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ECMOR XII  12th European Conference on the Mathematics of Oil Recovery
 Conference date: 06 Sep 2010  09 Sep 2010
 Location: Oxford, UK
 ISBN: 9789073781894
 Published: 06 September 2010
1  20 of 117 results


Upscaling of Fractured Oil Reservoirs Using Homogenization Including Nonequilibrium Capillary Pressure
Authors H. Salimi and J. BruiningRecovery in incompletely waterwet fractured reservoirs can be extremely low. In the laboratory, these systems are often mistaken for oilwet reservoirs, because imbibition only starts after removal of the oil layer, which originally covers the grains. The long time required to remove the oil film will be referred to as delay time. There are two theories that describe the delay time necessary for removal of an oil film, leading to a capillary pressure that depends on time. One of the theories is developed by Barenblatt et al. and it modifies both the capillary pressure and the relative permeabilities. The other theory is developed by Hassanziadeh et al. and it only deals with the nonequilibrium effect for the capillary pressure. No attempt has yet been made to model nonequilibrium effects in fractured reservoirs for a fieldscale problem and this is an innovative aspect of this paper. To examine whether the nonequilibrium effect has any effect on largerscale problems, we apply homogenization to derive an upscaled model for fractured reservoirs in which the nonequilibrium effects are included. We formulate a fully implicit threedimensional upscaled numerical model. Furthermore, we develop a computationally efficient numerical approach to solve the upscaled model. We use the simulation to determine the range of delay times for which discernable effects occur in terms of oil recovery. It is shown that at low Peclet numbers, i.e., when the residence time of the fluids in the fracture is long with respect to the imbibition time, incorporation of delay times of the order of few months have no significant effect on the oil recovery. However, when the Peclet number is large, the delay times reduce the rate of oil recovery. We will discuss for which values of the delay time (Barenblatt) and capillarydamping coefficient (Hassanizadeh), equivalent results are obtained. This is the first time that such a comparison is made for a field scale project and it shows that both approached show the importance of taking to account delay effects in the capillary pressure behavior.



Incorporation of Global Effects in Twophase Upscaling for Modeling Flow and Transport with Fulltensor Anisotropy
More LessUpscaling is often applied to coarsen highlydetailed geological descriptions. The upscaling of multiphase flow functions is challenging due to their strong dependency on global flow effects. In this work, we present two approaches to generate upscaled twophase flow functions with global flow effects incorporated. In global twophase upscaling, the upscaled twophase functions are directly computed from global finescale twophase solutions. In a new adaptive localglobal twophase upscaling approach, local boundary conditions (for both pressure and saturation) are determined from timedependent global coarsescale solutions. This avoids solving global finescale twophase flow. In both approaches, the upscaled twophase flow functions are adapted to a specific flow scenario, thus providing more accurate coarse models than the use of generic flows. The methods are applied to heterogeneous permeability fields with fulltensor anisotropy. We demonstrate the impact of fulltensor effects on the global flow dependency in twophase upscaling. It is also shown that the fulltensor effects in twophase flow are appropriately accounted for by the upscaled twophase functions with the global flow effects incorporated. The use of those upscaled functions in conjunction with a twopoint flux approximation can effectively capture the twophase crossflow due to the fulltensor anisotropy on the coarse scale.



Meshless Upscaling Method and Its Application to a Fluid Flow in Porous Media
By A. LukyanovIt is known that the twopoint flux approximation, a numerical scheme used in reservoir simulators, has O(1) error when grids are not Korthogonal. The multipoint flux approximations have found significant interest in the research community. However, nonphysical oscillations can appear in the developed multipoint flux approximations when the anisotropy is really strong. In this paper, the meshless multipoint flux approximation (MMPFA) for general fluid flow in porous media is proposed. The MMPFA is based on a gradient approximation commonly used in meshless method and can be extended to include higherorder terms in the appropriate Taylor series. The MMPFA is combined with the mixed corrections which ensure linear completeness. The mixed correction utilizes Shepard Functions in combination with a correction to derivative approximations. Incompleteness of the kernel support combined with the lack of consistency of the kernel interpolation in conventional meshless method results in fuzzy boundaries. In corrected meshless method, the domain boundaries and field variables at the boundaries are approximated with the default accuracy of the method. The resulting normalized and corrected MMPFA scheme not only ensures first order consistency O(h) but also alleviates the particle deficiency (kernel support incompleteness) problem.



