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Creating Streams

In this section, we will use the classic 4SP1 example (Papoulias & Grossmann, 1983) to show you how to work with EnergyIntegration.jl.

Consider the four-stream problem 1 (4SP1) shown below. The stream data in Table 1 are taken from Papoulias & Grossmann (1983).

StreamsFCp (kW/°C)Ts (°C)Tt (°C)Q (kW)
C1 (Cold)7.6260160+762
H2 (Hot)8.7916093-589
C3 (Cold)6.08116260+876
H4 (Hot)10.55249138-1171
S (Steam)270270
CW (Cooling water)3882
Table 1. Data for problem 4SP1.

Process Streams​

For process streams, the framework requires at least the following parameters:

  • stream name
  • stream flow rate, on either a mass or molar basis, F
  • inlet temperature, Tin
  • outlet temperature, Tout
  • per-side temperature contribution, Tcont
  • the six coefficients of the enthalpy polynomial, Hcoeff
  • heat-transfer coefficient, HTC

For example:

using EnergyIntegration
using Unitful: °C
Cold(:C1, F=1u"kmol/s", Tin=60°C, Tout=160°C, Tcont=5°C, Hcoeff=(0, 7.62, 0, 0, 0, 0), HTC=1u"kW/(K*m^2)")

Here, the per-side temperature contribution is used to split the minimum approach temperature into two parts, one assigned to the hot side and the other to the cold side. When a hot stream exchanges heat with a cold stream, the minimum temperature difference between them is treated as the sum of their individual Tcont values.

Hcoeff is a six-element tuple and is used in Equation (1):

H(T)=a0+a1T+a2T2+a3T3+a4T4+a5T5H(T) = a_0 + a_1 T + a_2 T^2 + a_3 T^3 + a_4 T^4 + a_5 T^5
(1)

Its second element is the constant-pressure molar or mass heat capacity. In most cases, the molar or mass heat capacity of a stream can be treated as a constant. When that is the case, you only need to provide the second element of Hcoeff and set the remaining elements to zero.

This also means that the stream tables commonly reported in the literature cannot usually be used directly in this framework, so some data conversion is required first. In Table 1, FCp is the heat-capacity flowrate, i.e. the product of the molar flowrate and the constant-pressure molar heat capacity, or equivalently the product of the mass flowrate and the specific heat capacity. In this framework, however, the stream flow rate and the constant-pressure molar or mass heat capacity must be specified explicitly. You therefore need to split the published data into those two parts. The split itself is arbitrary. For example, if FCp = 7.62 kW/°C, you may set F = 1 kmol/s and the molar heat capacity to 7.62 J/(kmol*K), or set F = 7.62 kmol/s and the molar heat capacity to 1 J/(kmol*K). The result will be the same.

Another point worth noting is the notation used in Table 1. Here, Ts denotes the supply temperature and Tt denotes the target temperature. In the context of heat exchanger networks, supply temperature is equivalent to inlet temperature, and target temperature is equivalent to outlet temperature. Therefore, for stream C1, you should set Tin = 60°C and Tout = 160°C.

We assume a minimum approach temperature of 10 K and split it equally between the hot and cold sides, so we set Tcont = 5°C. The paper does not provide heat-transfer coefficients for the individual streams because this example is used to solve an energy-targeting problem rather than an economic one. For that reason, in this example we simply assume HTC = 1u"kW/(K*m^2)".

With these assumptions, we can now prepare the four process streams:

Cold(:C1, F=1u"kmol/s", Tin=60°C, Tout=160°C, Tcont=5°C,
    Hcoeff=(0, 7.62, 0, 0, 0, 0), HTC=1u"kW/(K*m^2)"
),
Hot(:H2, F=1u"kmol/s", Tin=160°C, Tout=93°C, Tcont=5°C,
    Hcoeff=(0, 8.791, 0, 0, 0, 0), HTC=1u"kW/(K*m^2)"
),
Cold(:C3, F=1u"kmol/s", Tin=116°C, Tout=260°C, Tcont=5°C,
    Hcoeff=(0, 6.0833, 0, 0, 0, 0), HTC=1u"kW/(K*m^2)"
),
Hot(:H4, F=1u"kmol/s", Tin=249°C, Tout=138°C, Tcont=5°C,
    Hcoeff=(0, 10.54954, 0, 0, 0, 0), HTC=1u"kW/(K*m^2)"
),

Utilities​

Table 1 also includes steam, which acts as the hot utility, and cooling water, which acts as the cold utility. However, their heat duties Q are unknown, and their FCp values are also unknown. In the context of this framework, that means the flow rates of steam and cooling water are not fixed in advance, while their molar or specific heat capacities are still treated as constants. At a given temperature and pressure, the heat capacity of steam or water is a physical property and does not vary arbitrarily with the optimization problem.

