A multi-objective genetic algorithm for the design of pressure swing adsorption

Pressure Swing Adsorption (PSA) is a cyclic separation process, more advantageous over other separation options for middle scale processes. Automated tools for the design of PSA processes would be beneficial for the development of the technology, but their development is a difficult task due to the complexity of the simulation of PSA cycles and the computational effort needed to detect the performance at cyclic steady state. We present a preliminary investigation of the performance of a custom multi-objective genetic algorithm (MOGA) for the optimisation of a fast cycle PSA operation, the separation of air for N2 production. The simulation requires a detailed diffusion model, which involves coupled nonlinear partial differential and algebraic equations (PDAEs). The efficiency of MOGA to handle this complex problem has been assessed by comparison with direct search methods. An analysis of the effect of MOGA parameters on the performance is also presented

A multi-criteria design framework for the synthesis of complex pressure swing adsorption cycles for CO2 capture

Pressure Swing Adsorption (PSA) is the most efficient option for middle scale separation processes. PSA is a cyclic process whose main steps are adsorption, at high pressure, and regeneration of the adsorbent, at low pressure. The design of PSA cycles is still mainly approached experimentally due to the computational challenges posed by the complexity of the simulation and by the need to detect the performance at cyclic steady state (CSS). Automated tools for the design of PSA processes are desirable to allow a better understanding of the the complex relationship between the performance and the design variables. Furthermore, the operation is characterised by trade-o�ffs between conflicting criteria. A multi-objective flowsheet design framework for complex PSA cycles is presented. A suite of evolutionary procedures, for the generation of alternative PSA con�figurations has been developed, including simple evolution, simulated annealing as well as a population based procedure. Within this evolutionary procedure the evaluation of each cycle confi�guration generated requires the solution of a multi-objective optimisation problem which considers the conflicting objectives of recovery and purity. For this embedded optimisation problem a multi-objective genetic algorithm (MOGA), with a targeted fi�tness function, is used to generate the approximation to the Pareto front. The evaluation of each alternative design makes use of a number of techniques to reduce the computational burden. The case studies considered include the separation of air for N2 production, a fast cycle operation which requires a detailed di�ffusion model, and the separation of CO2 from flue gases, where complex cycles are needed to achieve a high purity product. The novel design framework is able to determine optimal configurations and operating conditions for PSA for these industrially relevant case studies. The results presented by the design framework can help an engineer to make informed design decisions

Direct current (DC) resistivity and Induced Polarization (IP) monitoring of active layer dynamics at high temporal resolution

With permafrost thawing and changes in active layer dynamics induced by climate change, interactions between biogeochemical and thermal processes in the ground are of great importance. Here, active layer dynamics have been monitored using direct current (DC) resistivity and induced polarization (IP) measurements at high temporal resolution and at a relatively large scale at a heath tundra site on Disko Island on the west coast of Greenland (69 degrees N). At the field site, the active layer is disconnected from the deeper permafrost, due to isothermal springs in the region. Borehole sediment characteristics and subsurface temperatures supplemented the DC-IF measurements. A time-lapse DC-IP monitoring system has been acquiring at least six datasets per day on a 42-electrode profile with 0.5 m electrode spacing since July 2013. Remote control of the data acquisition system enables interactive adaptation of the measurement schedule, which is critically important to acquire data in the winter months, where extremely high contact resistances increase the demands on the resistivity meter. Data acquired during the freezing period of October 2013 to February 2014 clearly image the soil freezing as a strong increase in resistivity. While the freezing horizon generally moves deeper with time, some variations in the freezing depth are observed along the profile. Comparison with depth-specific soil temperature indicates an exponential relationship between resistivity and below-freezing temperature. Time-lapse inversions of the full-decay IF data indicate a decrease of normalized chargeability with freezing of the ground, which is the result of a decrease in the total unfrozen water and of the higher ion concentration in the pore-water. We conclude that DC-IP time-lapse measurements can non-intrusively and reliably image freezing patterns and their lateral variation on a 10-100 m scale that is difficult to sample by point measurements. In combination with laboratory experiments, the different patterns in resistivity and chargeability changes will enable the disentanglement of processes (e.g., fluid migration and freezing, advective and diffusive heat transport) occurring during freezing of the ground. The technology can be expanded to three dimensions and also to larger scale

Re-parameterisations of the Cole-Cole model for improved spectral inversion of induced polarization data

