Many and severe uncertainties affect offshore processing of NG:

• Variability of raw gas composition, pressure and flow rate [3];

• Sales gas price and consumer market, equipment and operational costs [4];

• Meteorological events in high seas and even high operational risks of subsea equipment and topside processes, among others.

Feed composition and flow rate, ambient temperature and pipeline pressure [5] are critical load conditions as their variations propagate effects [6] throughout the plant disturbing operating conditions and product specifications [7]. In industrial practice, uncertainties are usually compensated by the use of conservative decisions like over-design of process equipment and then retrofits to overcome operability bottlenecks, or overestimation of operational parameters caused by worst-case assumptions of uncertain parameters [4], which, despite making the design feasible, drastically decrease profitability [8].

Another relevant uncertainty concerns the impact of the CO₂ re-injection in the reservoir for Enhanced Oil Recovery (EOR). Although EOR increases the efficiency of oil recovery and provides a safe destination for the large volume of CO₂ removed from the NG, it results in a long-term increase of CO₂ content in raw NG. In fact, up to 60% of the re-injected CO₂ can be retained in the reservoir [9], meaning that 40% (or more) stay in the gas phase, rising its CO₂ content, leading to incremental costs and risks throughout the lifetime of offshore NG processing.

Such uncertainties recommend using decision-making techniques under influence of stochastic factors. A classic and powerful technique for decision under non-deterministic scenarios is the Monte Carlo (MC) method. Given advances in computer-aided engineering [10], MC is an adequate technique to estimate the probability of process designs to accomplish all specification or targets within defined stochastic scenarios of interest. MC method is based on obtaining realizations of the proposed process (responses) under stochastic scenarios randomly sampled according to Probability Density Functions (PDF) of the non-deterministic factors that influence process response [11].

Currently, the process industry is moving towards the design of innovative and more sustainable processes that show improvements in both economic and environmental factors [12]. Corporations worldwide are realizing that sustainability makes good business sense and is fundamental to their survival and growth [13]. Especially, concerns about the impacts of Oil and Gas (O&G) exploitation on the wellbeing of the environment and society have led to increasing pressures for the O&G industry to move towards more sustainable processes [14].

For designing more sustainable processes, besides multiple metrics [15], ‘ad hoc’ criteria [16] and tools for quantifying sustainability, statistics algorithms for evaluating performance metrics and for supporting decision making have been developed [17]. In the procedure of achieving superior environmental performance, several alternative process flowsheets are generated by combining multiple unit operations, rendering performance assessment of alternatives cumbersome. Therefore, it is beneficial the use of Computer-Aided Engineering (CAE) methods to evaluate all possible alternatives for defining the most sustainable option [12].

It is presented a CAE tool (MCAnalysis) which automatically integrates the process simulator HYSYS (Aspentech) for obtaining chemical process responses with MATLAB (Mathworks) for generation of graphical statistical analysis using the Waste Reduction (WAR) algorithm (US Environmental Protection Agency) [18] for obtaining statistics of PEI’s. In this application, ‘MCAnalysis’ manages process uncertainties and generates sustainability performance [19] as the result of multiple MC samples of the process responses. ‘MCAnalysis’ is herein applied to an FPSO plant processing CO₂ rich NG under uncertainties in order to assess the environmental pillar of sustainability, using WAR to evaluate PEI’s [20] and PCA to identify the most relevant ones [21]. The assessed process is submitted to probabilistic uncertainties affecting raw NG conditions: flow rate and %mol CO₂, both following normal PDF’s. Two scenarios of CO₂ content were compared to evaluate the environmental impact of the increase of %mol CO₂ in raw NG.

This analysis consubstantiates an original work and has potential use for probabilistic sustainability assessments of FPSO gas-oil plants, which are well-known very risky systems operating at very special conditions in terms of safety concerns and exposition to hazards. The developed CAE tool ‘MCAnalysis’ is also an original achievement as it is reliable, robust and flexible computing resort allowing building several different scenarios of analysis. In the present work, it was configured for environmental assessment of complex offshore gas plant with CO₂ rich NG, but it can also be used for technical, profitability, reliability and safety studies.

