Mateusz Budnik

Yannis

Yannis Avrithis

Asymmetric metric learning for knowledge transfer

come

Introduction

Originating in metric learning, loss functions based on pairwise distances or similarities [START_REF] Hadsell | Dimensionality reduction by learning an invariant mapping[END_REF][START_REF] Wang | Learning fine-grained image similarity with deep ranking[END_REF][START_REF] Song | Deep metric learning via lifted structured feature embedding[END_REF][START_REF] Wang | Multi-similarity loss with general pair weighting for deep metric learning[END_REF][START_REF] Cakir | Deep metric learning to rank[END_REF] are paramount in representation learning. Their power is most notable in category-level tasks where classes at inference are different than classes at learning, for instance fine-grained classification [START_REF] Song | Deep metric learning via lifted structured feature embedding[END_REF][START_REF] Wang | Multi-similarity loss with general pair weighting for deep metric learning[END_REF], few-shot learning [START_REF] Vinyals | Matching networks for one shot learning[END_REF][START_REF] Snell | Prototypical networks for few-shot learning[END_REF] local descriptor learning [START_REF] Han | MatchNet: Unifying feature and metric learning for patch-based matching[END_REF] and instance-level retrieval [START_REF] Gordo | Deep image retrieval: Learning global representations for image search[END_REF][START_REF] Radenović | CNN image retrieval learns from bow: Unsupervised fine-tuning with hard examples[END_REF]. There are different ways to use them without supervision [START_REF] Iscen | Mining on manifolds: Metric learning without labels[END_REF][START_REF] Ye | Unsupervised embedding learning via invariant and spreading instance feature[END_REF][START_REF] Cao | Unsupervised deep metric learning via auxiliary rotation loss[END_REF] and indeed, they form the basis for modern 1 https://github.com/budnikm/aml 2 This work was supported by Conseil Régional de Bretagne and Rennes Métropole (Images & Réseaux AAP-PME-2017 grant MobilAI). It was performed using HPC resources of GENCI-IDRIS (Grant 2019-AD011011245).

unsupervised representation learning [START_REF] Misra | Self-supervised learning of pretext-invariant representations[END_REF][START_REF] He | Momentum contrast for unsupervised visual representation learning[END_REF][START_REF] Chen | A simple framework for contrastive learning of visual representations[END_REF].

Powerful representations come traditionally with powerful network models [START_REF] He | Deep residual learning for image recognition[END_REF][START_REF] Huang | Densely connected convolutional networks[END_REF], which are expensive. The search for resource-efficient architectures has lead to the design of lightweight networks for mobile devices [START_REF] Andrew G Howard | MobileNets: Efficient convolutional neural networks for mobile vision applications[END_REF][START_REF] Sandler | Mobilenetv2: Inverted residuals and linear bottlenecks[END_REF][START_REF] Zhang | ShuffleNet: An extremely efficient convolutional neural network for mobile devices[END_REF], neural architecture search [START_REF] Pham | Efficient neural architecture search via parameter sharing[END_REF][START_REF] Liu | DARTS: Differentiable architecture search[END_REF] and model scaling [START_REF] Tan | EfficientNet: Rethinking model scaling for convolutional neural networks[END_REF]. Training of small networks may be facilitated by knowledge transfer from larger networks [START_REF] Hinton | Distilling the knowledge in a neural network[END_REF]. However, both network design and knowledge transfer are commonly performed on classification tasks, using standard cross-entropy.

Focusing on fine-grained classification and retrieval, several recent methods have extended metric learning loss functions to allow for knowledge transfer from teacher to student models [START_REF] Chen | Dark-Rank: Accelerating deep metric learning via cross sample similarities transfer[END_REF][START_REF] Kim | Deep metric learning beyond binary supervision[END_REF][START_REF] Yu | Learning metrics from teachers: Compact networks for image embedding[END_REF][START_REF] Park | Relational knowledge distillation[END_REF]. However, two questions are in order: (a) since transferring a representation from one model to another is inherently a continuous task, can't we just use regression? (b) apart from knowledge transfer, is the original metric learning task still relevant and what is a simple way to combine the two?

In this work, we focus on the task of instance-level image retrieval [START_REF] Philbin | Object retrieval with large vocabularies and fast spatial matching[END_REF][START_REF] Radenović | Revisiting oxford and paris: Large-scale image retrieval benchmarking[END_REF], which is at the core of metric learning in the sense of using pairwise distances or similarities. In its most well-known form [START_REF] Gordo | Deep image retrieval: Learning global representations for image search[END_REF][START_REF] Radenović | CNN image retrieval learns from bow: Unsupervised fine-tuning with hard examples[END_REF], the task is supervised, but the supervision is originating from automated data analysis rather than humans. As such, apart from noisy, supervision is often incomplete, in the sense that although class labels per example may exist, not all pairs of examples of the same class are labeled. Hence, one has to work with pairs rather than examples, unlike e.g. face recognition [START_REF] Deng | ArcFace: Additive angular margin loss for deep face recognition[END_REF].

Our work is motivated by the scenario where a database (gallery) of images is represented and indexed according to a large model, while queries are captured from mobile devices, where a smaller model is the only option. In such scenario, rather than re-indexing the entire database, it is preferable to adapt different smaller models for different end-user devices. In this case, knowledge transfer from the large (teacher) to the small (student) model is not just helping, but the student should really learn to map inputs to the same representation space. We call this task asymmetric testing.

More importantly, even if we consider the standard symmetric testing task, where both queries and database examples are represented by the same model at inference, we 1 introduce a novel paradigm of using asymmetric representations at training, as a knowledge transfer mechanism. We call this paradigm asymmetric metric learning. By representing anchors by the student and positives/negatives by the teacher, one can apply any metric learning loss function. This achieves both metric learning and knowledge transfer, without resorting to a linear combination of two loss functions.

In summary, we make the following contributions:

• We study the problem of knowledge transfer from a teacher to a student model for the first time in pairbased metric learning for instance-level image retrieval.

• In this context, we study the asymmetric testing task, where the database is represented by the teacher and queries by the student.

• In both symmetric and asymmetric testing, we systematically evaluate different teacher and student models, metric learning loss functions (subsection 3.3) and knowledge transfer loss functions (subsection 3.4), serving as a benchmark for future work.

• We introduce the asymmetric metric learning paradigm, an extremely simple mechanism to combine metric learning with knowledge transfer (subsection 3.2).

Related work

Metric learning Historically, metric learning is about unsupervised learning of embeddings according to a pairwise distances [START_REF] Tenenbaum | Mapping a manifold of perceptual observations[END_REF] or similarities [START_REF] Schölkopf | Nonlinear component analysis as a kernel eigenvalue problem[END_REF][START_REF] Belkin | Laplacian eigenmaps for dimensionality reduction and data representation[END_REF]. Modern deep metric learning is mostly supervised, with pair labels specifying a set of positive and negative examples per anchor example [START_REF] Xing | Distance metric learning with application to clustering with side-information[END_REF]. Standard loss functions are contrastive [START_REF] Hadsell | Dimensionality reduction by learning an invariant mapping[END_REF] and triplet [START_REF] Xing | Distance metric learning with application to clustering with side-information[END_REF][START_REF] Wang | Learning fine-grained image similarity with deep ranking[END_REF], operating on one or two pairs, respectively.

Global loss functions rather operate on an arbitrary number of pairs [START_REF] Song | Deep metric learning via lifted structured feature embedding[END_REF][START_REF] Wang | Multi-similarity loss with general pair weighting for deep metric learning[END_REF][START_REF] Cakir | Deep metric learning to rank[END_REF], similarly to learning to rank [START_REF] Cao | Learning to rank: From pairwise approach to listwise approach[END_REF][START_REF] Xia | Listwise approach to learning to rank: theory and algorithm[END_REF]. The large number of potential tuples gives rise to mining [START_REF] Harwood | Smart mining for deep metric learning[END_REF][START_REF] Chao-Yuan Wu | Sampling matters in deep embedding learning[END_REF] and memory [START_REF] Wang | Cross-batch memory for embedding learning[END_REF][START_REF] Wu | Improving generalization via scalable neighborhood component analysis[END_REF] mechanisms. At the other extreme, extensions of cross-entropy operate on single examples [START_REF] Wang | CosFace: Large margin cosine loss for deep face recognition[END_REF][START_REF] Deng | ArcFace: Additive angular margin loss for deep face recognition[END_REF]. We focus on pair-based functions in this work, due to the nature of the ground truth [START_REF] Radenović | CNN image retrieval learns from bow: Unsupervised fine-tuning with hard examples[END_REF][START_REF] Radenović | Finetuning CNN image retrieval with no human annotation[END_REF]. Unsupervised metric learning is gaining momentum [START_REF] Iscen | Mining on manifolds: Metric learning without labels[END_REF][START_REF] Ye | Unsupervised embedding learning via invariant and spreading instance feature[END_REF][START_REF] Cao | Unsupervised deep metric learning via auxiliary rotation loss[END_REF]], but we focus on the supervised case, given that it requires no human effort [START_REF] Radenović | CNN image retrieval learns from bow: Unsupervised fine-tuning with hard examples[END_REF][START_REF] Gordo | Deep image retrieval: Learning global representations for image search[END_REF].

Image retrieval Instance-level image retrieval, either using local features [START_REF] Tolias | To aggregate or not to aggregate: Selective match kernels for image search[END_REF] or global pooling [START_REF] Jégou | Triangulation embedding and democratic kernels for image search[END_REF], has relied on SIFT descriptors [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF] for more than a decade. Convolutional networks quickly outperformed shallow representations, using different pooling mechanisms [START_REF] Sharif Razavian | Visual instance retrieval with deep convolutional networks[END_REF][START_REF] Tolias | Particular object retrieval with integral max-pooling of cnn activations[END_REF] and fine-tuning on relevant datasets, initially with cross-entropy on noisy labels from the web [START_REF] Babenko | Neural codes for image retrieval[END_REF] and then with contrastive [START_REF] Radenović | CNN image retrieval learns from bow: Unsupervised fine-tuning with hard examples[END_REF] and triplet [START_REF] Gordo | Deep image retrieval: Learning global representations for image search[END_REF] loss on labels generated from the visual data alone. While the best performance comes from large networks [START_REF] He | Deep residual learning for image recognition[END_REF][START_REF] Radenović | Revisiting oxford and paris: Large-scale image retrieval benchmarking[END_REF], we focus on small networks [START_REF] Sandler | Mobilenetv2: Inverted residuals and linear bottlenecks[END_REF][START_REF] Tan | EfficientNet: Rethinking model scaling for convolutional neural networks[END_REF] for the first time. Our asymmetric test scenario is equivalent to that of prior studies [START_REF] Hu | Towards visual feature translation[END_REF][START_REF] Shen | Towards backward-compatible representation learning[END_REF], but with different motivation and settings. Feature translation [START_REF] Hu | Towards visual feature translation[END_REF] is meant for retrieval system interoperability, so both networks may be large and none is adapted. The recent backward-compatible training (BCT) [START_REF] Shen | Towards backward-compatible representation learning[END_REF] is meant to avoid re-indexing of the database like here, but the new model used for queries is actually more powerful than the old one used for the database, or trained on more data.

Small networks While large networks [START_REF] He | Deep residual learning for image recognition[END_REF][START_REF] Huang | Densely connected convolutional networks[END_REF] excel in performance, they are expensive. One solution is to compress existing architectures, e.g. by quantization [START_REF] Gong | Compressing deep convolutional networks using vector quantization[END_REF] or pruning [START_REF] Liu | Rethinking the value of network pruning[END_REF]. Another is to manually design more efficient networks, e.g. by using bottlenecks [START_REF] Forrest N Iandola | Squeezenet: Alexnet-level accuracy with 50x fewer parameters and <0.5 mb model size[END_REF], separable convolutions [START_REF] Andrew G Howard | MobileNets: Efficient convolutional neural networks for mobile vision applications[END_REF], inverted residuals [START_REF] Sandler | Mobilenetv2: Inverted residuals and linear bottlenecks[END_REF] or point-wise group convolutions [START_REF] Zhang | ShuffleNet: An extremely efficient convolutional neural network for mobile devices[END_REF]. MobileNetV2 [START_REF] Sandler | Mobilenetv2: Inverted residuals and linear bottlenecks[END_REF] is such a network that we use as a student in this work. More recently, neural architecture search [START_REF] Pham | Efficient neural architecture search via parameter sharing[END_REF][START_REF] Liu | DARTS: Differentiable architecture search[END_REF][START_REF] Tan | MnasNet: Platform-aware neural architecture search for mobile[END_REF][START_REF] Howard | Searching for Mo-bileNetV3[END_REF] is making this process automatic, although expensive. Alternatively, a small model can first be designed (or learned) and then its architecture scaled by adding depth [START_REF] He | Deep residual learning for image recognition[END_REF], width [START_REF] Zagoruyko | Wide residual networks[END_REF], resolution [START_REF] Huang | GPipe: Efficient training of giant neural networks using pipeline parallelism[END_REF] or a compound of the above [START_REF] Tan | EfficientNet: Rethinking model scaling for convolutional neural networks[END_REF]. We use the latter as another student in this work. We show that pruning [START_REF] Wang | Progressive local filter pruning for image retrieval acceleration[END_REF] cannot compete designed or learned architectures.