The Selfflattening Nature of Trailing Shocks in Augmented Waterflooding – Segregationinflow Reestablish Selfsharpness
Authors A.M. AlSofi and M.J. BluntOne of the challenges for reservoir simulation is numerical dispersion. For waterflooding applications the effect is controlled due to the selfsharpening nature of a BuckleyLeverett shock. In this paper, we show that for augmented waterflooding – due to the coupling of compositional dispersion with fractional flow – the trailing shock is no longer selfsharpening. Thus, the simulation of such processes suffers from even higher numerical dispersion effects compared to pure waterflooding. Rather than implementing a higherorder discretization method, we propose a simple scheme based on segregation within a grid block. Compared to current mixing schemes, it differs in that segregation not only affects fluid properties but the transport, too. The scheme is shown to reestablish selfsharpness across the trailing shock. Simulations are performed that demonstrate the effectiveness of the scheme. The simulations also illustrate the possible effects of numerical dispersion on the predictions of augmented waterflooding. Finally, we discuss the extension of this technique to compositional simulation through a coupled limitedflash/segregationinflow assumption. Preliminary results demonstrate the potential of the approach as a heuristic method to control numerical dispersion for the simulation of miscible and nearmiscible gas injection processes.



A Multiscale Framework for Simulating Multiphase Flow on Flexible Grids
Authors A. Sandvin, J.O. Skogestad, E. Keilegavlen and J.M. NordbottenThe geological structure of porous rocks include irregular geometries and heterogeneities on a multiple of scales. Reservoir simulations (e.g. oil recovery, CO2 storage, ground water flow) often involve large spatial scales, where local finescale heterogeneities might have an important impact on the global flow. Discretisations of the governing equations of multiphase flow in general render large systems of nonlinear equations. The multiscale nature of the geology is inherited by the discrete mathematical problem, which can be illconditioned and thereby hard to solve. In this work, we apply domain decomposition (DD) as a solution strategy for the equations. The splitting of the global system into local subproblems can be done either prior to, or after linearisation of the nonlinear system. Comparison between DD as a nonlinear and linear solver strategy indicates that splitting into subproblems should be considered for use as preconditioners, also for nonlinear systems of equations. When applied after linearisation, DD is best suited as a preconditioner in an iterative solution procedure. In this work, we consider a twolevel DD framework for linear systems. The framework is flexible, and can be used both as an upscaling procedure, and as a preconditioner.



On the StokesBrinkman Equations for Modeling Flow in Carbonate Reservoirs
Authors I. Ligaarden, M. Krotkiewski, K.A. Lie, M. Pal and D. SchmidCavities and fractures can significantly affect the flow paths of carbonate reservoirs and should be accurately accounted for during flow simulation. Herein, our goal is to compute the effective permeability of rock samples based on highresolution 3D CTscans containing millions of voxels. Hence, we need a flow model that properly accounts for the effects of Darcy flow in the porous material and Stokes flow in the void volumes on relevant scales. The presence of different length scales and large contrasts in the petrophysical parameters lead to highly illconditioned linear systems that make such a flow model very difficult to solve, even on largescale parallel computers. To identify simplifications that render the problem computationally tractable, we analyze the relative importance of the Stokes and Darcy terms for a wide variety of parameter ranges on an idealized 2D model. We find that a system with a throughgoing free flow region surrounded by a low permeable matrix can be accurately modeled by ignoring the Darcy matrix and simulating only the Stokes flow. Using this insight, we are able to compute the effective permeability of a specific model from a CTscan that contains more than eight million voxels.



