SPE-173218-MS

SPE-173218-MS

Adaptive Local-global Multiscale Simulation of the In-situ ConversionProcess

Faruk O. Alpak, Shell International Exploration and Production Inc.; Jeroen C. Vink, Shell Global Solutions (US)Inc.

Copyright 2015, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Reservoir Simulation Symposium held in Houston, Texas, USA, 2325 February 2015.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contentsof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the writtenconsent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations maynot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

Numerical modeling of the In-situ Conversion Process (ICP) is a challenging endeavor involving thermalmultiphase flow, compositional PVT behavior, and chemical reactions that convert solid kerogen intolight hydrocarbons and are tightly coupled to temperature propagation. Our investigations of grid-resolution effects on the accuracy and performance of ICP simulations have demonstrated that ICPsimulation outcomes, e.g., oil/gas production rates and cumulative volumes, may exhibit relatively largeerrors on coarse grids, where coarse means a gridblock size of more than 3-5 m. On the other hand,coarse-scale models are attractive because they deliver favorable computational performance, especiallyfor optimization and uncertainty quantification workflows that demand a large number of simulations.Furthermore, field-scale models become unmanageably large, if gridblock sizes of 3-5m or less have tobe employed. Therefore, there is a clear business need to accelerate the ICP simulations with minimalcompromise of accuracy.

We have developed a novel multiscale modeling method for ICP that reduces numerical modelingerrors and approximates the fine-scale simulation results on relatively coarse grids. The method uses atwo-scale adaptive local-global solution technique. One global coarse-scale and multiple local fine-scalenear-heater models are timestepped in a sequentially coupled fashion. At a given global timestep, theglobal model solution provides accurate boundary conditions to the local near-heater models. Theseboundary conditions account for the global characteristics of the thermal-reactive flow and transportphenomena. In turn, fine-scale information about heater responses is upscaled from the local models, andused in the global coarse-scale model. These flow-based effective properties correct the thermal-reactiveflow and transport in the global model either explicitly, by updating relevant coarse-grid properties for thenext time step, or implicitly, by repeatedly updating the properties through a convergent iterative scheme.Upon convergence, global coarse-scale and local fine-scale solutions are compatible with each other.

We demonstrate the much improved accuracy and efficiency delivered by the multiscale method usinga 2-D cross-section pattern-scale ICP simulation problem. The following conclusions are reached vianumerical testing: (1) The multiscale method significantly improves the accuracy of the simulation resultsover conventionally upscaled models. The method is particularly effective in correcting the globalcoarse-scale model through the use of the fine-scale information about heater temperatures to regulate the

heat-injection rate into the formation more accurately. The effective coarse-grid properties computed bythe multiscale method at every timestep also enhance the accuracy of the ICP simulations, as demonstratedin a dedicated test case, where a constant heat-injection rate is enforced across models of all investigatedresolutions. (2) Multiscale ICP models result in accelerated simulations with a speed-up of 4 to 16 timeswith respect to fine-scale models out-of-the-box without any special optimization effort. (3) Ourmultiscale method delivers high-resolution solutions in the vicinity of the heaters at a reduced compu-tational cost. These fine-scale solutions can be used to better understand the evolution of the fluids andsolids, e.g., kerogen conversion and coke deposition, in the vicinity of the heaters (a few feet-long spatialscale). Simultaneously with the fine-scale near-heater solutions, the local-global coupled multiscalemodelprovides key commercial ICP performance indicators at the pattern-scale (a few hundreds offeet-long spatial scale) such as production functions.

IntroductionICP utilizes tightly-spaced electrical heaters inserted into regularly spaced wellbores to heat the in-situ oilshale resources to temperatures of approximately 650 F (Fowler and Vinegar 2009). ICP convertsinitially unrecoverable, solid organic material (kerogen) in the oil shale formations into recoverablehydrocarbons. Long-chain kerogen molecules within the oil shale are thermally cracked into smaller oiland gas molecules at pyrolysis conditions (Fowler and Vinegar 2009; Shen 2009). The converted productsare mobile hydrocarbons (light oil and gas) which are recovered through production wells. Coke, a solid,low-hydrogen-content organic component, is also formed as part of the thermal cracking reactions. Water,H2, CO2, CO, and other components are generated during the ICP process (Shen 2009).

High liquid recovery efficiencies (higher than 60% of the Fischer assay oil content of the kerogen inplace1) have been observed due to relatively uniform heating through heat conduction and predominantlyvapor-phase transport under reservoir conditions (Shen et al. 2010). ICP circumvents fundamentaldifficulties associated with direct rock-extraction driven recovery techniques, such as mining/retort,especially for deeply located oil-shale deposits. A historical perspective for ICP and associated pilotprojects are documented in Fowler and Vinegar (2009).

ICP is a complex and technically challenging process in a number of aspects. These include, but arenot restricted to, heater design, subsurface phenomena (non-isothermal compositional flow and transport,chemical reactions, and geomechanical deformation), surface facilities design, subsurface/surface instru-mentation for monitoring, and economic analysis. A good understanding of the reservoir performance iscrucial for designing an optimal production scheme while minimizing the environmental footprint. Thus,we focus on the coupled modeling of non-isothermal subsurface flow, transport, and thermal crackingreactions.

Tight coupling between thermally-driven flow and transport, compositional phase behavior, andchemical reactions, render the simulation of ICP a difficult endeavor. Various thermal reservoir simulationapproaches have been developed for ICP and results of a few studies have been reported in the literature(Shen 2009; Fan et al. 2010). These studies feature simulation models designed for pilot projects, whichare typically small in size and therefore require only relatively small simulation models. Shifting the focusof ICP modeling from pilot to larger commercial-scale patterns will clearly require the application ofapproximate techniques that retain sufficient accuracy of the fine-scale solutions, but reduce the simula-tion times significantly. The near-wellbore upscaling method reported in Aouizerate et al. (2012) can beviewed as a step in this direction. Li et al. (2014) describe a preliminary effort to apply multiscale methodsto ICP modeling.

