Parameters for simulating proppant transport.
\n\n
\n\nThe research leading to these results has received funding from the European Community\'s Seventh Framework Programme (FP7/2007-2013) under grant agreement number 285417. The publishing of this book was funded by the EC FP7 Post-Grant Open Access Pilot programme. 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\r\n\tStatistical machine learning merges statistics with machine learning which falls in the field of computer science, systems science and optimization. Much of the agenda in statistical machine learning is driven by applied problems in science and technology, where data streams are increasingly large-scale, dynamical and heterogeneous, and where mathematical and algorithmic creativity are required to bring statistical methodology to bear. Fields such as bioinformatics, artificial intelligence, signal processing, communications, networking, and information are all intervened here.
\r\n\tStatistical machine learning specifically poses some of the most challenging theoretical problems in modern statistics, the crucial among them being the general problem of understanding the link between inference and computation. This book intends to provide the reader with a comprehensive overview of linear method for regression, non linear method for regression, deep learning, unsupervised learning, artificial neural network, and support vector machine (SVM).
Extracellular vesicles (EVs) are spherical fragments released from biological membranes of various cell types under both physiological and pathological conditions. So far, many terms have been used to describe EVs, such as exosomes, microvesicles (MVs), membrane microparticles, ectosomes, and apoptotic bodies. Recently, based on their size and origin, EVs are classified as exosomes, MVs, and apoptotic bodies. Under stimulating or storage conditions, human red blood cells (RBCs) release EVs. This chapter focuses on the formation and release of MVs from human RBCs and considers the isolation and characterization of MVs in order to apply MVs as potential vehicles for nucleic acid delivery. Similar to EVs released from nucleated cells, MVs from human RBCs carry biomarkers originated from plasma membrane and also microRNAs but not DNA. These properties suggest that MVs can be used as potential vehicles to transport proteins, nucleic acids, or signal molecules. While the understanding of the biogenesis of MVs in human RBCs and their physiological role remains limited, accumulating data suggest that MVs may be applied in cancer therapy. This chapter reviews our current knowledge pertaining to MVs released from human RBCs. It describes the formation and biological properties of MVs and mentions the potential application of MVs as a molecular vehicle for drug and nucleic acid delivery. Furthermore, it gives an introduction in the application of MVs for cancer treatment. In addition, MVs and exosomes released from other cell types are also taken into consideration to provide findings of the nature of the membrane-derived vesicles, their mechanism of action, and their possible role in biological processes both under in vitro and in vivo conditions.
Under physiological and pathological conditions, various cell types release small spherical fragments called membrane vesicles or extracellular vehicles (EVs). So far, many different terms such as ectosomes, MVs, shedding vesicles, apoptosomes, membrane microparticles, or apoptotic bodies have been used in a vast number of reports on EVs [1–8]. Fifty years ago, in 1967, Wolf first identified small procoagulant structures deriving from activated platelets in human blood and created the initial term “platelet dust” [9]. Twenty years later, in 1987, Johnstone described the vesicle formation during maturation of sheep reticulocytes in vitro [10]. These findings were seen as a milestone in EV research allowing further studies on their function at various physiological conditions and in certain diseases. Since then, EVs have been detected in different body fluids such as peripheral blood, urine, saliva, semen, cerebrospinal fluid, synovial fluid, bronchoalveolar lavage, and bile. The mechanism of EV formation and the biochemical composition of EVs depend on cell types, physiological conditions, and the function of the cells from which they originate [11–16]. Recently, based on their size and biogenesis, EVs have been classified into exosomes, MVs, and apoptotic bodies. Exosomes are generally accepted to have size from 40 to 100 nm in diameter. They are secreted from endosomal compartments or multivesicular bodies of cells. In contrast, MVs including microparticles or membrane particles are larger in size varying from 50 to 1000 nm in diameter. The biogenesis of MVs arises through direct outward budding and fission of the plasma membrane following different kinds of cell activation or during early state of apoptosis [11, 17, 18]. Distinct from exosomes and MVs, apoptotic bodies are much larger with 1–5 μm in diameter. They are formed by cell-membrane blebbing when the cells undergo apoptosis [7, 11, 19–21]. Three subtypes of EVs, namely exosomes, MVs, and apoptotic bodies, are shown in Figure 1. In fact, it is still a challenge to separate one EV type from another because of their overlapping biophysical characteristics. Nevertheless, some discriminating markers have been reported [22]. In this chapter, the term MVs will be used for MVs, microparticles, or membrane microparticles (MPs) and EVs for both exosomes and MVs.
Potential vesicular structures of circulating DNA. Depending upon the mechanism of release, three subtypes of EVs, namely, exosomes, MVs, and apoptotic bodies, are described [28]. The figure is taken from Rykova et al. [29].
It has been reported that MVs are released from various types of activated or apoptotic cells including platelets, monocytes, endothelial cells (ECs), red blood cells, THP-1 monocytic cells, and granulocytes. MPs were also collected from the culture media, cell supernatants, and plasma by centrifugation at 20,000 g for 30 min. The average diameter of all types of MVs was varying much comparing different reports [19, 23–25]. The plasma MPs had the smallest size similar to MPs released from platelets and THP-1 cells, while MPs from monocytes were larger, and MPs from granulocytes and ECs were the largest ones. The data obtained from various reports indicate that the size of membrane MPs depends on the type of the cells from which they originate [23]. Although MVs have been discovered for years, the understanding of the mechanism of the formation as well as the biological roles of MVs is still a matter of debate. Recent reported findings led to advances of our understanding of the mechanism of formation and the role of MVs in many different diseases such as vascular diseases, cancer, infectious diseases, diabetes mellitus, diabetes, inflammation, and pathogen infection [24]. Inhibition of the production of MPs may serve as a novel therapeutic strategy for some diseases, especially for cancer treatment [11, 23, 26, 27]. In the next part of this chapter, the biogenesis, properties, and biological function of MVs released from human red blood cells (RBCs) are mainly addressed.
In the past decade, extracellular vesicles (EVs) have been recognized as potent vehicles of intercellular communication due to their capacity to transfer proteins, lipids, and nucleic acids, thereby influencing various physiological and pathological functions of both recipient and donor cells [30]. In addition, EVs also represent an important mode of intercellular communication by serving as vehicles for transfer between cells of membrane and cytosolic proteins, lipids, and RNA. Shortage of our knowledge of the molecular mechanisms for EV formation and lack of methods to interfere with the packaging of cargo or with vesicle release leads to a difficulty in identification of their physiological relevance in vivo [6]. EVs have been implicated in important biological processes such as surface-membrane trafficking and horizontal transfer of proteins and RNAs among neighboring cells, and distant tissues. Therefore, they play an important role in cell-to-cell communication under both physiological and disease conditions [11].