To model that situation, give the flow rate as a range. The framework will then automatically treat it as a decision variable:

F=(0u"kmol/s", 1000u"kmol/s") # F isa Tuple{Number,Number}

Because steam releases heat at essentially constant temperature, we have Tin = Tout. In that case, the actual heat released by the stream is determined by its molar or mass enthalpy of vaporization rather than by its heat capacity. Whenever a stream has Tin = Tout, you should provide a latent-heat parameter instead of heat-capacity coefficients. A complete steam-stream definition is shown below:

Hot(:HU1, F=(0u"kmol/s", 1000u"kmol/s"), Tin=270°C, Tout=270°C, Tcont=5°C,
    Hvap=100u"kJ/kmol", HTC=100u"kW/(K*m^2)",
    cost=200u"(kJ*yr)^-1", pricing_basis=:energy
),

Here we specify Hvap instead of Hcoeff because the steam stream has Tin = Tout. Even if you do provide Hcoeff, it will be ignored automatically.

Utilities are usually not free, so we use the cost keyword argument to define the utility price. The pricing_basis can be either :energy or :flowrate. In classical heat exchanger network synthesis problems, pricing based on energy is the more common choice. Here we set cost = 200u"(kJ*yr)^-1", meaning that each 1 kJ of utility consumption costs 200 units of currency.

Similarly, the cooling-water stream can be defined as follows:

Cold(:CU1, F=(0u"kmol/s", 1000u"kmol/s"), Tin=38°C, Tout=82°C, Tcont=5°C,
    Hcoeff=(0, 1.0, 0, 0, 0, 0), HTC=100u"kW/(K*m^2)",
    cost=20u"(kJ*yr)^-1", pricing_basis=:energy
),

Finally, place all of the streams we have defined into a single vector, stream_data = [...]. You will obtain:

stream_data = [
    Cold(:C1, F=1u"kmol/s", Tin=60°C, Tout=160°C, Tcont=5°C,
        Hcoeff=(0, 7.62, 0, 0, 0, 0), HTC=100u"kW/(K*m^2)"
    ),
    Hot(:H2, F=1u"kmol/s", Tin=160°C, Tout=93°C, Tcont=5°C,
        Hcoeff=(0, 8.791, 0, 0, 0, 0), HTC=100u"kW/(K*m^2)"
    ),
    Cold(:C3, F=1u"kmol/s", Tin=116°C, Tout=260°C, Tcont=5°C,
        Hcoeff=(0, 6.0833, 0, 0, 0, 0), HTC=100u"kW/(K*m^2)"
    ),
    Hot(:H4, F=1u"kmol/s", Tin=249°C, Tout=138°C, Tcont=5°C,
        Hcoeff=(0, 10.54954, 0, 0, 0, 0), HTC=100u"kW/(K*m^2)"
    ),
    Hot(:HU1, F=(0u"kmol/s", 1000u"kmol/s"), Tin=270°C, Tout=270°C, Tcont=5°C,
        Hvap=100u"kJ/kmol", HTC=100u"kW/(K*m^2)",
        cost=200u"(kJ*yr)^-1", pricing_basis=:energy
    ),
    Cold(:CU1, F=(0u"kmol/s", 1000u"kmol/s"), Tin=38°C, Tout=82°C, Tcont=5°C,
        Hcoeff=(0, 1.0, 0, 0, 0, 0), HTC=100u"kW/(K*m^2)",
        cost=20u"(kJ*yr)^-1", pricing_basis=:energy
    )
]

Summary​

In this section, we discussed how to define streams and used 4SP1 as an example to show how literature data can be converted into the data structures expected by EnergyIntegration. In most cases, some conversion is necessary, because EnergyIntegration is designed to be more general: it separates stream flow rate from heat capacity so that the same framework can be applied in a wider range of situations.

In the next section, we will discuss how to configure the temperature intervals and then move on to building the heat exchanger network with build_hen.

References​

Papoulias, S. A., & Grossmann, I. E. (1983). A Structural Optimization Approach in Process Synthesis—II. Heat Recovery Networks. Computers & Chemical Engineering, 7(6), 707–721. https://doi.org/10.1016/0098-1354(83)85023-6