Knowledge transfer Rather than training a small network directly, it is easier to optimize the same small network (student) to mimic a larger one (teacher), essentially transferring knowledge from the teacher to the student. In classification, this can be done e.g. by regression of the logits [START_REF] Ba | Do deep nets really need to be deep?[END_REF] or by cross-entropy on soft targets, known as knowledge distillation [START_REF] Hinton | Distilling the knowledge in a neural network[END_REF]. BCT [START_REF] Shen | Towards backward-compatible representation learning[END_REF] fixes the classifier (last layer) of the student to that of the teacher, similarly to [START_REF] Hoffer | Fix your classifier: the marginal value of training the last weight layer[END_REF]. Such ideas do not apply in this work, since there is no parametric classifier. Metric learning is mostly about pairs rather than individual examples, and indeed recent knowledge transfer methods are based on pairwise distances or similarities. This includes e.g. learning to rank [START_REF] Chen | Dark-Rank: Accelerating deep metric learning via cross sample similarities transfer[END_REF] and regression on quantities involving one or more pairs like distances [START_REF] Yu | Learning metrics from teachers: Compact networks for image embedding[END_REF][START_REF] Park | Relational knowledge distillation[END_REF], log-ratio of distances [START_REF] Kim | Deep metric learning beyond binary supervision[END_REF], or angles [START_REF] Park | Relational knowledge distillation[END_REF]. The most general form is relational knowledge distillation (RKD) [START_REF] Park | Relational knowledge distillation[END_REF]. Direct regression on features is either not considered or shown inferior [START_REF] Yu | Learning metrics from teachers: Compact networks for image embedding[END_REF], but we show it is much more effective than previously thought. We also show that the original metric learning task is still beneficial when training the student and we combine with knowledge transfer in a simple way.

Asymmetry Asymmetric distances or similarities are common in approximate nearest neighbor search, where queries may be quantized differently than the database, or not at , , : anchor, positive, negative (student). , , : anchor, positive, negative (teacher). f θ : student (with parameters θ). g: teacher (fixed).

, : distance measurements. , : attraction, repulsion (mutual). , : attraction, repulsion (unilateral). all [START_REF] Dong | Asymmetric distance estimation with sketches for similarity search in highdimensional spaces[END_REF][START_REF] Gordo | Asymmetric distances for binary embeddings[END_REF][START_REF] Jégou | Product quantization for nearest neighbor search[END_REF][START_REF] Jain | Asymmetric hamming embedding[END_REF][START_REF] Behnam Neyshabur | The power of asymmetry in binary hashing[END_REF][START_REF] Davis | Asymmetric sparse kernel approximations for large-scale visual search[END_REF]. In image retrieval, there are efforts to reduce the asymmetry of k-nearest neighbor relations [START_REF] Jégou | A contextual dissimilarity measure for accurate and efficient image search[END_REF], or use asymmetry to mitigate the effect of quantization [START_REF] Jégou | Improving bag-offeatures for large scale image search[END_REF], or handle partial similarity [START_REF] Zhu | Queryadaptive asymmetrical dissimilarities for visual object retrieval[END_REF] or alignment [START_REF] Tolias | Asymmetric feature maps with application to sketch based retrieval[END_REF]. In classification, it is common to use asymmetric image-to-class distances [START_REF] Boiman | In defense of nearest-neighbor based image classification[END_REF] or region-to-image matching [START_REF] Kim | Asymmetric region-toimage matching for comparing images with generic object categories[END_REF]. In metric learning, asymmetry has been used in sample weighting [START_REF] Liao | Efficient PSD constrained asymmetric metric learning for person re-identification[END_REF], different mappings per view [START_REF] Yu | Crossview asymmetric metric learning for unsupervised person re-identification[END_REF], or hard example mining [START_REF] Xu | Deep asymmetric metric learning via rich relationship mining[END_REF]. Asymmetric similarities are used between cross-modal embeddings [START_REF] Frome | Devise: A deep visual-semantic embedding model[END_REF][START_REF] Kiros | Unifying visual-semantic embeddings with multimodal neural language models[END_REF][START_REF] Faghri | VSE++: Improving visual-semantic embeddings with hard negatives[END_REF], but not for knowledge transfer. They are also used over the same modality to adjust embeddings to a memory bank [START_REF] He | Momentum contrast for unsupervised visual representation learning[END_REF] or to treat a set of examples as a whole [START_REF] Vinyals | Matching networks for one shot learning[END_REF], but again not for knowledge transfer.

f θ (a) f θ (p) f θ (n) g(a) g(p) g(n) f θ (a) f θ (p) f θ (n) g(a) g(p) g(n) f θ (a) f θ (p) f θ (n) g(a) g(p) g(n) f θ (a) f θ (p) f θ (n) g(a) g(p) g(n) (a)

Asymmetric metric learning

Preliminaries

Let X ⊂ X be a training set, where X is an input space. Two sources of supervision are considered. The first is a set of labels: a subset of all pairs of examples in X is labeled as positive or negative and the remaining are unlabeled. Formally, for each anchor a ∈ X, a set P (a) ⊂ X of positive and a set N (a) ⊂ X of negative examples are given. The second is a teacher model g : X → R d , mapping input examples to a feature (embedding) space of dimensionality d. The objective is to learn the parameters θ of a student model f θ : X → R d , such that anchors are closer to positives than negatives, the teacher and student agree in some sense, or both. When labels are not used, an additional set of examples U (a) may be used for each anchor a, e.g. a neighborhood of a space or the entire set X \ {a}. The teacher is assumed to have been trained on X using labels only.

Training amounts to minimizing the error function

J(X; θ) := a∈X (a; θ) (1)
with respect to parameters θ over X. There is one loss term per anchor a ∈ X, which however may depend on any other example in X; hence, J is not additive in X. The loss function may depend on the labels or the teacher only, discussed respectively in subsection 3.3 and subsection 3.4; it may depend on the teacher indirectly via a similarity function, as discussed in subsection 3.2. At inference, a test set Z ⊂ X and a set of queries Q ⊂ X are given, both disjoint from X. For each query q ∈ Q, a set P (q) ⊂ Z of positive examples is given. Symmetric testing is the task of ranking positive examples P (q) before all others in Z by descending similarity to q in the student space, for each query q ∈ Q. Asymmetric testing is the same, except that similarities are between queries in the student space and test examples in the teacher space.

Asymmetric similarity

We use cosine similarity in this work:

sim(v, v ) := v, v /( v v ) for v, v ∈ R d .
The symmetric similarity s sym θ (a, x) between an anchor a ∈ X and a positive or negative example x ∈ P (a) ∪ N (a) is obtained by representing both in the feature space of the student:

s sym θ (a, x) := sim(f θ (a), f θ (x)).
(

) 2
This is the standard setting in related work in metric learning. By contrast, we introduce the asymmetric similarity s asym θ (a, x), where the anchor a is represented by the stu-dent, while positive and negative examples x are represented by the teacher:

s asym θ (a, x) := sim(f θ (a), g(x)). (3)
In this setting, g(x) is fixed for all x ∈ X, because the teacher is fixed. Figure 1 illustrates the idea. When used with loss functions discussed in subsection 3.3, (3) (Figure 1(d)) uses both the labels and the teacher, essentially combining metric learning and knowledge transfer. With the same loss functions, (2) (Figure 1(a)) uses the labels only, focusing on metric learning only. Instead, as discussed in subsection 3.4, relational distillation [START_REF] Yu | Learning metrics from teachers: Compact networks for image embedding[END_REF][START_REF] Park | Relational knowledge distillation[END_REF] uses the teacher only, focusing on knowledge transfer only (Figure 1(b,c)). In practice, these other solutions require a linear combination of two error functions for metric learning and knowledge transfer.

Loss functions using labels

When using the labels, we have access to positive and negative examples P (a) and N (a) per anchor a. The teacher g may be used in addition to labels or not by using the asymmetric (3) or symmetric (2) similarity, respectively. We write either as s θ (a, x) below.

Contrastive The contrastive loss [START_REF] Hadsell | Dimensionality reduction by learning an invariant mapping[END_REF] encourages independently positive examples p to be close to the anchor a and negative examples n farther from a by margin m in the student space:

C (a; θ) := n∈N (a) [s θ (a, n) -m] + - p∈P (a)
s θ (a, p). (4)

Triplet The triplet loss [START_REF] Wang | Learning fine-grained image similarity with deep ranking[END_REF] encourages positive examples p to be closer to the anchor a than negative examples n by margin m in the student space:

T (a; θ) := (p,n)∈L(a) [s θ (a, n) -s θ (a, p) + m] + , (5)
where typically L(a) := P (a)×N (a). Positive and negative examples are not used independently: if similarities are ranked correctly, the corresponding loss term is zero.

Multi-similarity

The multi-similarity loss [START_REF] Wang | Multi-similarity loss with general pair weighting for deep metric learning[END_REF] treats positives and negatives independently:

MS (a; θ) := 1 α log   1 + p∈P (a)
e -α(s θ (a,p)-m)

  + 1 β log   1 + n∈N (a) e β(s θ (a,n)-m)   . (6)
Here, multiple examples are taken into account together by a nonlinear function: positives (negatives) that are farthest from (nearest to) the anchor receive the greatest relative weight.

Loss functions using the teacher only

When not using the labels, the only source of supervision is the teacher model g. Symmetric similarity (2) is not an option here; we either use use [START_REF] Belkin | Laplacian eigenmaps for dimensionality reduction and data representation[END_REF] or other ways to compare the two models. Given anchor a, the loss may depend on a alone, or also the additional examples U (a). We write S(a, x) := sim(g(a), g(x)) for the similarity of a and some x ∈ U (a) in the teacher space.

Regression The simplest option is regression, encouraging the representations of the same input example a by the two models to be close by using asymmetric similarity (3): R (a; θ) := -s asym θ (a, a) = -sim(f θ (a), g(a)). [START_REF] Cao | Learning to rank: From pairwise approach to listwise approach[END_REF] For each anchor, it does not depend on any other example. It is the same as the absolute version of metric learning knowledge distillation (ML+KD) [START_REF] Yu | Learning metrics from teachers: Compact networks for image embedding[END_REF] and as contrastive loss (4) on asymmetric similarity (3) (using only the anchor as a positive for itself ).

Relational distillation Given an anchor a and one or more other vectors x, . . . ∈ R d , relational knowledge distillation (RKD) [START_REF] Park | Relational knowledge distillation[END_REF] is based on a number of relational measurements ψ(a, x, . . . ). One such ψ(a, x, . . . ) is the distance ax for x ∈ R d . Another is the angle sim(a -x, ay) formed by a, x, y, for x, y ∈ R d . The loss is called distance-wise and angle-wise, respectively. The RKD loss encourages the same measurements by both models, RKD (a; θ) := (x,... )∈U (a) n r(ψ(f θ (a), f θ (x), . . . ), ψ(g(a), g(x), . . . )), [START_REF] Chen | A simple framework for contrastive learning of visual representations[END_REF] where n is e.g. 1 for distance and 2 for angle and r is a regression loss, taken as Huber [START_REF] Park | Relational knowledge distillation[END_REF]. RKD encompasses regression by ψ taken as the identity mapping on the anchor feature alone and r taken as -sim. It also encompasses the relative setting of ML+KD [START_REF] Yu | Learning metrics from teachers: Compact networks for image embedding[END_REF] by ψ(a, x) := ax and the direct match baseline of DarkRank [START_REF] Chen | Dark-Rank: Accelerating deep metric learning via cross sample similarities transfer[END_REF] by ψ(a, x) := ax 2 .

DarkRank Let V (a, x) := {y ∈ U (a) : S(a, y) ≤ S(a, x)} be the set of examples in U (a) that are mapped farther away from anchor a than x in the teacher space. For each x ∈ U (a), DarkRank [START_REF] Chen | Dark-Rank: Accelerating deep metric learning via cross sample similarities transfer[END_REF] encourages those examples to be farther away from a than x in the student space: 1. FLOPS and parameters for the networks used in this work, absolute and relative to teacher (%). Top: the teacher networks are adapted for image retrieval, i.e. the fully connected layers are removed. Bottom: the student networks adapted in the same way and also with an added layer (or not) to match the output dimensionality of the teacher.

DR (a; θ) := - x∈U (a)   s sym θ (a, x) -log y∈V (a,x) e s sym θ (a,y)   . (9)
It is an application of the listwise loss [START_REF] Cao | Learning to rank: From pairwise approach to listwise approach[END_REF][START_REF] Xia | Listwise approach to learning to rank: theory and algorithm[END_REF], where the ground truth ranking is obtained by the teacher rather than some form of annotation.

