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Pinch analysis based on rigorous physical properties

Abstract

Pinch Analysis is a methodology that allows the calculation of minimum hot and cold utilities consumption in a process from the knowledge of some data of the hot and cold streams. These energy targets are calculated through the Problem Table Method, that is based on the description of the process using constant heat capacity flowrates. This hypothesis is not valid in certain situations, particularly when phase changes are involved. A modification to Problem Table Method is proposed, that allows the use of enthalpies rigorously calculated from thermodynamic correlations. One case study is provided, where an error of 240% in hot target is verified if phase changes are neglected.

Pinch analysis; phase changes; enthalpies


Pinch analysis based on rigorous physical properties

D. L. WESTPHALEN1 and M.R.WOLF MACIEL2

1Departamento de Engenharia Química e de Alimentos, Escola de Engenharia Mauá, (IMT), Estrada das Lágrimas 2035, São Caetano do Sul - SP, Brazil, 09580-900, Phone: (55) (11) 4239-3060, Fax: (55) (11) 4239-3131, E-mail: dlw@maua.br

2Faculdade de Engenharia Química, Laboratório de Desenvolvimento de Processos de Separação (LDPS) / DPQ, UNICAMP, C. P. Box 6066, 3081-970, Campinas - SP, Brazil, Phone: (55) (192) 39-8534, Fax: (55) (192) 39-4717, E-mail: wolf@feq.unicamp.br

(Received: August 18, 1998; Accepted: May 20, 1999)

Abstract - Pinch Analysis is a methodology that allows the calculation of minimum hot and cold utilities consumption in a process from the knowledge of some data of the hot and cold streams. These energy targets are calculated through the Problem Table Method, that is based on the description of the process using constant heat capacity flowrates. This hypothesis is not valid in certain situations, particularly when phase changes are involved. A modification to Problem Table Method is proposed, that allows the use of enthalpies rigorously calculated from thermodynamic correlations. One case study is provided, where an error of 240% in hot target is verified if phase changes are neglected.

Keywords: Pinch analysis, phase changes, enthalpies.

INTRODUCTION

Pinch Analysis is a methodology developed for the integrated chemical processes design. This methodology, that emerged at the final of the 70's, is based on thermodynamic fundamentals and was originally conceived for the design of heat exchanger networks (Linnhoff et al., 1982). It has established new thermodynamic concepts for process engineers, and therefore process design activity does not rely on "black-box" methods. As a result, process engineers can associate some project constrains as control, operability, flexibility, safety, and lay-out to the energy targets calculated by Pinch Analysis. A feature of Pinch Analysis is the fact that engineers are not removed from the decision-making activity. The successful application of these techniques has enabled the extension of the original proposed concepts in a such way that Pinch Analysis can be considered nowadays a general process design tool. It provides a framework where the integration of separation systems (distillation columns, evaporators, dryers), refrigeration systems, multiple utilities systems, combined heat and power systems, wastewater, and others can be evaluated (Linnhoff, 1994).

Traditionally, process streams are specified with the use of initial and final temperatures and its mean heat capacity flowrate, defined by the equation:

(1)

Heat capacity flowrate values are taken from material and energy balances and are assumed as constants. In case of phase changes in multicomponent mixtures, this assumption is not reasonable, and the temperature range in which the stream heat capacity is assumed constant must be shortened. The definition of the number of temperatures intervals used to describe the thermal behavior of the stream relies exclusively on the engineer experience and there is no established criteria for the optimum number of splits.

Nowadays, process simulators are available to almost every engineer (Evans, 1990), and so, manual procedures, based exclusively on intuition or experience, are no longer justified. In this context, this work proposes a methodology for energy targets calculation based on rigorous physical properties calculation, that can be easily performed with the help of a process simulator.

PROBLEM TABLE METHOD

Linnhoff and Flower (1978) published an algorithm for setting algebraically the energy targets and pinch position for a set of hot and cold streams, known as "Problem Table". This algorithm is described in detail by Linnhoff et al. (1982) and Douglas (1988), and can be summarized by the following steps:

Step 1) After setting a DTmin, shift all hot streams in –DTmin/2 and all cold streams in DTmin/2;

Step 2) Set up temperature intervals from the temperatures calculated at the previous step;

Step 3) Evaluate the enthalpy balance for each temperature interval, checking if this balance results in an energy deficit or excess;

Note that, these procedure guarantees that all heat exchange between process streams occurs with a temperature difference equal or greater than the minimum temperature difference;

Step 4) Cascade the heat flow through temperature intervals;

Step 5) Look for the greatest negative heat flow and assign this value as positive to QH;

Step 6) Cascade again the heat flow through temperature intervals, starting with QH into the first interval . The value of QC is obtained from the last interval heat flow and the position of pinch point is taken at the temperature where the heat flow is equal to zero.

As an example, for process streams presented in Table 1 the following results were obtained for a minimum temperature difference of 10°C with the preceding algorithm: pinch position 85°C, hot utility target 20 MJ/h and cold utility target 60 MJ/h (Linnhoff et al., 1982).

Table 1:
Process data adapted from Linnhoff et al. (1982)

PROPOSED ALGORITHM

Initially, process streams have to be entirely defined, that is, all necessary information for enthalpy calculations have to be known, as flowrate, pressure, temperature and composition. Following the Problem Table Method, hot and cold streams have to be shifted in temperature. The difference of the proposed method is in the definition of the temperature intervals.