It is evident that direct investigation of the biological function of MVs in vivo is extremely complicated. Most of the studies regarding physiological roles of exosomes or MVs have to carry out in vitro, especially in the context of the immune system and cell-cell communication [31]. In 1996, a pioneering study by Raposo and colleagues demonstrated that exosomes derived from both human and mouse B-lymphocytes spread antigens bound to the class II major histocompatibility complex (MHC). These vesicle-associated complexes were capable of activating MHC class II leading to a restriction of T-cell responses. This finding suggests a role for exosomes in antigen presentation in vivo [32]. Furthermore, B cell–derived exosomes specifically interacted with the membrane of follicular dendritic cells derived from human tonsils. This finding is also an example for further supporting the idea of the active secretion of exosomes in vivo [33]. In addition, Montecalvo and colleagues demonstrated that different subsets of miRNAs are exchanged between follicular dendritic cells through exosomes at different maturation stages [34].
In a study, Wu showed that cancer cells release MVs and exosomes under both in vivo and in vitro conditions. MVs and exosomes carry different types of molecules on their surfaces, which are seen as biomarkers [24]. That is the reason why MVs or exosomes are used in cancer diagnosis. For example, circulating levels of MVs are elevated in gastric cancer patients. In these patients, MPs released from CD41a-positive platelets are significantly increased in stage IV compared with stage I or II/III [35]. It has been recently demonstrated that MVs released by cells represent another important mediator of cell-cell communication and are also an integral part of the intercellular microenvironment [3, 36, 37]. This opens a new scenario to understand signal and molecule transfers between cells even at long distances. For human RBCs, released MVs in both resting state (storage at 4°C) and stimulating conditions showed the ability to adhere together. It might be suggested that MVs are involved in the blot clot formation and also play a substantial role in the aggregation of stimulated RBCs [38, 39]. Further investigations have to be carried out to understand the role of MVs in both physiological and disease conditions.
It has been described that blood cells are able to generate a great variety of EVs. First identified in 1967, MVs are cell plasma membrane-derived small vesicles which are 0.1–1 mm in diameter. Later, the formation and release of EVs have been demonstrated in platelets, monocytes, endothelial cells, RBCs, and granulocytes [9]. EVs have been thought to serve as a disseminated storage pool of bio-effectors that circulate and play important roles in physiological homeostasis of the body under both physiological and disease conditions. Recent functional assays and analysis of MVs by multicolor flow cytometry have shown that MPs possess a broad spectrum of biological activities and may play an important role in multiple cellular processes including intercellular communication, immunity, apoptosis, and homeostasis [24, 40]. In case of human RBCs, MVs have a phospholipid bilayer structure exposing coagulant-active phosphatidylserine and expressing various membrane receptors [40]. It should be mentioned that mature human RBCs do not contain DNA but RNAs including mRNA and other non-coding RNAs. Therefore, it suggests that MVs from human RBCs may not only be involved in thrombosis, amplifying systemic inflammation or cell adhesion, but also in cell-cell interactions in term of nucleic acid transfer [38, 39, 41, 42].
Recently, it has been reported that negatively charged membranes of erythrocyte-derived microparticles display procoagulant activity [38, 39]. However, relatively little is known about the possible fibrinolytic activity of such MVs. This issue becomes particularly important during RBC storage, which significantly increases the number of MVs [43]. Regarding the ability of carrying nucleic acid, recently, a novel system composed of MVs from RBCs was created for efficient delivery of ultra-small superparamagnetic iron oxide particles into human bone marrow mesenchymal stem cells for cellular magnetic resonance imaging in vitro and in vivo. It showed that MVs are highly bio-safe to their autologous (exosomes) as manifested by cell viability, differentiation, and gene microarray assays. The data suggest that MVs could be used as potential intracellular delivery vehicles for biomedical applications [44]. More recently, a study of the function of MVs from human RBCs infected with Plasmodium falciparum parasites showed that infected RBC-derived MVs contain miRNAs that can modulate target genes in recipient cells. In addition, multiple miRNA species in EVs have been identified. They are bound to Ago2 and form functional complexes. The infected RBC-derived MVs were transfected successfully into endothelial cells repressing miRNA target genes and changed endothelial barrier properties [45]. In addition, role of RBCs-derived MVs in malaria response showed that the development of MVs by Plasmodium sp. has a major impact in disease outcomes and serves as an integral part in controlling stage switching in its life cycle. Clinical studies have highlighted elevated levels of EVs in patients with severe malaria disease, and EVs have been linked to increased sequestration of infected RBCs to the endothelium [46].
It has been known that during their 120-day of lifespan, RBCs lose approximately 20% of their volume through vesicle release, whereas their hemoglobin concentration increases by 14% [47]. Although a number of mechanisms explaining the formation of MVs have been proposed, the creation and the role of RBC microparticles are far from being completely understood. It has been pronounced that the formation of MVs involves the activity of certain components of the plasma membrane as well as cytoskeletal proteins [19]. Under physiological conditions, the phospholipids of the cell membrane are distributed asymmetrically. In particular, phosphatidylcholine (PC) and sphingomyelin (SM) are predominantly present in the outer membrane leaflet, while phosphatidylserine (PS) and phosphatidylethanolamine (PE) are located predominantly in the inner membrane leaflet. This asymmetric distribution is controlled by a group of enzymes, flippase, floppase, and scramblase [48–51]. The flippase is responsible for the transfer of PE and PS from the outer to the inner leaflet of the cell membrane, while the floppase has been shown to have the opposite effect. Their activity is regulated by ABCC1 protein, also known as a multidrug-resistant protein 1 [19]. In contrast, the distribution of the phospholipid PS is determined by the activity of the scramblase. In human RBCs, the mechanism of the formation of MVs has been investigated and described by many research groups [50–54].
The integrity of RBC membrane is supported from many components of cytoskeleton structure, e.g., hexagonal actin–spectrin lattice anchoring with other proteins such as glycophorin A and band 3 protein [55]. It has been described that the vesiculation would be a mean for RBCs to get rid of specific harmful agents such as denatured hemoglobin, C5b-9 complement attack complex, band 3 neoantigen, and IgG that tend to accumulate in RBCS or on their membrane during their lifespan [22]. An influx of Ca2+ through nonspecific cation channels leads to the activation of several enzymes such as calpain or scramblase leading to the externalization of phosphatidylserine of the RBC membrane and degradation of cytoskeleton proteins and aggregation of band 3 leading to vesiculation [41, 56]. In our recent study, the kinetics of membrane blebbing and formation of MVs were characterized by using annexin V-FITC and fluorescence microscopy. The kinetics of budding and shedding of MVs were captured in every 30 s. Treatment of RBCs with a calcium inonophore (as positive control), lysophosphatidic acid (LPA), or phorbol-12-myristate-13-acetate (PMA) led to the externalization of PS at the outer membrane leaflet of RBCs as well released MVs. Moreover, it was interesting to see that a stimulation of RBCs by PMA in the absence of Ca2+ also led to the release of MVs [17, 41]. This suggests that the formation of MVs is also under the control of a calcium-independent pathway related to the activity of the PKC (Figure 2).
Bright field imaging of the formation of MVs in human RBCs depending on time (up to 120 min) stimulated by 6 µM PMA in the presence of 2 mM Ca2+ (upper row) and in the absence of Ca2+ and with 2 mM EGTA (lower row).