1 Fischer assay (more precisely, modified Fischer assay, ASTM D3904-90 (1984)) is a common method to evaluate the liquid yield of a particular oil shaleresource, measured in U.S. gallons per short ton of raw shale.

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We have developed a novel multiscale modeling method for ICP that reduces numerical modelingerrors and approximates fine-scale simulation results on relatively coarse grids. The method uses atwo-scale local-global solution technique. The rationale of the method can be traced back to thelocal-global single-phase flow-based upscaling method first introduced by Chen et al. (2003) and laterextended by Chen and Durlofsky (2006) for adaptivity. Their method was applied as a pre-processing stepprior to simulations of relatively simple (compared to ICP) isothermal two-phase flow problems. Thesingle-phase local-global upscaling method is later extended to multiphase flow-based upscaling (Chenand Li 2009; Alpak 2014). Alpak et al. (2012) implemented the adaptive local-global computation ofvelocity basis functions within the framework of a multiscale mixed finite-element simulator developedfor high-resolution isothermal two-phase flow simulations of stratigraphically complex clastic reservoirson surface-based cornerpoint grids. In this work, we formulate the adaptive local-global coupling (Chenand Durlofsky 2006) within the framework of a proprietary finite-volume simulator and solve a dynamicmultiscale thermal-reactive-compositional multiphase-flow problem. One global coarse-scale and multi-ple local fine-scale near-heater models are timestepped in a sequentially coupled fashion. At a givenglobal timestep, the global model solution provides boundary conditions to local near-heater models.These boundary conditions account for the global characteristics of the thermal-reactive flow andtransport phenomena. In turn, upscaled properties and fine-scale information about the heater responsesare derived from the local models. These fine-scale flow-based attributes effectively correct the thermal-reactive flow and transport in the global model either at the given global timestep through a convergentiterative scheme or at the next timestep if no iterations are performed. The multiscale method isimplemented using a proprietary scripting language (DCL) to generically moderate the multiscalesimulation operations (e.g., global/local gridding, upscaling, downscaling, global/local timestepping, etc.)by taking advantage of the functionalities in a proprietary upscaling package (REDUCE) and aproprietary reservoir simulator (MoReS) (Por et al. 1989).

The organization of the paper is as follows: We first present the governing equations for ICP describingmass and energy conservation, and chemical reactions. The operating principles of the local-globalmultiscale method for ICP are described subsequently. A detailed proof-of-concept study featuring apattern-scale ICP model is presented next for the multiscale method. Simulation results obtained with themultiscale method are compared to the ones from a reference fine-scale model and two conventionallyupscaled coarse-scale models. The multiscale method is evaluated in terms of accuracy and computationalefficiency including parallelization. The effects of various choices that can be made in operating themultiscale method are briefly investigated. These choices include the number of fixed-point iterationsneeded for the convergence of the iterative multiscale scheme and the size of the local near-heaterdomains. In a dedicated limited-scope study, the influence of dynamic effective properties is evaluated inisolation from the more obvious accurate heater-temperature benefit of the multiscale method. Theconclusions section closes the paper.

Mathematical Model for ICPICP is a complex process, which requires the modeling of thermal flow and fluid transport, chemicalreactions, and multiphase thermodynamics. Oil shale consisting of solid kerogen is heated by (electrical)heater wells and then decomposes into coke and lighter hydrocarbon components, oil and gas, which arein turn extracted from the subsurface through production wells. Simulation of ICP requires solving massand energy conservation equations and phase equilibrium relationships in combination with chemicalreactions.Governing EquationsLet us define a spatial domain, , in 3 with boundary, . No-flow boundary condition is imposed on .The mass conservation equation for component i in a thermal-reactive-compositional multiphase flow (i.e.ICP) problem in can be expressed as follows:

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(1)

where t represents time, is the void porosity, Sj is saturation of phase j, j is the mass density of phasej, Xij is the mass fraction of component i in phase j, vj is the Darcy velocity of phase j, s=ik and sik are the(mole-based) stoichiometric coefficients for component i as product and reactant in reaction k, rk is themolar rate of reaction k, mi is the molar weight of component i, and is the well production or injectionrate of phase j. The void porosity is different from the fluid porosity. In addition to the pore-volumefractions occupied by oil, gas, and water phases, it also includes the pore-volume fraction taken up by thesolid phase composed of reactive solid components. The remaining non-reactive solids, i.e. the rock grain,constitute the remaining nonporous volume. In this formulation, oil, gas, water, and solid phase saturationsadd up to 1.0. The first part in Eq. 1 is the mass accumulation term, the second part represents the massflow term, the third part accounts for the mass change from chemical reaction, and the fourth part capturesthe mass in- or out-flow from wells. The Darcy velocity can be expressed as

(2)

where k is the permeability tensor, krj represents the relative permeability for phase j, j is the viscosityof phase j, pj is the pressure of phase j, j is the gravitational term for phase j, and D is the depth belowa reference point. For simplicity, we ignore the capillary effects. In ICP, a given solid component i onlypartitions in the solid phase. Hence, there are no mass flow terms, and the mass conservation equation (Eq.1) for a solid componenti simplifies to

(3)

where ci is the molar concentration of the solid component i, ciisSs/mi (with Ssdenoting the solidsaturation).

Modeling of energy flow is also required to account for the thermal processes in ICP. The energyconservation equation for ICP can be written as

(4)

where uj is the internal energy density of phase j, ur is the internal energy density of the rock, hj is theenthalpy density (as a fraction of mass, i.e. energy per unit mass) of phase j, k is the thermal conductivitytensor of the reservoir, T is the temperature, Hk is the molar enthalpy of reaction k, and q

H is the energyinput from heater wells. Thus, the first term in Eq. 4 accounts for energy accumulation; the second termrepresents the energy flow; the third term corresponds to the energy transport from heat conduction; thefourth term represents the energy generation/consumption due to chemical reactions; the fifth termaccounts for the energy in- or out-flow from wells; and the last term represents the energy input fromheater wells. As in the case of the mass conservation equation for component i in the solid phase, thereare no energy flow terms and energy in- or out-flow terms due to solid-phase transport in the energyconservation equation (i.e. the Darcy velocity of the solid phase is zero, vs 0).