Effective Local and Extended Local Singlephase Upscaling
Authors S. Du, S.A. Hosseini, Y. Zhou and M.J. KingEffective strategies for upscaling of flow in porous media rely upon (1) the characterization of flow in the reservoir (intercell transmissibility), (2) flow near wells (effective permeability) and (3) an a priori analysis of error. Transmissibility upscaling represents approximately constant gradient Darcy flow and, compared to permeability upscaling, maximizes the spatial resolution of intercell fluid flow available within a simulator. Near well permeability upscaling replies upon the line source approximation and the calculation of well productivity for radial flow near wells. It provides a characterization of the local reservoir quality. It can be performed without knowledge of the location or rates of physical wells. The error analysis has three components. It relies upon a connectivity analysis, an analysis of variance of velocity or slowness, and an estimate of offdiagonal flow terms in the permeability tensor. All three of these error components can be estimated using local flow information. This a priori error analysis allows a practicing engineer or a spatially adaptive algorithm to adjust the resolution of the upscaled model in order to minimize the most egregious upscaling errors. All three of these calculations can be performed using local or extendedlocal boundary conditions. This is in contrast to global upscaling approaches which have been previously used in the literature but which rely upon knowledge of a global flow field. Although global upscaling approaches can be quite accurate, their utility is limited as specific well locations and flow rates are not available at the point in the life of a project when the geologic model is typically upscaled in preparation for reservoir flow simulation. The utility of this combined upscaling and error analysis approach is demonstrated using the SPE10 test model, which is simple structurally but which has a fairly complex and heterogeneous permeability field.



Upscaling of Twophase Immiscible Flows in Communicating Stratified Reservoirs
Authors X.Z. Zhang, A.S. Shapiro and E.H.S. StenbyA new analytical upscaling method is described. It is applicable for stratified reservoirs or with vertically distributed properties. The interlayer communication is assumed to be perfect, corresponding to viscous or gravity dominant regimes. We apply asymptotic analysis to 2D flow equations of two incompressible immiscible fluids and reduce 2D BuckleyLeverrett system to 1D flow problem. Flow velocities in the layers depend on saturations of other layers, which reflects interaction between layers; the exchange terms between the layers may be expressed explicitly. The resulting quasilinear hyperbolic equations allow a selfsimilar solution, which makes it possible to express the pseudofractional flow function as a function of average saturation. The system is solved by the finite difference method. Both cases of discontinuous and continuous (lognormal) distributed layer permeabilities are studied. As comparison, the complete 2D waterflooding problems with very good vertical communication are solved in COMSOL. Generally, saturation profiles of the pseudo 1D model are only slightly different from the 2D simulation result by Comsol. The difference between recovery curves is marginal. This proves validity of the proposed method. Our method is much more advantageous over the classical HearnKurbanov procedure. It is better at predicting displacement fronts and oil recovery.



Analytical Solutions for Co and Countercurrent Imbibition of Sorbing – Dispersive Solutes in Immiscible Twophase Flow
Authors K.S. Schmid, S. Geiger and K.S. SorbieWe derive a set of analytical solutions for the transport of adsorbing solutes in an immiscible, incompressible twophase system. Our analytical solutions are new in two ways: First, we fully account for the effects of both capillary and viscous forces on the transport for arbitrary capillaryhydraulic properties. Second, we fully take hydrodynamic dispersion for the variable twophase flow field and adsorption effects of the solutes into account. All previously obtained results for component transport in immiscible twophase systems account for changes in the flow field due to the components’ presence but they ignore dispersive effects. This is surprising given the enormous practical importance of diffusive effects both in hydrological settings and for situations that arise in the context of oil production for chemical flooding, polymer flooding and the transport of wettability altering agents. In both cases, one often faces the situation of fractured media or thinlayer structures where the diffussive transport processes of components dominate over viscous forces. We consider a situation where the components do not affect the flow field and focus on dispersive effects. For the purely advective transport we combine a known exact solution for the description of flow with the method of characteristics for the advective transport equations to obtain solutions that describe both co and countercurrent flow and advective transport in one dimension. We show that for both cases the solute front can be located graphically by a modified Welge tangent and that the mathematically obtained solutions correspond to the physical notion that the solute concentrations are functions of saturation only. For the advectiondispersion case, we derive approximate analytical solutions by the method of singular perturbation expansion. We give some illustrative examples and compare the analytical solutions with numerical results.



