T3 at a certain pressure.We also determined T3 by the three-phasedirect coexistence method. The results of both methods agree, andwe suggest 295(2) K as the value of T3 for this system. We also analyzed the impact of curvature on thesolubility of methane in water. We found that the presence of curvatureincreases the solubility in both the gas–liquid and hydrate–liquidsystems. The change in chemical potential for the formation of hydrateis evaluated along the isobar using two different thermodynamic routes,obtaining good agreement between them. It is shown that the drivingforce for hydrate nucleation under experimental conditions is higherthan that for the formation of pure ice when compared at the samesupercooling. We also show that supersaturation  increases the driving force fornucleation dramatically. The effect of bubbles can be equivalent tothat of an additional supercooling of about 20 K. Having highly supersaturatedhomogeneous solutions makes possible the spontaneous formation ofthe hydrate at temperatures as high as 285 K . The crucial role of the concentration ofmethane for hydrate formation is clearly revealed. Nucleation of thehydrate can be either impossible or easy and fast depending on theconcentration of methane which seems to play the leading role in theunderstanding of the kinetics of hydrate formation.Inthis paper, the solubility of methane in water along the 400bar isobar is determined by computer simulations using the TIP4P/Iceforce field for water and a simple LJ model for methane. In particular,the solubility of methane in water when in contact with the gas phaseand the solubility of methane in water when in contact with the hydratehas been determined. The solubility of methane in a gas–liquidsystem decreases as temperature increases. The solubility of methanein a hydrate–liquid system increases with temperature. Thetwo curves intersect at a certain temperature that determines thetriple point  I1 The molecules of water form an open structure, and the guest moleculesof the gas occupy the lattice positions . The simplest hydrate structureis denoted as sI1 and is the one formedby methane and carbon dioxide. The unit cell of the sI solid belongsto the cubic system. Hydrates are of interest both from a fundamentalpoint of view and from a practical point of view.1 Hydrates are found close to the shores of the coast, andone could obtain natural gas from them. From a fundamental point ofview, they are formed from a mixture of rather small and simple molecules.Hydrates are compounds formed when water is in contact with a gasphase of a small molecule  at moderateto high pressures and at low temperatures.6 We have implemented the technique of seeding4 which allows one to estimate nucleation rates by combining simulationresults and classical nucleation theory. The technique of seedinghas been applied successfully to a number of systems from simple onessuch as hard spheres (HS) and Lennard-Jones (LJ) to more complex suchas water or salty water,7 obtaining goodagreement with results obtained from more rigorous techniques. Itwould be interesting to extend the methodology of seeding to morecomplex systems, as is the case of hydrates. In fact, in 2012, Molineroet al. implemented the technique of seeding8 to obtain a first estimate of the nucleation rate of hydrates usingthe mW model of water.9Over the past few years, we have studied in detail the nucleationin a number of systems.10 suggested in 2011 to usedirect coexistence of the three phases to estimate T3. It was observed that combining TIP4P/Ice11 and a simple LJ model for methane gives theestimates of T3 that are in good agreementwith the experimental ones . Notice that, to obtain values of T3 in good agreement with experiment, water models with a good predictionof the experimental melting point of ice Ih are required.13 After this study, a number of groups have revisitedthe problem using the same force field.18 Although the agreement between different groups isreasonable, some differences still exist, with values of T3 at 400 bar being in the range of 290–300 K forthis force field. It would be of interest before addressing nucleationstudies to reach some consensus on the value of T3 for this system.Before consideringnucleation using seeding, there are some issuesthat should be solved. First of all, the estimate of the temperatureat a certain pressure at which the three phases can coexist is needed.Conde and Vega20 However, the solubility of methane from the hydrate is rarely studiedeither in experiments or in simulations.21 In this work, we shall perform a study of the solubility of thehydrate. It will be shown that solubility studies allow us to estimate T3. Thus, in principle, the values of T3 obtained from the direct coexistence of thethree phases and those of the solubility should be coincident. Weshall show that this is the case and that they are the same to withinthe estimated uncertainty which is of about 2 K.The solubility of methane inwater increases as the temperaturedecreases. This has been studied both in experiments and in simulation.Δμnucleation. This is the change in chemical potential ofthe “reaction” where a molecule of the hydrate is formedfrom the molecules of methane and water both in the aqueous solution.Although it would be possible to determine Δμnucleation from experiments, often this is not possibledue to the lack of information about the thermodynamic propertiesof the system . Estimates of Δμnucleation are rare with the exceptionof the work of Kashchiev and Firoozabadi.23 In this work, we shall address the issue of the evaluation of Δμnucleation using two slightly differentthermodynamic routes. Results of both routes will be coincident (withinthe combined error bar).A key quantityin classical nucleation theory (CNT) is the drivingforce for nucleation, which is denoted as 24 The analysisreveals that the concentration of methane dramatically affects thevalue of Δμnucleation. Ingeneral, increasing the concentration of methane increases the drivingforce for nucleation. We found, in agreement with the work of otherauthors,26 that bubbles increase the solubility ofmethane, and we will quantitatively estimate the impact of this incrementin solubility on the driving force for nucleation. It will be shownthat bubbles increase the driving force, but there is a limit, asit is not possible to have bubbles which are mechanically stable belowa certain size of about 1.2 nm radius. However, we will show thatanother strategy is possible by generating homogeneous supersaturatedsolutions in which the nucleation of methane hydrates can occur evenat temperatures just 10 K below T3. Also,it will be shown that the solubility of methane in water when thesolution is in contact with the hydrate increases by introducing curvaturein the interface.An interesting issue is whether onecan modify the driving forcefor nucleation artificially.T3 and in Δμnucleation. Itcan be said that the study of the solubility of methane in water (eitherfrom the gas or from the hydrate) contains a lot of interesting physicsand the key ingredients to understand hydrate nucleation in futurestudies following the increasing activity in the field of the lastyears.41Thus, in this paper, we address the firststeps toward addressingthe issue of the homogeneous nucleation of hydrates under experimentalconditions with special interest in II43 in the NpT ensemble. Threetypes of barostats were used depending on the problem. Either isotropic NpT , anisotropic NpT (where each sidechanged independently), or NpzT  simulations will be performed in this work.A time step of 2 fs was used. To keep the temperature constant, theNosé–Hoover thermostat45 was employed,with a coupling constant of 2 ps. The pressure was kept constant withthe use of the Parrinello–Rahman barostat,46 and the time constant used was equal to 2 ps. For all ofthe simulations, the pressure was equal to 400 bar. For electrostaticand van der Waals interaction, a cutoff of 9 Å was used. Coulombicinteractions were treated using the PME method.47 Long-range energy corrections to energy and pressure wereincluded for the Lennard-Jones part of the potential. For water, theTIP4P-Ice11 water model was used, while,for methane, the parameters were taken from refs . Simulations were performed using the GROMACSpackagerom refs  and 49)43 in thePm3̅n) with a lattice constant ofabout 12 Å. In this solid,52 one has8 molecules of methane and 46 molecules of water in the unit cell. The 8 moleculesof methane occupy the 8 cavities available in the solid structure. Oxygens occupy the crystallographicpositions c(6), k(24), and i(16), whereas the methanes occupy the d(6) and a(2) crystallographic positions. We usedfull occupancy .Experimentally occupancies around 95% are often found.53 In the hydrate structure, one finds proton disorder. Proton disorderedconfigurations satisfying the Bernal–Fowler rules54 were generated using the algorithm of Buch etal.55For simplicity throughout this paper, the phase of pure methanewill be denoted as “gas phase”, as in the literatureone often uses the term “gas hydrates” even though methaneis studied under supercritical conditions. In certain cases, we havesimulated the solid phase of the hydrate with structure sI (56 We found that 5758). While 61 it is reasonable, simple, and adequate for our purpose of detectingmolecules of the solid phase. Details about the implementation of Supporting Information.To analyze the melting of thehydrate or its stability with time,we shall determine the size of the largest solid cluster of the hydrate. For this purpose, we shall use the order parameter proposedby Lechner and Dellago.62 in the thermodynamicdescription of mixtures so that we will have a dominant component(solvent) which in this case will be water and a minor component (solute)which in this case will be methane. The chemical potential of waterin the mixture is given by63x2OH is the molar fraction of water, μ2OH*  is the chemical potential of pure water at the same T and p of the mixture and kB is the Boltzmann constant . γ2OH is the activity coefficient of water. The chemical potentialof methane in the aqueous solution is given by4CH0 is the standard state of methanewhich depends on T and p but noton composition. Notice that the standard state of water is a “real”state, as it corresponds to pure water at the same T and p. However, the standard state of methane isa “virtual” state, as it does not correspond to anyphysical realization. It corresponds to a “virtual”state of pure methane where intermolecular interactions are identicalto those obtained at infinite dilution. From a statistical mechanicspoint of view, μ4CH0 is related to the residual chemical potential of methane in waterat infinite dilution (after adding the constant kBT ln(ρ2OH·Λ4CH3·q4CH), where ρ2OH is the number densityof pure water, Λ4CH is the thermal deBroglie wavelength of methane, and q4CH is the ideal gas partition function of methane containingall degrees of freedom but translation) and can also be related tothe Henry constant.64 In the unsymmetricalconvention, it holds that when x2OH → 1 both γ2OH and γ4CH go to 1.62 Sincethe solubility of methane in water is quite small, it is reasonable to assume that the activity coefficients forboth methane and water are close to 1. We shall assume that this isthe case in our “approximate” treatment of the aqueoussolution of methane.Since the solubility of methane in wateris small, we shall usethe unsymmetrical conventionIIIIII.A3. The planar interface is located in the XY plane, and pressure is applied perpendicular to the interfaceusing the NpzT ensemble. Simulations were run for more than 500 ns, andaverages were obtained using the last 250 ns . From thesimulations, we also obtained the surface tension of the water–methaneinterface using the pressure tensor:6566 , we roughly estimated a long-rangecorrection of about 2 mJ/m2. Moreover, for some temperatures,we repeated the runs using a much larger cutoff and some results are also presented in 2 higherthan those presented in By using the direct coexistence method, we shallcompute the solubility of methane in water for several