The well fluid production rates in a gridblock l are calculated using a numerical well index by thefollowing (Peaceman) formula

(5)

where

(6)

for phase joil, gas, and water, but not for the solid phase since there is no mass flow in the solidphase. In Eq. 5, WI is the numerical well index for fluid flow, p is the gridblock pressure, and pf is the

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bottomhole well flowing pressure. In Eq. 6, k is the average permeability of the gridblock, hw is the welllength inside the gridblock, rw is the wellbore radius, ro is the equivalent wellblock radius that dependson the gridblock size, and S is the skin factor.

Similarly, the energy injection rate through heater wells in a gridblock l is given by

(7)

where

(8)

In Eq. 7, WIth. is the numerical well index for thermal energy flow, T is the gridblock temperature, andTh is the heater temperature. In Eq. 8, k is the average thermal conductivity of the gridblock, hw is theheater well length inside the gridblock, rw is the wellbore radius, ro is the equivalent wellblock radius thatdepends on the gridblock size, and Sth. is a thermal skin factor.

To model the fluid properties (PVT data), the densities, enthalpies, and viscosities (of the flowingphases), as well as the partitioning of the fluid components into the water, oil, gas, and solid phases mustbe provided. An equation-of-state compositional formulation is not readily available for such a thermalmultiphase system. Thus, we use a conventional K-value description, with K-values that only depend onpressure and temperature. The pressure and temperature dependence of the K-values and viscosities areprovided in a tabulated format to the simulator. Low-order polynomials in p and T are used for thecomponent specific densities and enthalpies along with suitable mixing rules to compute these propertiesfor fluids with arbitrary composition.

Chemical Reaction ModelAccurate representations of the chemical reactions are fundamentally important for ICP. A chemicalreaction model within a reservoir simulation framework describes how components are transformed intoother components. For each reaction, the conversion occurs in fixed ratios defined by the stoichiometry.The rate at which the conversion takes place is determined by the reaction rate.

In this work, we consider a first-order reaction model for which the reactions occur in a single step.For the reaction A nB mC, the reaction rate at temperature T is given by

(9)

where r is the molar reaction rate and cA represents the molar concentration of the source componentA; n and m are (not necessarily integer) stoichiometry coefficients that determine the relative amounts ofthe reactants B and C; K(T) is the temperature dependent rate constant given by the Arrhenius equation:

(10)

where Ko is the frequency factor, Ea is the activation energy, and R is the gas constant. The reactionrate r (Eq.9) is an exponential function of temperature. Eq. 9 and Eq. 10 together determine the speed ofthe mass conversion, which will be used to provide the reaction source terms in the mass conservationequation (Eq. 1). To improve the accuracy of the reaction kinetics for the lumped/pseudo components weuse in our simulation models, some reaction constants are made pressure dependent, K(T,P). This pressuredependence is prescribed in a tabulated form.

Permeability Development ModelIn the initial state, the oil shale (non-pore volume) consists of inert solids and kerogen, which are thenpartially converted to light oil, gas, and coke during ICP. The volume fraction of the kerogen typically isquite significant, whereas the initial fluid porosity can be low, for example, in the order of 0.01 to 0.05in certain target zones, or larger, e.g., 0.10 to 0.40 in others. Often, the initial permeability of the oil shaleis rather low, for example, in the order of 1.0103 1.0 md. During ICP, when the formation is heated,

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the solid kerogen is converted predominantly into mobile hydrocarbon products, and hence the fluidporosity increases significantly. This increase in fluid porosity significantly increases the permeability. Itis crucially important to include the subsequent change in fluid mobility in the simulation model. Wetypically use experiment-based tabulated relationships between fluid porosity and permeability which canbe expressed as

(11)

where k and are the dynamically changing permeability and fluid porosity, respectively, while ko ando respectively denote the initial permeability and fluid porosity. Dynamic changes to gridblock perme-abilities are propagated to transmissibilities via permeability multipliers, , computed by k/ko. Thesame relationship in Eq. 11 is used in fine-scale, upscaled, and multiscale models, which will beintroduced later in the paper. A similar approach is applied to the dynamic updating of thermaltransmissibilities (instead of conductivities) via thermal-transmissibility multipliers, th., as a function ofthe changes in the gridblock thermal conductivity due to fluid saturation and temperature changes.

Multiscale Model for ICPA multiscale protocol is constructed for fast and accurate simulations of ICP. The multiscale modelconstitutes of a global coarse-scale model and multiple local fine-scale near-heater models. In ICPsimulations, high-resolution solutions are required for improved accuracy where temperature, pressure,and saturation gradients are high, and thermal-cracking reactions and porosity/permeability developmenttake place relatively more rapidly, i.e. predominantly near the heaters. Hence, local fine-scale models areconcentrated to the vicinity of the heaters in our multiscale approach. An example multiscale model withdiscretized local and global domains is shown in Fig. 1. As will be explained below, the local near-heatermodels have high resolution, but are disconnected from each other and hence are easy to solve. Wedescribe below the ingredients of the multiscale model and its operation principles.

Global Coarse-scale Model via Flow-based UpscalingThe global coarse-scale model is the product of local flow-based scale-up of a detailed fine-scale modelthat is computationally expensive to simulate. Upscaling of the initial permeability and initial thermalconductivity in the fine-scale model to computationally more efficient coarse-grid representations isperformed by use of an extended local fluid/heat flow-based transmissibility (interface property) upscalingmethod (White and Horne 1987; Romeu and Noetinger 1995; Farmer 2002). Upscaling of the initialporosity field relies on the conventional net-volume averaging stencil. Fluid porosity develops due to

Figure 1An example multiscale model with discretized local near-heater domains inside the global domain.