Classic and Hybrid MCMC Methods to Approximate Pore Size Distributions of Carbonate Reservoirs Using Porenetwork Models
Authors J.E Juri, M.I.J. van Dijke, K.S. Sorbie and S.K. MasalmehCarbonate reservoirs contain a large fraction of the remaining oil reserves, but their highly heterogeneous structures, at the pore scale, make them difficult to characterize and this is one of the main reasons for their low recovery factors. Pore space imaging and reconstruction techniques are often used to characterize the pore space topology and geometry. However, the wide range of pore sizes encountered in carbonates, including submicron microporosity, usually renders these techniques unsuitable. A classic technique to approximate the pore size distribution (Ritter and Drake) is based on inversion of the mercury intrusion capillary pressure (MICP) curve. However, this technique is inaccurate due to the lack of accessibility of the large pores before the percolation threshold is reached. In this paper, we use a simple lattice network, characterized by an average coordination number, a pore volumevsradius power law and a pore (radius) size distribution (PSD) with an arbitrarily large range of radii, to match the MICP curve. Efficient optimization methods have been implemented to estimate these principal parameters, as outlined below. The overall aim of this work is to predict rock flow functions for different floods or saturations paths that are difficult and expensive to obtain from laboratory experiments, based on the PSD estimations. In the present approach the PSD has a given number of nonconstant radius classes (bins), for which the probabilities need to be determined. As an initial guess, we take the Ritter and Drake PSD, based on which the nonfixed bin widths are determined, using principal theorems derived in information theory and data compression. Then, the porenetwork parameters including the PSD class probabilities are optimized to match the experimental MICP, using two methods that are based on the link between the Boltzmann  Maxwell equation describing the molecular state probabilities in statistical physics and the Bayes method for posterior distribution. The first method is the classic Metropolis Markov Chain Monte Carlo method and the second, hybrid, method adds Hamiltonian Dynamics to avoid the random nature of the classic Metropolis algorithm, thus enhancing the convergence of the classical approach. The methods have successfully been applied to two synthetic cases and three carbonate samples from a Middle East reservoir presenting three different carbonate facies. The hybrid method improves the Markov Chain Monte Carlo efficiency in terms of the accepted system parameters states by a factor of 4 to 5.



Porescale Modelling of Chemically Induced Effects on Twophase Flow
Authors Y. Zaretskiy, S. Geiger, K. Sorbie and M. FoersterWe present a finite element  finite volume simulation method for modelling fluid flow and solute transport accompanied by chemical reactions in experimentally obtained 3D pore geometries. We solve the stationary Stokes equation on the computational domain with the FE method using the same set of nodes and the same order of basis functions for both velocity and pressure. The resulting linear system is solved by employing the algebraic multigrid library SAMG. To simulate large 3D samples we partition them into subdomains and treat each separately on a different computing node. This approach allows us to use meshes with millions of elements as input geometries without facing limitations in computer resources. We apply this method in a proofofconcept study of a digitized Fontainebleau sandstone sample. We use the calculated velocity profile with the finite volume procedure to simulate porescale solute transport and diffusion. This allows us to demonstrate the correct emerging behaviour of sample’s hydrodynamic dispersivity. Finally, we model the transport of an adsorbing solute and the surface coverage dynamics is demonstrated. This information can be used to estimate the local change of a sample wettability state and the ensuing changes of the twophase flow characteristics.