Offshore processing of raw NG with high CO₂ content is supposed to occur on oil-gas FPSO platforms. Raw NG is first separated from oil and water and then goes to the gas plant at given flow rate, composition, temperature, and pressure. The raw gas is saturated in water (from 2,000 to 3,500 ppm) and its most critical variables are the flow rate and the high content of CO₂. The gas plant is normally designed for a given gas flow rate and CO₂ content, but both variables change along the FPSO campaign, the former because the oil flow rate can change for several reasons at constant GOR, while the latter changes (increases) along the campaign due to continuous injection of CO₂ in the reservoir for EOR. Evidently, several other variables associated with the raw gas can affect the process, but the flow rate and CO₂ content can seriously impact the processing if exceed the design condition. In this work, only the raw gas flow rate and the CO₂ content are considered as relevant process input factors subjected to uncertainties.

Gas processing description

The gas plant for offshore processing of CO₂ rich NG is sketched in Figure 1. This process was designed to comply with NG specifications assuming the mean values of critical input factors subjected to uncertainties – flow rate and CO₂ content of the raw gas. This design is denominated as the Base-Case. The objective is to test the Base-Case in terms of environmental impacts via MC sampling. The main operations in the Base-Case (Figure 1) are:

• NG dehydration for WDPA;

• Separation of condensable hydrocarbons for HCDPA;

• CO₂ removal.

Figure 1.

Block diagram of offshore processing of CO₂ rich NG (JT ‒ Joule-Thomson, TEG ‒ Triethylene Glycol, EOR ‒ Enhanced Oil Recovery, WDP ‒ Water Dew Point, HCDP ‒ Hydrocarbon Dew Point, NGL ‒ Natural Gas Liquids)

Triethylene Glycol (TEG) dehydration was chosen for WDPA as the most economic option [22], despite requiring a stripping column for TEG regeneration. HCDPA is achieved by Joule-Thomson Expansion (JTE) [23], while CO₂ is removed from NG by Membrane Permeation (MP) due to its operational simplicity, low costs, modularity, capability of processing CO₂ rich feeds, and reduced weight and footprint [24]. The process starts with compression of raw NG, which is sent to TEG dehydration for WDPA to avoid ice and gas hydrates in pipelines [25]. Rich TEG is regenerated producing flare gas residue and recirculates to WDPA column, while the dry NG flows to HCDPA, where a saleable stream of Natural Gas Liquids (NGL) is a sub-product. HCDPA must precede MP CO₂ removal to avoid membrane damage by condensable hydrocarbons. In MP CO₂ removal, dry NG flows through a battery of two MP modules, whose outlet MP retentate is the final conditioned NG. Final NG is compressed to be exported to onshore facilities. The MP permeate is a low-pressure CO₂ rich stream which is compressed for re-injection as EOR agent.

Gas plant uncertainties

Uncertainties related to the raw NG were selected for MC analysis. Independent normal random populations were assumed for feed flow rate (MM Sm³/d) and for its CO₂ content as molar fraction because these are the feed factors with the highest influence on the process response and also with the highest subjection to uncertainties. Normal PDF’s were chosen due to their relevance for describing multiple physical, meteorological, biological and financial phenomena. One can argue that normal PDF’s are not adequate to represent real stochastic disturbances because they have infinite tails spread on (−∞, +∞) domains, whereas the reality is not akin to infinite amplitude inputs. Well, this is not the case. First of all, there are, indeed, (very) rare natural events with relatively gigantic catastrophic amplitudes (someone does not have to be especially imaginative to cite one). Secondly, the 99.73% probability domain of normal PDF’s corresponds to the finite interval [μ − 3σ, μ + 3σ], while the 99.99% probability domain corresponds to [μ − 4σ, μ + 4σ], where μ and σ are, respectively, the population mean and standard deviation. This implies that more than 10,000 outcomes have to be sampled to have a single one outside the [μ − 4σ, μ + 4σ] interval, while MC searches are applied with finite samples containing from 1,000 to 3,000 outcomes, which is sufficient for ergodicity [27]. In other words, on practical grounds normal PDF’s give rise to bounded unimodal samples. Other advantages of normal PDF’s are:

• By the Central Limit Theorem a normal input is appropriate to represent the contribution of several other independent inputs following arbitrary distributions (which is, in real applications, the case of some unimodal disturbances that represent a collection of contributions);

• Normal PDF’s may degenerate to other simpler PDF’s like the Dirac PDF.