temperaturesalong the 400 bar isobar. For that purpose, a slab of water (2959molecules) was put in contact with a slab of gas with an initial size of the simulation box of around 3.6 × 3.6× 14.4 nmIn 68 As can be seen, the value that we obtained reproduces theexperimental value reasonably well. It is true, however, that theagreement between simulation and experimental results could be improvedby introducing a small scaling factor to the default Lorentz–Berthelotcombination rule.In It goes without saying that, when the systemreaches equilibrium,the temperature in the two phases is the same, the pressure is thesame (as one has a planar interface), and the chemical potential ofmethane in water is the same, so that it holds thatThe change in the chemical potential of methane along an isobarcan be obtained from the thermodynamic relation:Tref. Then, we can integrate the previous equationto obtain4CH is the chemical potential of methane and h4CH is its partial molar enthalpy. Of course in the case of a pure substance, the partialmolar enthalpy is simply the molar enthalpy. By performing simulationsof pure methane along the 400 bar isobar, we can compute the enthalpy,and using the previous equation, we can compute the chemical potentialof methane. We shall not include the kinetic energy when computingthe enthalpy , as this term cancels out when computingchemical potential differences evaluated at constant T and p. Results for the chemical potential of methaneas a function of T are presented in Tref = 295 K).For reasons thatwill be clear later, let us set the chemical potentialof pure methane at 400 bar to zero at a certain reference temperature An interesting question is whether there is anypossible temperaturelimit to perform the simulations to compute the solubility. As wedid not observe nucleation of the hydrate, the simulations can beperformed at any temperature without any difficulty, although of courseas the temperature decreases the dynamics slows down and equilibrationis more difficult.III.B3  in the hydrate).We used complete occupancy of the methane in the cages of the hydratestructure. Again, the interface was located in the XY plane and the Z axis was perpendicular to the interface.An anisotropic barostat was applied along the three axes so that thedimensions of the simulation box could change independently. The pressuresused were identical and equal to 400 bar in all three directions.The anisotropic barostat was important to remove any stress in thesolid and to obtain the correct solubility. Simulations were performedfor temperatures in the range 250–330 K. The length of thesimulations was greater than 500 ns in all cases. The averages wereobtained after removing the first 250 ns. It should be mentioned thatto evaluate the solubility of methane in water when in contact withthe hydrate it is convenient to use an initial configuration witha concentration of methane in water not too far from the equilibriumvalue to reach equilibrium as fast as possible. For all temperatures,we performed two runs, the first one to estimate the value of thesolubility and the second one to determine it with high accuracy.When equilibrium is reached, the chemical potential of the two components(water and methane) is the same in the two phases, the temperatureis the same, and the pressure is the same (as we have a planar interface).We shall also compute the solubility of methanein water when the solution is in contact with the hydrate along the400 bar isobar. For that purpose, we shall use the direct coexistencemethod. A slab of the hydrate will be put in contact with water solution.The dimensions of the simulation box were 4.8 × 4.8 × 8.7nmResults for the solubility of methane when solution is in contactwith the hydrate are presented in 21 butto the best of our knowledge were never reported in simulations.Some plots of the solubility of the hydrate as a function of temperature(for pressures different from the one considered in this work) weredescribed in an experimental paperIII.CT3. To the best of our knowledge, this is the first time T3 is determined from solubility calculationsof two independent two-phase coexistence runs. However, this methodis routinely used in the context of the classical equations of stateto determine three-phase coexistence conditions for gas and/or solidphases.71It is now interesting to plot both solubilitycurves (the solubility of methane in water from the gas and the solubilityof methane in water from the hydrate) in the same plot. This is donein T3 is 297(2) K. Our value is consistent with the valuesreported by other groups using the three-phase coexistence approach.18 A comprehensive study of the impact of the cutoff of the potentialon T3 is beyond the scope of this work,as it will require using a much larger cutoff or even to use PME methodsto properly account for the LJ interactions and that will make thecalculations terribly expensive. However, we have included in The value obtained from our calculations for T3. Let us discuss brieflythe advantages and disadvantages of this approach. The advantage ofthis methodology (with respect to the three-phase method) is thatthe simulations reach equilibrium and one needs to simulate two phases(rather than three). From a computational point of view, it couldbe a little bit cheaper, as 500 ns is usually enough to reach equilibrium,whereas, in the three-phase method, one may need runs of the orderof microseconds or more to clearly detect melting/growing of the methanehydrate. In addition to that, the three-phase method exhibits somedegree of stochasticity, since some trajectories, especially at T close to T3, must usuallybe repeated using different initial seeds to ensure the hydrate phasegrows or melts. These repetitions are unnecessary for the simulationsfor calculating solublities if the systems are well equilibrated.In any case, there is no free lunch and the method is also expensive.The efficiency of both routes is similar in terms of computer time,with the solubility route being slightly less demanding. Nevertheless,both routes are correct and should lead to consistent values of T3.The summary is that solubility calculations arealso a (relativelysimple) route to T3, there should be nohydrate, and the reasonwhy we can observe it is because the nucleation of the gas phase isan activated process. On the other hand, below T3, one of the two phases (either water or methane dependingon their relative amounts) should not exist. One should expect thenucleation of the hydrate, and then the growth of the hydrate untilone of the two components (either water of methane) is totally consumed required to determine thesolubility with high accuracy. We confirmed that in the simulationsused to determine the solubilities no nucleation of a hydrate wasobserved.Notice that, from a thermodynamic pointof view, above 1 of ref ). The reIII.D10 by usingthe three-phase direct coexistence method obtained T3 of 302 and 297 K, respectively, using two differentsystem sizes and much shorter runs. It is of interest to revisit thesecalculations. For that purpose, we have used a three-phase systemwith the hydrate, water, and the gas phase. Interfaces were parallelto the XY plane. The system consisted of 5944 watermolecules and 1512 methane molecules, and the size of the simulationbox was equal to about 4.8 × 4.8 × 12.2 nm3.Simulations were carried out for a few temperatures in a range of290–298 K. In order to maintain constant pressure, anisotropicscaling of the box was applied. The three-phase system was preparedin order to determine the temperature of coexistence of three phasesat a pressure of 400 bar. In order to accomplish that, the changesin time of the amount of the solid phase in the system at differenttemperatures were evaluated, with the use of the Supporting Information for additional information).The temperature of the three-phase coexistence was determined as anaverage of the lowest temperature at which the melting of the solidphase was observed and the highest temperature at which the hydratewas seen to grow. Results for the evolution of the number of solidmolecules are presented in T3 for this system from direct coexistence simulations,which is consistent with the value 297(2) K obtained from the solubilitycalculations using a cutoff of 9 Å or the value of 295 K usinga cutoff of 17 Å. With all of these results, we recommend 295(2)K as the temperature of T3 for this system.For the system consideredin this work, Conde and VegaT3 reported by various authorsfor the same model TIP4P/Ice and a LJ center for methane are presented.As can be seen, there is some scatter, some of which results fromdifferent values of cutoffs used in the simulations. The two calculationsof this work are in agreement with the error bar. Taking all factorsinto consideration, our current estimated value is 295(2) K. Thisvalue (with its error bar) is consistent with a number of previousstudies73 , although certainly lower than the value reported by Jensenet al.15 and lower than one of the valuesreported by Conde and Vega.10In T3 at 400 bar, which is equalto 297 K.74 As was shown before,75 water models with melting points of ice close to the experimentalvalue give good values of T3, which isfurther confirmed in this work.The value of this work is also in good agreement with the experimentalvalue of III.ENpT simulations.The system consists of a bubble of methane in the center of the simulationbox (notice that the bubble is subject to Brownian motion and it cancertainly move) surrounded by water. Radial density profiles of methanearound the center of mass of the bubble were computed. The positionof the center of mass of the bubble was evaluated separately in everyframe of the trajectory based on the locations of the density maximaof methane in the X, Y, and Z directions, as was done in our previous work with LJ bubbles.77In Simulations were performed for 500 ns, and averages were obtainedover the last 250 ns. Notice that the bubbles were stable all alongthe simulation. Once the system reaches equilibrium, it is possibleto compute the solubility of methane for this spherical (gas–water)interface. Notice that when the system reaches equilibrium the chemicalpotentials of methane and water are identical in the two phases, andthe same is true for all temperatures. However, pressure is now aninhomogeneous property and is different in the two phases. The conditionof chemical equilibrium for this spherical interface is now writtenas65 In a homogeneoussystem, the pressure tensor is identical in all points of the sample.However, this is not the case in an inhomogeneous system. It is interestingto point out that the average value of a certain component of thepressure tensor in the entire system does not depend on the choice(IK or H) used to define it locally. The second interesting pointis that for a system with a spherical interface  theaverage of the trace of the pressure tensor in the entire system isidentical to the pressure of the external phase (see the Appendixof ref (79 that states that the divergence of the pressuretensor should be zero ∇·p = 0). In short, in an inhomogeneous system, the pressure of the system is identicalto the pressure of the external phase  and corresponds to the pressure applied by the isotropicbarostat.Forconvenience, when having a spherical interface, the aqueoussolution will be denoted as phase I, whereas the gas phase formingthe bubble will be denoted as phase II. Before continuing, it is importantto clarify some aspects about the pressure in inhomogeneous systems.It is possible to define locally (at each point in space) a pressuretensor using, for instance, the Irving–Kirkwood (IK) criteriaor that proposed by Harasima (H) .xof ref  for prooR). As can be seen, the bubble has acertain size which will be assigned as Rbubble. There is not a unique criteria65 todefine the radius of a bubble . For the time being, we shall use a simple criterion. We shalldetermine the radius of the bubble Rbubble as the value of R at which the density of methanein the density profile is just the arithmetic average of the densityof methane in water and in the bubble. In previous work77 