Surrogate-based Optimisation of Integrative
Process Systems for Resource Recovery from Wastewater

Alex Durkin, alexander.durkin14@imperial.ac.uk

Marcos Millan-Agorio, marcos.millan@imperial.ac.uk

Miao Guo, miao.guo@imperial.ac.uk

Department of Chemical
Engineering, Imperial College London, London, SW7 2AZ

Increasing global population and
economic development, particularly in non-OECD countries, is projected to add
2.5 billion to the world’s urban population by 2050 (United Nations, Department
of Economic and Social Affairs, Population Division, 2018). This socio-economic
development will be accompanied by a rapid growth in demand for water, energy
and food (WEF) resources, whilst simultaneously increasing the production of
waste. In response to the resulting challenges (e.g. increased cost of waste
treatment and WEF resource scarcity), waste is increasingly being considered as
an alternative supply of resources.

Consequently, a paradigm shift is
underway to shift the focus of wastewater treatment plant (WWTPs) from
end-of-pipe treatment towards sustainable resource recovery facilities. Within
these wastewater streams are considerable carbon-containing and nutrient-rich
compounds which could be converted into biofuels and value-added bioproducts.
For example, oxidation of domestic wastewater organics has a maximum energy
potential of 1.93 kWh/m³, whilst the potential fossil energy
displaced by recovering fertiliser elements (P/N) is 0.79 kWh/m³ (McCarty,
Bae, & Kim, 2011).

With the interest of realising a
bioeconomy from waste, widespread technology innovation is focussing on
recovering diverse value-added bioproducts from wastewater and sludge. To
achieve maximum waste utilisation, process systems engineering (PSE) can assist
in sustainable process design and technology deployment. PSE has widespread
implementation of process design and optimisation in traditional chemical and
petroleum industries, however, PSE research in environmental engineering
processes (e.g. wastewater treatment) is comparatively lacking.

A resource recovery biorefinery can
be modelled to produce a spectrum of bio-derived products from wastewater by
integrating different technologies into a unified flowsheet design. However, a
major challenge lies in selecting an optimal combination of processes to
satisfy multiple conflicting decision criteria. This knowledge gap can be
addressed with superstructure optimisation methodology which considers a
network composed of all potential process technologies and the interconnections
between them (Henao
& Maravelias, 2011; Yeomans & Grossmann, 1999). The superstructure
flowsheet can then be optimised whilst simultaneously accounting for
conflicting objectives and various feasibility and design constraints. The
individual process units can be designed using commercial simulators, however,
the complexity of the underlying models, particularly in the case of wastewater
treatment, increases computational cost and poses challenges regarding
initialisation of decision variables and boundaries.

Surrogate models of process units can be derived to reduce computational
complexity and enable more tractable optimisation problems. By treating the
process units as “black-box” models, surrogate functions can be fit to sampled
input-output data from commercial simulators. This is particularly useful when
including biochemical technologies in the superstructure, where these processes
usually exhibit high dimensionality and model complexity. In this research,
surrogate models considered are kriging and artificial neural networks (ANNs). The
former is an interpolation method that models the underlying function as a
stochastic process and has the benefit of quantifying the uncertainty in the
surrogate model predictions. However, the requirement for the inversion of a
covariance matrix in the model formulation means high-dimensional problems can
become computationally demanding (Bhosekar
& Ierapetritou, 2018). Alternatively, ANNs can correlate multiple
input-output relationships and have a high degree of accuracy (Gonzalez-Garay
& Guillen-Gosalbez, 2018; Ibrahim, Jobson, Li, & Guillén-Gosálbez,
2018).

The modelling framework presented
in this study is shown in Figure 1. The procedure begins with selecting which
pool of technologies will be considered in the superstructure and, for each of
these technologies, which design variables will simultaneously optimised. Commercial
process simulation software, GPS-X 7.0, is coupled with MATLAB R2015b to
facilitate input-output sampling based on Sobol’ sequences, which provide good
input space coverage in a minimal number of samples (Sobol′,
2001; Zuniga, Kucherenko, & Shah, 2013). Support vector machines (SVMs) are
integrated into the sampling methodology to filter out infeasible designs,
thereby increasing sampling efficiency within the feasible design space. Kriging
and ANNs are used as surrogate models and the solutions are compared for these
different methods.

A set of optimal flowsheet
designs is identified by coupling mixed integer programming (MIP) optimisation
with adaptive sampling techniques within this framework. The MIP problem can be
solved using gradient-based solvers or direct-search algorithms (e.g. genetic
algorithms) and the results are compared in this work. The variables are
tightened around the optimal solutions and the procedure is repeated until convergence
occurs for the optimal solution as well as surrogate models. Each resulting set
of solutions provides optimal flowsheet designs for resource recovery from a
given wastewater as well as optimal process configurations to achieve the
trade-off between conflicting decision criteria. The conflicting decision
criteria are considered by multi-objective optimisation where objectives can
include economic potential and various environmental impact categories.

A case study on resource recovery
from fermentation industrial wastewater, characterised by high carbon and
nutrient concentrations, is presented in this study to demonstrate the
framework’s functionality. Different separation and conversion technologies
were considered to co-recover energy and nutrients in a flowsheet optimised by
economic and environmental decision criteria. Overall, we demonstrate that
process systems engineering insights can be effectively implemented to the
topic of resource recovery. A computational framework is presented for
modelling optimal flowsheets for recovery resources from wastewater. Such a
framework ultimately assesses process viability within an integrated flowsheet,
under multiple design criteria, therefore assisting in resource recovery
technology deployment.

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