Additionally, there is a very special reason to adopt normally distributed input factors. This has to do with the traceability of normal signals throughout the process. When submitted to uncertainties following normal PDF’s, process output variables shall present behaviours close to the normal pattern for approximately linear cause-effect relationships, whereas behaviours very different from normal (e.g. bimodal, multi-modal or stone-wall responses) would be observed for very non-linear causality relationships. In other words, using normal inputs one can identify where there is great non-linearity in the process response. This may be useful in sensitivity studies, design of process control strategies and when applying design safe margins to some critical process units. The normal PDF of variable x is given by eq. (1) with its parameters μ (mean) and σ (standard deviation). In the present case, the raw NG flow rate population is supposed to follow a normal PDF with μ = 6.0 MM Sm³/d and σ = 1 MM Sm³/d, meaning that it practically varies from 3.0 to 9.0 MM Sm³/d. Meanwhile, two scenarios were devised for the CO₂ content populations of raw NG: Case 20% – using normal PDF with μ = 0.20 and σ = 0.03 (i.e. CO₂ molar fraction approximately varies from 0.10 to 0.30), and Case 50% – using normal PDF with μ = 0.50 and σ = 0.03 (i.e. CO₂ molar fraction approximately varies from 0.40 to 0.60), as shown in Figure 2:

$PDF(x,\mu ,\sigma )=\frac{1}{\sqrt{2\pi {\sigma }^2}}{e}^{(-\frac{{(x-\mu )}^2}{2{\sigma }^2})},-\infty <x<\infty ,\sigma >0$ (1)

Figure 2.

PDF’s of: raw NG flow rate population [MM Sm³/d] (a), feed NG CO₂ molar fractions populations for: Case 20% CO₂ (b) and Case 50% CO₂ (c)

MC is a relevant methodology based on stochastic analysis for evaluating systems under non-deterministic scenarios when analytical solutions are complex or impossible due to non-deterministic components which are not known a priori [11]. Such methodology provides an approximation of the problem solution by stochastic sampling of the independent system variables obeying known PDF instead of solving the numeric-mathematical problem directly. The objective of MC analysis is the stochastic appraisal of the performance of a given dependent variable of interest (output variable) according to the behaviour of uncertain independent variables (input variables). The method consists on creating samplings of the independent variables by generating pseudo-random numbers distributed between 0 and 1 which are converted to random samples obeying PDF’s of the independent variables, given that the behaviour of these independent variables is random and follows specific PDF’s. When a large sample of random values of independent variables is used, the calculated values of output variables can be plotted as histograms, leading to approximations of PDF’s of output variables, which are the main objectives of MC analysis jointly with some statistics for estimating parameters of these PDF’s (e.g. sample mean and sample standard deviation).

This work uses the Inverse Transform Method [28] to generate normal pseudo-random populations. This method employs random number properties and the Cumulative Distribution Function (CDF) of a random variable to generate its sample PDF. The correlation of a random number with the CDF is given by eq. (2), which can be inverted to generate eq. (3) based on the iCDF (inverse of CDF) for expressing the mapping of a set of values of the variable of interest from a set of random values uniformly distributed between 0 and 1:

${\displaystyle {\int }_a^{x1}PDF(x)dx}=CDF(x1)=CDF(rnd1)={\displaystyle {\int }_0^{rnd1}PDF(rnd)d(rnd)=rnd1}$ (2)

$\text{x}1=i\text{CDF}(\text{rnd}1)$ (3)

where rnd is a random number uniformly distributed between 0 and 1, rnd1 is a sample of rnd between 0 and 1, x is another random number varying along the domain $a\le x\le b$, x1 is a sample of x between a and b, PDF(rnd) and PDF(x) are the PDF’s of variables rnd and x, and CDF(rnd) and CDF(x) the integrals of PDF(rnd) and PDF(x).