dealing with bubbles within a liquid for the Lennard-Jones system,we denoted this radius as the equidensity radius Req. Mathematically, Req isdefined as4CH isthe density of methane, either in phase I or in phase II (right-handside) or in the density profile (left-hand side).In 25In 4CH0 isjust the standard state of methane in water which depends only on T and p but not on composition. By assumingideal behavior (which seems reasonable taking into account the lowsolubility of methane in water), the change in the chemical potentialof methane in the aqueous phase when in contact with a spherical bubbleand with a planar interface can be estimated approximately  asThe increase in the solubility of methane in the presenceof bubbleswith respect to the planar interface at constant temperature can beexplained easily by noting that the local pressure inside the bubblesis not 400 bar  but higher,as can be understood from the Laplace equation. Higher pressures meanhigher chemical potentials, and assuming ideal behavior for methanein water, that also means higher molar fraction. Let us try to understandthe values obtained of the solubility on a theoretical basis. Letus assume that the chemical potential of methane in the water phase(phase I in our case) can be described askBT units). Estimates of the chemical potential obtained from this routeare shown in Since the solubilitycan change by a factor of 5, the chemicalpotential of methane changes significantly when in the presence ofbubbles the volume per molecule of pure methaneV/N) is thevolume per molecule of a bulk phase of methaneat pressure p, which can be obtained easily fromsimulations of pure bulk methane in the NpT ensemble.Notice that this thermodynamic pressure pII,μ is the one that enters into the thermodynamic description of theinternal phase in Gibbsian formalism . Results for this thermodynamic pressure are presented in It is interesting todetermine what would be the pressure of abulk phase of methane needed to have the same chemical potential asmethane in the external phase. We shall call that the thermodynamicpressure s for thebubble–water interface using the Laplace equationRs is theradius at the surface of tension80 andσs is the interfacial free energy at the surfaceof tension  to have a stable inhomogeneous system.86 Depending on the values of N, V, and T, one can find inhomogeneous systems withspherical, cylindrical, or planar interfaces as the most stable ones.87 One can even have local minima in F which are metastable with respect to others .88 These local minimacan be separated by free energy barriers so that one can stay in theseminima for a long time. However, for pure components, as soon as oneswitches to the NpT ensemble, the inhomogeneous systemis unstable89 and it will evolve toward oneof the two phases at equilibrium . The summary is thatin pure components the existence of a stable (or metastable) inhomogeneoussystem is possible in the NVT ensemble  can be at equilibrium (eitherstable or metastable) in the N1N2pT ensemble. Thus, the inhomogeneoussystem will be stable/metastable, as it would live in global/localminima of the Gibbs free energy G. Obviously, theinhomogeneous system will be unstable if one changes to the semigrandensemble90 where N1, μ2, p, and T are constant as it will evolve toward one of the two phases at equilibrium.Thus, mixtures in the N1, N2, p, T ensemble followthe behavior of pure component systems in the NVT ensemble and mixtures in the N1, μ2, p, T ensemble follow thebehavior of pure component systems in the NpT ensemble.What is the situationfor mixtures? A finite size mixture is defined by four variables.For instance, one could use N1, N2, p, and T one can have local minima of G describingeither a homogeneous system or several inhomogeneous systems withspherical, cylindrical, or planar interfaces. In general, there willbe free energy barriers separating these states. If the free energybarriers are large, the system can stay for quite long times in theseconfigurations. If the free energy barriers are small, the systemwill overcome these free energy barriers and will evolve to the globalminima in G. It goes beyond this study to analyzeif the curved interfaces considered so far  theycorrespond to local minima in G.The message is that for a certain value of Now we shallanalyze in detail the thermodynamic driving forcefor the formation of the solid hydrate.III.HT3, one should not have waterin contact with methane (regardless of whether one has planar or curvedinterfaces). One should have the hydrate in contact with either wateror the gas. If the ratio N2OH/N4CH > 5.75, one shouldhavea hydrate–water system. If the ratio is smaller, one shouldhave a hydrate–gas phase system. The formation of the hydratein the aqueous phase can be written as a chemical reaction (see Kashchievand Firoozabadi22) occurring at constant p and T:4(H2O)5.75]solid will be denoted simply as the “hydrate”and one molecule of the hydrate means one molecule of [CH4(H2O)5.75] in the solid.Below Δμnucleation, and it is given by23p and T. Obviously the value of Δμnucleation depends also on the value of the variable x4CH. There is a particular valueof x4CH of great interest froma practical point of view. It corresponds to the case in which thevalue of x4CH is given by thesolubility of methane from the gas phase . This is the way experiments on the nucleationof hydrate are performed . We shall denote this valuesimply as ΔμnucleationEC . Notice that in this case the value of x4CH is not an independent variable,as it is entirely determined by p and T. The chemical potential of the hydrate does not depend on compositionand is also entirely determined by p and T. Unfortunately, very little is known on the experimentalvalues of ΔμnucleationEC. Kashchiev and Firoozabadi used experimentalinformation to roughly evaluate its magnitude.23 It seems of interest to determine it for the force field used inthis work. It could be useful for future studies of nucleation usingthe same force field. It can also provide clear trends of the experimentalvalues. However, force fields are approximate so that the obtainedvalues will not be identical to those found in experiments.What is thevalue of the driving force for nucleation of the hydrate from thesolution? We shall denote it as III.H.1ΔμnucleationEC whichby definition is Δμnucleation when the molar fraction of methane is given by the solubility ofmethane from the gas phase via a planar interface. We shall illustratehow to compute it along the p = 400 bar isobar. Thefirst route to ΔμnucleationEC is simple: one willevaluate each of the terms of ΔμnucleationEC. When evaluated in this way, it will be denoted as ΔμnucleationEC1. At T3 for 400 bar, we know that ΔμnucleationEC = 0 , althoughwe do not know the individual values of μ4CH and μ2OH. However, this is nota problem, as we are interested in changes in chemical potentialsand not in individual values. For this reason, we shall set to zerothe chemical potential of methane, water, and hydrate at T3 .Let us estimate 4CH, weshall use hydrate is bothsimple and exact and is given byhhydrate is the enthalpy of one “molecule” ofthe hydrate 5.75).To estimate μΔμnucleationEC, wealso need to evaluateμ2OH. Let us write theexpression of the chemical potential of water in the solution at T3 and at TT, p, and the composition. Since the solution is diluted, onemay approximate the value of γ2OH to 1to obtainTo evaluate T:Let us now write the same expression at Therefore, the change in chemical potentialalong the isobar isobtained asC1 and C2). The firstone accounts for changes in the chemical potential of pure water dueto the temperature and the second one for changes in the molar fractionof water. Since the standard state for water is pure water, one simplyobtains As can be seen, the chemicalpotential has two contributions . Systems were simulated ata few temperatures in the range 250–310 K for 100 ns.As has been discussed above to evaluate ΔμnucleationEC1 are presented in kBT units. Using experimental results,Kashchiev and Firoozabadi22 estimated avalue of ΔμnucleationEC of about 1.5 kBT at a pressure of 194 bar for a supercoolingof 20 K route to determine When calculating dissociation enthalpies, one assumes thatthehydrate dissociates into pure water and pure methane. Of course, althoughthis is the definition of the enthalpy of dissociation, one shouldkeep in mind that when the actual hydrate dissociates there will alwaysbe a small amount of methane dissolved in water and an even smalleramount of water dissolved in the methane gas phase. The dissociationenthalpy of the model used in this work is obtained simply by performingsimulations of the pure phases  at severaltemperatures along the isobar. Dissociation enthalpies obtained fromsimulations are reported in 98 Notice thatone can obtain a simple (but approximate) expression to estimate thevalue of ΔμnucleationEC by assuming that the enthalpy of dissociationdoes not change with the temperature and can be taken from its valueat T3 and by neglecting the change incomposition with temperature of the aqueous solution containing methane,thus obtainingThe values obtained are in good agreementwith previously reportedvalues for a similar system.The values obtained from this route are includedin Δμnucleation.Let us now present another possible route to estimate III.H.2p, T, and x4CH = x4CH along an isobar starting from a point wherethe chemical potential of water and methane was identical in the solutionand in the hydrate. However, it is also possible to arrive to thestate p and T and composition x4CH arriving from another state withthe same p and T but with differentcomposition and where the chemical potentials of methane and waterare identical in the solution and in the hydrate. In fact, along thesolubility curve of methane from the hydrate, this condition is satisfiedso that ΔμnucleationEC = 0. Therefore, we just need to computethe change in chemical potential with composition at constant p and T. Notice that standard states dependonly on p and T and not on composition,and since the hydrate chemical potential does not change when changingthe composition of the solution, one obtains a new route (labeledwith the superindex 2) to determine ΔμnucleationEC2ΔμnucleationEC2 isdepicted in ΔμnucleationEC in the direction of freezing so that onesubtracts the chemical potential of methane and water in the aqueoussolution. Since the solubility of methane is quite small, the molarfraction of water is close to 1 and one can neglect the second termon the right-hand side. This was done by Molinero and co-workers8 in previous work.In the previousroute, we arrived to the state of interest with ΔμnucleationEC2 obtained from this second route are shownin ΔμnucleationEC2—as can be seen in ΔμnucleationEC2.The values of Δμnucleation for the formation of ice Ih . For instance, for a supercooling of 35 K, we found a valueof 0.29 in kBT units.91 At the same supercooling, the chemical potentialchange per unit of hydrate molecule is around 2.30 kBT, which after being divided by 5.75yields a value of 0.40 kBT per molecule of water. The summary is that the driving force forthe nucleation of the methane hydrate (at 400 bar) is significantlyhigher than that of the nucleation of ice (at 1 bar) when comparedat the same supercooling. Other things being equal , that means that nucleation of the hydrate should be morefavorable than that of ice Ih.92In previous work, we have determined values of III.IΔμnucleation for hydrate nucleation under “experimentalconditions”, i.e., ΔμnucleationEC. Byexperimental conditions, we mean that the concentration of methanein water is that obtained at equilibrium for a planar water–gasinterface at the considered values of p and T.In theprevious section, we have shown how to compute p and T, by using brute force simulation, Sum andco-workers25 were able to nucleate thehydrate in less than a microsecond (provided that the gas phase wasforming a bubble and the concentration of methane in water was inthe range x4CH = 0.02–0.04).Under the same conditions of p and T, nucleation never occurred for the planar interface even after runningfor