The induced polarization phenomenon, both in time domain and frequency domain, is often parameterised using the empirical Cole-Cole model. To improve the resolution of model parameters and to decrease the parameter correlations in the inversion process of induced polarization data, we suggest here three re-parameterisations of the Cole-Cole model, namely the maximum phase angle Cole-Cole model, the maximum imaginary conductivity Cole-Cole model, and the minimum imaginary resistivity Cole-Cole model. The maximum phase angle Cole-Cole model uses the maximum phase \u3c6max and the inverse of the phase peak frequency, \u3c4\u3c6, instead of the intrinsic charge-ability m0 and the time constant adopted in the classic Cole-Cole model. The maximum imaginary conductivity Cole-Cole model uses the maximum imaginary conductivity \u3c3max\u2033 instead of m0 and the time constant \u3c4\u3c3 of the Cole-Cole model in its conductivity form. The minimum imaginary resistivity Cole-Cole model uses the minimum imaginary resistivity \u3c1min\u2033 instead of m0 and the time constant \u3c4\u3c1 of the Cole-Cole model in its resistivity form. The effects of the three re-parameterisations have been tested on synthetic timedomain and frequency-domain data using a Markov chain Monte Carlo inversion method, which allows for easy quantification of parameter uncertainty, and on field data using 2D gradient-based inversion. In comparison with the classic Cole-Cole model, it was found that for all the three re-parameterisations, the model parameters are less correlated with each other and, consequently, better resolved for both time-domain and frequency-domain data. The increase in model resolution is particularly significant for models that are poorly resolved using the classic Cole-Cole parameterisation, for instance, for low values of the frequency exponent or with low signal-to-noise ratio. In general, this leads to a significantly deeper depth of investigation for the \u3c6max, \u3c3max\u2033, and \u3c1min\u2033 parameters, when compared with the classic m0 parameter, which is shown with a field example. We believe that the use of reparameterisations for inverting field data will contribute to narrow the gap between induced polarization theory, laboratory findings, and field applications

A Mathematical Study of the Influence of Hypoxia and Acidity on the Evolutionary Dynamics of Cancer

Hypoxia and acidity act as environmental stressors promoting selection for cancer cells with a more aggressive phenotype. As a result, a deeper theoretical understanding of the spatio-temporal processes that drive the adaptation of tumour cells to hypoxic and acidic microenvironments may open up new avenues of research in oncology and cancer treatment. We present a mathematical model to study the influence of hypoxia and acidity on the evolutionary dynamics of cancer cells in vascularised tumours. The model is formulated as a system of partial integro-differential equations that describe the phenotypic evolution of cancer cells in response to dynamic variations in the spatial distribution of three abiotic factors that are key players in tumour metabolism: oxygen, glucose and lactate. The results of numerical simulations of a calibrated version of the model based on real data recapitulate the eco-evolutionary spatial dynamics of tumour cells and their adaptation to hypoxic and acidic microenvironments. Moreover, such results demonstrate how nonlinear interactions between tumour cells and abiotic factors can lead to the formation of environmental gradients which select for cells with phenotypic characteristics that vary with distance from intra-tumour blood vessels, thus promoting the emergence of intra-tumour phenotypic heterogeneity. Finally, our theoretical findings reconcile the conclusions of earlier studies by showing that the order in which resistance to hypoxia and resistance to acidity arise in tumours depend on the ways in which oxygen and lactate act as environmental stressors in the evolutionary dynamics of cancer cells

Comparison of stabiliser functions for surface NMR inversions

Surface nuclear magnetic resonance is a geophysical technique providing non-invasive aquifer characterization. Two approaches are commonly used to invert surface nuclear magnetic resonance data: (1) inversions involving many depth layers of fixed thickness and (2) few-layer inversions without predetermined layer thicknesses. The advantage of the many-layer approach is that it requires little a priori knowledge. However, the many-layer inversion is extremely ill-posed and regularisation must be used to produce a reliable result. For optimal performance, the selected regularisation scheme must reflect all available a priori information. The standard regularisation scheme for many-layer surface nuclear magnetic resonance inversions employs an L-2 smoothness stabiliser, which results in subsurface models with smoothly varying parameters. Such a stabiliser struggles to reproduce sharp contrasts in subsurface properties, like those present in a layered subsurface (a common near-surface hydrogeological environment). To investigate if alternative stabilisers can be used to improve the performance of the many-layer inversion in layered environments, the performance of the standard smoothness stabiliser is compared against two alternative stabilisers: (1) a stabiliser employing the L-1-norm and (2) a minimum gradient support stabiliser. Synthetic results are presented to compare the performance of the many-layer inversion for different stabiliser functions. The minimum gradient support stabiliser is observed to improve the performance of the many-layer inversion for a layered subsurface, being able to reproduce both smooth and sharp vertical variations of the model parameters. Implementation of the alternative stabilisers into existing surface nuclear magnetic resonance inversion software is straightforward and requires little modification to existing codes

Increasing the resolution and the signal-to-noise ratio of magnetic resonance sounding data using a central loop configuration