The iCDF – inverse of the CDF – for the standard normal distribution (μ = 0, σ = 1) is numerically approximated in eq. (4) and eq. (5) [29]. Eq. (4) and eq. (5) correspond to the conversion of a population of pseudo-random numbers sampled from 0 to 1 into a population following the standard normal PDF with an absolute error smaller than 4.5 × 10⁻⁴, where c₀ = 2.515517, c₁ = 0.8202853, c₂ = 0.010328, d₁ = 1.432788, d₂ = 0.189269 and d₃ = 0.001308. The symmetry of normal PDF is considered so that eq. (4) and eq. (5) are valid for $0<p\le 0.5$. For $0.5<p\le 1$, eq. (4) and eq. (5) are used with 1 − p, switching the signal of the calculated abscissa z. With eq. (4) and eq. (5) the population of z values generated from the population of p values approximately follows the standard normal PDF. Eq. (6) converts the population of standard normal z to a normal population x with mean μ and standard deviation σ. Figure 3 depicts the relationships between samples via iCDF and CDF to generate samples according to normal PDF’s:

$t=\sqrt{-2lnp}$ (4)

${\text{z}}_p=\text{t}-\frac{{\text{c}}_0+{\text{c}}_1\text{t}+{\text{c}}_2{\text{t}}^2}{1+{\text{d}}_1\text{t}+{\text{d}}_2{\text{t}}^2+{\text{d}}_3{\text{t}}^3}$ (5)

$\text{z}=\frac{(\text{x}-\text{μ})}{\text{σ}}\to \text{x}=\text{μ}+\text{z}\times \text{σ}$ (6)

Figure 3.

Interrelationships among iCDF, CDF, and PDF of normal populations

The Quasi-MC (Quasi Monte Carlo) is an alternative sampling method for multi-dimensional numerical integrations and similar contexts where conventional MC sampling is applied. Quasi-MC uses low-discrepancy sequences – such as, the Halton and Sobol sequences – also called quasi-random or sub-random sequences [30]. Quasi-MC is presented in opposition to the regular MC sampling applications such as multi-dimensional MC integrations, which are based on pseudo-random sequences. MC and Quasi-MC samplings are adequate for multi-dimensional integrations where common numerical strategies – such as Newton-Cotes quadrature formulas – face severe difficulties. The advantage of Quasi-MC is its faster rate of convergence [O(1/N)] relatively to regular MC [$O(1/\sqrt{N})$], where N is the number of samples. On the other hand, Quasi-MC has some drawbacks comparatively to MC [31], such as:

• Its superiority over MC only appears if N is really high and the dimensionality (number of independent factors) is not too high;

• A majoring of the involved Quasi-MC error sometimes cannot be found for very non-linear response functions – e.g. multi-modal responses;

• Regular MC is very easy to implement even for very non-linear response functions as in the present case with offshore gas plants processing CO₂ rich NG;

• The high non-linear behaviour of some response functions may bring multi-modal responses for unimodal inputs (e.g. with normal PDF’s) – as shown in the present study in Figures 9-15 – such that the higher performance of Quasi-MC may be hampered by such patterns, vis-à-vis the resiliency of regular MC in such cases.

Despite the apparent superiority of Quasi-MC over MC, in the present work, only regular MC sampling is used. The main reason has to do with the much easier and robust implementation of MC sampling in the environment of ‘MCAnalysis’ juxtaposed to the fact that the number of flowsheet simulations is not too high for statistical convergence of the sample mean and variance of responses – from 1,000 to 2,000 simulations are normally required with two stochastic input factors – and also the fact that the real time-consuming step is the simulation of the complex gas plant (i.e. evaluation of the process response) and not the sampling management algorithm itself.

Several methodologies for characterizing the environmental impact of products and processes are available in the literature, as Life Cycle Assessment (LCA) and Waste Reduction (WAR), both well-established techniques to include environmental considerations into process design [32]. The LCA methodology assesses the environmental performance of a product or process thorough its life cycle: from the primary resources to recycling or safe disposal [33]. However, this methodology requires a large amount of information and few data are publicly available due to legal or intellectual property concerns [34]. The WAR methodology considers only the product manufacturing step [19] as Figure 4 shows. WAR is selected to be used in this work due to its simplicity when compared to LCA. It is worth noting that WAR, contrarily to LCA, is restricted to ‘gate-to-gate’ analysis (Figure 4).