Based on the current understanding, a scheme with the interaction of protein components in the cells has been proposed. The proposed mechanism for the budding and shedding of MVs in human RBCs is shown in Figure 3.
Proposed mechanisms of the formation of MVs in human RBCs. Lysophosphatidic acid (LPA) or prostaglandin E2 (PGE2), which are two typical substances released from activated platelets, activate a nonselective voltage-dependent cation (NSVDC) channel. The opening of this channel leads to an increase of the intracellular Ca2+ content. An increase of the intracellular Ca2+ level activates the phospholipid scramblase (PLSCR) and the protein kinase C (PKC). The activated PKC moves from the cytoplasma to the membrane. The amino-phospholipid translocase (APLT) is inhibited by high concentrations of intracellular Ca2+, PKC, and ATP depletion. The PKC also activates and opens Cl− channels leading to an efflux of Cl−. The efflux of Cl− leads to an intracellular acidification. Under stress conditions, ceramide is formed and caspases are activated. Calpains are a family of calcium-dependent non-lysosomal cysteine proteases activated by Ca2+. When caspase and calpain are activated, they are able to break down the cytoskeleton by a proteolysis activity leading to membrane blebbing and vesicle formation [41].
Although many factors influence the formation and release of MVs, Ca2+ and PKC play essential roles in the process of MV formation [17, 19, 41]. An increase of intracellular calcium inactivates the flippase and activates the scramblase as well as the floppase leading to a reorganization of phospholipids in the cell membrane [21, 22, 41, 53, 54, 57]. The activation of calpain and degradation of actin filaments leads to breaking of bonds between the cytoskeleton filaments and the phospholipids. The weakening of the protein fibrils of the cytoskeleton initiates the budding and shedding of MVs [52, 58–60]. It has been demonstrated that reorganization or disruption of the cytoskeleton plays an important role in the release of MVs [36]. Another study showed that the activation of the scramblase requires a larger increase of the calcium concentration and therefore it is considered as being less important for the formation of MVs [19, 50]. By using a special compound R5421, a scramblase-specific inhibitor, it has been shown that vesicle shedding was attenuated in human RBCs [52, 61]. By adding ascorbic acid to RBCs during storage, a significant decrease in MVs formation was observed [62]. In our study, the MVs formation was observed within 1 hour when RBCs were treated with the PKC activator, phorbol-12-myristate-13-acetate (PMA), even in the absence of Ca2+. In addition, the kinetics of the formation of MVs in human RBCs has recently investigated by real-time measurement using fluorescence microscopy [17].
In recent years, numerous works have focused on providing a comprehensive characterization of the content of exosomes and MVs. Recently, information about molecules including proteins, mRNAs, microRNAs, or lipids observed within these vesicles has been deposited in EVpedia and Vesiclepedia [48, 63, 64]. By the end of 2015, Vesiclepedia stores records for 92,897 proteins, 27,642 mRNAs, 4934 miRNAs, and 584 lipids from 538 studies in 33 different species [48]. These numbers suggest that exosomes and MVs contain an extremely broad and heterogeneous range of molecules. Although these databases are extremely valuable, it still needs more evidences to elucidate the biological role of MVs and exosomes because the processes of biogenesis and packing molecules into these vesicles are complicated. It should be also mentioned here that the interpretation of the content of exosomes and MVs may be influenced or interfered by artifacts in sample preparation, isolation procedures, and analysis methods [65]. In comparison to MVs, exosomes are vesicles secreted upon fusion of multivesicular endosomes with the cell surface. Thus, exosomes transfer not only membrane components but also nucleic acid among different cells. Therefore, in order to understand the function of exosomes, it is necessary to have more evidences at subcellular compartments and mechanisms involved in the biogenesis and secretion of these vesicles [66]. Moreover, for many years, it is commonly thought that human mature RBCs do not contain nucleic acids because they are terminally differentiated cells without nuclei and organelles. However, transcriptomic analysis of a purified population of human mature RBCs from individuals with normal hemoglobin (HbAA) and homozygous sickle cell disease (HbSS) showed that there was a significant difference in microRNA expression in HbAA in comparison with HbSS [67]. This finding is very important to understand that MVs released from human mature RBCs carry nucleic acid and are likely involved in the biological processes of cell-cell communication and nucleic acid delivery.
It is known that the antigens occurring on MVs are typical for cells from which the MVs are released. Depending on the origin of formation, MVs contain numerous markers that determine their origin, e.g., CD41 for platelets, CD235a and Ter-119 for RBCs [55, 68], and CD11c for dendritic cells [69]. Additionally, MVs released from B cells, dendritic cells, and melanoma cell lines are richer in sphingomyelin, rather than in cholesterol which are also characteristics of their parental cells [70]. Some glycoproteins on the surface of RBCs expressed at low and variable levels protect RBCs from damage and elimination. These include complement inhibitors, such as DAF and CD59, and signaling molecules such as CD47 [71, 72] and SHPS-1, a multifunctional transmembrane glycoprotein [72]. These makers inhibit phagocytosis of RBCs by macrophages because CD47 prevents this elimination by binding to the inhibitory receptor signal regulatory protein alpha (SIRPα) [73]. Therefore, these markers also exist on the surfaces of MVs released from RBCs [11, 74, 75]. In human RBCs, if the released MVs carry CD47 on their surface, they may be avoided from the clearance by macrophages [76, 77].
Studies on proteomics of MVs released from human RBCs were first carried out by Bosman presenting pioneering investigations [78–80]. In these series of studies, membranes of intact RBCs and MVs were compared, allowing the identification of several proteins differentially expressed between the two types of samples. Together with further studies on the oxidation and the depletion of spectrins and cytoskeletal proteins such as proteins 4.1 and 4.2, band 3 followed by the time course of storage, it has been concluded that RBCs have the ability to get rid of harmful materials by vesiculation such as denatured hemoglobin, C5b-9 complement attack complex, and band 3 neoantigen [81, 82]. In human RBCs, the formation of MVs has been described as part of the RBC senescence process [47, 78] and also proposed as part of an apoptosis-like form of these cells [20, 21].
It should be also mentioned that due to the variation of the lateral composition of the cell membrane, MVs originated from the same cell may contain different proteins or lipid components. Proteomic analyses have revealed that the spectrum of proteins found in MVs released from cultured cells is influenced partly by the stimulating conditions, which were used to trigger the vesiculation [36]. A study on the components of proteins in human RBC-derived MVs by two-dimensional gel electrophoresis discovered that the protein components in MVs under various stimulating conditions (cold storage and increased intracellular calcium level) are different. This was especially the case for sorcin, grancalcin, PDCD6, and particularly annexins IV and V [83]. Therefore, the molecular pathways to form MVs are different under both in vivo and in vitro conditions. In addition, this finding suggests that MVs may be also classified based on the presence of proteins. Recently, a method has been reported using carboxyfluorescein diacetate succinimidyl ester, which allows to detect the phospholipid component PS in the outer membrane leaflet of MVs that fail to react with annexin V [84]. This study is very important for screening blood products during storage in blood bank because the formation of MVs with PS in the outer membrane leaflet may lead to thrombus formation or aggregation of RBCs or phagocytosis.