Experiments

Setup

Datasets We use the SfM dataset [START_REF] Radenović | Finetuning CNN image retrieval with no human annotation[END_REF] for training, containing 133k images for training and 30k images for validation. We use the revisited ROxford5k and RParis6k datasets [START_REF] Radenović | Revisiting oxford and paris: Large-scale image retrieval benchmarking[END_REF] for testing, each having 70 query images. All datasets depict particular architectural landmarks under very diverse viewing conditions. We follow the standard evaluation protocol, using the medium and hard settings [START_REF] Radenović | Revisiting oxford and paris: Large-scale image retrieval benchmarking[END_REF]. We report mean average precision (mAP) here, while mean precision at 10 (mP@10) results are included in the supplementary material. Comparisons are based on mAP. Also included in the supplementary material are additional symmetric and asymmetric testing results for both datasets and both metrics in the presence of 1M distractors [START_REF] Radenović | Revisiting oxford and paris: Large-scale image retrieval benchmarking[END_REF], denoted as R1M. To compare with pruning [START_REF] Wang | Progressive local filter pruning for image retrieval acceleration[END_REF], we also use the original Oxford5k [START_REF] Philbin | Object retrieval with large vocabularies and fast spatial matching[END_REF] and Paris6k [START_REF] Philbin | Lost in quantization: Improving particular object retrieval in large scale image databases[END_REF] datasets, reporting mAP only.

Networks All models are pre-trained for classification on ImageNet [START_REF] Russakovsky | ImageNet large scale visual recognition challenge[END_REF] and then fine-tuned for image retrieval on SfM, following the setup of the same work. We use VGG-16 [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF] and ResNet101 [START_REF] He | Deep residual learning for image recognition[END_REF] as teacher models with the feature dimensionality d of 512 and 2048, respectively. We use MobileNetV2 [START_REF] Sandler | Mobilenetv2: Inverted residuals and linear bottlenecks[END_REF] and EfficientNet-B3 [START_REF] Tan | EfficientNet: Rethinking model scaling for convolutional neural networks[END_REF] as student networks, removing any fully connected layers and stacking one 1 × 1 convolutional layer to match the dimensionality of the teacher. All networks use generalized mean-pooling (GeM) [START_REF] Radenović | Finetuning CNN image retrieval with no human annotation[END_REF] on the last convolutional feature map. 1 gives the number of parameters and computational complexity (in FLOPS) for the networks used in this work. It is important to note that the versions of the teachers are already adapted for image retrieval by removing the fully connected layers, hence our version of VGG16 has significantly fewer parameters than the original (around 138M). Student networks are adapted in the same way, that is, fully connected layers removed. In addition, each student is shown with or without the 1 × 1 convolutional layer per teacher.

Complexity and parameters Table

Implementation details

The image resolution is limited to 362 × 362 at training (fine-tuning). At testing, a multiscale representation is used, with initial resolution of 1024 × 1024 and scale factors of 1, 1 √ 2 and 1 2 . The representation is pooled by GeM over the features of the three scaled inputs. We use supervised whitening, trained on the same SfM dataset [START_REF] Radenović | Finetuning CNN image retrieval with no human annotation[END_REF]. In asymmetric testing, whitening is learned in the teacher space. Our implementation is based on the official code of [START_REF] Radenović | Finetuning CNN image retrieval with no human annotation[END_REF] in PyTorch [START_REF] Radenović | CNN image retrieval in PyTorch: Training and evaluating CNNs for image retrieval in Py-Torch[END_REF], as well as [START_REF] Wang | Multi-similarity loss with general pair weighting for deep metric learning[END_REF][START_REF] Park | Relational knowledge distillation[END_REF][START_REF] Chen | Dark-Rank: Accelerating deep metric learning via cross sample similarities transfer[END_REF]. Teacher models are taken from [START_REF] Radenović | Finetuning CNN image retrieval with no human annotation[END_REF]. Our implementation is publicly available, including trained student models for all loss functions and all pairs of teacher/student models 3 .

Training and hyper-parameters We follow the training setup of [START_REF] Radenović | Finetuning CNN image retrieval with no human annotation[END_REF] for loss functions that use labels. We use the validation set to determine the hyperparameter values and the best model. We train all models using the SGD with learning rate decay of 0.99 per epoch. Symmetric training (2) takes place for 100 epochs or until convergence based on the validation set. For asymmetric training (3), this is extended to 300 epochs. Each epoch consists of 2000 tuples. A mini-batch has 10 tuples, each composed of 1 anchor, 1 corresponding positive and 5 negatives. For unsupervised losses we create tuples of the same overall size. We use weight decay of 10 -6 in each experiment. [START_REF] Davis | Asymmetric sparse kernel approximations for large-scale visual search[END_REF]. GeM pooling and learned whitening [START_REF] Radenović | Finetuning CNN image retrieval with no human annotation[END_REF] used in all cases.

Loss functions For contrastive loss (4), we set the margin m = 0.7 and the initial learning rate η to 10 -5 and 10 -3 for symmetric and asymmetric training, respectively. For triplet (5), we set m = 0.1 and η = 10 -8 . For multisimilarity (6) we set m = 0.6, α = 1, β = 1 and η = 10 -8 for all setups. For regression (7), we set η = 10 -3 . We use the DA variant or RKD [START_REF] Park | Relational knowledge distillation[END_REF] (8), with the anglewise and distance-wise loss weighted by a factor of 2 and 1 respectively, and η = 10 -2 . For DarkRank (DR) ( 9), we set η = 10 -6 for the VGG16 teacher; for ResNet101, η = 10 -5 for MobileNetV2 and η = 10 -7 for EfficientNet-B3. We do not discriminate between the student training being supervised or not, since labels are already used for teacher training.

Mining When using labels, we use hard negative mining as a default, following [START_REF] Radenović | Finetuning CNN image retrieval with no human annotation[END_REF]. Negatives are mined each epoch from a random subset of 22k images of the training set.

The negatives closest to the anchor (according to (2) or (3), depending on the setting) are selected. There is no mining for positives, because there are only few (1-2) positives per anchor. When not using labels, we draw additional examples uniformly at random as a default. There is no mining for regression.

Example of asymmetric hard example mining Depending on the similarity we use in the loss function, i.e., symmetric (2) or asymmetric (3), we follow the same choice for hard negative mining. This means that, in mining based on asymmetric similarity, the features of anchor a come from the student model f θ (a), while the database is represented by the teacher g. The database is fixed and does not need to be re-computed after each epoch. Only the anchors are updated, which makes training more efficient. Figure 2 gives an example of the hard negatives mined for one anchor across different epochs. Before the training starts (epoch 0) the results are not very informative, which is not surprising giving that the feature spaces of the teacher and the student do not match. However, after just a few epochs we see harder negatives being selected. This example illustrates how asymmetric similarity acts as a knowledge transfer mechanism from the teacher to the student model.

Results

Contrastive-regression ablation As will be shown in the following results, contrastive loss and regression turn out be most effective in general. Moreover, by comparing ( 4) with ( 7), contrastive with asymmetric similarity (3) encompasses regression by setting each anchor as a positive for itself, without any other positive or negatives. To better understand the relation between these two loss functions, we perform an ablation study where we investigate versions of contrastive on (3) having negatives, or not, and the anchor itself as positive, or not.

The results are shown in Table 2 for the case of VGG16→MobileNetV2. In symmetric testing, it turns out that the best combination is having both negatives and the anchor itself. The same happens in almost all cases for other teacher and student models, as shown in the supplementary material. We denote this combination as Contr + and we include it in subsequent results:

C + (a; θ) := n∈N (a) [s θ (a, n) -m] + - p∈P (a) s θ (a, p) -s θ (a, a), (10)
where s θ is asymmetric (3). Asymmetric testing is much more challenging. The best is regression in this case, but Contr + is still the second best.

Symmetric testing According to the left part of Table 3, Contr + works best on MobileNetV2, while on Efficient-Net, either contrastive and Contr + works best, with the two options having little difference. The difference to other loss functions using labels is large, reaching 20% or even 30% on ROxford5k. Triplet is known to be inferior to contrastive [START_REF] Radenović | Finetuning CNN image retrieval with no human annotation[END_REF], but the difference is more pronounced in our knowledge transfer setting. This result is particularly surprising for multi-similarity, which is state of the art in finegrained classification [START_REF] Wang | Multi-similarity loss with general pair weighting for deep metric learning[END_REF]. Also surprisingly, regression works best among loss functions not using labels, including recent knowledge transfer methods RKD [START_REF] Park | Relational knowledge distillation[END_REF] and Dark-Rank [START_REF] Chen | Dark-Rank: Accelerating deep metric learning via cross sample similarities transfer[END_REF]. It is second or third best in all cases. This finding is contrary to [START_REF] Yu | Learning metrics from teachers: Compact networks for image embedding[END_REF], where the regression baseline is found inferior. DarkRank is inferior to RKD, in agreement with [START_REF] Park | Relational knowledge distillation[END_REF].

The superiority of contrastive or Contr + over regression confirms that, by using our asymmetric similarity, the original metric learning task is still beneficial. Unlike knowledge distillation on classification tasks, knowledge transfer alone is not the best option. Focusing on the best results (contrastive or Contr + ), we confirm that, with just one exception (VGG16→EfficientNet on RParis6k hard), knowledge transfer always helps compared to training without the teacher, using the same d. The gain is more pronounced, reaching 7-10% on ResNet101→MobileNetV2, when the teacher is stronger and the student is weaker (the exception corresponds to the weakest teacher and strongest student). MobileNetV2 performs only 2-3% below its teacher. Remarkably, Effi-cientNet outperforms its teacher: this happens on RParis6k for VGG16 and on all settings for ResNet101. This is also the case in the presence of R1M distractors for ResNet101 teacher. This result can be found in the supplement, where symmetric testing results for all losses and models are included on ROxford5k +R1M and RParis6k +R1M.

Asymmetric testing Here, similarities are asymmetric at testing, with the database being represented by the teacher and queries by the student. According to the right part of Table 3, regression is the clear winner in this case. This is contrary to [START_REF] Shen | Towards backward-compatible representation learning[END_REF], where regression fails. In a sense, this can be expected since the student should learn to map images to features exactly like the teacher. Contr + is clearly the second best, with the differences varying between 1-2% on RParis6k and up to 8% on ROxford5k. Contrastive is the third, with a further loss of roughly 5-10% or more. Knowledge transfer of weak information like relations or ranking fails completely in this case. This is totally expected, because it is the absolute coordinates that should match. What is unexpected is that triplet and multi-similarity fail too. The former may be due to also relying on relations: a positive may not be attracted to an anchor when it is closer than a negative. The latter may be due to soft weighting: a positive may not be attracted to an anchor when its loss contribution is dominated by harder positives.

When compared with symmetric testing using the corresponding teacher alone, the loss of using the student on queries is 8-16%. There is no substantial difference in this behavior between MobileNetV2 and EfficientNet. Asymmetric testing is considerably more challenging than symmetric. The closest work in terms of asymmetric testing is feature translation [START_REF] Hu | Towards visual feature translation[END_REF], where a shallow translator is learned instead of fine-tuning the student end-to-end. This approach performs poorly, with up to 40% mAP loss. Students are still large networks, so there is no computational gain. Additional asymmetric testing results for ROxford5k and RParis6k with R1M distractors can be found in the supplement.

Results on Paris6k and Oxford5k

We consider this experiment primarily for comparison with progressive local filter pruning (PLFP) [START_REF] Wang | Progressive local filter pruning for image retrieval acceleration[END_REF], which performs symmetric testing with a pruned version of VGG16. For the sake of comparison, there is no whitening in this case. According to Table 4, MobileNetV2 has substantially lower FLOPS and parameters than the pruned VGG16, yet with either teacher it performs better on Paris and nearly the same on Oxford. ric testing, matching teacher and student features requires the same absolute coordinates in the feature space. This is done best by regression, but Contr + also works well. Losses that rely on pairwise or higher-order relations, like RKD or DR, fail in this task. Triplet also fails, presumably because it also relies on relations.

Asymmetric embedding visualization

Conclusions

There are certain unexpected or surprising findings in this work. First, regression is particularly effective in knowledge transfer. It appears that the more the constraints on student mappings (e.g. ranking → distance/angle relations → positions), the better the performance in standard symmetric testing. Second, the standard contrastive loss is particularly effective with asymmetric similarity at training, outperforming by a large margin state of the art methods like multi-similarity. A straightforward combination with regression-treating the anchor itself as positive-performs best on symmetric testing. These two solutions are the only ones where knowledge transfer helps, i.e., outperforms the student trained alone. In the new asymmetric testing task, regression is unsurprisingly a winner.

We have shown that using the original metric learning task while transferring knowledge is still beneficial in symmetric testing. It remains to be investigated whether the same can happen in asymmetric testing. We consider the same dataset in teacher and student training, so the latter is as supervised as the former. An interesting extension would be to consider a different, unlabeled dataset in student training. This would be a semi-supervised solution, like data distillation [START_REF] Radosavovic | Data distillation: Towards omnisupervised learning[END_REF].

Figure 1 .

 1 Figure 1. Metric learning and knowledge transfer. (a) Symmetric: Positive (negative) pairs of examples mutually attracted (repulsed) in student space; teacher not used.(b) Regression (absolute ML+KD[START_REF] Yu | Learning metrics from teachers: Compact networks for image embedding[END_REF]): Examples in student space attracted to corresponding examples in teacher space; labels not used. (c) Relational (relative ML+KD[START_REF] Yu | Learning metrics from teachers: Compact networks for image embedding[END_REF] or distance-wise RKD[START_REF] Park | Relational knowledge distillation[END_REF]): Distances encouraged to be the same in both spaces; labels not used. (d) Asymmetric (this work): Anchors in student space attracted to (repulsed from) positives (negatives) in teacher space; both labels and teacher used.

