Evaluation of VOC recovery strategies

Abstract

Many manufactured items receive surface coatings for decoration and/or protection against damage. In a number of places along the production line emissions of (VOC) Volatile Organic Compounds can occur. Because VOC are a major contributor to photochemical smog, control of VOC emissions is a major concern for the industries' commitment to the environment. Approaches for process optimisation have a long tradition within chemical and process engineering for the systematic identification of cost- and resource-efficient production options. The challenge in the context of supply chain management is the optimal recovery and reuse of materials not only for single substances or energy flows in large chemical installations, but also for smaller production processes and various mass and energy flows within and between enterprises. Based on a case study from the industrial coating of bicycle frames, an approach for Multi Objective Pinch Analysis (MOPA) for the evaluation of overall recovery potentials for energy, water and VOC is presented. Moreover, a metric for resource efficiency is introduced as a measure for the possible savings potential and for the savings ultimately realised. This integrated approach requires a tight coupling of mass, energy, economic and environmental assessment methods and demands a highly interdisciplinary approach.

Annex: Pinch analysis as a transportation problem

The Pinch problem can be solved graphically or with computer based software, e.g. flow-sheeting-tools such as ASPEN Plus (AspenTech), DIVA (Max Planck Institute for Dynamics of Complex Technical Systems) or PROII (SimSci-Esscor - Invensys) which already include algorithms for the pinch analysis with a repertoire of different heat exchangers. By linearising the hot and cold flows, the transformation of the Pinch problem into an automated solving procedure as a transportation problem from Operations Research can be demonstrated (Cerda et al. 1983), where efficient algorithms exist for solving the ‘minimal energy input’-optimisation problem. The objective function of the classical minimisation equation of transportation problems is stated in Eq. (7).

$${\mathop {\min }\limits_{x_{{ij}} } }{\sum\limits_i {{\sum\limits_j {c_{{ij}} \cdot x_{{ij}} } }} }$$

(7)

Where the parameter c _ij indicates the costs per unit transported material from production site i to customer j and x _ij denotes the transported quantity (for a complete description of the transport problem see Neumann and Morlock 1993). Analogous to this, the extended objective function as the minimum utility problem can be stated as follows:

$${\mathop {\min }\limits_{q_{{ik,jl}} } }{\sum\limits_{i = 1}^C {{\sum\limits_{k = 1}^L {{\sum\limits_{j = 1}^H {{\sum\limits_{l = 1}^L {C_{{ik,jl}} \cdot q_{{ik,jl}} } }} }} }} }$$

(8)

The variable q _ik,jl (heat transferred) corresponds to x _ij (material transported), but is extended by different temperature intervals, since a transfer of heat against the temperature gradient is not possible. The transport prices c _ij per unit transported material are translated to the parameter C _ik,jl , which defines the possible exchanges by weighting possible process flow combinations with zero, utility consumption with one, and impossible combinations with an infinitely high value (see Eq. (9)).

$$C_{{ik,kl}} = \left\{ {\begin{array}{*{20}l} {0 \hfill} & {{{\text{for }}i,\;j\;{\text{are}}\;{\text{both}}\;{\text{process}}\;{\text{and}}\;{\text{match}}\;{\text{is}}\;{\text{allowed}},\;{\text{i}}{\text{.e}}{\text{.}}\;{\text{k}}} \hfill} \\ {0 \hfill} & {{{\text{for}}\;i,j\;{\text{are}}\;{\text{both}}\;{\text{utility}}\;{\text{streams}}{\left( {i = C,j = H} \right)}} \hfill} \\ {1 \hfill} & {{{\text{only}}\;i\;{\text{or}}\;j\;{\text{is}}\;{\text{a}}\;{\text{utility}}\;{\text{stream}}} \hfill} \\ {M \hfill} & {{{\text{otherwise}},\;{\text{where}}\;M\;{\text{is}}\;{\text{a}}\;{\text{very}}\;{\text{large}}{\left( {{\text{infinite}}} \right)}\;{\text{number}}} \hfill} \\ \end{array} } \right.$$

(9)

With the linear approximation of all process streams within each temperature interval, the composite curves are a combination of straight lines aggregated from the different streams in the intervals k and l (k,l ∈ L) for all cold streams i (i ∈ C) and all hot streams j (j ∈ H). Cerda et al. 1983 prove that only corner points (points where at least one of the composite curves changes its slope) and end points can be potential Pinch Points. These are the boundaries of the different intervals k and l of L. In a preceding step, a set of viable Pinch Points can be identified, in general reducing the size of the initial problem significantly. Since only points with a change in the slope of the composite curves can be candidate Pinch Points, intervals without any change in the mass flow rate or the heat capacity can be merged. This distinction is even more precise because points on the cold composite curve are only candidates if the slope becomes flatter at this point, whereas points on the hot composite curve are only candidates if the slope is steeper above the point.

The objective function (Eq. (7)) is accompanied by a series of constraints and assumptions:

$$\begin{array}{*{20}c} {{{\sum\limits_{j = 1}^H {{\sum\limits_{l = 1}^L {q_{{ik,jl}} = a_{{ik}} } }} }}} & {{i = 1,2, \ldots C;k = 1,2, \ldots ,L}} \\ \end{array} $$

(10)

$$\begin{array}{*{20}c} {{{\sum\limits_{i = 1}^C {{\sum\limits_{k = 1}^L {q_{{ik,jl}} = b_{{jl}} } }} }}} & {{j = 1,2, \ldots H;l = 1,2, \ldots ,L}} \\ \end{array} $$

(11)

$$\begin{array}{*{20}c} {{q_{{ik,jl}} \geqslant 0}} & {{\forall \;i,j,k\;{\text{and}}\;l}} \\ \end{array} $$

(12)

$$a_{{Cl}} \geqslant {\sum\limits_{j = 1}^{H - 1} {{\sum\limits_{l = 1}^L {b_{{jl}} } }} }$$

(13)

$$b_{{HL}} \geqslant {\sum\limits_{i = 1}^{C - 1} {{\sum\limits_{k = 1}^L {a_{{ik}} } }} }$$

(14)

with:

• a _ik : thermal energy flow in temperature interval k required by cold stream i

• b _jl : thermal energy flow in temperature interval l to be removed from hot stream j

• C : cold utility stream

• C−1 : number of cold process streams

• H : hot utility stream

• H−1 : number of hot process streams

• L : number of intervals

• c _ik : cold process stream i in temperature interval k

• h _jl : hot process stream i in temperature interval k

• C _ik,jl : cost of transferring a single unit of heat from heat source h _jl to heat sink c _ik

• q _ik,jl : thermal energy transferred from source h _jl to heat sink c _ik

• T : Temperature

Equation (10) for example states that the heat required by cold stream i in interval k must be transferred from any hot stream. In the same manner, Eq. (11) states that the cooling of hot stream j in interval l must come from any cold stream. This transferred heat must be nonnegative (Eq. (12)), which ensures that there is no heat moving from a cold stream to a hot stream. Furthermore, there is the assumption that there is enough cooling (Eq. (13)) and enough heating capacity (Eq. (14)) of the utility streams to satisfy all cooling and heating requirements. Additionally, the problem stated assumes a given minimum ΔT _min driving force, implicitly given in the required heat a _ik and the available heat b _ij per interval k and l respectively.

Furthermore, constraints can be chosen in such a way, that certain energy flow combinations are excluded, e.g. due to distances from sources to sinks that are too large (for an in-depth description of the application of the transport algorithm to the pinch analysis see Cerda et al. 1983). Moreover, apart from the target function “minimal energy input%rdquo; a minimisation of the costs can also be achieved.