It seems relatively simple to isolate EVs from human plasma with available protocols described elsewhere. However, to isolate MVs from RBCs, it requires a step to separate only RBCs without contamination of platelets or white cells. Upon the purpose of study, MVs can be collected by differential centrifugation. Menck and colleagues isolated and distinguished MVs and exosome from human blood cells using Western blot analysis. The data revealed that MVs pelleted from EDTA-anticoagulated plasma samples by differential centrifugation were 100–600 nm in diameter. MVs can be distinguished from exosomes by detecting the presence of proteins tubulin, actinin-4, or mitofilin, while antibodies for CD9 and CD81 were used as markers for exosomes [85].
Jayachandran and colleagues isolated MVs from platelet-free plasma (PFP) and platelet poor plasmas (PPP) and stored the MVs at either −40 or −80°C for more than a year. No effect on MV counts irrespective of initial counts was observed after three freeze thaw cycles of PFP [86]. Another investigation on the stability of MVs after different times of storage at 4 and −80°C by using flow cytometry analysis showed that there was no significant difference by counts and size distribution of MVs stored at 4°C for 3–4 days or 1 week and MVs frozen at −80°C for 1 or 4 weeks [87]. In another study, Gallart showed that plasma containing exosomes and MVs frozen at −150°C can keep vesicles intact for long time [88]. Investigation was carried on the effect of short-term storage and temperature on the stability of exosome by incubating at temperatures ranging from −70 to 90°C for 30 min. Immunoblot results showed that all exosome-associated proteins incubated at 90°C were mostly degraded for a short period of time. The effect of long-term storage was carried out by incubating isolated exosomes for 10 days at wide range of temperature from −70°C to room temperature (RT). It revealed that protein and RNA amounts were significantly reduced at RT compared with data obtained at −70 and 4°C. Incubation at 4°C and RT resulted in major loss of CD63, and decreasing level of HSP70 was shown only at RT. In addition, flow cytometry result showed that exosome population became more dispersed after RT incubation for 10 days compared with −70°C incubated or freshly isolated exosomes [88]. Study on exosomes isolated from urine defined that freezing at −20°C caused a major loss of the integrity of these exosomes. In contrast, storage at −80°C increased the recovery almost complete (86%). Vortexing after thawing resulted in a significantly increased recovery of exosomes in urine frozen at −20 or −80°C, even if it was frozen for 7 months [89]. A similar study has been done to evaluate the stability of MVs released in whole blood samples under the influence of different anticoagulants. Analysis of MVs stored at 4°C and RT using nanoparticle tracking analysis (NTA) showed that total MV counts increased after 24 hours in sodium citrated or heparinized blood. The presence of EDTA showed stable platelet-derived MVs and RBC-derived MV counts at RT over a period of 48 h [90].
Currently, there is no standard protocol for isolation of EVs for either therapeutic application or basic research [91]. However, a conventional method to obtain EVs is ultrafiltration followed by differential centrifugation. Ultrafiltration and size-exclusion liquid chromatography is suitable for EV isolation at large scale [92]. In fact, many research groups use differential centrifugation combined with filtration to isolate and define the MVs or exosomes. For example, a centrifugation force from 10,000 to 20,000 g is commonly applied to pellet MVs and from 70,000 to 100,000 g or even higher for exosomes. Although the centrifuge force is indicated in a number of publications, it is still varying among research groups. Nevertheless, there is always an overlap in the size of collected MVs or exosomes when analyzed by using dynamic light scattering (DLS) method. Therefore, the procedure for sample preparation and also isolation of MVs should be simplified as much as possible with minimal steps. In general, four critical steps should be taken into consideration: (i) removal of intact cells and large cell debris by low-speed centrifugation of the extracellular fluid (200–1000 g for 3–15 min); (ii) pelleting of large, secreted vesicles from the cell-free supernatant by medium-speed centrifugation (10,000 g for 30 min, a minimum of 2 times); (iii) collection of small, secreted vesicles by ultracentrifugation at 70,000–100,000 g, and (iv) noting all other parameters and type of rotors used in experiments [7].
At present, there is still a lack of studies assessing EV products after periods of storage. However, our unpublished investigations showed that the polydispersity (PI) of MV increased proportionally with the storage time at −20°C in deionized water. Vortexing was useful to recover MVs after storage. Further studies have to be done investigating the stability and the polydispersity of MVs in different solvents or buffers. The results of such analyses will facilitate defining provisional shelf-life times of EV-based products. The materials used for sample preparation, isolation, and storage should also be taken into consideration, especially for human therapeutics because solvents and buffers have a strong influence on the stability of EVs, especially after storage [93]. There is a wide range of solvents from water, sodium chloride solution, to phosphate-buffered saline (PBS), Tris-HCl, HEPES, and glycerol. However, glycerol and dimethyl sulfoxide (DMSO) showed a significant influence to the stability of EVs [94]. For investigation of the function and physical properties of EVs, isotonic buffers are recommended to prevent pH shifts during storage as well as during freezing and thawing procedures. Although PBS or other phosphate-containing buffers are widely used, it has to be considered to avoid calcium even at a very low concentration due to the formation of calcium phosphate aggregated in the buffer as nanoparticles, which can interfere with EV quantification assays [93]. Storage vials can also affect the quality of EVs due to unexpected or irreversible binding to certain materials. Thus, vials should be carefully selected to eliminate the factors that influence the concentration or integrity of stored EVs [93, 95].
So far, a variety of techniques have been commonly used to study MVs released from human RBCs. Traditionally, nanoparticle analysis is available to analyze the particles at nanosize including flow cytometry, DLS, and electron microscopy. Most widespread is flow cytometry; however, commercial flow cytometry typically has a lower practical size limit (for polystyrene beads) of around 300 nm at which point the signal is hard to distinguish clearly from the baseline noise level or so-called “dust” [96]. Fluorescence labeling can be efficient to detect particles at lower sizes. DLS has also been used, but being an ensemble measurement, the results comprise either a simple z-average (intensity weighted) particle size and polydispersity (PI), or a very limited-resolution particle size distribution profile. Electron microscopy is a useful research tool for studying micro- and nanovesicles but at high running costs and extensive sample preparation [22]. Atomic force microscope (AFM) is also an applicable method to measure the size and also the morphology of MVs [17]. An alternative approach for measuring EVs is using the NTA method. In NTA, the size is derived from the measurement of Brownian motion of EVs in a liquid suspension [22].
In recent study, under stimulating conditions, MVs from RBCs were collected by differential centrifugation and characterized by using SEM, AFM, and DLS. Data from the measurement using a Zetasizer (Nano ZS) for both size and zeta potential showed that the sizes of two subpopulations of MVs were 125.6 ± 31.4 nm and 205.8 ± 51.4 nm. There was an overlapping in the size of the two populations in the region from 150 to 200 nm. Zeta potential of released MVs was measured in different solvents showing negative values from −40 to −10 mV depending on the solvent used [17]. The morphology and size of MVs released from human RBCs were also analyzed using AFM and SEM (Figure 4).