Figure 4.

WAR algorithm with plant life cycle (adapted from [19])

WAR was proposed by Cabezas et al. [18] as a general theory for the flow and generation of PEI’s through a chemical process and is used to quantify its environmental performance. By definition, PEI is the unrealized average effect or impact that the emission of mass and energy would cause to the environment, being essentially a probability function associated to a potential effect. A PEI conservation equation based on an accounting of the flow of PEI in/out of the product manufacturer and energy generation [20], is introduced by WAR in eq. (7) for steady state balance, where ${\stackrel{\text{•}}{\text{I}}}_{in}^{(cp)}$ and ${\stackrel{\text{•}}{\text{I}}}_{out}^{(cp)}$ are the input and output rates of PEI of the chemical process, ${\stackrel{\text{•}}{\text{I}}}_{in}^{(ep)}$ and ${\stackrel{\text{•}}{\text{I}}}_{out}^{(ep)}$ are the input and output rates of PEI of the energy generation process, ${\stackrel{\text{•}}{\text{I}}}_{we}^{(cp)}$ and ${\stackrel{\text{•}}{\text{I}}}_{we}^{(ep)}$ are the output of PEI associated with the waste energy lost from the chemical and energy generation processes and ${\stackrel{\text{•}}{\text{I}}}_{gen}^{(t)}$ represents the creation or consumption of PEI by chemical reactions inside the chemical process and the power plant. Figure 5 illustrates eq. (7):

$\stackrel{}{{\stackrel{\text{•}}{\text{I}}}_{in}^{(cp)}+}{\stackrel{\text{•}}{\text{I}}}_{in}^{(ep)}-{\stackrel{\text{•}}{\text{I}}}_{out}^{(cp)}-{\stackrel{\text{•}}{\text{I}}}_{out}^{(ep)}-{\stackrel{\text{.•}}{\text{I}}}_{we}^{(cp)}-{\stackrel{\text{•}}{\text{I}}}_{we}^{(ep)}+{\stackrel{\text{•}}{\text{I}}}_{gen}^{(t)}=0$ (7)

PEI is calculated by a unified score obtained by the weighted sum of eight environmental impact categories, listed in Table 1, and a specific PEI for each impact category is associated to the components of the process streams as shown in eq. (8), where l is an indicator for input or output, α_i is the weighting factor for environmental impact category i, $\stackrel{•}{M_{j,l}}$ is the mass flow of stream j, x_kj is the mass fraction of component k in stream j and ${\psi }_{ki}^s$ is the specific PEI of component k associated with environmental impact category i. The measures for calculating each ${\psi }_{ki}^s$ are also listed in Table 1. The calculation of ${\psi }_{ki}^s$ is given by eq. (9) where (Score)_ki represents the impact score of component k correlated with environmental category i and <(Score)_k>_i represent the average impact score of all components in category i. This normalization of the component impact eliminates unnecessary bias within the category. The specific correlations among each category score and its corresponding measure of impact are described in Young and Cabezas [19]. The environmental assessment in this work presents the output PEI’s for each individual category caused by the offshore processing of CO₂ rich NG and identifies the most relevant as performance indicators using PCA. Impacts from product streams are not considered:

${\stackrel{{}_{\text{•}}}{\text{I}}}_{\text{l}}={\displaystyle \sum _i^{EnvCats}{\text{α}}_{\text{i}}}{\displaystyle \sum _{\text{j}}^{Streams}\stackrel{\text{•}}{{\text{M}}_{\text{j,l}}}}{\displaystyle \sum _{\text{k}}^{Comps}{\text{x}}_{\text{kj}}{\text{ψ}}_{\text{ki}}^{\text{s}}}$ (8)

${\text{ψ}}_{\text{ki}}^{\text{s}}=\frac{{(Score)}_{\text{ki}}}{<{(Score)}_{\text{k}}{>}_{\text{i}}}$ (9)

Figure 5.