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conversion of kerogen and other components that exist in the solid phase. It can also increase/decrease dueto geomechanical deformation, which exerts itself through pressure-dependent changes in porositygoverned by rock compressibility. As fluid porosity varies, this induces permeability changes determinedvia Eq. 11. Similar to the fine-scale model described above, dynamic changes to permeability arepropagated to upscaled flow transmissibilities via automatically calculated . A dynamic th. approach(where a reference thermal transmissibility is scaled by the dynamically changing thermal transmissibil-ity) is applied to update the upscaled thermal transmissibilities as a function of the changes in thegridblock thermal conductivity due to fluid-saturation and temperature variations.

ICP models are typically initialized with solids that have layer-by-layer varying composition describedin terms of their molar density. We implemented the pore-volume weighted averaging approach for theupscaling of molar densities of the solid components (relevant to the initialization process). Since the(reactive) solid phase is part of the pore volume (not the grain volume) analogous to fluid saturations inour formulation, a pore-volume weighted method is appropriate for their upscaling. The upscaled globalcoarse-scale model is fully described by the Eqs. 1 through 11 similar to the global fine-scale model.Without multiscale treatment, it employs a coarse-scale mesh and conventionally upscaled properties. Thewell driven simulation outcomes, e.g., cumulative oil and gas recovery, are thereby affected both by thehomogenization of property heterogeneity and the coarser discretization of the underlying reservoirsimulation equations.

Local Fine-scale ModelsNon-overlapping local fine-scale models are automatically generated around the heater wells in the globalcoarse-scale model as part of our implementation. Near heater models are comprised of local internal-model blocks and boundary-condition blocks (Fig. 1). The significance of each type of local model blockis described below. i denotes the spatial domains of the local near-heater models in

3 with boundary,i, where i 1, . . ., Nh, and Nh stands for the number of heater wells. In the current implementation, iare non-overlapping domains generated via local grid refinement (LGR) of selected sets of coarsegridblocks, i.e. the near-heater zones, in the global model domain, . Since the coarse-model is a productof upscaling as discussed in the previous section, during the generation of local fine-scale models it ispossible to not only generate a fine grid via LGR for high-resolution simulations of near-heater zones, butalso populate the locally-refined grid with downscaled thermal-reactive-compositional flow properties byusing the information in the fine-scale model. This is possible thanks to the flexible implementation fordata exchange between the upscaler and the simulator. The grid in-between the locally refined regions isdeactivated by voiding them out. Hence, all fine-grid regions are disconnected from each other. We referto this process as the background grid masking. The LGR, downscaling, and background grid maskingprocesses are performed in a separate copy of the coarse-scale model, which is specifically used forgenerating and timestepping these local disconnected sets of LGR regions around heaters.

Local models solve mass and energy conservation equations, Eq. 1 and Eq. 4 respectively, in localdomains, i. The only exception is that the terms that describe the mass and energy in- or out-flow fromproduction wells are absent in the local models because these wells are not contained in the fine-scale gridareas. Production wells are accounted for in terms of dedicated boundary condition blocks in the currentimplementation, which will be described later. The local models for each heater neighborhood areinitialized via downscaling of the global model initialization to local-model grid resolution. They are inturn solved at every global timestep (timestep of the global coarse-scale model) subject to pressure andmass/energy concentration boundary conditions imposed on i. This approach requires the use ofdedicated edge blocks wrapping around i. Numerical experiments indicate that pressure and mass/energyconcentration boundary conditions imposed using edge blocks operate more robustly compared to themass/energy flux boundary conditions. The boundary conditions are obtained from the global modeldownscaled into the grid resolution of the local models.

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A multiscale treatment of the production wellneighborhoods is not considered at this stage of thework for the multiscale method. The focus of thework is near-heater zones. The effects of the pro-duction well blocks are accounted for via a dedi-cated set of boundary condition blocks. The local-model grids are designed such that the productionwell intervals always coincide with the boundary-condition blocks in the global coarse-scale model.Despite the sink-block based treatment of produc-tion well intervals in the local models, based on thefine-scale flow information, we derive upscaledwell indices ( ) to be used for the production wellintervals in the global coarse-scale model. This pro-cess is explained in the following section. In thefuture, we intend to extend the multiscale methodfor ICP to include the production well neighbor-hoods in a more sophisticated fashion to cater formore general well configurations and placements.

Multiscale AlgorithmA multiscale protocol is constructed by coupling theglobal coarse-scale and local fine-scale models (Fig.2). The algorithm of the multiscale protocol is out-lined by the following steps:

1. The global model and local near-heatermodels are constructed via upscaling, LGR,and background grid masking processes.The pressures and mass/energy concentra-tions in the global model are initialized attime tk but the local models remain non-initialized.

2. The local models are initialized using pres-sure and mass/energy concentration datafrom the global model using appropriatedownscaling techniques. The INTENSIVEdownscaling approach is used for intensiveproperties (e.g., pressure) where each fine-scale block (inside a coarse block) is popu-lated with the value of the coarse-scale par-ent block. The EXTENSIVE downscalingtechnique is used for extensive properties (e.g., mass). An extensive property of the parentcoarse-scale block is then distributed over the offspring fine-scale blocks. Depending on the LGRscheme (uniform or not), nature of the downscaled property (bulk, pore, etc.), and whether or notthe downscaling process is linked to an existing fine-scale model, the extensive property isdistributed over the offspring fine-scale blocks with a uniform or non-uniform, bulk- or pore-volume weighted scheme.

3. The global model is simulated for one timestep (tk to t(k1)).

Figure 2Adaptive local-global multiscale simulation algorithm forICP. GM Global coarse-scale model, LM Local fine-scale models.

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4. The boundary conditions on i are computed by projecting the global model solutions for pressureand mass/energy concentration, and downscaling them to the grid resolution of the local fine-scalemodels. This operation is performed only in the target LGR regions. In the boundary conditionblocks, pressure and mass/energy concentration solutions of the coarse-scale global model arelocally refined to the fine grid and imposed as boundary conditions to fine-scale local models. Allfine-scale blocks derived from the parent coarse-scale boundary condition block are used asboundary condition blocks in the fine-scale model. In the future, the implementation can beimproved to only use a single ring of fine-scale blocks per near-heater model. Also, variousinterpolation schemes could be considered to improve continuity. The local models are solved forthe next timestep (tk1) using the updated boundary conditions on i. Since the local fine-scalemodels are decoupled from each other, they can be simulated concurrently, using one CPU/corefor each model.