Topographical imaging of stimulated RBCs and released MVs. Glutaraldehyde-fixed samples of PMA-stimulated RBCs using AFM (A) and SEM (D); MVs scanning using AFM (B, C) and SEM (E) [17].
The structural feature that makes EVs especially attractive for drug delivery purpose is due to their analogy to liposomes. This means that EVs originated from an organism can be used as conventional liposome with an advantage when they are administered to the same organism in vivo. EVs are able to deliver molecules through hard-to-cross barriers like the blood-brain barrier. Therefore, EVs can be used for loading with drugs or other bioactive molecules and then work as efficient delivery systems. Several strategies are described for loading small molecule and genetic materials into liposomes; however, most of these strategies are not feasible for exosomes [97–99]. Two major strategies have been applied to load small molecules or drugs to EVs. The first possibility is the loading after EV isolation, and the second is the loading during EV biogenesis. In addition to loading, labeling of MVs is required to detect or investigate the efficiency of delivery to target cells and the expression of protein or function of miRNAs in recipient cells. So far, several techniques and methods have been applied to label MVs. Most common methods are incubation with fluorescence lipophilic dye, biotinylated radioisotope, substrate of luciferase (for in vivo trial), streptavidin-conjugated fluorescence dyes, or other modified proteins [100].
When nucleic acid (DNA, RNA) is directly introduced to the body, it will be rapidly removed out of the circulation via degradation by nucleases or by kidneys before reaching the target tissues or cells of interest. Recent evidence has shown that different kinds of RNAs are transported by EVs during cell-cell communications. It has been shown that miRNAs are enriched in EVs in form of miRNA-RISC complexes and transferred from exosomes and MVs to many different cells. As such, EVs can be applied as a new attractive alternative approach for therapeutic miRNA delivery [14]. Recently, a study showed that embryonic stem cell MVs likely are useful therapeutic tools for transferring mRNA, microRNAs, protein, and siRNA to cells and also important mediators of signaling within stem cell niches [101]. It has been known that the lipids, proteins, mRNA, and microRNA (miRNA) delivered by these vesicles change the phenotype of the receiving cells [11, 102]. The ability to encapsulate and deliver different types of nucleic acid of both exosomes and MVs has been investigated. The results showed that MVs delivered functional plasmid DNA, but not RNA, whereas exosomes from the same source did not deliver functional nucleic acids. These results have significant implications for understanding the role of EVs in cellular communication and also the role of MVs for development of tools for nucleic acid delivery [11]. MVs from human RBCs infected with P. falciparum parasites contain miRNAs that can modulate target genes in recipient endothelial cells and serve as an integral part in controlling stage switching in the life cycle of the parasites [45, 46]. A typical example of application of EVs as vehicle for drug transport is the loading of curcumin, chemotherapeutic compounds paclitaxel and doxorubicin to EVs using electroporation. After transfecting loaded EVs to implanted breast tumor tissues, the results showed that the loaded EVs suppressed the growth of tumors without causing any toxicity [103]. As such, curcumin-loaded EVs have already made their way into the clinic to specifically suppress the activation of myeloid cells [93, 104].
The strategy for cancer treatments is specifically killing malignant cells by vehicles, which carry appropriate substances or compounds to the target cells. Unfortunately, so far, it was not successful to cure the disease. The current concept in tumor treatment is to control the microenvironment of the tumor because the tumor is not only composed of malignant cells but also consists of other groups of cells that work together [105, 106]. Future research directions should draw more attention to EVs as biological targets for diagnosis, prognosis, and therapy of cancer. In addition, EVs participate and play a significant role in cell communication, and therefore they may become a valuable drug delivery system [107]. So far, a vast number of investigation on exosomes in carrying and transport of nucleic acid to target cells have been carried out; however, more information about using MVs to carry nucleic acid for transfection to cultured cells is required. Recently, an investigation of the capacity of MVs to deliver functional nucleic acids was carried out by using recipient HEK293FT cells cultured with exosomes and MVs derived from transfected donor cells with the fusion protein Luc–RFP as reporter. The data revealed that only loaded MVs led to Luc–RFP expression in the recipient HEK293FT cells, even though both MVs and exosomes encapsulated the reporter proteins. After the MV-mediated transfer, the bioluminescence signal increased over 3 days that was not observed in case of exosomes. The finding suggested that nucleic acids were delivered and led to a de novo expression of reporter proteins in recipient HEK293FT cells. By comparison with HEK293FT cells transfected by lipofectin with Luc-encoding pDNA, there was a different time course of Luc expression of the two methods. This observation suggested that the mechanism of MV-mediated delivery of nucleic acids and protein expression may be different from that of cationic liposome-based delivery of pDNA, which is typically used for transfection to culture cells [11]. Although this finding was very important to confirm the ability of MVs in carrying nucleic acid and transfection to recipient KEK293FT cells, experiments with different cell types are required. Another example is the study using MVs shed from the monocytic cell line THP-1 enriched with miR-150 to transfect to endothelial cells promoting angiogenesis of these cells [108]. MicroRNA-223 delivered by platelet-derived MVs promotes lung cancer cell invasion via targeting tumor suppressor EPB41L3 [109]. Another example of using MVs in nucleic acid delivery was the work of Zhang to prove the inhibitory effect of TGF-β1 siRNA delivered by mouse fibroblast L929 cell-derived MVs (L929 MVs) on the growth and metastasis of murine sarcomas 180 cells both in vitro and in vivo. By comparing to the same concentration of free TGF-β1 siRNA, TGF-β1 siRNA delivered by L929 MVs efficiently decreased the level of TGF-β1 in the recipient tumor cells [110]. Other works dealing with miR-150 proved that MVs can be an excellent carrier for nucleic acid delivery [108, 110]. Taken all together, MVs carrying microRNAs can influence the recipient cell phenotypes.
Protein expression induced by MV-mediated pDNA delivery is a slower process than after transfection using cationic lipid complexes. It may be due to that fact that loaded MV need to fuse with the endosomal membrane before releasing nucleic acid contents into the cytosol. Studies on EVs from transiently transfected cells may be confounded by a predominance of pDNA transfer. Compare the efficiency of transfection of MVs loaded with pDNA or RNA, it revealed that MVs functionally deliver DNA much better than RNA. Further studies of the nature of this transfer are necessary to understand the specificity of pDNA loading pathways and delivery mechanisms [11]. So far, small RNAs have been successfully loaded into MVs for a variety of delivery applications; however, the potential use of MVs for DNA delivery has been abandoned. By using electroporation, Lamichhane investigated the ability of loading MVs with linear DNA. Loading efficiency and capacity of DNA in MVs were dependent on DNA size as well as on the conformation of DNA. By using this approach, linear DNA molecules with less than 1000 bp in length were more efficiently associated with MVs compared to larger linear DNAs and pDNA. In addition, MV size was also influencing the potential of DNA loading, as larger MVs encapsulated more linear and plasmid DNA than smaller vesicles and exosomes. These results demonstrated critical parameters that define the potential use of MVs for gene therapy [111]. Another example is the application of EVs isolated from media of cultured cardiomyocytes derived from adult mouse heart. These EVs, which were transfected to target fibroblasts, led to a change in the gene expression patterns in comparison with controls [112]. Recently, a study on delivery of a therapeutic mRNA or protein via MVs for treatment of cancer was carried out. Genetically engineered MVs by expressing high levels of the suicide gene mRNA and protein–cytosine deaminase (CD) fused to uracil phosphoribosyl transferase (UPRT) in MV from HEK-293T cells. Isolated MVs from these cells were used to treat pre-established nerve sheath tumors (schwannomas) in a mouse model. MV-mediated delivery of CD-UPRT mRNA or protein by direct injection into schwannomas led to regression of these tumors. This finding suggests that MVs can serve as novel cell-derived vehicle to effectively deliver therapeutic mRNA/proteins for treatment of diseases [113]. Taken all together, the results from these studies suggest that MVs can be used as new vehicles for nucleic acid transfer.