several microseconds. Definitely the bubbles helped, and the reasonis simple. The solubility of methane increases. We shall denote as Δμnucleation* (with an asterisk) values of the change inchemical potential for the formation of the hydrate  obtainedunder conditions where the solubility of methane is higher than thatobtained for a planar water–gas interface at the consideredconditions of p and T . Forsimplicity, we shall denote as x4CHeq and x2OHeq the molar fractions of methane and water in the aqueous phase whenin equilibrium with the gas phase via a planar interface at a certainvalue of p and T. We shall denote x4CH* and x2OH* values of the molar fractions in theaqueous phase different from these. If the composition of the aqueoussolution is changed but p and T areunchanged, then the chemical potential of the hydrate phase does notchange. However, there will be a change in the chemical potentialof water and methane. One then obtainsWould it be possible to help the nucleation ofhydrate under “special conditions”? The answer to thisquestion is positive. In fact, for certain values of If we neglect the third termon the right-hand side , then one obtainsΔμnucleation* becomes larger  by1.1–1.6 kBT unitswith respect to ΔμnucleationEC. This is quite a significantincrease. Around 20 K of additional supercooling would be needed toobtain a similar change in ΔμnucleationEC. Ofcourse, 20 K of further supercooling slows down the dynamics. Therefore,bubbles help in the nucleation of the hydrate and would provoke asimilar increase in the driving force as 20 K of further supercoolingwhile keeping the dynamics fast. However, there is a limit in thehelp that bubbles can provide for brute force nucleation studies.As bubbles cannot be smaller than 1.25 nm , the maximum increase that they can providefor nucleation is of around 1.6 kBT units. This is enough to force nucleation for moderateto high supercooling . However, this is not enough to provoke spontaneousnucleation at small supercoolings . In fact, forpressures below 500 bar, Sum and co-workers26 were not able to nucleate hydrate at temperatures above 255 K evenwith bubbles.According to thisexpression, if the solubility of methane is increasedby a factor of 3–5, then the value of x4CH*. A possibility is to start froma highly supersaturated solution . The systemwould be now in a doubly metastable state. In fact, it will be metastablewith respect to the formation of the hydrate, but it would also bemetastable with respect to the formation of the gas phase . The phasethat will appear first is the one with the lowest free energy barrierfor nucleation. This was the approach used by Sarupria and Debenedetti,94 and it is also the path followed in pioneering studies on hydratenucleation. We shall follow this approach. We will start from a homogeneousmixture having around 5000 molecules of water and the number of methanemolecules required to have a certain molar fraction of methane. Wetypically used values of x4CH* in the range 0.042–0.117(notice that 0.117 is only slightly below the composition of the hydratewhich has a molar fraction of methane of around 0.15). Results ofthese runs are shown in T3!). These results are in line with the resultsobtained previously95 for a similar systemat p = 500 bar—in this case, nucleation ofhydrate was observed for temperatures in the range 250–285K (up to 14 K below T3 for these pressureconditions).Would it be possible to nucleate the hydrate ateven higher temperatures? Bubbles are not enough, but extra help can befound. In fact, all that is needed is to have an “artificially”high value of kBT units. Since ΔμnucleationEC at this T is of about 0.7 kBT, it can be seen that a value of Δμnucleation* around 4 kBT is enoughat this temperature to provoke nucleation in brute force runs. Ingeneral, values of Δμnucleation* higher than 4 kBT are enough to guaranteenucleation in brute force simulations. These values can be obtainedbelow 255 K using bubbles or above this temperature using highly supersaturatedhomogeneous solutions.At a temperature of 285 K, thesupersaturation needed to observethe nucleation is almost 20 times the equilibrium solubility for theplanar interface. Such a supersaturation provokes a shift in the chemicalpotential of methane of about 3 It is worth pointing out that the hydratenucleation is a transitionfrom a disordered phase to an ordered phase with solid-like characteristicsthat are not necessarily crystalline. In our work, we were only interestedin detecting the nucleation events, for which we used the T3. We also observed the formation of bubbles at lower temperatures but only for the highest concentration ofmethane considered—x4CH = 0.117. At 270 K, both the hydrate and the bubble were formed atthe beginning of the simulation; however, the hydrate melted soonafter. Although it is not an accurate method to determine T3, it is obvious that the highest temperatureat which spontaneous formation of the hydrate was observed in a highlysupersaturated solution provides a lower bound to a rough estimateof T3.We triedto obtain nucleation even at higher temperatures  using high supersaturation. However, we were not successful.If the supersaturation was low, then there was no nucleation, andif the supersaturation was high, then the spontaneous formation ofthe bubbles of the gas phase took place and supersaturation was reducedto normal , which is not enough to inducenucleation at these high temperatures close to T3 is remarkable. Theconcentration of methane in water is the key to dramatically changethe driving force for nucleation. This can be increased either byintroducing bubbles or by starting from an homogeneous highly supersaturatedsolution.We must confess that we neversucceed in forming ice Ih in bruteforce simulations of pure water using the TIP4P/Ice model. The factthat we are able to nucleate the hydrate in a few hundreds of ns whilejust 10 K below IVT3 value at which the three phases—gas,water, and hydrate—can remain at equilibrium at a certain pressure.Therefore, we show that a new method to evaluate T3 in hydrate research is available that requires performingsimulations that reach equilibrium in all cases. Above T3, the hydrate is not thermodynamically stable. Below T3, one of the two fluid phases will not be thermodynamicallystable. However, we observe metastability. Therefore, it is possibleto have a water–gas interface at temperatures below T3, as the formation of hydrate is an activatedprocess, and it is also possible to have the hydrate–waterinterface above T3, as the formation ofthe gas phase is an activated process. Since there is some scatteraround the value of T3 for this system,we revisited also the direct coexistence method using larger systemsthan in our previous work. The final conclusion is that for this system T3 is located at 294(2) K from direct coexistencesimulations and at 297(2) K from the solubility calculations (fora cutoff of 9 Å) and 295(2) K (for a cutoff of 17 Å). Thesevalues are lower than one of the values we reported some time ago and in better agreement with the estimates of othergroups. With all of this information, we suggest 295(2) K as the T3 value for this system at a pressure of 400bar.Inthis paper, we have studied at 400 bar the solubility of methanein water when in contact with either the gas or the hydrate with computersimulations using the TIP4P/Ice model for water and a simple LJ modelto describe the methane molecule. The solubility of methane from thegas decreases as the temperature increases, revealing that the processis exothermic. The solubility of methane from the hydrate increaseswith temperature, showing that the process is endothermic. There isa temperature at which both curves intersect, and this determinesthe NVT ensemble for pure components has beendescribed before for HS (solid–fluid) and LJ systems (bothsolid–fluid and fluid–fluid). For pure components, itis not possible to have a stable spherical interface in the NpT ensemble. Here we show that this is possible for mixturesand not only for the gas–water interface but also for the hydrate–waterinterface.We have analyzed the impact of a curved interface on thesolubilityof methane, concluding that the curvature increases the solubility.Both the solubility of methane from the gas and the solubility ofmethane from the hydrate increase due to curvature. The explanationis simple—the higher pressure inside the phase forming thesphere increases the chemical potential of methane and therefore increasesthe solubility . We have estimated the change in the chemical potentialof methane due to curvature. The fact that bubbles increase the solubilityhas been described previously. We show here that the smallest bubblethat is mechanically stable has a radius of about 1.25 nm. Below thissize, the bubbles collapse. Therefore, by using bubbles, one can increasethe solubility of methane with respect to a planar interface by amaximum factor of 4–6. It is not possible to increase the solubilitybeyond this value. However, the fact that it is possible to have stablesolid clusters of the hydrate in contact with the solution has notbeen reported before. The existence of spherical stable interfacesin the 23 Even from experiments, it is difficult to estimate this magnitudedue to the lack of many experimental results for some properties thatare required to evaluate the change in chemical potential. Here weestimate the change in chemical potential by using an almost exactroute. For methane and the hydrate, we estimate the chemical potentialexactly. For water, it was necessary to assume ideal behavior of theaqueous solution of methane, which seems reasonable given the lowsolubility of methane. We obtained the value of the change in chemicalpotential for the formation of the hydrate using two different thermodynamicroutes obtaining values that are fully consistent. At a temperatureof 260 K, this change was of 2.4 in kBT units per molecule of hydrate 5.75). This is higher than the magnitudewe found for ice formation for a supercooling of 35 K (when computedper molecule of water). We have also evaluated how this chemical potentialis modified when the solubility of methane increases with respectto the value of the planar interface. By inserting methane bubblesinto the solution, we have shown that the chemical potential of methaneincreases by about 1.6 kBT units, inducing an increase in the driving force for nucleationthat is comparable to that produced by 20 K of additional supercooling.That explains why nucleation of the hydrate in brute force simulationsis much easier when having bubbles. However, one can go beyond thebubbles. In fact, one can start from a homogeneous solution of methanehaving a supersaturation in the range 5–20 (reaching molarfractions up to 0.117) and then hydrate formation is observed fortemperatures up to 285 K . Notice that for the TIP4P/Ice model we werenever able to obtain ice in brute force studies regardless of thetemperature considered. Again, the facility to nucleate hydrate nowarises from the fact that, although one can not modify much neitherthe chemical potential of the hydrate nor that of water at a certain T and p, one can increase dramaticallythe chemical potential of methane by inducing supersaturation  either byusing bubbles or by starting from a homogeneous supersaturated solution.This increases the value of the driving force for nucleation in simulations, thus reducing thefree energy barrier which is proportional to the third power of theinterfacial free energy and inversely proportional to the second powerof Δμnucleation*. Increasing Δμnucleation* by a factor of 2 reduces the free energy barrier by a factor of4. Since the free energy barrier enters in an exponential term whendetermining nucleation rates by CNT, the change in Δμnucleation* provokes a dramatic change in the nucleation rates.The driving force for nucleation is the change inchemical potentialwhen forming the hydrate. There are almost no estimates of its valuewith the exception of the work of Kashchiev and Firoozabadi.T3; however it is likely thatin this case the process occurs via heterogeneous nucleation.It wasnot possible to nucleate the hydrate at temperatures above285 K in the homogeneous highly supersaturated system. This is sobecause the system is in a doubly metastable state (both with respectto the formation of hydrate and with respect to the formation of thebubble). The transition with the smallest value of the free energybarrier will take place first. It seems that for temperatures below285 K the smaller free energy barrier corresponds to that of hydrateformation, whereas for temperatures above that it corresponds to bubbleformation. In experiment, it is possible to nucleate hydrate at temperaturesjust below 97 in conditions where brute forcesimulations are useless (due to the high induction time). What isclear now is that nucleation of hydrates can be either an event withalmost zero probability or an event observed in just dozens of nanoseconds.The concentration of methane is the start of this movie. Somewhatsurprisingly, one can nucleate methane hydrates using the TIP4P/Icemodel in brute force simulations, whereas this was never observedfor this model (to the best of our knowledge) for the formation ofice.It is clear that a lot of physics can be learned by studying thesolubility of methane in water. Although the system is simple, itcontains a number of interesting features. In the future, it wouldbe of interest to determine in a quantitative way the nucleation ratesfor this system