WAR algorithm (adapted from [20])

Principal Component Analysis (PCA) consists in re-organizing data sets (e.g. data from process plants), which often exhibit correlated patterns, in order to find a set of new uncorrelated variables as linear combination of the original ones. The new variables are assigned to fractions of the variance in the original data in decreasing order [21]. The original data set is organized as a matrix $\underset{\_}{\underset{\_}{X}}$_{m × n}, where the scalar variables of the problem correspond to the columns and their samples correspond to the rows, meaning that each vector of sampled data ${\underset{\_}{X}}_i$ _{m× 1} for variable X_i corresponds to a column of the matrix $\underset{\_}{\underset{\_}{X}}$, as illustrated by eq. (10). Each vector ${\underset{\_}{X}}_i$ originates a sample scalar mean $<X_i>$ given by eq. (11). Such sample means are gathered in the vector of means $<\underset{\_}{X}>$ as shown in eq. (12). $\underset{\_}{U}$_{m × 1} is a compatible vector of ones:

$\begin{array}{l}{\text{X}}_1{\text{X}}_2\mathrm{...}{\text{X}}_{\text{n}}\\ \downarrow \downarrow \mathrm{....}\downarrow \\ \underset{\_}{\underset{\_}{\text{X}}}=\left[\begin{array}{l}{\text{x}}_{11}{\text{x}}_{12}\cdot \cdot \cdot {\text{x}}_{1\text{n}}\\ {\text{x}}_{21}{\text{x}}_{22}\cdot \cdot \cdot {\text{x}}_{2\text{n}}\\ \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \\ {\text{x}}_{\text{m}1}{\text{x}}_{\text{m}2}\cdot \cdot \cdot {\text{x}}_{\text{mn}}\end{array}\right]=[{\underset{\_}{\text{X}}}_1{\underset{\_}{\text{X}}}_2\mathrm{...}{\underset{\_}{\text{X}}}_{\text{n}}];{\underset{\_}{\text{X}}}_1=\left[\begin{array}{l}{\text{x}}_{11}\\ {\text{x}}_{21}\\ \cdot \cdot \cdot \\ {\text{x}}_{\text{m}1}\end{array}\right];{\underset{\_}{\text{X}}}_2=\left[\begin{array}{l}{\text{x}}_{21}\\ {\text{x}}_{22}\\ \cdot \cdot \cdot \\ {\text{x}}_{\text{m}2}\end{array}\right];{\underset{\_}{\text{X}}}_{\text{n}}=\left[\begin{array}{l}{\text{x}}_{1\text{n}}\\ {\text{x}}_{2\text{n}}\\ \cdot \cdot \cdot \\ {\text{x}}_{\text{mn}}\end{array}\right]\end{array}$ (10)

$<X_i>={\underset{\_}{U}}^T{\underset{\_}{X}}_i/m$ (11)

$<\underset{\_}{X}>={[<X_1>\mathrm{...}<X_n>]}^T$ (12)

PCA factorizes the matrix of sample variance-covariance ${\underset{\_}{\underset{\_}{R}}}_X$_{n × n} – symmetric and positive definite – obtained by eq. (13). The n eigenvalues of ${\underset{\_}{\underset{\_}{R}}}_X$ are calculated and expressed as a column vector of positive eigenvalues $\underset{\_}{\lambda }$ sorted in decreasing order, while the respective orthogonal normalized n eigenvectors (n × 1) are stored as columns of matrix $\underset{\_}{\underset{\_}{P}}$ as illustrated in eq. (14):

${\underset{\_}{\underset{\_}{\text{R}}}}_{\text{X}}=\frac{{(\underset{\_}{\underset{\_}{\text{X}}}-\underset{\_}{\text{U}}\text{.<}\underset{\_}{\text{X}}{\text{>}}^{\text{T}})}^{\text{T}}(\underset{\_}{\underset{\_}{\text{X}}}-\underset{\_}{\text{U}}\text{.<}\underset{\_}{\text{X}}{\text{>}}^{\text{T}})}{\text{m}-1}$ (13)

$\underset{\_}{\text{λ}}=\left[\begin{array}{c}{\text{λ}}_1\\ ⋮\\ {\text{λ}}_{\text{n}}\end{array}\right],\underset{\_}{\underset{\_}{\text{P}}}=\left[\begin{array}{ccc}{\underset{\_}{\text{P}}}_1& \cdots & {\underset{\_}{\text{P}}}_{\text{n}}\end{array}\right]$ (14)