Determination of Connectivity in Vuggy Carbonate Rock Using Image Segmentation Techniques
Authors T.P.G. Gurholt, B.F.V. Vik, I.A. Aavatsmark and S.I.A. AanonsenIt is commonly understood that carbonate reservoirs hold much of the worlds' oil and gas reserves. In this study we examine a heterogeneous vuggy pore class. The vuggy pore space is imaged using xray computed tomography (CT). MicroCT ($mu$CT) is used to better image parts of the interparticle (matrix) porosity. Image segmentation is applied to obtain a threedimensional (3D) map of the vuggy pore space, which is used to determine its connectivity. We evaluate the performance of selected image segmentation techniques applied for segmenting CTscans of vuggy carbonate rocks at varying resolutions. Computations are performed for both twodimensional (2D) and threedimensional (3D) image segmentation. The computations show that the methods perform well on high resolution $mu$CT scans. For a CT scan with low and nonuniform resolution they wrongly classify a large portion of the voxels. This makes it challenging to determine the connectivity. The computed porosity is, due to image resolution, underestimated when compared to measured porosity from laboratory experiments.



Roles of Transient and Local Equilibrium Foam Behavior in Porous Media – Traveling Wave
Authors E. Ashoori, D. Marchesin and W.R. RossenIn foam EOR, complex dynamics of bubble creation and destruction controls foam properties. We assume that local equilibrium applies throughout a foam displacement on the field scale, with the exception of an entrance region and at shock fronts, where saturations and bubble size change abruptly. We find a range of conditions in which the localequilibrium condition applies even within the shock front. In a waterflood the width of a shock transition zone is determined by capillarypressure gradients. For foam, this equation is joined by one for evolving foam texture. If there is no gas ahead of the foam, we prove that foam texture is everywhere at local equilibrium within the shock, regardless of the foam model. If there is gas initially in the formation, slow foam generation and coalescence processes can narrow the shock from that assuming local equilibrium. In other cases, the dynamics of the traveling wave leads to oscillations near the shock; these are not numerical artifacts, but reflections of the models. Multiple steady states seen in experiment for some injection rates can be predicted by certain foam models. The approach of solving for the traveling wave can give rule out some of these states.



Extended Kvalue Method for Multicontact Miscible Displacements
Authors G. Rannou, D.V. Voskov and H.A. TchelepiAccurate predictions of gasinjection processes usually require a compositional formulation based on an Equation of State (EoS). Because the thermodynamic behavior of multicomponent multiphase systems is highly nonlinear and coupling to the flow equations is quite complex, EoSbased simulations can become computationally prohibitive. For immiscible displacements an efficient approximation of the general compositional problem can be used if the phaseequilibrium ratios (Kvalues) are assumed to be weak functions of composition; however, this assumption is questionable for nearmiscible displacements. The standard Kvalue approach suffers from significant difficulties, both in terms of robustness and accuracy, in the critical region. Here, we describe an extended Kvalues method that takes advantage of the solutionpath invariance in the compositional space with respect to the hydrodynamic properties. Specifically, we propose an additional degreeoffreedom, which captures the composition dependence of the phase behavior, for use in the tabulation and interpolation of the Kvalues. An important aspect of the method is the use of the socalled Minimal Critical Pressure criteria (MCP), which indicates when a given composition becomes supercritical. We compare results obtained with EoS and Kvalues based simulations for several (isothermal) compositional problems, and we demonstrate the efficiency and accuracy of the proposed method.