The discontinuous and unstable characteristics of solar energy limit its application in the space heating field, while aquifer thermal energy storage (ATES), as a seasonal thermal energy storage pattern, is a feasible way of solving these problems faced by solar space heating and however, low temperature ATES must not exceed 25–30 °C while high temperature ATES has low recovery efficiency. Here a novel scheme of storing high temperature solar thermal energy into a shallow depth artificial reservoir (SDAR) is proposed. By innovatively storing thermal energy into rocks rather than aquifer, the recovery efficiency improves from 46% for ATES to 90% for SDAR, and the thermal power increases from 309 kW for deep borehole heat exchanger to 1970 kW for SDAR. SDAR has no special requirement to rock temperature and can thus be created in shallow buried depth rocks, leading not only to a reduction of engineering cost but also an expansion of application scope. To further avoid risk of induced seismicity caused by hydraulic fracturing and reduce cost, the abandoned oil and gas fields and mines can be reused as the artificial reservoir. The district heating area in China reached 122.66 × 108 m2 by 2020, and 83% of this area was heated by coal-based fuel5, consuming a lot of energy and causing serious pollutant. Therefore, it is essential to increase the share of renewable energy in the space heating fields in order to reduce greenhouse gas emission.The total floor area in China is 644 × 107, and they should be the primary choice for renewable energy space heating. However, the total area of geothermal heating (cooling) only reached 13.9 × 108 m2 by 2020 due to the dependence on the hydrothermal resources and their unbalanced space distribution9. While for solar space heating, the area was only 16.50 × 106 m2 by 2020 due to the discontinuous and unstable energy characteristics10. Seasonal thermal energy storage (STES) is a feasible way of solving the problems faced by solar space heating, among them underground thermal energy storage (UTES) is considered to be the most promising storage technology13. Aquifer thermal energy storage (ATES), especially low temperature ATES (LT-ATES), is the most suitable UTES system, and about 3000 LT-ATES projects were in operation in Europe by the end of 201714. The temperature of the injected water in LT-ATES system is not allowed to be above 25–30 °C in most countries16, and it is thus inappropriate to store solar thermal energy with high temperature. Recently, high temperature aquifer thermal energy storage (HT-ATES) has received more and more attentions due to higher storage temperature and larger storage capacities and however, low thermal recovery efficiency due to the effects of free convection caused by the density difference limits its application and this is an urgent and important task that need to be solved at present20.Geothermal and solar energy resources are abundant in China23. During the non-heating season, the high temperature solar thermal energy is stored into the shallow depth artificial reservoir (SDAR), leading to an increase in the rock temperature inside the artificial reservoir. During the heating season, more thermal energy can be extracted from the artificial reservoir for space heating due to having high rock temperature caused by the thermal energy storage, at the same time the temperature of rocks inside the artificial reservoir also decreases due to the thermal energy extraction. Similarly, more solar thermal energy can be stored into the artificial reservoir during the non-heating season due to having low rock temperature caused by the thermal energy extraction. The thermal transfer medium (water) flows in the fractures created in the artificial reservoir and exchanges heat with the surrounding rocks, thus realizing thermal energy storage mainly in the rocks rather than aquifer (water). Storing thermal energy into the rocks is mainly by heat conduction, which can restrain the natural conversion causing a low thermal recovery efficiency in HT-ATES. It is thus expected that the thermal recovery efficiency can be greatly improved by storing thermal energy in the rocks instead of water. The shallow depth artificial reservoir  has no special requirement to temperature, depth and storage space for water, and thus leading not only to a considerable reduction of project cost but also a great expansion in the application scope. Fortunately, consolidated sandstone, limestone and granite resources and so on with the shallow buried depth are found to be widely distributed in northern China. For this reason, SDAR or SDEGS is suitable for storing high temperature thermal energy, and however, the thermal performance especially the thermal recovery efficiency for SDAR needs to be testified further by numerical simulation and experiment as well as theoretical analysis. Therefore, the key point of this study is to evaluate and discuss the performance of thermal energy storage and thermal recovery efficiency for HTSTESSDAR from technological perspective by means of numerical simulation.The hydrothermal resources are not rich in most regions in China, and therefore the thermal energy and underground space have not been exploited in these regions. Enhanced geothermal system (EGS) is a feasible way to extract geothermal energy stored in the rocks without rich hydrothermal resources and however, the conventional EGS generally requires high rock temperature with a shallow buried depth in order to acquire more thermal energy and reduce the project expenses, limiting the scope of its use. If more thermal energy can still be acquired even if EGS project is built with a shallow depth and a normal rock temperature, it will reduce engineering cost and expand application scope. On this basis, a novel scheme of high temperature solar thermal energy storage into a shallow depth artificial reservoir (HTSTESSDAR) created in the rocks without rich hydrothermal resources is proposedThe physical model of the artificial reservoir system created in the shallow buried depth rocks is shown in Fig. The system diagram of high temperature solar thermal energy storage in shallow depth artificial reservoir (HTSTESSDAR) is shown in Fig. To get more thermal energy, the heat pump is used in order to attain a lower injection temperature during the heating season.25:Mathematical model for well tube and artificial reservoirEnergy equation in the well tube and insulation tube:The heat transfer item in the insulation tube is expressed as:The heat transfer item in the injection channel is given as:The convective heat transfer coefficient between fluid and the tube wall is calculated according to the following formula:The energy conservation for the surrounding rocks around the well section above the artificial reservoir is calculated by:The artificial reservoir is assumed to be isotropic and homogeneous and is equivalent to a porous medium having uniform porosity and permeability. The local thermal equilibrium between the porous rock matrix and fluid is considered, and the effective specific heat and thermal conductivity in the artificial reservoir are given as the following.The energy conservation in the artificial reservoir is given by:The mass and momentum conservation equations in the artificial reservoir are calculated according to the following formulas:Mathematical model for the evacuated tubular solar collectorThe thermal efficiency for the evacuated tubular solar collector is given below:2 for 7 h per day during the non-heating season with external average temperature of 21.2 °C, and it is 500 W/m2 for 5 h per day during the heating season with external average temperature of 4.6 °C in North China.Solar direct radiation intensity can reach 750 W/mBased on the conservation of mass, momentum and energy, the mathematical model describing the flow and heat exchange in the well tube, artificial reservoir and insulation tube is given as follows3/h. During the non-heating season with duration of 245 days, the high temperature thermal energy produced from the evacuated tubular solar collector is injected into the artificial reservoir with a temperature of 90 °C and a volume flow rate of 20 m3/h. For HTSTESSDAR, the thermal energy storage comes before its extraction.The surface temperature is 15 °C and the geothermal gradient is 30 °C/km. The heating duration is 120 days and during this period the heat is extracted from the artificial reservoir with an injection temperature of 10 °C and a volume flow rate of 50 m3/h in the process of experiment. The experiment was carried out from November 19, 2017 to April 6, 201825. At the same time, the above equations are also used to simulate the performance of DBHE, and the simulation and experimental results are shown in Fig. P represents the thermal power extracted from DBHE, and Tin and Tout respectively denote the temperature of injection and extraction water. The average thermal power from DBHE during the experiment process is 448.49 kW. According to the data analysis the maximum deviation between simulation and experimental data in Fig. The deep borehole heat exchanger (DBHE) was designed and built in 2016 at Qingdao in China, and its schematic and casing profile are shown in Fig. 5 m3, and it will release or store 751.49 GJ heat when its temperature changes 1 °C. When the system runs stably, the average total stored or extracted heat each year are respectively 22,390.66 and 20,427.70 GJ . Moreover, the integrated analysis of Figs. In Fig. 2 are installed. Due to the storage tank storing the short-term heat energy on a diurnal basis, the daily average thermal power of solar energy over 24 h during the non-heating season is 1067 kW, and it is 520 kW during the heating season. During the heating season, the artificial reservoir system and solar energy system are combined to provide heat for buildings. Due to the instability of solar energy, the artificial reservoir should thus have a higher ability of thermal load regulation in order to keep the heating system to run stable during the heating season. Figure 3/h, and they are respectively 1598.85, 1954.49 and 2252.58 kW for the volume flow rate of 40, 50 and 60 m3/h at a constant injection temperature of 10 °C. That is to say, the thermal power of the artificial reservoir can be adjusted by changing the injection temperature and volume flow rate. Further, the thermal power of the artificial reservoir during the heating season reaches 2553.33 kW at an injection temperature of 5 °C and a volume flow rate of 60 m3/h with a thermal load regulation ability of 583.33 kW compared with the average thermal power of 1970 kW obtained at an injection temperature of 10 °C and a volume flow rate of 50 m3/h. The heating system can be designed