5. Upscaled coarse-scale properties are computed from fine-scale solutions in i. These propertiesare upscaled permeability multipliers, , for updating the coarse-scale permeabilities and fluid-flow transmissibilities, upscaled thermal-transmissibility multipliers, , for updating thecoarse-scale conductive heat-flow transmissibilities, and upscaled production and heater wellindices and , respectively. Another important fine-scale property is the heater welltemperature, T(h,i). Initially, heater wells are operated by imposing a constant power (heat-injectionrate). The fine-scale heater temperature T(h,i) is used in the updated global model to determine, onindividual basis for each heater, whether a criterion in the form, , is satisfied to activatethe gradual power reduction strategy the so-called tap-down for a reliable heater operation andsustained heater life.

6. Using the upscaled coarse-scale properties, the global model is (optionally) re-simulated to adaptthe global model to the local model solutions. The global timestep (tk to tk1) is repeated using acustom script-level (monitor) functionality. In each iteration, improved global model solutionsprovide more accurate boundary conditions to the local models.

7. Optionally, the steps 4 through 7 are repeated until upscaled global coarse-scale and averaged localfine-scale solutions are adapted to each other, i.e. until they do not exhibit an appreciable changecompared to the previous iteration. In the current implementation, the number of iterations is afixed, user-specified number, nRTS. Convergence of this fixed-point iterative scheme is observedin the tested cases for nRTS values between 1 and 3. Thus, nRTS is set to 1 by default. In fact, ina number of investigated problems, nRTS0 approach (i.e. using the upscaled properties in the nextglobal timestep without repeating the current timestep) delivered sufficient accuracy, predomi-nantly because the global timesteps in the ICP model are already rather small when rapid changesare taking place. Typically, when the timesteps are large, fluid/energy transport and chemicalreactions evolve rather slowly, thereby rendering the time-delayed updates of the upscaledproperties sufficient for reasonable accuracy. Rather than using a constant typeconvergence criterion, more intelligent convergence criteria using the convergence in heat/energyfluxes, pressures, and temperatures can be implemented in a future work for enhanced computa-tional efficiency.

8. Upon convergence of the iterative global timestep repeating process, the converged upscaledproperties are assigned to the global coarse-scale model as starting values for the next (global)timestep and the model is simulated for one timestep.

9. The steps 4 through 9 are repeated until the final simulation time (ICP pattern life-time) is reached.

Fine-scale at the end of a given global timestep are computed using the permeability developmentmodel in Eq. 11 based on the porosity development, which is in turn driven by the flow and transportphysics in the local fine-scale near-heater models. In the global-timestep level upscaling process,

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fine-scale are homogenized over coarse blocks using a pore-volume weighted averaging scheme2 toyield . The resulting act on the coarse-scale fluid-flow transmissibilities3 to incorporate the evolutionof permeability during ICP. Note that this procedure yields different (presumably more accurate) resultsthan using the coarse-scale porosities in Eq. 11, because the function in Eq. 11 is usually highly non-linear.

Fine-scale th. at the end of a given global timestep are computed using a thermal conductivity model.Fine-scale th. are homogenized over coarse blocks using a bulk-volume weighted averaging scheme4 toyield The resulting act on the coarse-scale heat-flow transmissibilities5 to incorporate theevolution of fine-scale conductivity during ICP.

and evolve permeability and thermal conductivity fields respectively in the coarse-scale modelfor ICP related changes, and yield upscaled permeability, , and thermal conductivity, , tensor fields.An inspection of Eq. 6 reveals that with the information in the production well gridblocks, one cancompute . Similarly, via Eq. 8 and using information in heater well gridblocks, it is possible tocompute . and are computed for updating the global coarse-scale model at every globaltimestep, as pointed out above. In the future, we intend to investigate the upscaling of relative mobilitiesof the flowing phases, krj/j and chemical reaction parameters in the spirit of Li et al. (2014) and Li etal. (2015).

Numerical Experiments

Fine-scale ModelThe multiscale model is constructed via upscaling, LGR, and background grid masking operations. Thus,the fine-scale model (FM) is not only the reference (for accuracy and performance comparisons) but alsothe starting point for multiscale modeling. A number of characteristics of the model remain unchangedduring upscaling, LGR, background grid masking, and ensuing multiscale treatment (e.g., PVT/kineticmodel, etc.).

A single-pattern, cross-section model with one vertical producer well and three horizontal heater rowsis used for the numerical experiments (Fig. 3). The model encompasses 2-D layered-type geologicvariability and is composed of 45 1 99 4455 (NX NY NZ) gridblocks. The initialpermeability and void porosity values for the formation layers are also shown in Fig. 3. In total, there arethree heaters in each row, resulting in a total of nine heater wells in the pattern. Initial reservoirtemperature is 95 F and the initial reservoir pressure is 343.6 psi.

The PVT/reaction-kinetics model described in Shen (2009) encompasses 7 mobile (fluid) componentsand 6 solid components. The model used in this work is the one described in Shen (2009) with a few smalldifferences, which have no implications for the multiscale model. In fact, the PVT/reaction-kinetics modelis immaterial to the multiscale method, so long as the same model is used for the fine-scale, coarse-scale,and multiscale simulations. Capillary forces are assumed negligible for the transport phenomena.

The production well is operated with a 50 psi minimum bottomhole pressure and 1500 bbl/daymaximum liquid production constraints. Currently, no gas production rate constraint is imposed on themodel. Simulations are run for a 20 year-long pattern life-time to achieve sufficient in-situ conversion inthe heated zones. The heaters are operational starting from the reference time (t 1.0 day). Heaterlife-time is assumed to be 10 years, i.e. all heaters are turned-off at t 10 year.