Figure 2 .

 2 Figure 2. Asymmetric hard negative mining. One anchor a shown on the first column, followed by the hard negatives N (a) mined for this anchor, over different epochs. The anchor is represented by the student and the database of potential negatives by the teacher.

Figure 3 Figure 3 .

 33 Figure 3. T-SNE embeddings of 5 color-coded ROxford5k classes 5 , 20 random easy [54] examples each, represented by a VGG-16 teacher (circles) and a MobineNetV2 student (diamonds). A line connects the two representations of each example.

Table

	NETWORK	TEACHER	d	GFLOPS ABS %	PARAM (M) ABS %
	VGG16 [54]		512 79.40	14.71
	ResNet101 [54]		2048 42.85	42.50
			1280 1,74	2.22
	MobileNetV2	VGG16	512	1.94 2.44 2.88 19.6
		ResNet101 2048 2.50 5.83 4.85 11.4
			1536 5.36	10.70
	EfficientNet-B3	VGG16	512	5.56 7.00 11.48 78.0
		ResNet101 2048 6.26 14.6 13.84 32.6

Table 2 .

 2 Contrastive-regression ablation. Symmetric and asymmetric testing mAP on ROxford5k and RParis6k [52]. LAB: using labels in student model training. POS, NEG: Using positives, negatives. SELF: Using anchor (by teacher) as positive for itself (by student). ASYM: Using asymmetric similarity (3) at training. The second row is Contr +

					SYMMETRIC TESTING ASYMMETRIC TESTING
	STUDENT	TEACHER LAB LOSS SELF POS NEG MINING	ASYM MEDIUM	HARD	MEDIUM	HARD
					ROxf RPar ROxf RPar ROxf RPar ROxf RPar
			Contr (4)	hard	57.3 67.1 31.1 41.3 38.3 49.8 18.4 23.8
			Contr (4)	hard	57.3 68.4 31.5 42.2 42.9 55.9 22.6 31.4
	MobileNetV2 VGG16	Contr (4)	hard	55.9 66.7 31.1 40.6 34.1 47.3 17.0 24.5
			Contr (4)	hard	55.5 67.0 30.4 40.9 38.2 52.2 15.3 28.9
			Reg (7)	-	53.3 67.5 28.9 40.9 48.0 57.9 26.5 32.6

Table 3 .

 3 Symmetric and asymmetric testing mAP on ROxford5k and RParis6k[START_REF] Radenović | Revisiting oxford and paris: Large-scale image retrieval benchmarking[END_REF]. LAB: using labels in student model training. ASYM: Using asymmetric similarity (3) at training (our work). Best result highlighted per teacher-student pair. GeM pooling and learned whitening[START_REF] Radenović | Finetuning CNN image retrieval with no human annotation[END_REF] used in all cases.

					SYMMETRIC TESTING ASYMMETRIC TESTING
	STUDENT	d TEACHER LAB	LOSS	MINING	ASYM MEDIUM	HARD	MEDIUM	HARD
					ROxf RPar ROxf RPar ROxf RPar ROxf RPar
	VGG16 [54]	512	Contr (4)	hard	60.9 69.3 32.9 44.2
	ResNet101 [54] 2048	Contr (4)	hard	65.4 76.7 40.1 55.2
	MobileNetV2	512 2048	Contr (4) Contr (4)	hard hard	53.6 66.4 28.8 39.7 56.1 68.5 30.3 42.0
	EfficientNet-B3	512 2048	Contr (4) Contr (4)	hard hard	53.8 70.9 26.2 46.0 59.6 75.1 33.3 51.9
			Contr + (10) hard	57.3 68.4 31.5 42.2 42.9 55.9 22.6 31.4
			Contr (4)	hard	57.3 67.1 31.1 41.3 38.3 49.8 18.4 23.8
			Triplet (5)	hard	37.0 62.7 11.6 36.4 1.8 4.3 0.7 2.8
		512 VGG16	MS (6)	hard	36.8 62.8 11.5 36.5 1.9 4.3 0.8 2.7
			Reg (7)	-	53.3 67.5 28.9 40.9 48.0 57.9 26.5 32.6
			RKD (8) random	46.2 64.3 21.8 37.6 2.0 4.1 0.8 2.6
			DR (9)	random	45.2 60.6 24.6 33.1 1.7 3.8 0.7 2.4
	MobileNetV2		Contr + (10) hard	63.2 75.0 37.9 52.0 47.1 61.5 21.8 37.7
			Contr (4)	hard	60.8 72.1 36.1 47.6 32.3 51.5 9.6 28.2
			Triplet (5)	hard	45.5 68.0 19.6 43.4 1.3 3.7 0.7 2.4
		2048 ResNet101	MS (6)	hard	44.5 68.1 17.9 43.2 1.4 3.6 0.7 2.3
			Reg (7)	-	59.8 73.1 35.7 49.5 49.2 65.0 23.3 40.7
			RKD (8) random	56.1 69.8 31.8 44.2 1.6 4.1 0.8 2.5
			DR (9)	random	43.4 59.3 20.8 31.6 1.5 3.7 0.6 2.3
			Contr + (10) hard	56.9 69.0 31.1 43.5 44.7 58.0 23.9 32.4
			Contr (4)	hard	56.8 70.4 31.2 45.4 43.8 24.9 23.0 6.1
			Triplet (5)	hard	33.7 64.6 8.0 40.3 1.4 4.0 0.6 2.5
		512 VGG16	MS (6)	hard	33.9 64.9 8.1 40.6 1.4 3.9 0.6 2.5
			Reg (7)	-	55.0 69.4 27.1 44.5 49.4 58.2 26.0 33.0
			RKD (8) random	51.6 67.0 26.2 41.1 1.3 3.8 0.6 2.5
			DR (9)	random	52.4 65.2 26.5 37.2 1.4 3.8 0.6 2.5
	EfficientNet-B3		Contr + (10) hard	66.8 77.1 42.5 55.5 45.2 63.7 19.6 40.9
			Contr (4)	hard	66.3 77.4 41.3 55.5 37.4 57.4 10.9 33.7
			Triplet (5)	hard	39.5 69.4 11.6 45.8 1.5 4.0 0.7 2.5
		2048 ResNet101	MS (6)	hard	39.9 69.7 11.7 46.2 1.5 4.0 0.7 2.4
			Reg (7)	-	64.9 74.4 40.5 52.4 52.9 65.2 27.8 42.4
			RKD (8) random	56.3 73.0 30.5 50.4 1.6 3.8 0.7 2.4
			DR (9)	random	52.2 66.3 27.3 40.1 2.0 3.5 0.7 2.2

Table 4 .

 4 Symmetric testing mAP on Paris6k and Oxford5k. FLOPS and parameters relative to VGG16. LAB: using labels in student model training. Using asymmetric similarity (3) in all teacherstudent settings. GeM pooling[START_REF] Radenović | Finetuning CNN image retrieval with no human annotation[END_REF] used in all cases but not learned whitening.

	STUDENT	%FLOPS %PARAM TEACHER LAB LOSS	mAP Oxf Par
	VGG16 [54]	100	100		Contr (4) 82.45 81.37
	VGG16-PLFP [74] 57.37	61.05		Contr (4) 76.20 73.18
	MobileNetV2	2.44	19.58	VGG16	Contr (4) 74.14 78.26 Reg (7) 66.58 74.45
		3.14	32.97 ResNet101	Contr (4) 75.30 83.23 Reg (7) 63.57 76.96

https://github.com/budnikm/aml

Corresponding to landmarks: All Saints College, Christ Church College, Magdalen College, Radcliffe Camera and Hertford Bridge.


Yan Cao

M Kasaeian

H Abbasspoor

Moein Shamoushaki

M A Ehyaei
email: aliehyaei@yahoo.com

Stéphane Abanades

Energy, exergy, and economic analyses of a novel biomass-based multigeneration system integrated

Keywords: Multi-generation system, Multi-effect distillation, Electrodialysis, Exergy, Economic

Energy, exergy, and economic analyses of a novel biomass-based multigeneration system integrated with multi-effect distillation, electrodialysis, and LNG tank

Yan Cao, M. Kasaeian, H. Abbasspoor, Moein Shamoushaki, M.A. A Ehyaei,

Stéphane Abanades

To cite this version:

Yan Cao, M. Kasaeian, H. Abbasspoor, Moein Shamoushaki, M.A. A Ehyaei, et al.. Energy, exergy, and economic analyses of a novel biomass-based multigeneration system integrated with multi-effect distillation, electrodialysis, and LNG tank. Desalination, 2022, 526, pp.115550. 10.1016/j.desal.2022.115550. hal-03529911

1) Introduction

One of the most severe challenges threatening human society is global warming. Based on recent studies, greenhouse gas (GHG) release is expected to rise by 50% and become the most dominant adverse factor responsible for climate change by 2050 [START_REF] Subramaniam | Biofuels, environmental sustainability, and food security: A review of 51 countries[END_REF]. The GHG principally originates from fossil fuels combustion.

Therefore, the substitution of fossil fuels with clean energies is vital. The application of biomass-originated energy systems has been identified as a promising solution [START_REF] Abanades | A critical review of biogas production and usage with legislations framework across the globe[END_REF][START_REF] Rajaei | Feasibility of using biogas in a micro turbine for supplying heating, cooling and electricity for a small rural building[END_REF]. Biomass gasification is an economic and high-efficiency method that makes possible biomass transformation to clean and flammable gaseous stocks using a gasifier [START_REF] Gallucci | Experimental demonstration of chemical-looping combustion of syngas in packed bed reactors with ilmenite[END_REF]. The method's effectiveness remarkably influences the provided syngas yield and quality [START_REF] Sikarwar | Progress in biofuel production from gasification[END_REF].

Besides, deficiency of water is a significant vital global concern endangering nowadays [START_REF] Mir | Integration of electrodialysis with renewable energy sources for sustainable freshwater production: A review[END_REF]. The United Nations reported that in 2050, nearly seven billion people in sixty nations would face drastic scarcity of water [START_REF] Ihsanullah | Carbon nanotube membranes for water purification: Developments, challenges, and prospects for the future[END_REF]. Seawater desalination is noticed as a viable and most used technique to cope with the growing requirement for cleaner water [START_REF] Ehyaei | Energy, exergy, economic, exergoenvironmental, and environmental analyses of a multigeneration system to produce electricity, cooling, potable water, hydrogen and sodium-hypochlorite[END_REF]. There are two main kinds of seawater desalination processes to produce distilled water (DW). The first is named the thermal desalination system (TES). Seawater is transformed to vapor by evaporation process and then chilled into purified water. Another approach comprises desalination methods promoted through diverse separation techniques like reverse osmosis (RO) [START_REF] Cao | Energy, exergy, exergoenvironmental, and economic assessments of the multigeneration system powered by geothermal energy[END_REF]. Two attractive approaches in thermal desalination are the multi-effect evaporation desalination (MED) and multi-stage-flash (MSF) evaporation desalination [START_REF] Alonso | Alternatives of seawater desalination using nuclear power[END_REF]. MED continues as an attractive choice due to the lower rate of corrosion, the power needed, and the costs of desalted water compared with MSF [START_REF] Wang | Proposal and analysis of a high-efficiency combined desalination and refrigeration system based on the LiBr-H2O absorption cycle-Part 2: Thermal performance analysis and discussions[END_REF].

Desalination of seawater provides a rich source of fresh water, a crucial supply for people's well-being and farming. While the application of desalination proceeds to expand, high-salinity brine evacuation is an environmental matter, causes a possible adverse consequence on the ecosystems [START_REF] Roberts | Impacts of desalination plant discharges on the marine environment: A critical review of published studies[END_REF]. The global brine production is about 141.5 million m 3 /day, which is principally released into ocean habitats [START_REF] Van Wyk | Analysis of the energy consumption of supercritical water desalination (SCWD)[END_REF]. As desalination application continues to develop, discharge of high-salinity brine could harm the environment and ecosystems. To improve the economic and environmental aspects of the desalination of seawater, developing technology to generate HCl and NaOH with low power use is essential. Chemical products on-site production from brine could eliminate the need of purchasing and transporting chemicals from elsewhere. The negative consequences of discharge of the brine on the environment and ecosystem could be minimized by recovering the chemical resources of the brine. In addition, it makes it possible to recycle back brine to the freshwater partially [START_REF] Kumar | Direct electrosynthesis of sodium hydroxide and hydrochloric acid from brine streams[END_REF].

Junjie et al. [START_REF] Junjie | Improvement of a multi-stage flash seawater desalination system for cogeneration power plants[END_REF] proposed a cogeneration power cycle integrated with an improved MSF desalination mechanism. They showed that the concentration of the brine in each stage and the average yearly capital expense of freshwater generation is possible to decline by 21.8% and 10.7%, respectively, compared with conventional MSF. Meratizaman et al. [START_REF] Meratizaman | Introduction of an efficient small-scale freshwaterpower generation cycle (SOFC-GT-MED), simulation, parametric study and economic assessment[END_REF] studied a unified system composed of MED, solid oxide fuel cell (SOFC), and gas turbine (GT) cycles. For the economic assessment, the yearly expense is applied. Their conclusions revealed that the integration of MED and SOFC-GT systems improved the cycle economically.