according to the maximum heating load of 2490 kW , and the instability of the hybrid heating system  can be solved by adjusting the thermal power of the artificial reservoir even if solar energy system does not run. One of the fundamental design principles for the hybrid heating system is that the thermal load regulation ability of SDAR should not be less than the daily average thermal power of solar energy in the heating season. The above analysis results also show that two significant benefits can be achieved from the hybrid heating system ① the discontinuous and unstable energy supply problem for solar energy can be solved by storing thermal energy into the artificial reservoir; ② the thermal output of the hybrid system can keep stable by adjusting the thermal power of the artificial reservoir.According to Eq.  and ener31. To compare the performance between SDAR and DBHE, a numerical simulation on DBHE is carried out and the calculation results are shown in Figs. Tin and Tout remain stable for 20 years’ operation, and the thermal power in the heating season increases with time and however, the percentage increase of the thermal power is only 6.54% . Figure Deep borehole heat exchanger (DBHE) Fig.  is a cloCompared with DBHE, the artificial reservoir creates a lot of fissures in the rocks and thus increases the heat exchange area as well as reduces the thermal resistance between the rocks and the working fluid, leading to an increase in the thermal power from 309 kW (DBHE) to1970 kW (SDAR). From the point of view of heat transfer, two main factors contribute to the increase in the thermal power of SDAR ① both heat transfer coefficient and heat exchange area all increase in the artificial reservoir compared with DBHE. The coefficient of convection heat transfer between fluid and the rocks in SDAR is far greater than that of thermal conductivity of rocks in DBHE, and the heat exchange area between fluid and the rocks in SDAR having a lot of fissures is also far greater than that of between fluid and the well tube in DBHE; and ② the thermal resistance from the surrounding rocks to the artificial reservoir in SDAR is far less than that from the surrounding rocks to the geothermal well in DBHE due to the diameter of the artificial reservoir in SDAR is far greater than that of geothermal well in DBHE, and thus more heat transfers from the surrounding rocks to the artificial reservoir during the heating season and vice versa. In the case of the thermal conductivity of rocks and heat transfer temperature difference between the fluid and the rocks as well as the injection volume flow rate unchanged, increasing the contact area between the fluid and the rocks is the most effective measure to enhance the heat exchange. The increase of the contact area by creating the artificial reservoir in the shallow depth rocks (SDEGS) is technically easy and low-cost compared with that in the deep EGS. To reduce costs and risks further, the abandoned oil and gas fields and mines can be used to create the artificial reservoir for the storage of high temperature thermal energy.To improve the thermal recovery efficiency, a novel scheme of storing high temperature thermal energy into an artificial reservoir created in the shallow depth rocks is proposed in this study, and it is expected that the thermal recovery efficiency can be greatly improved by storing thermal energy in the rocks instead of aquifer. As expected, the results suggested the thermal recovery efficiency for HTSTESSDAR reaches 90% while it is only 46% for HT-ATES in Neubrandenburg, and the thermal power for HTSTESSDAR increases to 1970 kW while it is only 309 kW for DBHE at the same condition.For HTSTESSDAR, the artificial reservoir has no special requirement to the rock temperature, and it can thus be created in the shallow buried depth rocks, leading not only to a considerable reduction of project cost but also a great expansion in the application scope. In our opinion, HTSTESSDAR is the last piece of geothermal heating puzzle. Based on the above analysis, we give the most appropriate technical route for geothermal heating ① using LT-ATES in the regions with rich shallow groundwater or using shallow ground source heat pump; ② using geothermal heating or HT-ATES in the regions with rich hydrothermal geothermal resources or deep groundwater and ③ using HTSTESSDAR in the other regions.


Collaborative robots represent an evolution in the field of swarm robotics that is pervasive in modern industrial undertakings from manufacturing to exploration. Though there has been much work on path planning for autonomous robots employing floor plans, energy-efficient navigation of autonomous robots in unknown environments is gaining traction. This work presents a novel methodology of low-overhead collaborative sensing, run-time mapping and localization, and navigation for robot swarms. The aim is to optimize energy consumption for the swarm as a whole rather than individual robots. An energy- and information-aware management algorithm is proposed to optimize the time and energy required for a swarm of autonomous robots to move from a launch area to the predefined destination. This is achieved by modifying the classical Partial Swarm SLAM technique, whereby sections of objects discovered by different members of the swarm are stitched together and broadcast to members of the swarm. Thus, a follower can find the shortest path to the destination while avoiding even far away obstacles in an efficient manner. The proposed algorithm reduces the energy consumption of the swarm as a whole due to the fact that the leading robots sense and discover respective optimal paths and share their discoveries with the followers. The simulation results show that the robots effectively re-optimized the previous solution while sharing necessary information within the swarm. Furthermore, the efficiency of the proposed scheme is shown via comparative results, i.e., reducing traveling distance by 13% for individual robots and up to 11% for the swarm as a whole in the performed experiments. Swarm robotics is a field inspired by natural self-organizing swarms, such as birds, bees, ants, and fish . The aimOf particular interest is the problem of navigation of a swarm of autonomous robots in an unknown environment, such as a GPS-denied area or where no prior map information exists. Work in this field presents a wide array of research challenges, such as the ability to maintain formation, self-localization, collision avoidance, and path finding . SimultaThe sensing modes utilized for C-SLAM can be divided into two broad categories, namely, vision-based and laser/LiDAR-based. Due to their high resolution, robustness to varying weather conditions, and resilience against lighting conditions, several LiDAR C-SLAM techniques have been investigated ,20,21,22Minimization of the energy consumption of a swarm as a whole is another important research area with core emphasis on a varied set of themes, such as dealing with external influences ,24, optiThe organization of the rest of the paper is as follows: Navigation in environments with no prior map information raises several research challenges. The autonomous robots or agents, while navigating in unknown environments and not having to bank on acquiring information from central or remote servers, must utilize their onboard sensors to observe, analyze, and perform necessary actions based on the information at hand for collision-free navigation and successful completion of the mission . At the In SLAM, exploration is fundamental, and its importance becomes even more vital in swarm SLAM systems (or multi-robot SLAM). Various exploration methodologies are utilized to facilitate the exploration, such as random walk exploration ,34, poteLiterature differentiates collaborative SLAM (C-SLAM) as centralized or decentralized architectures, with centralized schemes gathering all the data into a central server  and assessing the trajectories for all the robots. Different sensing arrangements, such as laser or LiDAR-based ,38 and vOn the other hand, for swarms to function effectively, especially in conditions where communication range is limited or there are poor communication channels, distributed SLAM is a more appropriate approach. The authors of  presenteThe approach presented in  results We now present a collaborative sensing approach whereby individual agents form partial maps of known obstacles discovered by other agents, and utilize this information to find the shortest path to their respective goals. It is to be noted that all agents continue sensing their environment to avoid possible collisions with hitherto unknown obstacles or hidden parts of partially discovered obstacles, continuously passing on any such observation to all other agents to update their world view. ith agent and the goal, respectively, and i stands for the ith agent and jth obstacle in the list. The respective agent then checks whether this particular object has already been detected by any of the agents that may have navigated through the same path by calling the Merge Objects function. This Merge Objects function will perform the following actions if the detected obstacle is present in the obstacle list or if the detected obstacle is not present in the obstacle list. If  the latter is true, then based on the attributes of the detected obstacles in the obstacle list and the newly detected obstacle, it is determined whether the newly detected obstacle is a completely different obstacle or part of a previously partially detected obstacle. These attributes are then passed onto the Shortest Path Obstacle Avoidance function in order for the agent to be able to perform collision avoidance actively.Algorithm 1 NavigationAlgorithm 1 provides the general pseudocode for navigation and obstacle detection. All agents execute this top-level algorithm locally by utilizing their onboard processing units. In the beginning of the mission, all the agents are assigned IDs and connection between them is set up in a leader–follower manner. A global leader is declared, and in a hierarchical manner, the respective leaders are connected to the immediate respective followers, in the initialization phase of the algorithm. Afterwards, the respective agent starts navigation if it has not reached the designated goal, i.e., |When an agent is launched, it executes the obstacle avoidance algorithm to find the shortest path to its destination while avoiding known obstacles. It selects the nearest inflection point as its temporary goal or waypoint, and moves towards this waypoint while continuously sensing its environment for hitherto unseen obstacles. In the case that an obstacle is sensed on its way to the waypoint, the agent performs collision avoidance while simultaneously broadcasting the coordinates of the newly discovered parts of the obstacle. All agents update their individual maps by adding the newly gathered information and run the Merge Objects algorithm to merge multiple sections of the same obstacle into one obstacle. After the agent has moved clear of the obstacle, the process of selecting the waypoint towards its goal is repeated until it completes its mission.Algorithm 2 Merge Objects and Update MapAlgorithm 2 starts by checking whether the detected obstacle exists in the obstacle list  and immediate waypoint selection with obstacle avoidance (IWp-OA). First, we explain shortest path planning with the obstacle avoidance algorithm with reference to 1.The robot draws a straight line from its current position R to its goal G to determine whether it intercepts any edge of the known obstacles. In the instant case, the line 2.Next, it chooses two waypoints that are a minimum safe distance away from vertices C1 and C2; let us call these W1 and W2. Possible paths are 3.The robot iterates steps 1 and 2 above for all possible path segments, always progressing from left to right, creating a new waypoint for each edge that intercepts any path, and repeating steps 1 and 2.4.We now have a directed acyclic graph (DAG) with multiple obstacle-free paths from the robots current position to the goal.5.The robot now