2 are governed by the porosity development process during ICP. Limited number of numerical experiments showed that the pore-volume weightedaveraging of yields relatively more accurate solutions compared to other analytic homogenization approaches.3 Coarse-scale fluid-flow transmissibilities are the product of a conventional flow-based upscaling performed prior to simulation.4 Since both grain and fluid-phase conductivities govern the average thermal conductivity, fine-grid th. are homogenized over coarse gridblocks usingbulk-volume weighted averaging.5 Coarse-scale heat-flow transmissibilities are the product of a conventional flow-based upscaling performed prior to simulation.

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Multiscale ModelAn aggressively coarsened global coarse-scale model is generated for multiscale simulations throughupscaling. This model contains 15133 495 gridblocks resulting from a 9-fold (313) coarseningof the fine-scale model. Without multiscale treatment, this aggressively coarsened model is referred to asthe coarse-scale model, CM. When multiscale treatment is included, the global coarse-scale model isreferred to as the MM-GLOBAL. Preliminary upscaling tests showed that 3-fold vertical coarsening leadsto significant scale-up errors with respect to FM. In line with this learning, a more sensibly upscaled modelthat preserves the fine-scale layer structure, with 15199 1485 gridblocks and a gridblock size of 10ft in the x-direction, is also constructed via scale-up. This relatively finer coarse-scale model is referredto as the upscaled model, UM. Simulation results for UM are utilized to assess the accuracy andcomputational performance delivered by the multiscale model, MM, with respect to FM. Views of the 2-Dcross-sectional grids for FM, CM, and UM are shown in Fig. 4 for comparison purposes.

Non-overlapping local near-heater models are automatically generated in the MM-GLOBAL as part ofour implementation. Near-heater models of this particular example case are composed of local internal-model blocks shown in Fig. 5, and boundary-condition blocks illustrated in Fig. 6. Fine-scale localnear-heater models are automatically derived from the MM-GLOBAL via application of LGR for thenear-heater models and the background grid masking process. We apply a 313 LGR for thenear-heater models, recovering the spatial resolution of FM. The single-model containing the isolatedlocal fine-scale near-heater models is referred to as the MM-LOCAL (Fig. 7). The local-global couplingis iterated only once at every global timestep unless it is explicitly stated otherwise.

Figure 3Fine-scale ICP model: Views of the grid mesh, horizontal heaters, vertical producer, initial permeability [0.012-0.05 md], and initial voidporosity [0.08-0.66] fields.

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Results of the Proof-of-concept Test CaseThe results of the numerical experiments conducted on the example pattern-scale ICP model are discussedfrom the accuracy and computational efficiency perspectives below.

Accuracy of the Multiscale Model MM, UM, and MM responses are shown in terms of cumulative gasproduction and gas production rate profiles in Fig. 8. The same set of illustrations is documented for oil,water, and liquid production in Fig. 9, Fig. 10, and Fig. 11, respectively. Cumulative heat injection and

Figure 4Fine-scale [FM], upscaled coarse-scale [CM], and upscaled [UM] model grids. The X {horizontal} Y {vertical} cross-section is shown.

Figure 5Near-heater (local) model blocks in the global model [MM-GLOBAL] (left panel) and the local model [MM-LOCAL] (right panel). Redblocks indicate the local internal-model blocks. The black line in MM-GLOBAL indicates the production well blocks. Local models are enclosedwithin blue [MM-GLOBAL] and red [MM-LOCAL] boundaries. The X {horizontal} Y {vertical} cross-section is shown.

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Figure 6Near-heater (local) model blocks in the global model [MM-GLOBAL] (left panel) and the local model [MM-LOCAL] (right panel). Redblocks indicate the local boundary-condition blocks. The black line in MM-GLOBAL indicates the production well blocks. Local models are enclosedwithin blue [MM-GLOBAL] and red [MM-LOCAL] boundaries. The X {horizontal} Y {vertical} cross-section is shown.

Figure 7Near-heater (local) model blocks in the local model [MM-LOCAL] are enclosed by blue boundaries. Red blocks correspond to the internallocal-model blocks. The light-peach colored blocks are boundary-condition blocks. The X {horizontal} Y {vertical} cross-section is shown.

Figure 8Fine-scale, upscaled, and multiscale model responses: Cumulative gas production (left panel) and gas production rate (right panel). FM fine-scale model, UM upscaled model, and MM multiscale model.

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Figure 10Fine-scale, upscaled, and multiscale model responses: Cumulative water production (left panel) and water production rate (right panel).FM fine-scale model, UM upscaled model, and MM multiscale model.

Figure 11Fine-scale, upscaled, and multiscale model responses: Cumulative liquid production (left panel) and liquid production rate (right panel).FM fine-scale model, UM upscaled model, and MM multiscale model.

Figure 9Fine-scale, upscaled, and multiscale model responses: Cumulative oil production (left panel) and oil production rate (right panel). FM fine-scale model, UM upscaled model, and MM multiscale model. Note that oil production is very low, less than 0.5 bbl/day in FM.

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total heat-injection rate profiles are illustrated in Fig. 12. It is important to note that the heat-injection ratesstart at the same value but they all very rapidly reach the heater-element operating-limit temperature. Thisbehavior signifies that the formation heat-conductivity values are relatively low in this example, notallowing sufficient heat to be transported into the formation. The rapid heat build-up and associatedtemperature rise in the vicinity of the heater elements triggers early power tap-downs and prevents thedevelopment of a sustained plateau heat-injection rate. The test problem was purposefully designed tostress-test the multiscale method: By designing the fine-scale problem as described above, the heat-injection rate profiles are kept at a transient state as long as possible. The objective is then to evaluate thelevel of accuracy delivered by the multiscale method in correctly capturing the relatively more difficulttransient-behavior of the heat-injection rate profiles observed in the fine-scale model. Fig. 13 shows thecumulative gas and cumulative liquid production profiles respectively illustrated in Fig. 8 and Fig. 11 butthis time including the aggressively upscaled CM response without multiscale treatment. Note that theglobal model used in MM (MM-GLOBAL) is in fact CM with multiscale treatment. For all of themonoscale and multiscale models, temperature and gas saturation snapshots taken at t 10 year (the timeat which the formation was hottest) are shown in Fig. 14 and Fig. 15, respectively. Kerogen mass fractionsnapshots taken at t 20 year (the final simulation time) are shown in Fig. 16.