Najafi et al. [START_REF] Najafi | Exergetic, economic and environmental analyses and multi-objective optimization of an SOFC-gas turbine hybrid cycle coupled with an MSF desalination system[END_REF] analyzed a SOFC-GT-MSF linked system exegetically, economically, and environmentally.

They optimized this cycle by a multi-objective genetic algorithm (MOGA) to obtain the optimum operating variables. Their achieved outcomes confirmed that exergetic productivity and whole expense were achieved at optimum point, namely 46.7% and 3.76 million USD/year, respectively. Mokhtari et al. [START_REF] Mokhtari | Thermoeconomic and exergy analysis in using hybrid systems (GT+ MED+ RO) for desalination of brackish water in Persian Gulf[END_REF] evaluated a combined cycle including GT, MED, and RO systems to produce water and electricity in the Iran southern region in the outskirts of the Persian Gulf. According to their analysis, higher than required energy led to a decrease of 0.5 dollars per m 3 in unit product cost while a hybrid cycle is implemented. Shamoushaki et al. [START_REF] Shamoushaki | Exergy, economic and environmental analysis and multiobjective optimization of a SOFC-GT power plant[END_REF] conducted thermodynamic, exergy, economic and environmental evaluation of hybrid cycle composed of SOFC-GT systems. The multi-objective optimization of the integrated system by non-dominated sorting genetic algorithm II (NSGA-II) was conducted. They calculated the cost rate, 0.0435 US$/s, and efficiency of exergy of 57.7% at the optimum point. Also, the payback time was obtained at about 3.12 years. [START_REF] Khanmohammadi | Modeling and multi-objective optimization of a novel biomass feed polygeneration system integrated with multi effect desalination unit[END_REF] proposed a new multigeneration biomass-based cycle combined with a desalination unit to provide electricity, fresh water, and hot water. The optimization has been carried out using the genetic algorithm to determine the optimum design variables amount. The combustion chamber and gasifier had the highest values of exergy destruction ratio (approximately 84%).

Khanmohammadi and Atashkari

Moghimi et al. [START_REF] Moghimi | Energy and exergy investigation of a combined cooling, heating, power generation, and seawater desalination system[END_REF] assessed a combined cooling, heating, and power (CCHP) hybrid cycle composed of GT, MED-thermal vapor compression (TVC), and ejector refrigeration cycle (ERC). The obtained exergy efficiency of the combined system was 2.1% greater than the single Brayton system. Also, their analyzed cycle showed a power production of 30 MW, cooling and heating capacities of 3.14 MW, and freshwater production of 85.57 kg/s. Rashidi and Khorshidi [START_REF] Rashidi | Exergy analysis and multiobjective optimization of a biomass gasification based multigeneration system[END_REF] studied a biomass gasification-based system for generating CCHP based on the exergy concept. The multi-objective optimization and fuzzy clustering methods were applied to find the optimum solution. They compared the obtained results with two diverse optimization approaches, and the fruitfulness of the recommended process was validated employing different execution indicators. Ghaebi and Ahmadi [23] modeled a SOFC-GT system integrated with humidification-dehumidification (HDH) desalination and heat recovery steam generator (HRSG) units. The obtained results showed that the combined cycle produces heating, net electricity, and distilled water (370.2 kW, 1605 kW, and 345.7 kg/h, respectively). Mohammadi et al. [START_REF] Mohammadi | Hybrid systems based on gas turbine combined cycle for trigeneration of power, cooling, and freshwater: A comparative techno-economic assessment[END_REF] compared six different configurations of trigeneration systems based on the GT cycle. Diverse desalination and chiller systems were united with a coupled cycle. The consequences explicated the most reliable cost-effective arrangement was gas turbine combined cycle with wet cooling tower integrated with double effect absorption chiller (DEABC) and RO. Energetic and economic analysis of biomass-based integrated cycle with ORC to heat recovery and carbon storage has been performed by Georgousopoulos et al. [START_REF] Georgousopoulos | Thermodynamic and techno-economic assessment of pure and zeotropic fluid ORCs for waste heat recovery in a biomass IGCC plant[END_REF]. 4.61% efficiency of combined system improvement has been achieved by proposing this system.

Vojdani et al. [START_REF] Vojdani | A novel triple pressure HRSG integrated with MED/SOFC/GT for cogeneration of electricity and freshwater: Techno-economic-environmental assessment, and multiobjective optimization[END_REF] performed the techno-economic and environmental assessment and multi-objective optimization of a cogeneration system composed of MED and SOFC-GT. According to the proposed system, the generated power, efficiency of exergy, and emission increased up to 6.5%, 8.4%, and 5.8% as opposed to SOFC-GT standalone system. Zoghi et al. [START_REF] Zoghi | Multi-criteria analysis of a novel biomass-driven multigeneration system including combined cycle power plant integrated with a modified Kalina-LNG subsystem employing thermoelectric generator and PEM electrolyzer[END_REF] assessed a biomass-driven multi-production cycle composing a modified Kalina-LNG subsystem, electrolyzer, and thermoelectric generator. They calculated hydrogen and natural gas mass flow rates at 5.77 kg/h and 4.42 kg/s. Cao et al. [START_REF] Cao | A novel hybrid biomass-solar driven triple combined power cycle integrated with hydrogen production: Multi-objective optimization based on power cost and CO2 emission[END_REF] studied a new hybrid biomass-solar-based coupled system combined with hydrogen production. The multiobjective optimization of the system was carried out according to power cost and CO2 emissions. The results showed that at the optimum solution, exergetic efficiency, Levelized cost of energy (LCOE), and carbon dioxide emission were 30.4%, 61.4 $/MWh, and 0.46 kg/kWh. Lak Kamari et al. [START_REF] Kamari | Assessment of a biomass-based polygeneration plant for combined power, heat, bioethanol and biogas[END_REF] investigated an integrated system based on biofuel to generate electricity, bio-products, and heat. Their assessment showed 15% energy saving is possible with the designed system. Exergy, economic, exergonic, and optimization of a multipurpose cycle were done by Safder et al. [START_REF] Safder | Energetic, economic, exergetic, and exergorisk (4E) analyses of a novel multi-generation energy system assisted with bagasse-biomass gasifier and multi-effect desalination unit[END_REF]. The optimization outcomes determined that the combined system produced electricity, cooling, and freshwater (28.7 MW, 13.6 kg/s, and 3.4 MW, respectively). Thermo-economic evaluation of a biomass/natural gas-driven combined system has been studied by Jalili et al. [START_REF] Jalili | An integrated CCHP system based on biomass and natural gas co-firing: exergetic and thermo-economic assessments in the framework of energy nexus[END_REF]. The highest and lowest irreversibilities were related to gas cycle and double-effect absorption unit with 61% and 6% of total exergy destruction, respectively. Cao et al. [START_REF] Cao | Proposal and thermo-economic optimization of using LNG cold exergy for compressor inlet cooling in an integrated biomass fueled triple combined power cycle[END_REF] assessed a biomass gasification-fueled triple combined system from a thermos-economic aspect.

The optimization of the integrated cycle was performed by a genetic algorithm to minimize the LCOE. The system showed a 6.7% higher efficiency applying CO2 as a working fluid instead of helium. Xu et al. [START_REF] Xu | Optimization of a biomass-driven Rankine cycle integrated with multi-effect desalination, and solid oxide electrolyzer for power, hydrogen, and freshwater production[END_REF] studied a multi-production cycle including solid oxide electrolyzer, desalination, and ORC units supplied by biomass energy. Exergy efficiency and cost are obtained at 17.16% and 26 $/GJ at optimized results.

Musharavati et al. [START_REF] Musharavati | Multi-objective optimization of a biomass gasification to generate electricity and desalinated water using Grey Wolf Optimizer and artificial neural network[END_REF] conducted a combined system optimization to produce power and freshwater.

Optimized electricity generation and desalinated water are obtained at 5127 kW and 38.6 kg/s. Based on the above previous researches, there are no studies regarding a configuration of the multigeneration system (MGS) powered by biomass to produce electrical power, cooling, DW, sodium hydroxide (NaOH), and hydrogen chloride (HCl). In this MGS, steam is provided via biomass; then, this produced steam meets the energy needs of the CO2 cycle and MED. In addition, liquid natural gas (LNG) is used as a heat sink to decrease the condenser pressure and increase the electrical power production via the CO2 cycle. After absorbing heat from the condenser of the CO2 cycle, the NG is used via an expansion turbine and cooler to produce electrical power and cooling. Also, another subsystem is added to MGS for the brine (B) discharge treatment. To be brief, the innovative aspects of the present study are as follows:

(i)
Proposal of a novel configuration of MGS powered by biomass (ii) Investigation of brine treatment to decrease the effects of B release on the environment.

(iii) Comprehensive system analyses include energy, exergy, and economic analyses 2) Methodology

Model configuration

Figure 1 depicts the system configuration. In the gasifier, biomass in the presence of heat is converted to biogas (points 1, 2, 3). The hot syngas heats the pressurized water via heater (points 3, 4, 5, 23). The syngas is burned in the boiler to convert hot water to steam (points 6 to 8). The steam is divided into two streams (points 9 & 10). The steam in point 9 is used in a multi-effect distillation (MED) system to produce demineralized water (DW) from the seawater (SW) (points 12 & 13). The part of dissipated brine (B) is converted to NaOH and HCl via electrodialysis (ELECD) (points 14 to 16). Another part of steam (point 10) meets the energy needs of the carbon dioxide (CO2) cycle evaporator (Eva) (points 18, 20 to 21). In the CO2 cycle, the liquefied CO2 is used as a working fluid. This cycle operates similarly to the Rankine cycle.

The liquefied CO2 is pressurized via pump I (PI). Then, it transfers the heat with steam within the Eva to change to superheated steam (SHS) (points 10, 18, 20 to 21). The SHS rotates the expander I (EXP I) and generator (G) to produce electricity (points 21 & 22). The low-pressure steam flows through a condenser to dissipate heat and change to saturated liquid. Since the CO2 cycle condenser temperature is lower than the environment, the liquefied natural gas (LNG) is used for this target (points 19, 22, 24 to 25). In the LNG line, the high-pressure LNG absorbs the heat from the CO2 low-pressure steam (points 24 & 25). Then, it expands through expander II (EXP II) and G to produce electricity. Furthermore, the low pressure and cold LNG is used in the cooler to produce cooling (points 26 & 27). Figure 2 shows the layout of the MED. MED works based on subsequent evaporation and condensation in different stages named effects. This system converts the seawater (SW) to the demineralized (DW) and brine (B). Steam flows through tube bundles (point 9), and it is used to evaporate the sprayed SW on the tube bundles. Then, it is condensed as DW.

The parts of SW sprayed on tube bundles evaporate and go to the second effect, and part of it accumulates in the bottom of the effect and goes to the flash boxes, which contain more salt than seawater. This part of B is evaporated in the flash boxes due to pressure drop arising from the effect to the flash box, and it goes to the second effect. The non-evaporated B is dissipated to the environment. This process continues until the last effect. The connection between subsystems and components is depicted in Figure 3.

Energy and mass balance assessment

The following assumptions are noticed for the energy assessment [START_REF] Ehyaei | Exergy, economic & environmental (3E) analysis of inlet fogging for gas turbine power plant[END_REF][START_REF] Ehyaei | Exergy, economic and environment (3E) analysis of absorption chiller inlet air cooler used in gas turbine power plants[END_REF][START_REF] Ehyaei | Optimization of a triple cycle based on a solid oxide fuel cell and gas and steam cycles with a multiobjective genetic algorithm and energy, exergy and economic analyses[END_REF][START_REF] Mistry | An improved model for multiple effect distillation[END_REF][START_REF] Shamoushaki | Energy, exergy, economic and environmental (4E) analyses of a geothermal power plant with NCGs reinjection[END_REF]: 1. The system operates at steady-state conditions.

2. The dead-state temperature and pressure are 15 ℃ and 101.3 kPa.

3. The heat losses are neglected.

4. The thermodynamic procedure in P and EXP is supposed polytropic, and the efficiency is assumed to be 85%.

5. Kinetic and potential energy are ignored.

6. DW and B have the effect temperature at the exit.

7. The overall heat transfer coefficient in MED is a function of temperature.

8. The temperature difference between each effect is equal. 9. The MED feed water is distributed equally.

10. The heat exchanger effectiveness factor is 85%.

The general mass and energy balance equations are shown below [START_REF] Bejan | Advanced engineering thermodynamics[END_REF]:

∑ 𝑚i 𝑛 = ∑ 𝑚ȯ 𝑢𝑡 (1) 𝑄 ̇-𝑊 ̇+ ∑ 𝑚i 𝑛 (ℎ + 𝑉 2 2 + 𝑔𝑍) = ∑ 𝑚ȯ 𝑢𝑡 (ℎ + 𝑉 2 2 + 𝑔𝑍) (2)
where 𝑚̇ , h, V, 𝑊, ̇ Z, g and 𝑄 ̇ are the mass flow rate, enthalpy, velocity, power, height, gravitational acceleration, and heat transfer rate, respectively.