Although EVs were applied to humans already in the early 2000s for the treatment of cancer patients, no recommended standard techniques have been established for the production of EVs at clinical grade. Several manufacturing and safety considerations need to be addressed and appropriate quality controls have to be implemented and validated. It remains a challenge to set up platforms for the production of EVs at clinical grade that fulfill all necessary criteria for the successful approval of subsequent EV-based clinical trials [93]. The most relevant issue to be addressed at the various levels of the developmental processes is to bring MV-based therapeutics into the clinical application in treatment of diseases including cancers. It is obvious that MVs are part of parental plasma cells; therefore, their antigenicity is mainly determined by protein and lipid components, profile of miRNAs and mRNAs, and also other factors originated from the parent’s cells. Similar to exosomes, MVs are able to overcome limitations of cell-based therapeutics including safety, manufacturing, and availability. With a capability of crossing the blood-brain barrier, which classically acts as a major hurdle in the administration of therapeutic agents for targeting cells and tissue, especially of the central nervous system, MVs can be applied for the transport of molecules to target cells or tissues [114, 115] The presence of biomarkers on the surface may drive the loaded MVs to the specific target and help them to protect their cargoes from degradation [65, 116]. The standard procedure for isolation, purification, and storage of EVs at large scale should be established for certain cell types for trials at both in vitro and in vivo levels.
Another important issue in application of MVs is how to load bioactive compounds into these vesicles. For example, in order to load MVs with therapeutic small RNA molecules, two encapsulation approaches commonly used are post-loading or pre-loading. Post-loading method is using a specific method to introduce RNA into EVs (e.g., electroporation) while pre-loading is carried out during the EV formation (it is also called endogenous method that exploits the cellular machinery for small RNA loading into EVs). This endogenous method has been successfully used for the packaging of both siRNA and miRNA in EVs [99, 117, 118]. Functional delivery into recipient cells has been shown in several reports [119–121]. Several recent reports have shown functional siRNA delivery into recipient cells using EVs loaded by electroporation. However, the efficacy of this exogenous method has not been fully demonstrated, and other research groups stated that the loading of EVs with miRNA by using this method was not successful [120, 122]. Therefore, further studies are needed to confirm the feasibility and efficiency of this method for EVs loading. Nevertheless, the feasibility of the method likely varies depending on the siRNA or miRNA species. Furthermore, the efficiency of the overexpression or the direct transfection of particular small RNA-loaded EVs to recipient cells is still the matter of concern.
MVs are able to carry macromolecules, especially nucleic acid, and play a key role in cellular communication. In near future, MVs may efficiently support for the conventional treatment of tumor or cancer, which are using chemotherapeutic drugs, radiation therapy, or surgery. Recent findings suggest that released MVs from human RBCs can be applied as novel treatment for various diseases including cancer. Structurally, MVs contain various membrane receptors and also carry nucleic acids, proteins, or other molecules. With many advantages in overcoming many of the limitations of cell-based therapeutics including safety, manufacturing, and availability, MVs may serve as cell-to-cell shuttles for carrying bioactive molecules to target cells. Therefore, MVs involve biological processes, especially the interaction with tumors or cancers. Human RBCs, with a large number of cells in the human body, can be easily collected without requiring cell culturing or sophisticated instrumentation. In addition, MVs released from RBCs can move to almost all tissues in the body without being hindered by any biological barrier. Therefore, MVs from human RBCs are potential candidates for the transport of nucleic acid and other bioactive compounds to the target cells. However, to make MVs to become applicable and efficacious in therapeutic treatments, underlying functions of MVs still need to be better understood. Future research directions should pay more attention to MVs as biological targets for cancer diagnosis, prognosis, and therapy that enable MVs as new source and of new material and promising approach for practical therapeutics.
The authors would like to thank the Vietnam National Foundation for Science and Technology Development (NAFOSTED) for the support under the grant number 106-YS.06-2013.16. Nguyen Duc Bach received this grant including the travel expenses for working in the group of IB.
In unconventional oil and gas industry, there exists a significant granular flow process, which is known as the proppant transport [1]. It is necessary to pump high-strength granular materials such as ceramic particles and sand into the stimulated fracture networks with carrying fluid. Eventually after the flow-back of fluid, the granular materials remain in the fractures and fracture networks are efficiently propped, which contributes to a high conductivity for gas/oil exploitation. Therefore, it is important to reveal the physical mechanisms in the proppant transport process.
Essentially, proppant transport process is a two-phase flow problem constrained in a channel with various widths. In previous works, concentration transport approach was very popular for simulating the proppant transport. In the approach, proppant is considered as a continuum, and is quantitatively described using concentration. The motion of the particle phase is solved based on a concentration transport equation. This method is firstly established by Mobbs and Hammond [2]. They derived the governing equations for the fluid-particle mixture (i.e., slurry) by combining mass conservation laws of two phases and convection models. Then a Poisson equation for the fluid pressure is obtained. They proposed an important dimensionless number, that is, the Buoyancy number, to quantitatively describe the relative intensity of horizontal convection effect and the vertical settling effect. Their pioneering work is then adopted and extended in many later works. For example, Gadde and Sharma [3] and Gu and Mohanty [4] extended this framework by considering the effects of fracture propagation. Wang et al. [5] introduced a blocking function in order to consider the proppant bridging effect. Dontsov and Peirce [6] utilized a more accurate velocity retardation model based on their theoretical analysis. Roostaei et al. [7] applied the WENO (weighted essentially non-oscillation) scheme to solve the concentration transport equation, which greatly reduces the numerical diffusion.
The MP-PIC method [8, 9] is another numerical method for simulating large-scale fluid-particle coupling system, which is popular in chemical engineering. In the MP-PIC method, fluid motion is governed by the volume-averaged Navier-Stokes equation, and particle motion is solved using the Newton’s second law under the Lagrangian framework, which is different from those in the concentration approach. Due to its Lagrangian feature and high fidelity, the MP-PIC method is also shown to be a powerful tool for simulating proppant transport process.