MM delivers notably improved accuracy compared to UM and much improved accuracy with respectto CM. MM solutions are reasonably close to FM solutions. This is accomplished predominantly by use

Figure 12Fine-scale, upscaled, and multiscale model responses: Cumulative heat injection (left panel) and total heat-injection rate (right panel). FM fine-scale model, UM upscaled model, and MM multiscale model.

Figure 13Coarse-scale, fine-scale, upscaled, and multiscale model responses: Cumulative gas production (left panel) and cumulative liquidproduction (right panel). CM coarse-scale model, FM fine-scale model, UM upscaled model, and MM multiscale model.

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of fine-scale heater temperatures, Th, and near-heater effective properties, , , and , that moreaccurately moderate the heat-injection rate into the formation. On the other hand, values improve the

Figure 14Temperature snapshots at t 10 year for the fine-scale model FM, coarse-scale model CM, upscaled model UM, and multiscale modelglobal (MM-GLOBAL) and local (MM-LOCAL) domains. The unit of the temperature axis is Kelvin. The color scale varies between 300 and 650Kelvin (80.3 and 710.3 F) from bottom to top.

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accuracy of flow and transport in the vicinity of the production well intervals. Since we use extendednear-heater regions in the local models (rather than assigning the local models only to the coarse blocks

Figure 15Gas saturation snapshots at t 10 year for the fine-scale model FM, coarse-scale model CM, upscaled model UM, and multiscale modelglobal (MM-GLOBAL) and local (MM-LOCAL) domains. The color scale varies between 0.0 and 0.6 pore-volume fraction from bottom to top.

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that contain heater wells), the accuracy of the thermal-reactive flow and transport process is enhanced ina relatively larger zone within (MM-GLOBAL). There is however room for further improvementespecially with regards to oil production behavior and early-time rate response. We believe that the

Figure 16Kerogen mass fraction snapshots at t 20 year for the fine-scale model FM, coarse-scale model CM, upscaled model UM, and multiscalemodel global (MM-GLOBAL) and local (MM-LOCAL) domains. The color scale varies between 0.0 and 1.0 mass fraction from bottom to top.

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multiscale method can be rendered more accurate by extending it to compute effective relative mobilitiesand effective chemical reaction parameters at every timestep.

At a reduced computational cost compared to FM, MM delivers accurate high-resolution solutions inthe vicinity of the heaters (see, for example, Figs. 14 through 16). These fine-scale solutions can be usedto better understand the evolution of the fluids and solids, e.g., kerogen conversion, coke deposition, andpermeability development near the heaters. In addition to the fine-scale near-heater solutions, ICPperformance indicators and production functions are simultaneously computed at the pattern-scale withMM.

The Effect of Multiple Fixed-point Iterations The impact of fixed-point iterations on the multiscalemodel response is evaluated by running the MM model for three iterations per timestep for local-globalcoupling. This model is referred to as MM-ITER. Fig. 17 documents the cumulative oil, gas, and liquidrecovery profiles for FM, MM, and MM-ITER. Additional iterations do not yield an appreciableimprovement in the solution accuracy for the investigated problem. Nonetheless, a very close investiga-tion in Fig. 17 indicates a slight improvement in the cumulative gas production profile. We also noticedthat iterating once or not iterating (using one timestep lagged effective properties and fine-scale heatertemperatures) yields almost the same accuracy. This is likely because of the small timesteps taken by thesimulator to ensure convergence for the challenging thermal-reactive-compositional multiphase flowsimulation problem.

Computational Performance A number of tests are carried out to assess the computational speed-updelivered by the multiscale method implementation in DCL out-of-the-box without optimization. Aslight variant of the proof-of-concept problem is generated for testing the computational performance ofthe multiscale method. The modified problem features twelve heaters with four heaters in every row. Allother model characteristics remain unchanged. Speed-up information derived from a representative set ofsimulation times are reported below for single-CPU and parallel runs.

Single-CPU computational performance of UM and MM in terms of speed-up with respect to FM arecompared. CM yields very inaccurate results. It is therefore excluded from the performance comparison.As discussed above, MM-ITER with three iterations per global timestep does not improve the accuracyin a significant fashion. Thus, it is also excluded from the performance test. UM yields a speed-up of 6.9in reference to FM. MM delivers a more significant 16.1 fold speed-up. The speed-up benefit of MMcomes together with more accurate global and high-resolution near-heater solutions. Overall, MM delivers

Figure 17The impact of iterations on the multiscale model response (left panel). FM fine-scale model, MM multiscale model (one iteration pertimestep), and MM-ITER multiscale model with three iterations per timestep. The continuous line for MM is under the continuous line withdiamonds. The zoomed view of the cumulative gas production (CumGAS) time-function towards t 20 year (right panel). It indicates a tinyimprovement for MM-ITER.

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improved accuracy and a significant enhancementof computational performance without a specialcode optimization effort.

There is a lot of room for improving the perfor-mance of the multiscale models. The implementa-tion of the multiscale method is performed at theinput-deck level using the DCL. No special optimi-zation effort is dedicated to write the fastest possiblescript. Further speed-up can be achieved with amore efficient implementation of the multiscalemethod, especially as part of a dedicated low-levelsimulation code. As indicated by the above test, low-level code implementation of the multiscale methodcircumventing the monitor execution overhead is likely to provide an even larger speed-up. Anotherpotential enhancement to be addressed is the implementation of an adaptive convergence criterioneliminating the need to iterate for a fixed number of times per global timestep. Iterating even once as inthe above tests is likely to be unnecessary for the multiscale model, if the global timestep size is small orif the solutions are not evolving drastically from one timestep to the next. The size of the near-heaterdomains is another parameter that could be optimally selected for further improved computationalperformance.

