Viscosity of saturated nonpolar liquids at elevated pressures

Abstract

x(0) = and the control vector is bounded such that 0 6 ~1 1.0, -0.4167 4 ~2 4 0.972.This system meets the requirements of the algorithms since 1. u1 affects only x1 and u2 affects only XIj, 2. the normalized initial states are of the same sign, 3. and the xi's between x1 and x.3 cannot change sign as long as x1 and x6 do not change sign. The application of the proposed algorithm is as follows. First at t = 0, the constrained value of the controls u1 = 1.0 and u2 = 0.972 are applied. At t = 0.0586, XI = 0.000 so u1 is found from u1 = -(1/B1,1) [All 5 where [Ai] represents the ith row of the A matrix. u2 is kept at c972 until t = 0.2025. At that point %6 = 0.000 and u2 is found from u2 = -(11B6.2) [Ae] -5 From hence, u1 and u2 are calculated in a closed loop fashion until all the xi are within a desired tolerance of the origin. SUMMARYAn algorithm for generating the time-optimal deadbeat control policies for a class of lumped parameter systems has been presented and illustrated. The algorithm avoids the possibility of hidden oscillation, possible with other techniques proposed for solving this problem, because it is a continuous time algorithm. In addition, a portion of the algorithm is closed loop in nature, and only a small amount of computer storage is required to implement the solution.

Viscosity of liquid hydrocarbons and their mixtures

“…The most restrictive shortcoming of this procedure is that the viscosity acentric factor differs strongly from the acentric factor and cannot be predicted a pn'on'. For temperatures above a reduced temperature T, = 0.7, where the logarithmic viscosity is no longer a function of inverse temperature, Letsou and Stiel (1973) proposed a method that requires critical temperature, critical pressure, acentric factor, and molecular weight. The errors are usually high; applied to n-Decane, this method underpredicts the experimental data, as shown in Figure 1.…”

Viscosity: A critical review of practical predictive and correlative methods

“…The other common corresponding states method for calculating viscosity is based on an analogy of the Pitzer et al (1955a,b) expansion of the compressibility factor in acentric factor, Z = Z(') + wZ('), where Z(I) = aZ/aw, commonly known as the three-parameter corresponding states. Letsou and Stiel (1973) developed a model of this type for saturated liquids:…”

The Correlation and Prediction of the Viscosities of Mixtures Over a Wide Range of Pressure and Temperature

“…This was the approach adopted by Pitzer et al (1955) for thermodynamic properties. Similar expansions for transport properties have been proposed by Jossi et al (1962) and Letsou and Stiel (1973). For ease of computation, Lee and Kesler (1975) replaced the derivative in Eq.…”