3-D probabilistic simulation model - Geo-Engineering - TU Delft

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2 AN INTEGRATED 3D MODEL FOR UNDERGROUND COAL GASIFICATION SPE 30790mechanisms. Van Batenburgs’ modellO’ll includea bothchemical reactions and rock failure, but its purpose wasto show that acceptable gas compositions could be attainedin cavity ”gaaification. It does not predict a limitfor areal sweep efficiency.In this paper we present a3D model that can: (1)describe the transition from the early stagea to a fullydeveloped gssifier, and (2) predict the areal sweep efficiency.It is a 3D extension of a previously described2D model.*2 Main differences (apart from the extradimension) with the earlier presented 2D model lie inthe fact that a pressure formulation is used in stead ofthe stream function approach. In the model the essentialfeatures of the underground gasification process are--mA..--J XI..-.. ..-..-.4. L..*.sel.a.mr!v k-m wiamti~mar! inGapt!urcu. Am-y aiYpuN3 u-v. -1 .-J “-u ....”.. ”...- ..the 2D version, 12 but are repeated here to avoid tediouscross-referencing. We will addrees the influence of ashpermeability on overall cavity development, as well asthe thermo-mechanically induced spalling of both roofrock and coal.The model includes aspects of permeable bed gasification,natural convection driven cavity surface gasific&tion and roof-failure mechanisms. Important parametersare the ash content, permeabilities (of ash, roof debris,and char), well outlay and injection strategy. The modelcalculates the form and shape of the cavity. The longterm development of the cavity is dominated by naturalconvection driven cavity gasification.The main applications of this 3D model are the designand-evaluation -.——_-.—_ of underground —--—--qals,as well as the extrapolation of field teat results tocod gasification field tri.the deeplying thin coal seams such aa occur in North-Western Europe.PhysicalModelStructural configuration. Consider a horizontal coallayer with thickness h, length L, and width W with arock layer on top of it. A 3D representation is shown inFig. 2, and a vertical cross section at W/2 is shown inFig. 1. There are four subregions: the aah region ~A,.l–l— —: -—n AL- ..-:.I -.
sp~ 307CJQ E.N.J. BIEZEN, J. BRUINING, AND J. MOLENAAR 3Part of the combustion products and remaining oxygen(if there is insufficient combustible gas) react at thecoal wall driven by natural convection flows (cavity gasification;see below). The other part reacts with thecoal between the cavity wall through which it ie flowingand the production well (indirect permeable bed gasifietion). In spite of this, no distinction is made between directand indirect permeable bed gasification. We merelyuse a parameter (F’) to define how many carbon atomsreact with one molecule of oxygen (02).Because of the reactions the mass flux increases byaddition of coal atoms to the gaa. If gas reacts indirectlywe can (owing to the high cavity permeability)equivalently concentrate all mass flux increase at the interfaceI’vc without affecting the flow field. We assumea constant product gas composition. Thus the ratio ofthe mass flux downstream and the mass flux upstreamof the interfaces I’uc U r~c is constant. Furthermorewe assume ideal gas behavior. The temperature of theproduct gas is the adiabatic flame temperature.Cavity gasification by surface reactious. Cavitygasification is a complex process.’O’l’~” A detailedtreatment is outside the scope of this article. The coalsurface bounding the cavity reacts with the gases in tbecavity. For sufficiently high temperatures the coal consumptionrate is determined by the mass transfer ratethrough the boundary layer between the coal and thecavity. The forced convection flow in the cavity is negligiblewith respect to the natural convection flow.For turbulent natural convection flows, i.e., at highRayleigh numbers (Ra > 1. 1010), the transfer rateis constant: kj = 280 ‘D[m3/m2s], where D[m2/s]denotea the molecular diffusion coefficient. The value ofkf is distributed relatively uniformly over the cavity.*gThe reaction rate r = kj P [02] MC [kgcarbon/m2s],where [02 ] is the molar oxygen concentration. Thecomposition in the cavity may differ from the injectioncomposition, but this will be disregarded as oxygen isreplaced by carbondioxide which also reacts at the coalwall.Coal and roof failure. Three mechanisms of roof failureare distinguished, viz. rock/coal spalling, meltingand large scale roof collapse due to stress concentrationsnear the side boundaries of the cavity. Large scale roofcollapse occurs when a considerable part of the roof spanis unsupported. The critical span depends on the rockmass properties of the roof. The effect is less importantat the initial stagea of the gasification process and hasnot been taken into account.Spalling is the chipping of rock induced by thermaland mechanical stresses. 20 Spzdling occurs both for coaland rock. High span rates develop only in rock/coalexposed to cavity temperatures exceeding 500°C. Dueto the high temperature and pressure inside the cavi$y~P~lA enal hlmelm ar- immdiat.dv undid.5 We.Wu w“”. “.-”-” --- . . . . . ..- . . ..---.J ~— .. ..-.assume that spalling occurs at a constant rate. In ourpresent calculations we use a spatially uniform span931rate. Spalling is introduced in the model as a localphenomenon. The span locations are determined with aprobabilistic method. The span rates for rock and coalare model parameters. Melting effects can be modeledwith enhanced span rates and a low chipped rock permeability.Cavity evolution. The procedure to determine thecavity evolution is as follows: Let the dwtribution ofash, void, and coal be given at a certain time. Thwgeometry delines the permeability distribution. For thegiv~n permeability distribution we determine the flowfield by applying Darcy’s equation. As the coal consumptionrate is small with reepect to the gas velocitieswe can assume (quasi) stationary flow conditions. Coalis consumed at the interfaces roe U r~e at a rate proportionalto the normal flux on the interface. At the cavityboundary an extra amount of coal is gasified due to naturalconvection driven surface gasification. Finally, allspalled coal iz immediately gaafied.The volume of gasified coal becomes void space to beadded to the cavity, and its aah is d~placed verticallyto the bottom of the cavity. The ash-void interface rv~is displaced downward when the coal beneath it is g~ified. The rock and coal exposed to the cavity span ata constant rate and also fail vertically downward. Thevolume of spalled rock/coal per unit original rock/coalvolume are model parameters, The permeability distributionis updated and the calculation procedure entersthe next time step.Model equationsGeneralized mass flux vector.flux vector ~ is defined byA generalized masswhere ~ is the specific discharge and p is the density ofthe gas. The ratio x betwaen the maaz flux downstreamand the mass flux upstream of the interface between~A U S)V and f2c is constant. A similar ratio also occursin steam drive.21 The (stationary) conservation lawreads div ~ = Oin the whole domain Q ordiv~=Oin f2jA,n = jc,. on rae . . . . . . . . . . . . . . . . . . . . . . ...(2)W,n = W,nnn r. . -.. . “=where jA,n and ~v,n are the normal components ofthe upstream generalized mass flux vector at rUCandrac, respectively, and jc,n is the downstream generalizedmaas flux. Note that (~)A,~ # (pg)c,n and(P9)v,n #(P9)C.,n.Darcy equation and pressure equation. Substitutionof Darcy’s equation in Eq. 1 giveskmJ = –P--gradp iii “r-fi . . . . . . . . . . . . . . . . . . . ..\w)(Q)
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3-D probabilistic simulation model - Geo-Engineering - TU Delft

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