A New Variableset for Nonlinear Flow Simulation Based on Compositional Space Parameterization
By D.V. VoskovWe consider numerical modeling of compositional twophase flow in porous media, and we propose a nonlinear formulation that employs a variableset based on compositional space parameterization. In the formulation, the phasefraction and saturation change 'continuously' in the immiscible region of the compositional space. Inside the twophase region, these variables are identical to the saturation and phasefraction of the standard approach. In the singlephase regions, however, these variables can become negative, or larger that unity. We demonstrate that when this variable set is used, the EOS computations are resolved completely within the general Newton loop. That is, no separate phasestability or flash computations are necessary. The number of general Newton iterations grows only slightly, and overall savings lead to more efficient simulations. We discuss using this variable set, which can be thought of as an extension of the natural variable, in two ways. The first scheme honors the nonlinear dependence of the overall density on phasefractions and saturation, and the second employs a linearized relation for the overall density. Both schemes are compared with the standard naturalvariables formulation using several challenging compositional problems. We also describe how the proposed approach can be used for modeling multicontact miscible displacement processes.



Continuation of the Tiesimplex Space for Threephase Thermalcompositional Systems
Authors A. Iranshahr, D. Voskov and H. TchelepiModeling the phase behavior associated with compositional flow simulation of systems that form more than two phases (e.g., steam, or CO2 injection) is a challenging problem. In addition to the coupling of thermodynamics with the nonlinear equations of flow and transport, accurate phasestate identification for mixtures that form three (or more) phases, as function of pressure, temperature and composition, is the subject of active research. We describe a general negativeflash method for multicomponent thermal systems that can form three, or more, fluid phases, including a convergence proof. This extended negativeflash approach integrates quite nicely with flow simulation based on adaptive tiesimplex compositional space parameterization. We prove that tiesimplexes change continuously with pressure, temperature, or along a continuous trajectory in compositional space. Continuation of the tiesimplex space provides theoretical justification for the tiesimplex based flow modeling, in which interpolation in pressure and temperature for a limited number of tiesimplexes is performed during a simulation run. We also show how a tiesimplex associated with a given composition can degenerate as a function of pressure and temperature. We focus on the complex behaviors of the tietriangles and tielines associated with threephase, steaminjection problems. The algorithms that capture the degeneration of the tietriangles into tielines are described in detail. Interpolation in the parameterized compositional space is used to identify the phasestate and proves to be as reliable as a 'conventional' phasestability test for threephase mixtures. This extended negativeflash algorithm has been integrated into our tiesimplex based flow simulation framework. We demonstrate the effectiveness of the framework using several compositional steaminjection problems with complex behaviors.



New Models for Heater Wells in Reservoir Simulation
Authors G. Aouizerate, L.J. Durlofsky and P. SamierDownhole electrical heating can be used to achieve the high temperatures required for insitu upgrading of oil shale. Heaterwell models are needed if this process is to be simulated accurately. The traditional Peaceman approach used for fluid injection and production wells may not be applicable because it does not capture transient effects, which can be important in downhole heater models. Here we develop two new models for representing heater wells in reservoir simulators. The first model is applicable for homogeneous systems with properties that are not temperature dependent. For such cases we develop a semianalytical procedure based on Green’s functions to construct timedependent heaterwell indices and heaterblock thermal transmissibilities. For the general case, which can include both finescale heterogeneity and nonlinearity due to the temperature dependence of rock properties, we present a numerical procedure for constructing the heaterwell model. This technique is essentially a nearwell upscaling method and requires a local finescale solution in the well region. Local boundary conditions are determined using a localglobal treatment. The accuracy of the new heaterwell models is demonstrated through comparison to reference solutions for two example problems.