Steam/water line

The gasification reaction is as follows [START_REF] Jarungthammachote | Thermodynamic equilibrium model and second law analysis of a downdraft waste gasifier[END_REF][START_REF] Soltani | Thermodynamic analyses of a biomass integrated fired combined cycle[END_REF]:

𝐶𝐻 𝑎 𝑂 𝑏 𝑁 𝑐 + 𝑤𝐻 2 𝑂 + 𝑚 (𝑂 2 + 3.76𝑁 2 ) → 𝑛 𝐻 2 𝐻 2 + 𝑛 𝐶𝑂 𝐶𝑂 + 𝑛 𝐶𝑂 2 𝐶𝑂 2 + 𝑛 𝐻 2 𝑂 𝐻 2 𝑂 + 𝑛 𝐶𝐻 4 𝐶𝐻 4 + 𝑛 𝑁 2 𝑁 2 (3)
𝐶 𝐻 𝑎 𝑂 𝑏 𝑁 𝑐 represents the biomass general chemical formula. The a, b, c coefficients depict the stoichiometric content of H, O, and N in the biomass. 𝑤 and m denote the moisture and air content.

Regarding the mass balance in equation 1 for C, H, O, and N, the following relations can be written [START_REF] Jarungthammachote | Thermodynamic equilibrium model and second law analysis of a downdraft waste gasifier[END_REF][START_REF] Soltani | Thermodynamic analyses of a biomass integrated fired combined cycle[END_REF]:

𝑛 𝐶𝑂 + 𝑛 𝐶𝑂 2 + 𝑛 𝐶𝐻 4 = 1 (4)
2𝑛 𝐻 2 + 2𝑛 𝐻 2 𝑂 + 4𝑛 𝐶𝐻 4 = 𝑎 + 2𝑤 (5)
𝑛 𝐶𝑂 + 2𝑛 𝐶𝑂 2 + 𝑛 𝐻 2 𝑂 = 𝑏 + 𝑤 + 2𝑚 (6)
2𝑛 𝑁 2 = 𝑐 + 7.52𝑚

Also, the following equilibrium reactions should be taken into account [START_REF] Jarungthammachote | Thermodynamic equilibrium model and second law analysis of a downdraft waste gasifier[END_REF][START_REF] Soltani | Thermodynamic analyses of a biomass integrated fired combined cycle[END_REF]:

𝐶 + 2𝐻 2 ↔ 𝐶𝐻 4 𝐾 = 𝑛 𝐶𝐻 4 𝑛 𝑡𝑜𝑡 (𝑛 𝐻 2 ) 2 ( 𝑃 𝑔 𝑃 𝑜 ) = exp( -∆𝐺 𝑅 𝑢 𝑇 𝑔𝑎𝑠𝑖𝑓𝑖𝑒𝑟 ) (8) 𝐶𝑂 + 𝐻 2 𝑂 ↔ 𝐶𝑂 2 + 𝐻 2 𝐾 = 𝑛 𝐶𝑂 2 𝑛 𝐻 2 𝑛 𝐶𝑂 𝑛 𝐻 2 𝑂 = exp( -∆𝐺 𝑅 𝑢 𝑇 𝑔𝑎𝑠𝑖𝑓𝑖𝑒𝑟 ) (9)
P, T, ∆𝐺, 𝑅 𝑢 are the pressure, temperature, changes in the Gibbs free energy, and global gas constant.

The combustion reaction in the boiler can be written as [START_REF] Talebizadehsardari | Energy, exergy, economic, exergoeconomic, and exergoenvironmental (5E) analyses of a triple cycle with carbon capture[END_REF]:

1 𝑟 𝑎 𝐶 𝑥1 𝐻 𝑦1 𝑂 𝑧1 + (𝑥 𝑜 2 𝑂 2 + 𝑥 𝑁 2 𝑁 2 ) → 𝑦 𝐶𝑂 2 𝐶𝑂 2 + 𝑦 𝑁 2 𝑁 2 + 𝑦 𝑜 2 𝑂 2 + 𝑦 𝐻 2 𝑂 𝐻 2 𝑂 ( 10
)
𝑦 𝐶𝑂 2 = 𝑥 1 𝑟 𝑎 ( 11
)
𝑦 𝑁 2 = 𝑥 𝑁 2 ( 12
)
𝑦 𝐻 2 𝑂 = 𝑥 𝐻 2 𝑂 + 𝑦 1 2𝑟 𝑎 ( 13
)
𝑦 𝑂 2 = 𝑧 1 + 𝑥 𝑂 2 - 𝑥 1 𝑟 𝑎 - 𝑦 1 4𝑟 𝑎 (14)
𝑟 𝑎 = 𝑛 𝐴𝑖𝑟 𝑛 𝑆𝐺 (15)
𝑥 𝑖 and 𝑦 𝑖 are the mass and mole fractions of i. 𝑟 𝑎 specifies the ratio of air/syngas. SG stands for the syngas.

In the water/steam line, the mass and energy balance relations for each component are listed in Table 1.

Table 1. The mass and energy balance correlations for each component in the water/steam line

No. Component Mass balance

Energy balance

1 HW 𝑚̇5 = 𝑚̇6 ṁ 3 = ṁ 4 𝑚̇3(ℎ 3 -ℎ 4 )𝜂 𝐻𝑋 = ṁ 5 (ℎ 6 -ℎ 5 ) 2 P II 𝑚̇2 3 = 𝑚̇5 𝑊 ̇𝑃𝐼𝐼 = 𝑚̇5(ℎ 5 -ℎ 23 ) 3 MX 𝑚̇2 3 = 𝑚̇1 1 + 𝑚̇1 8 𝑚̇2 3 ℎ 23 = 𝑚̇1 1 ℎ 11 + 𝑚̇1 8 ℎ 18
In this table, HW and MX mean water heater and mixer, respectively.

CO2 cycle/LNG heat sink

The mass and energy balance equations for the CO2 cycle and LNG line are brought in Table 2. In Table 2, Eva and Cond mean evaporator and condenser.

Multi-effect distillation (MED)

The effect temperature difference is calculated by the following relation [START_REF] Alasfour | Thermal analysis of ME-TVC+MEE desalination systems[END_REF]:

𝑇 𝑖 -𝑇 𝑖-1 = ∆𝑇 == 𝑇 1 -𝑇 𝑁 𝑁 -1 (16)
N and T are the effects number and temperature. The subscript i denotes the effect number.

The vapor temperature in effects is calculated by [START_REF] Al-Mutaz | Development of a steady-state mathematical model for MEE-TVC desalination plants[END_REF]:

𝑇 𝑣𝑖 = 𝑇 𝑖 -𝐵𝑃𝐸 (17)
Subscript v denotes vapor. Boiling point elevation (BPE) is defined as a parameter for determining the effect of salt on evaporation temperature [START_REF] Al-Mutaz | Development of a steady-state mathematical model for MEE-TVC desalination plants[END_REF].

Considering the non-equilibrium allowance (NEA), the flash box temperature can be calculated by [START_REF] Miyatake | Fundamental experiments with flash evaporation[END_REF]:

𝑇 𝑖 ′ = 𝑇 𝑣𝑖 + 𝑁𝐸𝐴 ( 18
)
where NEA is calculated by [START_REF] Miyatake | Fundamental experiments with flash evaporation[END_REF]:

𝑁𝐸𝐴 = 0.33(𝑇 𝑣𝑖-1 -𝑇 𝑣𝑖 ) 𝑇 𝑣𝑖 (19)
The mass concentration and energy balance equations for each effect can be calculated by [START_REF] El-Dessouky | Fundamentals of salt water desalination[END_REF][START_REF] Alasfour | Thermal analysis of ME-TVC+MEE desalination systems[END_REF]:

𝑚̇𝐷 𝑊,𝑖 = 𝑚̇𝐵 𝑊,𝑖-1 + 𝑚̇𝑆 𝑊,𝑖 -𝑚̇𝐵 𝑊,𝑖 (20)
𝑚̇𝑆 𝑊,𝑖 𝑥 𝑆𝑊,𝑖 + 𝑚̇𝐵 𝑊,𝑖-1 𝑥 𝐵𝑊,𝑖-1 = 𝑚̇𝐵 𝑊,𝑖 𝑥 𝐵𝑊,𝑖

𝑥, 𝐿, and 𝑓𝑓 represent the salt concentration, latent heat, and flashing fraction. Subscript r denotes entrained steam.

The overall surface area of each effect and condenser is calculated by [START_REF] Alasfour | Thermal analysis of ME-TVC+MEE desalination systems[END_REF][START_REF] El-Dessouky | Multiple effect evaporation-vapour compression desalination processes[END_REF]:

𝐴 𝑒𝑓𝑓𝑒𝑐𝑡𝑠 = [(𝑚̇𝐷
LMTD and U denote logarithmic mean temperature difference and overall heat transfer coefficient.

Subscript cond denotes condenser.

U for the effects and condenser can be calculated by the following relations [START_REF] Alasfour | Thermal analysis of ME-TVC+MEE desalination systems[END_REF][START_REF] El-Dessouky | Multiple effect evaporation-vapour compression desalination processes[END_REF]:

𝑈 𝑒𝑓𝑓𝑒𝑐𝑡𝑠 = 1939.4 + 1.40562𝑇 𝑒𝑓𝑓𝑒𝑐𝑡 -2.07525 × 10 -2 𝑇 𝑒𝑓𝑓𝑒𝑐𝑡 2 + 2.3186 × 10 -3 𝑇 𝑒𝑓𝑓𝑒𝑐𝑡 3 (25)
𝑈 𝑐𝑜𝑛𝑑 = 1617.5 + 0.1537𝑇 𝑐𝑜𝑛𝑑 -0.1825𝑇 𝑐𝑜𝑛𝑑 2 + 8.026 × 10 -5 𝑇 𝑐𝑜𝑛𝑑 3

The recovery ratio (RR) and gained output ratio (GOR) of the MED can be calculated by the following relations [START_REF] Alasfour | Thermal analysis of ME-TVC+MEE desalination systems[END_REF][START_REF] El-Dessouky | Multiple effect evaporation-vapour compression desalination processes[END_REF]:

𝑅𝑅 = 𝑚̇𝐷 𝑊 𝑚̇𝑆 𝑊 (27)
𝐺𝑂𝑅 = 𝑚̇𝐷 𝑊 𝑚̇9

(28)

Electrodialysis (ELECD)

ELECD is a system to convert the B to NaOH and HCl. This system consumes electricity. In the ELECD, the following reaction can be considered [START_REF] Thiel | Utilization of desalination brine for sodium hydroxide production: technologies, engineering principles, recovery limits, and future directions[END_REF]:

𝑁𝑎𝐶𝑙 + 𝐻 2 𝑂 → 𝑁𝑎𝑂𝐻+𝐻𝐶𝑙 (29)
The minimum salt concentration for using this system is 26%. This system needs 0.73 kWh/kg NaOH of electrical energy [START_REF] Thiel | Utilization of desalination brine for sodium hydroxide production: technologies, engineering principles, recovery limits, and future directions[END_REF].

System energy efficiency

The CO2 cycle and system energy efficiencies (ENE) are calculated by the following relations:

ƞ 𝐶𝑂2 𝑐𝑦𝑐𝑙𝑒 = 𝑊 ̇𝑛𝑒𝑡,𝐶𝑂2 𝑐𝑦𝑐𝑙𝑒 𝑚̇1(ℎ 10 -ℎ 18 ) (30)
In which, 𝑊 ̇𝑛𝑒𝑡,𝐶𝑂2 𝑐𝑦𝑐𝑙𝑒 and 𝑊 ̇𝑛𝑒𝑡,𝑆𝑦𝑠 are calculated by the following relations:

𝑊 ̇𝑛𝑒𝑡,𝐶𝑂2 𝑐𝑦𝑐𝑙𝑒 = 𝑊 ̇𝐸𝑋𝑃𝐼 -𝑊 ̇𝑃𝐼 (32)
𝑊 ̇𝑛𝑒𝑡,𝑆𝑦𝑠 = 𝑊 ̇𝐸𝑋𝑃𝐼 -𝑊 ̇𝑃𝐼 + 𝑊 ̇𝐸𝑋𝑃𝐼𝐼 -𝑊 ̇𝑃𝐼𝐼 -𝑊 ̇𝐸𝐿𝐸𝐶𝐷 (33)

Exergy assessment and system exergy efficiency

Specific exergy is classified into four categories denoted as chemical, kinetic, physical, and potential as noticed below [START_REF] Lazzaretto | SPECO: a systematic and general methodology for calculating efficiencies and costs in thermal systems[END_REF][START_REF] Bejan | Thermal Design and Optimization[END_REF]:

𝛹 = ∑ 𝑥 𝑖 𝛹 𝑐ℎ𝑖 + 𝑉 2 2 + 𝑔𝑧 + (ℎ -ℎ 0 ) -𝑇 0 (𝑠 -𝑠 0 ) + 𝑇 0 ∑ 𝑥 𝑖 𝑅 𝑖 𝑙𝑛𝑦 𝑖 (34)
𝛹 and x denote specific exergy and mass fraction. g, z, and V are acceleration of gravity, velocity, and height. s and y depict specific entropy and mole fraction. ch, 0, and i are chemicals, standard conditions, and species. Table 3 presents the exergy destruction rate (EDR) for all equipment of the MGS. The CO2 cycle and system exergy efficiencies (EXE) are calculated by the following relations:

Ɛ 𝐶𝑂2 𝑐𝑦𝑐𝑙𝑒 = 𝑊 ̇𝑛𝑒𝑡,𝐶𝑂2 𝑐𝑦𝑐𝑙𝑒 𝑚̇1(𝛹 10 -𝛹 18 ) (35)
Ɛ 𝑆𝑦𝑠 = 𝑊 ̇𝑛𝑒𝑡,𝑆𝑦𝑠 + 𝑄 ̇𝐶𝑜𝑜𝑙𝑒𝑟 (

The biomass chemical exergy can be calculated by [START_REF] Kotas | The exergy method of thermal plant analysis[END_REF]:

𝛹 𝑐ℎ = 𝛽(𝐿𝐻𝑉 + 𝜔ℎ 𝑓𝑔 ) (37)
hfg denotes the enthalpy of vaporization.