In this work, the two above numerical methods are both applied in simulating the proppant transport process. Though the two numerical methods are built under different frameworks, there exist both similarities and differences between them. The hidden facts are revealed based on the analysis of the governing equation sets, as well as the numerical results. The remaining contents of this work are organized as follows. In Section 2, basic governing equation sets of the two methods are demonstrated, and relationship between the two methods are discussed. In Section 3, several numerical cases are designed to illustrate the performance of the two methods, and the numerical results are then discussed. Finally, conclusions are drawn in the Section 4.
Assume that there exists only one kind of proppant (same density and size, or mono-disperse) in the fracture and the particle phase is well distributed so that in the large scale we can take the derivative of the particle concentration in most regions (except discontinuity), and the particle and fluid phase are both incompressible. Then we have following unknown variables: fluid velocity
Let us start from the continuity equation. Figure 1 shows the fluxes and accumulation in a control volume. It is clear that for the particle phase we have the mass balance equation:
Control volume in concentration transport approach.
where w is the fracture width. Then it is trivial to obtain the differential form [2]:
Similarly, we have the mass balance equation for fluid phase:
Considering fluid leak-off, it is trivial to add a source term in the RHS:
where
In large-scale cases, we assume that in the horizontal direction, the velocities of the two phases are the same (homogeneous slurry flow), and in the vertical direction, the particle phase velocity differs from the fluid phase due to particle settling. Then we have the following formula:
where
Using Eqs. (2) and (4), we can obtain the fluid/particle mixture (slurry) continuity equation.
where
Eq. (6) is necessary for solving fluid pressure and it is illustrated below. As we know, for pure Newtonian fluid, we have the constitutive laws in which viscosity is a significant parameter. In viscous case (low Re number), based on the Poiseuille’s Law, we can derive the relationship between the pressure gradient and average velocity in a channel/fracture:
where
In the case of fluid/particle mixture, we also expect there exists a similar relationship between fluid pressure and slurry velocity. There are many previous literatures including experimental and numerical works revealing this relationship. It is well known that the apparent viscosity of the mixture is higher than that of the pure fluid and a formula similar to Eq. (7) can be obtained introducing the effective viscosity of the mixture [7]:
where
By substituting Eq. (8) into Eq. (6), we get the following pressure Eq. (7):
If the fracture width does not vary with time, then the time derivative vanishes, with the pressure Poisson equation remaining, and the sand concentration
The MP-PIC method is an Eulerian-Lagrangian method, in which fluid motion is solved in the Eulerian grids and particle motion is solved under the Lagrangian framework. The governing equation of fluid motion reads [10]:
where w is the fracture width,
In the MP-PIC method, the particle phase is discretized into parcels, and every parcel represents several physical particles, which possess the same properties such as density and size, and also similar kinetic behavior such as the velocity and acceleration. Parcel motion is governed by the Newton’s second law listed as follows:
where
First let us summarize the governing equations of the two approaches.
Concentration transport approach:
MP-PIC approach:
In Eq. (13), we need to introduce models for settling velocity
Next we will discuss the similarity and difference between these two equation sets, which are denoted as set I and set II, respectively:
Fluid part: it is clear that in set II unsteady and convection/inertial terms are considered. Set I is suitable for homogeneous slurry flow, which indicates that particles settle pretty slowly and Reynolds number is low. In slick water cases, set II is preferred. Actually set II shall converge into set I in low Re number cases. In steady cases, the unsteady terms vanish and the fluid-particle interaction term converges into additional gravity force of particle phase, then the second equation in set II is simplified as:
If the term
Particle part: obviously we solve particle phase motion under Eulerian framework in set I while under Lagrangian framework in set II. Density/size distribution is easier to be considered in set II. In set I we directly assign a settling velocity for the particle phase while in set II we can resolve the settling history with the drag relaxation term if the time step is set to be small enough. The terminal velocity in set II is determined by which drag force model is utilized. Both of the settling velocity model in set I and drag force model in set II are modifications of Stokes settling theoretical results. Also unsteady terms including fluid pressure and viscous stress effects are considered in set II.
In both of the two 2D large-scale equation sets, models are necessary for closure issues and they cannot exactly describe the full-scale fluid/particle behavior. “Large scale” has two meanings: large time scale and large spatial scale. Different physical mechanisms play significant roles in different scales. For the time scales, p-p collision occurs in the time scale of “μs,” f-p drag occurs in the time scale of “ms,” fluid leak-off and fracture width change have significant effects in the time scale of “s” or “min.” For the spatial scales, fluid viscous force dominates in the Kolmogorov length scale (mm), gravity convection dominates in the length scale of “m.” We expect that in our 2D large-scale models, we can capture the large-scale fluid/particle behavior. However, small-scale fluid/particle interactions shall affect the large-scale phenomena.
Using 3D DNS (direct numerical simulation) we can obtain the full-scale details; however, due to computational limits simulation time at most reaches several minutes and simulation length at most reaches 1 dm. Though it is not possible to perform 3D DNS even for an experimental-scale case, useful models can be extracted from the DNS data, for example effective viscosity, settling velocity, retardation factor etc.
In this work, Barree and Conway’s [11] effective viscosity model is utilized to calculate slurry viscosity for the concentration transport approach and calculate wall friction force for the MP-PIC method, which is expressed as follows:
where
Besides, Wen and Yu’s drag force model [12] is utilized for calculating the fluid-particle coupling drag force for the MP-PIC method and determining particle settling velocity for the concentration transport approach, which is expressed as follows:
where
Numerical simulation is performed in a rectangle domain as shown in Figure 2. The left side of the domain is set as inlet. Proppant is uniformly injected from the whole inlet and proppant concentration is set as 20%. Here the proppant concentration means the volume ratio of particles to total volume of fluid/particle mixture. The right side of the domain is set as outlet. The upper and bottom sides of the rectangle domain are set as the non-flow boundary. Particle deposition mechanisms are different in these two methods. In the concentration transport approach, if proppant concentration reaches the close packing limit, particle settling velocity is set to be approaching zero, and it is easy to implement the non-flow condition for a Eulerian approach. In the MP-PIC method, if proppant concentration reaches the close packing limit, additional forces due to particle stress gradient are exerted on parcels to make sure these parcels shall move away from the high-concentration region. When parcels move across the non-flow boundary, the displacements of these parcels are modified following a bounce-back way.
A sketch for the numerical simulation domain.
Parameters used in the simulation are listed in Table 1. Cases with different fluid viscosities, that is, 1, 10, and 100 cP are considered in this section. Because characteristic length is 0.005 m (fracture width) and characteristic velocity is 0.2 m/s (inlet velocity), the Reynolds numbers in these cases are 1000, 100, and 10 respectively.
Parameter | Value | Parameter | Value |
---|---|---|---|
Fluid density | 1000 kg/m3 | Particle density | 2500 kg/m3 |
Fluid viscosity | 1 and 10 and 100 cP | Particle diameter | 0.6 mm |
Time-step | Simulation time | 4 s | |
Inlet velocity | 0.2 m/s | Inlet concentration | 20% |
Domain size | Mesh size |
Parameters for simulating proppant transport.