Surface nuclear magnetic resonance technique, also called magnetic resonance sounding (MRS), is an emerging geophysical method that can detect the presence and spatial variations of the subsurface water content directly. In this paper, we introduce the MRS central loop geometry, in which the receiver loop is smaller than the transmitter loop and placed in its centre. In addition, using a shielded receiver coil we show how this configuration greatly increases signal-to-noise ratio and improves the resolution of the subsurface layers compared to the typically used coincident loop configuration. We compare sensitivity kernels for different loop configurations and describe advantages of the MRS central loop geometry in terms of superior behaviour of the sensitivity function, increased sensitivity values, reduced noise level of the shielded receiver coil, improved resolution matrix and reduced instrument dead time. With no extra time and effort in the field, central-loop MRS makes it possible to reduce measurement time and to measure data in areas with high anthropogenic noise. The results of our field example agree well with the complementary data, namely airborne electromagnetics, borehole data, and the hydrologic model of the area

Sequential and joint hydrogeophysical inversion using a field-scale groundwater model with ERT and TDEM data

Increasingly, ground-based and airborne geophysical data sets are used to inform groundwater models. Recent research focuses on establishing coupling relationships between geophysical and groundwater parameters. To fully exploit such information, this paper presents and compares different hydrogeophysical inversion approaches to inform a field-scale groundwater model with time domain electromagnetic (TDEM) and electrical resistivity tomography (ERT) data. In a sequential hydrogeophysical inversion (SHI) a groundwater model is calibrated with geophysical data by coupling groundwater model parameters with the inverted geophysical models. We subsequently compare the SHI with a joint hydrogeophysical inversion (JHI). In the JHI, a geophysical model is simultaneously inverted with a groundwater model by coupling the groundwater and geophysical parameters to explicitly account for an established petrophysical relationship and its accuracy. Simulations for a synthetic groundwater model and TDEM data showed improved estimates for groundwater model parameters that were coupled to relatively well-resolved geophysical parameters when employing a high-quality petrophysical relationship. Compared to a SHI these improvements were insignificant and geophysical parameter estimates became slightly worse. When employing a low-quality petrophysical relationship, groundwater model parameters improved less for both the SHI and JHI, where the SHI performed relatively better. When comparing a SHI and JHI for a real-world groundwater model and ERT data, differences in parameter estimates were small. For both cases investigated in this paper, the SHI seems favorable, taking into account parameter error, data fit and the complexity of implementing a JHI in combination with its larger computational burden

Efficient full decay inversion of MRS data with a stretched-exponential approximation of the distribution

We present a new, efficient and accurate forward modelling and inversion scheme for magnetic resonance sounding (MRS) data. MRS, also called surface-nuclear magnetic resonance (surface-NMR), is the only non-invasive geophysical technique that directly detects free water in the subsurface. Based on the physical principle of NMR, protons of the water molecules in the subsurface are excited at a specific frequency, and the superposition of signals from all protons within the excited earth volume is measured to estimate the subsurface water content and other hydrological parameters. In this paper, a new inversion scheme is presented in which the entire data set is used, and multi-exponential behaviour of the NMR signal is approximated by the simple stretched-exponential approach. Compared to the mono-exponential interpretation of the decaying NMR signal, we introduce a single extra parameter, the stretching exponent, which helps describe the porosity in terms of a single relaxation time parameter, and helps to determine correct initial amplitude and relaxation time of the signal. Moreover, compared to a multi-exponential interpretation of the MRS data, the decay behaviour is approximated with considerably fewer parameters. The forward response is calculated in an efficient numerical manner in terms of magnetic field calculation, discretization and integration schemes, which allows fast computation while maintaining accuracy. A piecewise linear transmitter loop is considered for electromagnetic modelling of conductivities in the layered half-space providing electromagnetic modelling of arbitrary loop shapes. The decaying signal is integrated over time windows, called gates, which increases the signal-to-noise ratio, particularly at late times, and the data vector is described with a minimum number of samples, that is, gates. The accuracy of the forward response is investigated by comparing a MRS forward response with responses from three other approaches outlining significant differences between the three approaches. All together, a full MRS forward response is calculated in about 20 s and scales so that on 10 processors the calculation time is reduced to about 34 s. The proposed approach is examined through synthetic data and through a field example, which demonstrate the capability of the scheme. The results of the field example agree well the information from an in-site borehole

Understanding the impact of constraints: A rank based fitness function for evolutionary methods

There are design problems where some constraints may be considered objectives as in “It would be great if the solution we obtained had this characteristic.” In such problems, solutions obtained using multi-objective optimisation may help the decision maker gain insight into what is achievable without fully satisfying one of these constraints. A novel fitness function is introduced into a multi-objective population based evolutionary optimisation method, based on a plant propagation algorithm extended to multi-objective optimisation. The optimisation method is implemented and applied to the design of off-grid integrated energy systems for large scale mining operations where the aim is to use local renewable energy generation, coupled with energy storage, to eliminate the need for transporting fuel over large distances. The latter is a desired property and in this chapter is treated as a separate objective. The results presented show that the fitness function provides the desired selection pressure and, when combined with the multi-objective plant propagation algorithm, is able to find good designs that achieve the desired constraint simultaneously