Economic evaluation

The annual income (AI) of the MGS is calculated by selling the products annually and it is calculated by the following relation [START_REF] Bellos | Parametric analysis and yearly performance of a trigeneration system driven by solar-dish collectors[END_REF][START_REF] Tzivanidis | Energetic and financial investigation of a stand-alone solar-thermal Organic Rankine Cycle power plant[END_REF]:

𝐴𝐼 = 𝑌 𝑒𝑙𝑒𝑐 𝑐 𝑒𝑙𝑒𝑐 + 𝑌 𝑐𝑜𝑜𝑙𝑖𝑛𝑔 𝑐 𝑐𝑜𝑜𝑙𝑖𝑛𝑔 + 𝑌 𝐷𝑊 𝑐 𝐷𝑊 + 𝑌 𝑁𝑎𝑂𝐻 𝑐 𝑁𝑎𝑂𝐻 + 𝑌 𝐻𝐶𝑙 𝑐 𝐻𝐶𝑙 (39)
c and Y represent products specific costs and annual products (Table 4). Subscript elec denotes electricity. The purchased equipment cost (PEC) for all components is depicted in Table 5.

277

For estimating the surface area of the HX, the logarithmic method is used and the following relation is 278 considered [START_REF] Pierobon | Multi-objective optimization of organic Rankine cycles for waste heat recovery: Application in an offshore platform[END_REF]: 279

𝑄 ̇= 𝑈𝐴𝐹 𝑡 Δ𝑇 𝐼𝑛 (40)
Where U, 𝑄 ̇, A, Ft, and Δ𝑇 𝐼𝑛 are the overall heat transfer coefficient, heat transfer rate, surface area, 280 correction factor, and logarithmic mean temperature difference. The overall heat transfer coefficient for 281 HX is considered to be 700 W/m 2 K. 282 According to ref [START_REF] Bejan | Thermal design and optimization[END_REF], total capital investment (TCI) is classified into three types. They are direct cost (DC), indirect cost (IC), and other costs (OC). Table 6 shows the components of DC, IC, and OC as a percentage of the PEC. The inflation rate effect on the TCI is calculated by [START_REF] Shafer | Calculating Inflation Factors for Cost Estimates[END_REF]:

𝑇𝐶𝐼 𝑛 = 𝑇𝐶𝐼 0 (1 + 𝑖) 𝑛 (41)
n and i depict the years' number and the rate of inflation (3.1%) [70]. Operation and maintenance cost (OMC) is considered to be 3% of the TCI [START_REF] Bellos | Parametric analysis and yearly performance of a trigeneration system driven by solar-dish collectors[END_REF][START_REF] Tzivanidis | Energetic and financial investigation of a stand-alone solar-thermal Organic Rankine Cycle power plant[END_REF].

Thus, the total cost (TC) is calculated as follows [START_REF] Bejan | Thermal design and optimization[END_REF]:

𝑇𝐶 = 𝑇𝐶𝐼 𝑛 + 𝑂𝑀𝐶 (42)
The simple payback period (ZS) index is calculated by [START_REF] Bellos | Parametric analysis and yearly performance of a trigeneration system driven by solar-dish collectors[END_REF][START_REF] Tzivanidis | Energetic and financial investigation of a stand-alone solar-thermal Organic Rankine Cycle power plant[END_REF]:

𝑍 𝑆 = 𝑇𝐶 𝐴𝐼 (43)
The payback period (ZP) index can be obtained by [START_REF] Bellos | Parametric analysis and yearly performance of a trigeneration system driven by solar-dish collectors[END_REF][START_REF] Tzivanidis | Energetic and financial investigation of a stand-alone solar-thermal Organic Rankine Cycle power plant[END_REF]:

𝑍 𝑃 = 𝑙𝑛( 𝐴𝐼 𝐴𝐼 -𝑟. TC ) 𝑙𝑛(1 + 𝑟) (44)
r depicts the discount factor (3%) [START_REF] Bellos | Parametric analysis and yearly performance of a trigeneration system driven by solar-dish collectors[END_REF][START_REF] Tzivanidis | Energetic and financial investigation of a stand-alone solar-thermal Organic Rankine Cycle power plant[END_REF].

The net present value (NPV) is calculated by the following relation [START_REF] Bellos | Parametric analysis and yearly performance of a trigeneration system driven by solar-dish collectors[END_REF][START_REF] Tzivanidis | Energetic and financial investigation of a stand-alone solar-thermal Organic Rankine Cycle power plant[END_REF]:

𝑍 𝑁 = 𝐴𝐼 (1 + 𝑟) 𝑁 -1 𝑟(1 + 𝑟) 𝑁 -TC (45)
N refers to the life cycle of the project (25 years) [START_REF] Bejan | Thermal design and optimization[END_REF]. The Internal rate of return (ZIR) can be obtained as follows [START_REF] Bellos | Parametric analysis and yearly performance of a trigeneration system driven by solar-dish collectors[END_REF][START_REF] Tzivanidis | Energetic and financial investigation of a stand-alone solar-thermal Organic Rankine Cycle power plant[END_REF][START_REF] Edalati | Technical and economic assessments of grid-connected photovoltaic power plants: Iran case study[END_REF]:

𝑍 𝐼𝑅 = 𝐴𝐼 TC [1 - 1 (1 + 𝐼𝑅𝑅) 𝑁 ] (46)

3) Results and discussion

For the MGS investigation, a computational program is developed in the engineering equation solver (EES). The thermodynamic properties of all working fluids are considered via the external library of EES.

The input data of the computational program is brought in Table 7. The biomass used in the gasifier is Alfalfa with the CH1.324O0.594N0.063 chemical formula, a molecular weight of 23.68 kg/kmole, and LHV of 12233.8 kJ/kg [START_REF] Kanagarajan | Emission and energy analysis of self-sufficient biomass power plant to achieve near net zero CO 2 emission[END_REF][START_REF] Basu | Biomass gasification and pyrolysis: practical design and theory[END_REF]. The flowchart of the computer code is depicted in Figure 4.

Model validation

Validation of model results is essential to use the research results in the related industry or further research. In this work, the configuration of the proposed system is novel. So, validation of the whole system is not feasible and each sub-system was validated individually.

The data from ref [START_REF] Kanagarajan | Emission and energy analysis of self-sufficient biomass power plant to achieve near net zero CO 2 emission[END_REF] is considered for the gasifier. The considered biomass feed type is bean straw with 0.1294 kg/s mass flow rate and 0.0006 kmole/kmole intake air to biomass ratio. The gasifier products predicted by the computer model and ref [START_REF] Kanagarajan | Emission and energy analysis of self-sufficient biomass power plant to achieve near net zero CO 2 emission[END_REF] are shown in Figure 5, confirming the good agreement. For the MED validation, ref [START_REF] Razmi | Thermodynamic analysis of compressed air energy storage (CAES) hybridized with a multi-effect desalination (MED) system[END_REF] is considered. Table 8 depicts the results of the comparison, which also validates the model. The ref [START_REF] Naseri | Exergy analysis of a hydrogen and water production process by a solar-driven transcritical CO2 power cycle with Stirling engine[END_REF] is considered to validate the CO2 cycle with the LNG heat sink. The CO2 and LNG turbines' power production and pumps power consumption are compared. Table 9 shows a comparison between the present work and reference [START_REF] Naseri | Exergy analysis of a hydrogen and water production process by a solar-driven transcritical CO2 power cycle with Stirling engine[END_REF]. From these comparisons, it can be concluded that the computer model provides reliable data.

Energy and exergy assessment results

The thermodynamic characteristics of all MGS streams, such as mass flow rate, pressure, temperature, specific enthalpy, and specific exergy, are reported in Table 10. The MED specification is summarized in Table 11. The electrical power production and consumption for various components and the cooling production of the MGS are shown in Table 12. It seems that the expander (EXP II) in the LNG line produces more electrical power than the expander in the CO2 cycle due to high pressure of NG after exchanging heat with the condenser of the CO2 cycle. The products of the system are shown in Figure 6 shows the energy and exergy efficiencies (ENE and EXE) of the CO2 cycle and MGS. According to Figure 6, the CO2 cycle ENE and EXE are 8.5% and 37.1%; however, the MGS ENE and EXE are 75.1% and 88.4%, respectively. So, it can be concluded that the MGS is beneficial from the energy and exergy point of view. In the CO2 cycle, the difference between the heat source and sink temperatures is T21-T18, while in the MGS, it is T7-T24. According to the Carnot efficiency, ((

T L T H 1 -
), T L and T H : heat sink and source temperatures), by increasing heat source and sink temperatures, the efficiency of all engines is improved. Thus, the ENE and EXE of the MGS are improved considerably.

In comparison between MGS and CO2 cycle, the ENE of the MGS is much higher due to the higher number of products than the CO2 cycle.

The EDR percentage of all MGS sub-systems including CO2 cycle, steam, LNG lines, MED, and ELECD, is Figure 10 shows the variation of ENE, EXE, and EDR of the CO2 cycle versus condenser pressure (P22).

Increasing the P22 from 600 to 1000 kPa causes reductions in ENE, EXE, and EDR of the CO2 cycle, since an increase in P22 causes a reduction in EXP I power production and P I power consumption. However, reduction in EXP I power production is more than P I power consumption. For the parametric study of the gasifier, other types of biomass were taken into account (Table 14). The chemical formula, LHV, and molecular weight of the different biomass types are summarized in this table.

The specifications of these biomass types were included in the computer code. Figure 11 displays the ENE and EXE of the MGS that uses these types of biomass. It is clear that with increasing the LHV of the biomasses, both the ENE and EXE of the MGS decrease. It can be concluded that by increasing the LHV of the biomass, the recovery ratio declines. Figure 14 shows the variation of the GOR of the MED system with xf. Increasing xf decreases the GOR of the MED system. By increasing xf from 15 to 50, the GOR of the MED system decreases by around 12.5%.

Since more steam should be consumed to separate salt from the seawater that has a direct effect on system performance.



The highest and lowest percentages of the AI are relevant to electricity and PW.

 SPP, PP, NPV, and IRR values are obtained at 2.78 years, 2.94 years, 3.929×10 7 $, and 0.36, respectively.

 Increasing the efficiency of the EXP I from 50% to 100% causes the ENE and EXE of the CO2 cycle being also doubled.

 With increasing the LHV of the biomasses, the ENE and EXE of the MGS are decreased. It can be concluded that by increasing the LHV of the biomass, the recovery ratio is decreased.

 Increasing biomass moisture content reduces the ENE and EXE of the MGS.

 Increasing the salt concentration of seawater from 15 to 50 leads to a reduction in DW mass flow rate while rising B mass flow rate, and further decreases the GOR of the MED system by around 12.5%.

 The SPP and PP decrease when raising the number of MED effects.

For future development of this MGS, the researches should concentrated on the power consumption of ELECD that all of dissipated brine can be converted to beneficial products and it does not harm the environment.

Nomenclature

  167

Figure 1 .Figure 2 .Figure 3 .

 123 Figure 1. The layout of the proposed system 168

  𝑆𝑦𝑠 + 𝑄 ̇𝐶𝑜𝑜𝑙𝑒𝑟 + 𝑚̇1 5 ℎ 15 + 𝑚̇1 6 ℎ 16 + 𝑚̇1 3 ℎ 13 𝑚̇1𝐿𝐻𝑉 + 𝑚̇2 4 (ℎ 24 -ℎ 27 )

Figure 4 .

 4 Figure 4. Flowchart of the computer code

Figure 5 .

 5 Figure 5. The comparison between gasifier products of the computer model and ref.[START_REF] Kanagarajan | Emission and energy analysis of self-sufficient biomass power plant to achieve near net zero CO 2 emission[END_REF]

depicted in Figure 7 .