selects the first waypoint on shortest obstacle-free path as its temporary goal and starts moving towards it.This algorithm will be re-run every time a new obstacle is discovered, a hidden part of a known obstacle is discovered by the robot’s onboard sensors, or such a finding is communicated by other robots in the swarm. As an alternate approach in the interest of saving computation time and energy, we propose a simplified version of the above algorithm. In this approach, the robot works backwards from the goal, choosing the shorter of two paths at each intersection upon reaching an obstacle. The simplified approach is explained below with reference to 1.The robot draws a straight line from its current position R to its goal G and determines whether it intercepts any edge of the known obstacles. In the instant case, the line 2.Since the top left corner C1 is nearer to I1 than the bottom left corner C2, it decides to circumvent the obstacle from the top left corner C1. It chooses a waypoint that is a minimum safe distance away from C1, let us call it W1, and sets this waypoint as its temporary goal.3.It repeats steps 1 and 2 above; this time, the line 4.The robot repeats step 1 by drawing a straight line The concept of fuzzification of objects is exemplified in Since there may be other obstacles in the way that are yet to be discovered, planning a complete path to the final goal may be an unnecessary effort at this stage. Additionally, for this reason, the robots continually scan their immediate environment for any hitherto unseen obstacles. They also continue listening to broadcasts from other robots for information about a discovery of a new obstacle or the discovery of further sections of a known obstacle. In either case, the path planning algorithm is executed again to ensure that the path followed by the robot is obstacle-free.v is the velocity, and A two-dimensional XY plane, i.e., all the objects (robots and obstacles) are at the same altitude, of 12 km × 6 km is used, with unknown obstacles randomly scattered in space. The number of agents are set to ten and are launched from the same coordinates one after the other. Robots move with a maximum speed of 72 km per hour, or 20 m per second. Python graphics are utilized for simulation purposes. For simulation and testing, we utilized the mathematical models of differential drive robots, and further equipped them with the output of a simulated LiDAR sensor in a two-dimensional plane. The following is a kinematic model of a differential drive robot:W is the width of the robot.The following equation is utilized to calculate the turning curve of the robot:The robots pass through a vast passage area between the launch zone and delivery zone.There are randomly placed multiple obstacles in the passage area.The communication channel between the robots is considered to be ideal and lossless.Utilizing onboard localization methods, the robots obtain their position vector.The range of LiDAR sensors is 100 m.In order to show the progress of the swarm graphically, the field was scaled to fit the available screen resolution, each pixel representing 10 m. The following are the initial conditions and assumptions defined for our work:Similarly, In this article, we present a methodology for finding an optimal solution for the navigation of a swarm of autonomous robots in environments with no prior map information, utilizing only local onboard sensors for observational purposes and inter-robot communication for the sharing of observations in a concise manner. In the presented technique, robots utilize their onboard ranging sensors to detect and avoid close-range obstacles while navigating towards their goal. The approach works by utilizing the information regarding maps built by leading robots for optimizing the routes for rest of the robots in the swarm. Interestingly, this partial map building approach is robust against communication failure of one or more robots, since the followers build upon whatever information is at hand and utilize onboard sensors to augment it. Thus, any gaps owing to lost information are quickly filled by followers. We have simulated various situations with multiple objects obstructing the straight path to the destination, and show that the proposed approach results in the swarm learning its environment in sufficient detail with the passage of few leading robots so that the remaining members of the swarm can find an optimal path.Thus, considering the arrival of the whole swarm at the destination as the mission to be carried out with optimal path traversal, some of the leading robots end up taking longer routes and discovering hidden parts of partially discovered obstacles. This additional information is shared with the rest of the swarm, and results in a more informed choice of route by following robots. This results in optimal path selection for the followers and up to 13% saving in the travel path for individual robots. Furthermore, utilizing the proposed approach results in efficiency of up to 11% in traveling distance for the swarm as a whole.Another contribution of this work is that communication cost is limited to transmitting only significant new discoveries rather than sending the whole point cloud with each detection event of LiDAR by each member of the swarm. This is a direct result of the fuzzification and merging of detected obstacles that reduces the number of obstacles. As long as an obstacle is within the sensing range of a robot’s LiDAR sensor, it receives several detection points in the point clouds for each scan. If this detection data were to be communicated to the rest of the swarm, it would result in high communication cost. Instead, the robot performs several preprocessing steps before transmission. Firstly, it evaluates whether a detection point belongs to an already detected object or not. Here, our fuzzification of the detected objects helps in returning affirmative answers for very close points. If the answer of the first step is negative, it is assumed that the said point belongs to an undetected object. The aforementioned point is fuzzified to form an object with dimensions equal to the minimum clearance distance, and the resulting object is added to the obstacle list. Next, the whole obstacle list is scanned to determine whether any two objects are adjacent or overlapping, merging such objects into one larger object. Since the obstacle list is maintained in a sorted order, only one scan is sufficient to merge all adjacent or overlapping objects. After this final step of merging, the updated obstacle list is broadcast to the rest of swarm. This scheme results in the saving of communication cost and economy of associated communication energy.In our future work, we aim to further develop the proposed methodology by extending the approach to dynamic environments with moving obstacles. Furthermore, other interesting aspects to analyze will be the effects of communication delays, IMU drifts, and other environmental disturbances in dynamic environments.


Vibrio natriegens, Escherichia coli, and Staphylococcus aureus. The results showed that the speckle analysis system is not only able to record the growth of the microbial colony but also to visualize the microbial growth activity in different parts of the colony. The developed speckle imaging technique visualizes the zone of “the highest microbial activity” migrating from the center to the periphery of the colony. The results confirm the accuracy of the previous models of colony growth and provide algorithms for analysis of microbial activity within the colony.The microbial colony growth is driven by the activity of the cells located on the edges of the colony. However, this process is not visible unless specific staining or cross-sectioning of the colony is done. Speckle imaging technology is a non-invasive method that allows visualization of the zones of increased microbial activity within the colony. In this study, the laser speckle imaging technique was used to record the growth of the microbial colonies. This method was tested on three different microorganisms:  Critical detection time, colony size, growth rate, and maximum colony size are the parameters, which may be quantified using the existing live imaging methods.The growth of colony size is used as a criterion for characterizing the microbial activity on agar media. Colony size growth is usually monitored by recording live images at different times and comparing the sizes of the colonies. Adopting this imaging technique, images are obtained by high-resolution cameras or flatbed scanners5. In many models, microbial colony growth is described to be uneven—colony growth depends on the active zones of the microbes which, in their turn, depend on nutrient supply from the media. For example, microbial growth on the edge of the colony is more active than in its center due to the constant supply of nutrients from the surrounding media or the constant push of the cells on the lateral ones. The microscopic structure of the colony supports many of these presumptions. The cells in the center of the yeast colony stop proliferating and lose viability while the cells on the edge of the same colony are alive and continue growing (proliferating)6. The differences in microbial activity in different parts of the colony cannot be accurately visualized with the existing live imaging methods. Currently, different microbial activity within colonies can be explored only with invasive procedures—colony cross-sectioning and viability staining6.There are several models describing colony growth7. Regarding this phenomenon, the laser speckle imaging technique has been proved useful in monitoring microbial activity in optically inhomogeneous media by analyzing time-varying laser speckle patterns.An interference pattern created by the coherent light reflected or scattered from different parts of the illuminated surface is a laser speckle. If an object that is irradiated with laser speckles does not change the scattering properties over time, the speckle image would not change either. If the scatterers move spontaneously , some speckles begin to change . The change in the scattering properties of objects creates a time‐varying speckle. That is, external events or influences, as well as processes occurring directly on the measured surface, can lead to changes in the speckle images8, identification of fungal infection in apple fruits9, and measuring peripheral blood flow in sclerosis patients10.The laser speckle imaging technique is an emerging technology for medical and food safety analyses. It allows for early detection of microbial growthIn this study, the speckle imaging technique was used to record the growth and structural features of the microbial colony. The results showed that the developed speckle analysis system is capable not only to record the growth of a microbial colony but also to visualize microbial growth activity in the different parts of the colony. The speckle imaging reveals that colony growth is driven by cell proliferation on its edges rather than its center. The results confirm the accuracy of the previous models of colony growth and provide algorithms for microbial activity analyses within the colony.Escherichia coli ATCC® 8739 (E. coli), Vibrio natriegens DSM 759 (V. natriegens), and Staphylococcus aureus ATCC® 6538P (S. aureus). Bacterial cultures were maintained on agar plates. E. coli and S. aureus were maintained on LB agar media consisting of Bacto Peptone 10 g/l, yeast extract 5 g/l, agar 20 g/l , and NaCl 5 g/l . V. natriegens was maintained at room temperature on agarized NB salt broth: Difco Nutrient Broth 8 g/l, NaCl 15 g/l, as suggested by Weinstock et al.11.The following microbial strains were used in the experiments: All microbial species were subcultured from a single colony in the respective liquid media and cultivated at + 30 °C overnight. Petri plates were inoculated with serially diluted bacterial culture to yield 20–200 colonies per plate. Petri plates with inoculated bacteria were placed at + 30 °C in an incubator . Colony growth was monitored in parallel by 635 nm laser illumination , and a CMOS camera  was divided into small sections of N × N pixels. The steps below were realized for each section separately. A two-dimensional normalized cross-correlation was performed between consecutive images of N × N pixels from the beginning to the end of the experiment13:In the previous studies, the authors described sensitive correlation subpixel analysis, which can help detect bacterial activity and its effects within a colonyIt was necessary to find out the exact shift of the cross-correlation peak. This value characterizes the changes that occur between consecutive NxN pixels images:14:To find a more accurate value of the offset, the parabolic interpolation was performed around the peak of the cross-correlation functionThe offsets obtained between each pair of adjacent NxN pixels images were accumulated from the start to the end of the experiment:Running the described algorithm for consecutive N × N pixels images for the entire sequence creates a “time signal”.This algorithm was implemented for all N × N pixel sections in the entire field of the experiment. Thus, a two-dimensional array from the “time signals”, where time is the third dimension, was obtained in place of the considered field of the experiment.15. The signal envelope function was used  or by applying spots from serial dilutions on the plates and thus obtaining macrocolonies. Micro and macro colonies on an agar medium were grown in the same incubator in parallel under a speckle imaging system and on the flatbed scanner (Canon Canoscan4400r). The growth of Comparing the growth of the tested colonies, very similar results were obtained with both systems. Therefore, it may be concluded that the established laser speckle system does not affect the growth of microbial colonies see Fig. . We compE. coli culture was serially diluted and inoculated on the LB agar media as macrocolonies (the volume of each inoculum was 5 μL). Macrocolony growth was recorded using a laser speckle imaging system. The time of the maximum signal value for each macrocolony was determined and plotted against the initial cell number per macrocolony. Signal peak time mean values and standard deviation of the three independent inoculation series were calculated , the maximum of the speckle signal is reached once and it never “recovers”.The first results demonstrated that colony growth within a speckle imaging system was the same as in a flatbed scanner. Slight differences between them arise from the individual growth of the colony, which can be affected by the localization of the colony within the plate or the distance to the nearest neighborsS. aureus, E. coli and V. natriegens. Even though in depth analyses on the structure of the speckle signal migration was done on several colonies from three different microbial species , signal migration away from the center to the edge of the colony is feature of every and each microbial colony. In Supplementary Fig. The signal obtained by sub-pixel correlation of laser speckle images, which characterizes bacterial activity, increased inside the colony, reached its maximum, and then decreased. The signal strength had a remarkable spatiotemporal distribution. Different parts of the colony had different maximum signal peak times. The maximum activity peak was initially observed at the center of the colony. Over time, activity “wave” migrated from the center to the edges of the colony  when the activity started to decrease: the blue color (in the center) represents the earliest, red color represents the latest (edge of the colony).15:The location of the first decrease on the map can be assumed as the starting point for the growth of a microbial colony. Knowing the coordinates of this starting point or center, it is possible to obtain a curve of the colony growth as a function of time. However, since the growth of the colony depends on various factors  the resulting curve will have a certain scatter of values  It does not try to fit the curve into a specific shape: a straight line, or a parabola, etc. (2) Unlike a moving average, it does not take outliers into account.The “ring” effect was obtained for all three types of the tested bacteria. The growth rate was the main difference that was observed Fig. .Figure 716, where the truncation was performed not in amplitude, but in the time of the activity peak:Taking the points corresponding to the distance from the center of the colony according to the curve described in Figs. By selecting several points in time on the map, it is possible to observe how the peak of activity will look as a function of the distance from the center of the colony. The width of the peak is proportional to the width of the activity “ring”, and its change in time is shown in the bottom graph of Fig. The spatial width of the signal at different times can be observed in Fig. 5.From Fig. 5 provides a formula for calculating the width of the active zone or the “ring”:−1), which can be found from the Gompertz equation17. Thus, having the experimental data , it is possible to calculate the width of the active zone or the width of the “ring” using Eq. , while it overestimates the width of the active edge of the microbial colony in the case of E. coli and S. aureus. It may be implied that the differences stem from the fact that growth rate α, h−1 in the Pirt equation is a constant, while in fact it changes (decreases) during colony growth4. Another aspect to consider is that in both cases experimental data were used for the calculations. However, as mentioned above, noise has influenced measurement accuracy.The Pirt model predicts that the actively growing edge of the microbial colony might be of the similar width as measured by the speckle activity  the calculation of colony growth dynamics21. However, the experimental data on the actual size of the activity zone of the growing colony are scarce.Microbial colony growth on the agar media is a technique used in microbiology in research and routine tests to analyze microbial contamination of environmental, food or medical samples. Many mathematical models are used to describe microbial colony growth5. However, in routine tests of environmental or medical samples, microcolonies growing at a random distance to the neighboring colonies are typically observed22. Additionally, due to the genomic or physiological make-up of microbial species, their colonies grow in different 3D shapes , which in turn might influence the width of the activity zone on the edge of the colony23.The Pirt model of microbial colony growth is among the first ones describing microbial colony radial growth over time. The model well aligns with real observations if there is no growth inhibition by the neighboring colonies and the size of the activity zone on the edge is constant. The Pirt model has been validated on the distantly growing macrocolonies arising from many cells24, the orientation of the microbial cells  together with the gradual nutrient depletion around the colony define the dynamics of the colony growth. Warren and colleagues in their simulations noticed the formation of a metabolically active “ring” structure around the colony, which is formed by cells having direct contact with the substrate, and where most proliferation activity takes place24.In one of the recent models suggested by Warren et al.In this (our) study, a laser speckle-based system was developed to record microbial colony growth together with a sub-pixel correlation analysis algorithm of laser speckle images, which allows discriminating and quantifying activity zones within the colony. The speckle signal is in good correlation with the colony growth rate and is dependent on the cell number per colony  is observed, which might be attributed to the changes of properties of the agar media, biological variability of the sample and/or accuracy of the measurements.25. Formation and strength of the speckle signal might be affected by the agar media dry out. According to our observations, in many experiments in the first 3–5 h, effects associated with the drying of the agar media might occur. However: (1) This effect spread throughout the Petri dish like a "wave" and then disappeared without causing additional effects. (2) The observed effect of "drying" occurred much earlier than the formation of "rings". Accordingly, even if drying appeared, this effect did not affect the formation of rings. An example of the drying effect is shown in Fig. It is known that agar plates tend to lose water (dry out) during microbial cultivationThe growth of the colonies on the agar media was similar after the inoculation-colonies tend to have the same initial growth rate see Fig.  and theiWhen a colony has ceased to be active, it is still visible on raw speckle images . After applying the subpixel correlation algorithm “”, the maSensitive correlation subpixel analysis revealed that distinct activity zone within the colony exist that migrate from the center to the edges during the growth of the colony. We observed a similar pattern of activity zone (''ring'') migration in the colonies of three different microbial species. Moreover, we observed the presence of the ring in every actively growing colony (see Supplementary Fig. Speckle imaging is promising, powerful technology which for the first time has helped to visualize activity zones within the microbial colony. Previously the presence of these zones were predicted mathematically. Current study also suggests the potential ways to further develop speckle imaging technology for microbial colony studies: to increase the sensitivity of optical and electronic systems for speckle detection, to minimize noise, to seek the options for multiplexing the technology. It would allow recording microbial proliferation activity as early as possible, as well as detecting slowly growing colonies, and identify microbial activity within the colony which makes the proposed technique suitable for many direct applications in research and development, medicine, and epidemiology.Supplementary Information.


Low GHG-producing energy alternatives to fossil fuels are at the center of these activities, and this includes hydropower development. Proponents of this alternative energy source emphasize its renewability, co-benefits provided by reservoirs and generation of electricity with little net release of GHGs to the atmosphere ,2. Howevumulated . And it et al. [In this issue, Ni et al.  provide et al. .et al. is their recognition that the influence of TGD extends far beyond the reservoir and its immediate surroundings. Their approach is based on the logic that a full accounting of  GHG consequences of the dam should encompass the full sphere of the dam's influence. This means expanding the study extent to include the impounded reach as well as thousands of kilometers of the middle and lower Yangtze and delivery of gases to the East China Sea. This methodology led to the unexpected result that aquatic emissions have declined rather than increased since the dam went into operation.While most studies of reservoir GHG emissions consider fluxes from reservoir surfaces and perhaps also the river immediately downstream from the dam where rapid degassing can occur, a second key strength of the work by Ni et al. note, the dam has disrupted physical, chemical and biological conditions over large spatial and temporal scales ‘far beyond our previous understanding’. Although TGD is unique in its size, it is unlikely to be unique in the scale and scope of its influence; Ni et al. provide us with a reason to reconsider effects of large dams worldwide from larger and more expansive perspective.The general lesson of this paper is that a larger whole-ecosystem view is needed to understand the effects of large dams. Expanding the spatial extent of study led to the revelation of declining GHG emissions from the Yangtze River. By itself, this conclusion may be viewed as a positive result regarding dam effects. However, expanding beyond this single process revealed fundamental and profound modifications of several other riverine processes following dam closure. As Ni Conflict of interest statement. None declared.