Matrix $\underset{\_}{\underset{\_}{P}}$ contains the directions capable of describing the variability of original data $\underset{\_}{\underset{\_}{X}}$ by decreasing relevance, meaning that $\underset{\_}{\underset{\_}{X}}$ data show more variability over the direction defined by the first column of $\underset{\_}{\underset{\_}{P}}$. This is the 1^st principal direction for describing the statistical behaviour of $\underset{\_}{\underset{\_}{X}}$. The second column of $\underset{\_}{\underset{\_}{P}}$ is the 2^nd principal direction and so on. A matrix of generalized scores $\underset{\_}{\underset{\_}{S}}$_{m × n} is obtained by projecting $\underset{\_}{\underset{\_}{X}}$ over the directions (columns) of $\underset{\_}{\underset{\_}{P}}$ after subtracting the respective sample means $<X_i>$ as eq. (15) shows, where ${\underset{\_}{P}}_i$ is the principal direction i of $\underset{\_}{\underset{\_}{P}}$ and ${\underset{\_}{S}}_i$ contains m × 1 samples of the generalized score S_i. The generalized scores are the new scalar variables S₁, S₂,…,S_n candidates to substitute the original variables X₁, X₂,…,X_n with the advantage of having the variability condensed to its maximum and decreasing along the elements of the set. Usually, the first elements represent most of the variability of the original set. The percentage of the variance associated to the general score S_i is calculated considering its contribution over the total variance of the sample as shown in eq. (16):

${\underset{\_}{S}}_i=(\underset{\_}{\underset{\_}{X}}-\underset{\_}{U}<{\underset{\_}{X}}^T>){\underset{\_}{P}}_i$ (15)

${\text{ν}}_{\text{i}}\left[\%\right]=100\frac{{\text{λ}}_{\text{i}}}{{\displaystyle \sum _{\text{i}}{\text{λ}}_{\text{i}}}}$ (16)

In order to enable the automatic execution of MC analysis for any chemical process representable as a simulation flowsheet, a set of random sample values of the process input stochastic variables must be generated, managed and submitted to process simulation to generate output samples which are then statistically processed to generated statistics results and figures. Therefore ‘MCAnalysis’ was designed as a HUB to manage MC analysis for several different scenarios of stochastic response like technical analysis of a process design, safety analysis, energy consumption assessment, economic assessments and environmental sustainability assessment (Figure 6). In this work only the environmental assessment is demonstrated.

Figure 6.

HUB architecture of ‘MCAnalysis’

‘MCAnalysis’ starts with the module “Generate Batch Data”, which processes a configurable XML (Configuration XML) containing the definition of the MC non-deterministic independent input variables, the respective PDF’s and how to identify them in the HYSYS simulation flowsheet. Populations of the input stochastic variables are randomly generated and graphically processed through MATLAB for generating histograms and plotting associated PDF curves. HYSYS simulation is then executed in batch for each sample of the input variables. The relevant simulated responses for the MC analysis, listed in another configuration XML (Read XML), are gathered and stored in an output XML file (HYSYS output XML). The batch data generated from the simulation can then be used for process design or assessment of environmental performance with MC analysis.

For technical analysis of a process design, HYSYS output XML is processed by the module ‘MCM Analysis’ together with a configurable XML (Configuration XML) containing the output variables relevant for MC analysis as well as their maximum or minimum specifications (if the variable is a design specification) for graphical presentation of MC analysis results through MATLAB: histograms, PDF curves and percentage of success achieved by the sampled cases. As for environmental performance assessment, HYSYS output XML is processed by the module ‘Environmental Indicators’ together with a configurable XML (WAR general data), which is extracted from HYSYS with components, input and output streams, where the output streams are classified by the user as product or waste. This module uses the WAR algorithm data [35] to generate an XML (WAR output) containing PEI’s classified according to the eight environmental impact categories for all the samples of MC analysis. For the environmental performance assessment itself, this output XML is processed by the module ‘MCM Analysis’ in the same way as the HYSYS output XML.