 7 The highest percentage of EDR belongs to the LNG line due to LNG's high mass flow rate in this line. After the LNG line, the steam line features the most significant percentage of the EDR owing to the high temperature and mass flow rate of steam. 14.7% and 10.4% of the EDR are related to the CO2 cycle and MED. The lowest portion of the EDR is related to ELECD due to the low mass flow rate of brine. In the CO2 cycle, the evaporator features the biggest portion of the EDR because of heat transfer taking place between steam and CO2. The P I has the lowest rate of the EDR arising from a slight difference within thermodynamic features in the inlet and outlet of the P I. The EXP I and Cond have 3.9% and 6.97% of EDR percentage. In the steam line, the most distinguished portion of the EDR belongs to the boiler because of burning syngas and changing the water to steam that two important sources of the EDR named heat transfer and combustion reaction. The EDR percentage of the gasifier and heater is similar. The EDR percentage of P II is negligible.

Figure 6 .Figure 7 .Figure 8

 678 Figure 6. The energy and exergy efficiencies of the CO2 cycle and MGS 407

Figure 8 .Figure 9 .

 89 Figure 8. The percentage of the annual income for all products of the MGS

Figure 11 .

 11 Figure 11. The energy and exergy efficiencies of the MGS that uses different types of biomass

Figure 12 .

 12 Figure 12. The energy and exergy efficiencies of the MGS versus moisture content (w) in the biomass

Figure 13 .Figure 14 .Figure 15

 131415 Figure 13. The variation of DW and brine with xf

Figure 15 .

 15 Figure 15. The variation of PP and SPP with number of MED effects (N)

  Abbreviations

Table 2 .

 2 The mass and energy balance equations for the CO2 cycle and LNG line

	No. Component Mass balance	Energy balance
	1	P I	𝑚̇1 9 = 𝑚̇2 0	𝑊 ̇𝑃𝐼 = 𝜂 𝑃 𝑚̇5(ℎ 5 -ℎ 23 )
	2	Eva	𝑚̇2 0 = 𝑚̇2 1 𝑚̇1 0 = 𝑚̇1 8	𝑚̇1 0 (ℎ 10 -ℎ 18 )𝜂 𝐻𝑋 =𝑚̇1 9 (ℎ 21 -ℎ 19 )
	3	EXP I	𝑚̇2 1 = 𝑚̇2 2	𝑊 ̇𝐸𝑋𝑃𝐼 = 𝜂 𝐸𝑋𝑃 𝑚̇2 1 (ℎ 21 -ℎ 22 )
	4	Cond	𝑚̇2 2 = 𝑚̇1 9 , 𝑚̇2 4 = 𝑚̇2 5	𝑄 ̇𝐶𝑜𝑛𝑑 = 𝜂 𝐶𝑜𝑛𝑑 𝑚̇2 4 (ℎ 25 -ℎ 24 )=𝑚̇1 9 (ℎ 22 -ℎ 19 )
	5	EXP II	𝑚̇2 5 = 𝑚̇2 6	𝑊 ̇𝐸𝑋𝑃𝐼𝐼 = 𝜂 𝐸𝑋𝑃 𝑚̇2 5 (ℎ 25 -ℎ 26 )
	6	Cooler	ṁ 26 = ṁ 27	𝑄 ̇𝐶𝑜𝑜𝑙𝑒𝑟 =𝑚̇2 6 (ℎ 26 -ℎ 27 )

Table 3 .

 3 The EDR for all system components

	No. Component	EDR (kW)
	1	Cooler	𝑚̇2 6 𝛹 26 -𝑄 ̇𝐶𝑜𝑜𝑙𝑒𝑟 (1 -	𝑇 26 𝑇 0	) -𝑚̇2 7 𝛹 27
	2	EXP II	𝑚̇2 5 𝑒 25 -𝑚̇2 6 𝑒 26 -𝑊 ̇𝐸𝑋𝑃𝐼𝐼
	3	Cond	𝑚̇2 2 𝛹 22 -𝑚̇1 9 𝛹 19 + 𝑚̇2 4 𝛹 24 -𝑚̇2 5 𝛹 25
	4	EXP I	𝑚̇2 1 𝑒 21 -𝑚̇2 2 𝑒 22 -𝑊 ̇𝐸𝑋𝑃𝐼
	5	Eva	𝑚̇2 0 𝛹 20 -𝑚̇2 1 𝛹 21 + 𝑚̇1 0 𝛹 10 -𝑚̇1 8 𝛹 18
	6	P I	𝑚̇1 9 𝛹 19 -𝑚̇2 0 𝛹 20 + 𝑊 ̇𝑃𝐼
	7	Gasifier	𝑚̇1𝛹 1 + 𝑚̇2𝛹 2 -𝑚̇3𝛹 3
	8	MED	𝑚̇9𝛹 9 + 𝑚̇1 2 𝛹 12 -𝑚̇1 0 𝛹 10 -𝑚̇1 3 𝛹 13 -𝑚̇1 4 𝛹 14
	9	ELECD	𝑚̇1 4 𝛹 14 + 𝑊 ̇𝐸𝐿𝐸𝐶𝐷 -𝑚̇1 5 𝛹 15 -𝑚̇1 6 𝛹 16
	10	P II	𝑚̇2 3 𝛹 23 -𝑚̇5𝛹 5 + 𝑊 ̇𝑃𝐼𝐼
	11	Heater	𝑚̇3𝛹 3 -𝑚̇4𝛹 4 + 𝑚̇5𝛹 5 -𝑚̇6𝛹 6
	12	MX	𝑚̇1 1 𝛹 11 + 𝑚̇1 8 𝛹 18 -𝑚̇2 3 𝛹 23
	13	Boiler	𝑚̇4𝛹 4 -𝑚̇7𝛹 7 -𝑚̇8𝛹 8 + 𝑚̇6𝛹 6

Table 4 .

 4 The specific cost of fuel and products

	No. Specific cost of products and fuel	Unit	Value Ref.
		Products
	1	Electricity	$/kWh 0.12 [56]
	2	Cooling	$/kWh 0.06 [57]
	3	Demineralized water	$/m 3	5.8	[58]
	4	Sodium hydroxide	$/kg	0.74 [59]
	5	Hydrochloric Acid	$/kg	0.35 [60]
	6	LNG	$/kg	0.009 [61]

Table 5 .

 5 PEC for all components 276

	[23]

Table 6 .

 6 The components of DC, IC, and OC as a percentage of the PEC

	No.	Items	Percentage
	1	Piping (PI)	10
	2	Instrumentation and controls (I&C)	6
	3	Electrical equipment and materials ( E)	10
	4	Land (L)	4
	5	Civil, structural, and architectural work (CSA)	17
	6	Service facilities (SF)	34
	7	Engineering and supervision (E&S)	25
	8	Construction costs including contractor's profit	30
	9	Contingencies	24
	10	Startup costs (S&C)	9
	11	Working capital (WC)	17

Table 7 .

 7 Input data of system modeling 322

	No. Parameter	Definition	Unit Values
	1	T24	LNG temperature	o C	T19-10
	2	P25	Outlet EXP II pressure	kPa 121.6
	3	𝑚̇1	Working fluid mass flow rate in CO2 cycle kg/s	10
	4	w	Moisture ratio in biomass	-	0.34
	5	TBT	Top brine temperature	o C	66.3
	6	BBT	Bottom brine temperature	o C	40
	7	x12	Seawater salt concentration	-	35
	8	x14	Brine salt concentration	-	60
	9	m	Equ 3	-	0.187
	10	N	Number of effects	-	4
	11	T25	Inlet EXP II temperature	o C	25
	12	P24	LNG tank pressure	kPa 658.5
	13	P22	Condenser pressure in CO2 cycle	kPa 607.8
	14	P21	Evaporator pressure in CO2 cycle	kPa 1519.5
	15	ra	Air/fuel ratio in boiler	-	2.1
	16	T4	Syngas outlet temperature from heater	o C	85
	17	T6	Water outlet temperature from heater

Table 8 .

 8 The compared results of the generated model and ref.[START_REF] Razmi | Thermodynamic analysis of compressed air energy storage (CAES) hybridized with a multi-effect desalination (MED) system[END_REF] for the MED validation

	No. Parameter Unit Model Ref [74] Error (%)
	1	𝑚̇1 3	kg/s 0.802	0.8125	1.6
	2	𝑚̇1 4	kg/s 0.056	0.055	1.8
	3	GOR	-	9.2	9.4012	2.1

Table 9 .

 9 Comparison between the model and ref.[START_REF] Naseri | Exergy analysis of a hydrogen and water production process by a solar-driven transcritical CO2 power cycle with Stirling engine[END_REF] for the CO2 cycle

		30
		25	Ref
	(%)	20	Model
	fraction	15
	Molar	10
		5
		0
			nH2	nCO	nCO2		nH2O	nCH4	nN2
					Components
			No. Parameters Unit Model Ref [75] Error (%)
			1	𝑊 ̇𝐸𝑋𝑃 𝐼	kW	14.2	14.66	3.1
			2	𝑊 ̇𝑃𝐼	kW	4.98	4.778	4.2
			3	𝑊 ̇𝐸𝑋𝑃 𝐼𝐼	kW	7.19	7.464	3.6
			4	𝑊 ̇𝑃 𝐼𝐼	kW	3.81	3.693	3.1

Table 13 .

 13 The MGS products are 73.17 GWh of cooling, 103 GWh of electrical energy, 1223 Ton of NaOH, 1114 Ton of HCl, and 212.6 m 3 of PW annually. This system consumes 17130.2 Ton/year of Alfalfa biomass. The calculated ratio of cooling to power is 71%. 370

Table 10 .

 10 The thermodynamic characteristics of all MGS streams 371

	No ṁ (kg/s) P (kPa) T( o C)	h (J/kg)	e (J/kg)
	1	0.5948	101.3	10	16300.0	11890000.0
	2	0.6476	101.3	10	283507.0	6692.0
	3	1.242	202.6	430.8	642994.0	5551000.0
	4	1.242	192.6	85	126876.0	5149000.0
	5	4.399	121.6	32.5	136240.0	3580.0
	6	4.399	121.6	75	314025.0	69086.0
	7	1.353	101.3	480	716477.0	641162.0
	8	4.399	101.3	125	2726000.0	607337.0
	9	2.2	101.3	125	2726000.0	607337.0
	10	2.2	101.3	125	2726000.0	607337.0
	11	2.2	101.3	40	167586.0	6213.0
	12	112.5	101.3	25	99766.0	1364.0
	13	7.384	101.3	39.46	165255.0	5905.0
	14	1.034	101.3	313.2	154184.0	7910.0
	15 0.03869 101.3	313.2	686848.0	214779.0
	16 0.04245 101.3	313.2	686848.0	589373.0
	17	9.303	101.3	313.2	154184.0	7910.0
	18	2.2	101.3	25	104844.0	1606.0
	19	10	607.8 -52.81 -419369.0	199761.0
	20	10	1520	-52.46 -418448.0	200504.0
	21	10	1520	115	71690.0	155362.0
	22	10	607.8	55.15	21267.0	97147.0
	23	4.399	101.3	32.5	136215.0	3552.0
	24	59.5	658.5 -62.81 -200676.0	297925.0
	25	59.5	658.5	48	46196.0	278333.0
	26	59.5	101.3 -51.17 -165844.0	66293.0
	27	59.5	101.3	20	-12119.0	381.9
	372
	373
	374
	375
	376
	377

Table 11 .

 11 The MED specification

	No. Variable	Unit	1	2	3	4
	1	Aeffects	m 2	13.02 177.4 194.9 210.3
	2	BPE	o C	0.417 0.452 0.49 0.538
	3	Tb	o C	66.3	57.5	48.8	40
	4	Tdv	o C	65.9	57.1	48.3	39.5
	6	Ueffect	W/m 2 K 6319 2605 2383 2219
	7	P	kPa	26.03 17.4	11.3	7.2
	8	Acondenser	m 2		277.7
	8	GOR	-		3.36
	9	RR	-		0.065

Table 12 .

 12 The electrical power production and consumption for various components

	No. Items Unit Values
	1	ẆEXP I	kW 504.23
	2	ẆEXP II	kW 12490
	3	ẆP I	kW	9.2
	4	ẆP II	kW	0.14
	5	ẆELECD	kW	111.5
	6	Q ̇Cooler kW	9146

Table 13 .

 13 The products of the system

	No.	Products	Unit	Values
	1	Electrical energy	GWh	103
	2	Cooling energy	GWh	73.17
	3	NaOH	Ton/year 1223
	4	HCl	Ton/year 1114
	5	PW	m 3 /year	212.6

Table 14 .

 14 The chemical formula, molecular weight, and LHV for different types of biomass[START_REF] Kanagarajan | Emission and energy analysis of self-sufficient biomass power plant to achieve near net zero CO 2 emission[END_REF][START_REF] Basu | Biomass gasification and pyrolysis: practical design and theory[END_REF]

	Cases Name	Chemical Formula Molecular weight (kg/kmole) LHV (kJ/kg)
	1	Oats strand	CH1.269O0.626N0.013	23.46	12480
	2	Rapeseed	CH1.491O0.832N0.011	24.95	13084
	3	Wheat straw CH1.434O0.675N0.031	24.69	13215.2