In a first approximation, the constant heat capacity flowrates are used, although this assumption does not represent correctly what happens when phase changes occur. When this assumption is inadequate, the temperature interval is split in two more intervals. The complete algorithm is described as follows:

Step 1) Shift all hot streams in –DTmin/2 and all cold streams in DTmin/2;

Step 2) Set up temperature intervals from the temperatures calculated at the prior step;

Step 3) For each temperature interval, check if the assumption of constant heat capacity flowrate is reasonable, as follows:

Step 3.1) For each stream located in the interval, the enthalpies are rigorously calculated at the initial (Ti) and final (Ti+1) interval temperatures. The enthalpy of initial and final temperatures are designated H(Ti) and H(Ti+1), respectively;

Step 3.2) Calculate the medium value of the enthalpies calculated at the prior step ();

Step 3.3) Calculate the medium temperature of the interval () and the enthalpy of this medium temperature ();

Step 3.4) For any stream located at the interval temperature, the difference between the medium enthalpy and the enthalpy at the medium temperature has to be checked. If, for any stream, the relative error (equation 2) between the medium enthalpy and the enthalpy at the medium temperature is greater than a specified tolerance, this temperature interval has to be split in two new intervals. Figure 1 illustrates how this division is set up. The first new interval has as initial and final temperatures the values Ti and , respectively. The second new interval has as initial and final temperatures the values and Ti+1, respectively.

Figure 1:
Temperature interval subdivision

This procedure (Step 3) is repeated for the new intervals until the relative error is smaller than the specified tolerance. From the temperature intervals set up by this procedure, the other steps from the Problem Table are performed in order to calculate QH, QC and the pinch point position.

The relative error is defined as follows:

(2)

CASE STUDY

In order to exemplify the proposed algorithm, it will be applied to the hot and cold streams presented in Table 2. All physical properties were calculated with the process simulator HYSIM, using the Peng-Robinson equation of state. These streams data were chosen in a such a way that all initial and final temperatures, and heat duties, are the same of those streams presented in Table 1.

Table 2:
Hot and cold streams

Calculating the energy targets for the streams presented in Table 2, using the proposed algorithm, it was obtained the values 5883 and 45882 kJ/h for the hot and cold utilities, respectively, for a minimum temperature difference of 10°C, and a tolerance of 1%. However, the energy targets for the same streams, assuming constant heat capacity flowrates were 20000 and 60000 kJ/h for the hot and cold utilities, respectively, representing an error of 240% for the hot utility. Pinch position remained at the same temperature value. Figure 2a presents the composite curves constructed from the Problem Table Method and Figure 2b presents the composite curves constructed using the method proposed in this work. Because of the phase change that occurs in stream 1, the heat duty necessary to increase the temperature of stream 1 from 20 to 135°C is not uniformly distributed, that is, the heat load is in reality concentrated in the temperature range where the phase change takes place. Consequently, the heat duties of the hot composite curve are differently distributed above and below the pinch when the Problem Table and the proposed method are employed. These differences in energy targets calculation can lead an engineer to misconceptions and as a result a wrong heat exchanger network will be designed.


(a) Problem Table Method

Figure 2:
Composite curves

(b) Proposed algorithm

CONCLUDING REMARKS

It was proposed a modified Problem Table Method in order to calculate energy targets of a process taking account rigorous physical properties calculation. This new method is particularly beneficial in situations were phase changes occur and the heat capacity flowrates can not be assumed as constant. Another advantage of this algorithm is that the existing methods for area target and minimum number of shells (Ahmad and Smith, 1989) can still be used in conjunction with the proposed method.

The availability of high speed computers and process simulators allows that rigorous physical properties can be calculated in a easy way. Therefore, it is desired that more rigorous methods should be used in place of traditional and approximated methodologies.

NOMENCLATURE

CP Heat capacity flowrate (kJ/h °C)

H Enthalpy flow (kJ/h)

Medium enthalpy flow (kJ/h)

i Temperature interval

T Temperature (°C)

Ts Supply temperature (°C)

Tt Target temperature (°C)

Medium temperature (°C)

QC Cold utility target (kJ/h)

QH Hot utility target (kJ/h)

DTmin Minimum temperature difference (°C)

e Relative error

  • Ahmad, S., Smith, R., Targets and Design for Minimum Number of Shells in Heat Exchanger Networks. Chem. Eng. Res. Des., v. 67, September (1989).
  • Douglas, J. M., Conceptual Design of Chemical Processes. McGraw-Hill, Inc, New York (1988).
  • Evans, L., Process Modeling: What Lies Ahead. Chem. Eng. Prog., October, 42 (1990)
  • Linnhoff, B., Ahmad, S., SUPERTARGETING: Optimum Synthesis of Energy Management Systems. J. Ener. Res. Tech., v 111, 121 (1989).
  • Linnhoff, B., Flower, J. R., Synthesis of Heat Exchanger Networks: I. Systematic Generation of Energy Optimal Netwoks. AIChE J., v. 24, 633 (1978).
  • Linnhoff, B., Towsend, D. W., Boland, D., Hewitt, G. F., Thomas, B. E. A., Guy, A. R., Marsland, R. H., A User Guide on Process Integration for the Efficient Use of Energy. The Institution of Chemical Engineers, Rugby (1982).
  • Linnhoff, B., Pinch Analysis. Chem. Eng. Prog., August, 33 (1994).

Publication Dates

  • Publication in this collection
    16 Dec 1999
  • Date of issue
    Sept 1999

History

  • Accepted
    20 May 1999
  • Received
    18 Aug 1998
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