50 to 7594,. SCOPEDistillation is the single most important separation unit operation in the process industry. It is widely used to upgrade feedstocks, separate reaction intermediates, arid purify products in processes ranging from cryogenic separation of oxygen, nitrogen, and helium to the recovery of aromatics from coal tar. In a recent study carried out under the auspices of the Governor's Energy Advisory Council of Texas, the energy usage of some forty-five refineries (in thirty-nine companies) and 226 chemical plants (in 140 companies) was surveyed (Prengle et al., 1974), and distillation was an important energy consumer in almost all of them. In petroleum refineries which are the largest energy consumers on a per plant basis (1.9 X 1016 J/plant), crude and vacuum distillation alone accounts for 22.5 to 51% of the total energy consumption. Any enhancement of efficiency of this important unit operation could have an impact which will significantly benefit a wide cross section of process industries.In the conventional distillation column, heat is sup-

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