Towards Temperature Transient Analysis in Horizontal Wells
Authors K.M. Muradov and D.R. DaviesTemperature modeling and analysis of horizontal wells has become increasingly important due to the extensive deployment of downhole temperature monitoring devices. Such sensors allow continuous monitoring of zonal production with a sufficiently high resolution. Published descriptions of the necessary analysis tools have concentrated on well temperature models and convective heat transfer in porous media. They rarely describe transient, reservoir temperature changes during conventional production. Here, fluid expansion effects are superimposed on heat conduction to the surrounding layers coupled to a transient inflow regime. This paper will discuss why these already available solutions to related problems cannot be employed directly. It will propose a comprehensive model of the reservoir temperature around a horizontal, liquid production well. The above task is treated as a multidimensional, heat transfer problem. Both an asymptotic, early time, solution in real space and an accurate, integral solution can be derived. The asymptotic, analytical solution has been tested against a scientific, simulation softwares. The applicability and practical importance of the solution will be discussed. It forms the basis of a Temperature Transient Analysis tool for horizontal, oil producing wells where both the flow properties of the reservoir fluid and the inflow distribution are to be evaluated.



Analysis of Coupled and Fully Integrated Models for Lowfrequency Electrical Heating Assisted Heavy Oil Recovery
Authors J.A. Torres, I.I. Bogdanov, V. Dabir and A.M. KampWe have studied low frequency heating for heavy oil recovery accompanied by salt water recirculation around electrode wells. The multiphysics nature of this problem naturally calls for a code coupling solution. The main objective of this work is to develop an efficient methodology for such coupling. We address the coupling paradigm which includes questions about the degree of coupling (with respect to synthesis), grid and solver type used in the simulation of each separate problem, problem stability and accuracy, interpolation strategy, parallelization, etc. The implemented solution was validated and applied. We coupled a finite volume (FV) reservoir simulator (Stars) to a general purpose finite element (FE) simulator (COMSOL Multiphysics) used to compute an approximation to Maxwell’s equations. These two simulators are coupled by an inhouse coupler written in Matlab, being its critical step the bidirection mapping of interpolation/integration of data between the FE and FV mesh. Selection of solver parameters has been confirmed to be critical in order to limit the effect of numerical dispersion. Coupling solutions, such as the one described in this paper, allow developing simulation tools that reuse as much as possible specialized and existing tools. Their application to practical problems proves to be useful.



Lowtemperature Insitu Combustion of Light Oil
Authors A.A. Mailybaev, D. Marchesin and J. BruiningWe consider flows possessing a combustion front when a gaseous oxidizer (air) is injected into the porous medium, a rock cylinder thermally insulated preventing lateral heat losses and filled with light or medium viscosity oil. When oxygen reacts with hydrocarbons at low temperatures, a series of reactions occur that will convert a part of hydrocarbons to oxygenated hydrocarbons and gaseous product (water, carbon dioxide etc.). The oxygenated hydrocarbons are compounds like ketones, alcohols, aldehydes and acids. This process is termed low temperature oxydation (LTO). Indeed, LTO only involves some 25 % of the possible sites that can react with oxygen. Therefore also the reaction heat per volume of fuel can at most be 25 % of full hydrocarbon combustion and consequently the temperature in the LTO reaction zone is very low. Upstream of the LTO reaction zone evaporization occurs. We formulate conservation laws for liquid oil, gaseous oil, oxygen and inert gas components (combustion products and nitrogen) that includes the reaction terms. Moreover we give the energy conservation equation. We give an analytical solution to the equations. It turns out that the solution consists, from upstream to downstream, of a thermal wave, an LTO wave that combines oxidation and evaporation and a BuckleyLeverett saturation wave. It is shown that in the solution a major role is played by the existence of a resonance line at which the derivatives of the oxygen and evaporated oil flux versus the oil saturation vanish. It means that the derivative of the oil flux versus saturation is positive upstream of the resonance line and negative downstream of the resonance line. The complete solution is described for typical parameters of LTO oil combustion. Computations show that only a small part of the oil vaporizes or reacts. The oil velocity is close to the LTO speed. Thus the LTO wave represents a mechanism of almost complete oil displacement by means of the temperature increase in the LTO wave, which leads to a decrease of oil viscosity and increase of the gas flux in the wave.