Figures 3–5 show the numerical results of three different Reynolds number cases of two methods. The results are contoured by the volume fraction of particle (denoted as “vfp”), or the proppant concentration. Here we denote the high Reynolds number case as case I, the moderate Reynolds number case as case II, and the low Reynolds number case as case III respectively.
Simulation results of high Reynolds number case (Re = 1000). (a)–(d) are the concentration transport results at time = 1, 2, 3, and 4 s respectively, and (e)–(h) are the MP-PIC results at time = 1, 2, 3, and 4 s respectively.
Simulation results of moderate Reynolds number case (Re = 100). (a)–(d) are the concentration transport results at time = 1, 2, 3, and 4 s respectively, and (e)–(h) are the MP-PIC results at time = 1, 2, 3, and 4 s respectively.
Simulation results of low Reynolds number case (Re = 10). (a)–(d) are the concentration transport results at time = 1, 2, 3, and 4 s respectively, and (e)–(h) are the MP-PIC results at time = 1, 2, 3, and 4 s respectively.
In case I the viscosity of carrying fluid is very low, that is, 1 cp, which indicates a poor capability of proppant transport. From Figure 3, it is clear that both of the two numerical methods illustrate the packing process during the transport process. In the figure, blue, white, and red regions indicate the pure fluid, suspending slurry, and sandbank regions respectively. In case II, settling behavior of proppant is weaker than that of case I, and instead gravity convection of the slurry front in the vertical direction is obvious as shown in Figure 4. In case III, it is obvious from Figure 5 that proppant settling behavior is hard to recognize and gravity convection is much weaker than that of case II.
By comparing the results at different Reynolds numbers, it can be summarized that as the slurry is injected into the domain, there are several significant mechanisms that determine the eventual proppant distribution listed as follows.
The first mechanism is proppant settling. Proppant settling is due to the net gravity force of the proppant if particle density is larger than the fluid density, and the terminal velocity of proppant is determined by the particle Reynolds number and particle volume fraction. According to the Wen and Yu’s drag force model, it is trivial to obtain the settling velocities of proppant in the above three tests, and they are 53.2, 11.8, and 1.28 mm/s, respectively. Therefore, within a same horizontal transport distance, the level of slurry-pure water interface declines more dramatically in case I compared to the other two cases with lower Reynolds numbers.
The second one is gravity convection. In case II and case III, proppant settling can be ignored compared to the inlet velocity, however the slurry fronts in these two cases still evolve and both trend from vertical direction to inclined direction. This is because of the horizontal pressure gradient on the slurry front due to the difference between slurry and pure fluid, which provides a driving force and keeps slurry on the bottom penetrating into the pure fluid region. This mechanism is then intuitively described as gravity convection. Gravity convection in case III is much weaker than that in case II. Though the horizontal pressure gradients on the slurry front are the same in these two cases, fluid viscosity is greater in case III, which leads to a smaller channel permeability for slurry flows. Therefore, the penetration velocity in case III is much smaller than that in case II. In case I, gravity convection also plays a significant role. According to the ratio of inlet velocity and proppant settling velocity, that is, about 4, without gravity convection slurry front is expected to be exact the diagonal line of the domain. However, numerical results of both methods show that the suspending region is far below the diagonal line, which indicates that fluid velocity field is greatly changed due to gravity convection compared to a uniform flow. Above all, gravity convection can be considered as a global effect reflecting the density difference between slurry and pure fluid, whereas proppant settling represents a local effect reflecting the density difference between proppant particle and pure fluid.
The third one is proppant packing. The two prior mechanisms affect the distribution of slurry suspending region, and proppant packing shall affect the distribution of sandbank. In case I, as time evolves proppant concentration increases at the bottom of the simulation domain. When proppant concentration reaches a maximum value, that is, close to the packing state, particle-particle interactions and particle-wall interactions become more frequent. Then, the early formed sandbank stays unmovable, and the fluid velocity also dramatically decreases in this region due to the fluid-particle coupling and particle-particle/wall damping effects.
By comparing the numerical results of two different methods based on the above mechanisms, similarities and differences between the two methods discussed in Section 2.3 are verified.
Firstly, in case III it is obvious that numerical results of methods are almost the same with each other. In case III, Reynolds number is pretty low and the fluid motion is dominated by the viscous mechanism. The slurry flow is approximately plug flow. Secondly, in case II of moderate Reynolds number, numerical results of concentration transport approach show that the gravity convection is a bit severe than those of MP-PIC method. However, transport patterns of these two methods are in general similar. Quantitatively, the relative length of top and bottom slurry fronts at the end of simulation time is 0.5 and 0.4 m, respectively. Thirdly, in case I, numerical results of two methods differ a lot from each other. For the slurry suspending region, the covering area of the MP-PIC results is obviously much larger than those of concentration transport approach. This is mainly because the transient term and convection term in the fluid governing equation are ignored in the concentration approach, and these two mechanisms play significant roles in low viscous or high Reynolds number cases. It is clear that losses of these two mechanisms shall under-estimate the transport capability when utilizing the concentration transport approach. Besides, sandbank packing process in the concentration transport results also differ a lot from that in the MP-PIC results, including the slopes of upstream and downstream sandbank region. This is because particle-particle interaction is considered in the MP-PIC method in some way, while it is not considered in the concentration transport approach.
It is worth noting here that in this work the fifth order WENO (weighted essentially non-oscillation) scheme is adopted for solving the concentration transport equation, thus the effect of numerical diffusion of concentration transport approach can be considered insignificant, and differences between the numerical results of two methods can exactly reflect the effects of different modeling strategy on proppant transport. Above all, both methods can precisely capture the proppant settling mechanism when the same drag force model is adopted in both methods, and concentration transport approach can capture the gravity convection mechanisms precisely when Reynolds number is smaller than 100. However, proppant packing mechanism is not captured very well in the concentration approach.
In this work, two numerical methods are adopted to simulate proppant transport: the concentration transport approach and the MP-PIC method. The first one is a typical Eulerian-Eulerian method and the second one is a typical Eulerian-Lagrangian method. With full discussions on their frameworks and comparisons between the numerical results, the following conclusions are then obtained:
From the view of pure horizontal proppant advection, numerical diffusion can be insignificant in the concentration transport approach if high-order scheme like WENO scheme is adopted, and the interfaces between slurry front and pure fluid can be clearly captured.
When fluid Reynolds number is smaller than 100, assumptions of ignoring velocity convection term and transient term for fluid governing equation adopted in the concentration transport approach are reasonable, and numerical results of both methods show similar transport patterns.
When fluid Reynolds number reaches 1000, that is, in the low viscous cases, numerical experiments prove that the concentration transport approach shows a low fidelity for capturing both the slurry suspending region and the sandbank packing process.
Generally, the more physical mechanisms, including particle-particle/wall interaction and fluid-particle interaction, accurately considered in a numerical framework, the better a simulator performs on capturing proppant transport behaviors.
This work is funded by the National Natural Science Foundation of China (nos. U1730111, 11972088, 91852207), the State Key Laboratory of Explosive Science and Technology (no. QNKT19-05), and the National Science and Technology Major Project of China (Grant no. 2017ZX05039-005).
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