The local heater domains are non-overlapping, fully isolated from each other via no-flow boundaries,and solved subject to the boundary conditions from the global model at every timestep. Therefore, for thesimulation of MM-LOCAL, one can readily employ a domain-decomposition approach, where everyisolated gridblock cluster i is assigned to a separate domain. Thus, by running the model MM-GLOBAL(which calls the model MM-LOCAL at every timestep) on INT(Nh) CPUs (where 01), one caneffectively solve both the global and the individual local models in parallel. The local models are thensolved in parallel without incurring a communication cost in this approach as they are isolated from oneother. Parallelization may not yield an appreciable speed-up for aggressively coarsened MM-GLOBALmodels. Communication costs may even render it less efficient compared to running it in the serial mode.However, this depends on the size of the coarse model and in any case it may be still beneficial to runthe non-overlapping fine-scale near-heater models within MM-LOCAL in parallel. We explore a differentparallelization approach to address such cases. The MM-GLOBAL run is still launched in the parallelmode but the parallelization is turned off within the MM-GLOBAL deck. Then, only the near-heatermodels within MM-LOCAL are solved on multiple CPUs. In Table 1, we document the speed-up gainedby running the 12-heater multiscale model on six CPUs for the above-discussed strategies. The referencecase FM is also simulated in the parallel mode on six CPUs. The performance improvement for MM inthe parallel mode is more modest compared to single-CPU runs. Nonetheless, simulating MM on multipleCPUs is still relatively more computationally efficient than simulating FM in parallel on the same numberof CPUs. Clearly, the local fine-scale models in MM-LOCAL contain in total a smaller number ofgridblocks than FM. Solving the isolated (smaller) local domains in the parallel mode is faster than solvingthe (larger) communicating domains of FM. The exact decoupling that comes with the uniform-sized localdomains in MM-LOCAL also helps the parallel performance of MM. Solving the MM-GLOBAL in theparallel mode in addition to the near-heater models in MM-LOCAL is more effective than restricting theparallelism to the MM-LOCAL only in the investigated case (Table 1).

The computational advantage of isolated (non-interacting) fine-scale local domains is not onlysignificant in the parallel mode but also in the serial mode. This is especially due to the conductiveheat-transport nature of ICP using a number of localized sources (heater wells). The conventionalfixed-LGR approach in a coarse-scale model is too rigid compared to the multiscale approach. Moreover,

Table 1PARALLEL COMPUTATIONAL PERFORMANCE COM-PARISON

Model Speed-up

FM 1.0

MM[p-global & p-local] 6.5

MM[p-local] 3.9

MM [p-local & p-global] The global model and the local models are simulatedin parallel.MM [p-local] Only the local models are simulated in parallel.

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prior experience with it indicates that its parallelization is less efficient. This is why a coarse-scale modelthat uses fixed LGR is not considered as a viable alternative to MM.

The Effect of Enlarging the Near-heater Zone The size of the extended near-heater zone is subject tooptimization, which is not attempted in this work. The size should be selected to strike a good balancebetween improved accuracy and enhanced computational performance, which are competing objectives.Here, we only investigate the impact of using a further extended near-heater zone. An alternativemultiscale model (MM-EXTENDED) was generated where the entire global model was decomposed intonine local models (Fig. 18). Fig. 19 shows the comparison of cumulative gas and cumulative oilproduction profiles for MM-EXTENDED to the ones computed for MM and FM. Further increasing thesize of the near-heater domains does not yield any appreciable improvement in accuracy in the investi-gated case. However, it increased the simulation time by 30 percent. This suggests that using a smallerLGR region around the heaters could lead to a faster MM model with acceptable accuracy. Anotherimportant point worth highlighting is that, when higher resolution simulation of near-heater zones isdesired, one can resort to multilevel LGR in the local models.

Figure 18Near-heater (local) model blocks in the global model are enclosed by blue boundaries for MM-GLOBAL (left panel) and MM-GLOBAL-EXTENDED (right panel). Red blocks indicate the local internal-model blocks. The light-blue blocks inside the dark-blue boundaries correspond tothe boundary-condition blocks. The black line indicates the production well blocks. The X {horizontal} Y {vertical} cross-section is shown.

Figure 19Comparison of cumulative gas and cumulative oil production profiles for MM-EXTENDED to the ones computed for MM and FM. Thered curve is under the blue curve in the left panel.

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Evaluating the Impact of Effective Properties The multiscale method is very effective in correctingthe global coarse-scale model by use of fine-scale information about heater temperatures to regulate theheat-injection rate more accurately, as shown in the previous test cases. In order to test the impact of thedynamically computed effective properties ( , , , and ) in MM, we devised a modified testcase in which the constraint is removed and the heaters are not tapped down. Therefore, a constantheat-injection rate is enforced in all heaters. The heater life-time is 10 years and the pattern life-time is20 years as in the case of the original test case. This way, the impact of effective properties is evaluatedin an isolated fashion from the heater-temperature discrepancy between global and local models, whichmay arise due to the tap-down process governed by heater temperature. The panels of Fig. 20 illustratethe comparison of cumulative gas production, cumulative liquid production, cumulative heat injected, andgas production rate profiles for the alternative ICP problem with enforced total energy injection for FM,UM, and MM. The accuracy of UM is much better in reference to FM when a constant heat-injection rateis enforced in the heaters. Nonetheless, dynamic effective properties computed via the multiscaleapproach help MM deliver more accurate simulation results compared to UM.

ConclusionsWe have developed a novel multiscale modeling method for ICP that reduces numerical modeling errorsand approximates fine-scale simulation results on relatively coarse grids. The method uses a two-scale

Figure 20Comparison of cumulative gas production, cumulative liquid production, cumulative heat injected, and gas production rate profiles forthe alternative ICP problem with enforced total energy injection for FM, UM, and MM.

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adaptive local-global solution technique. One global coarse-scale and multiple local fine-scale near-heatermodels are timestepped in a sequentially coupled fashion. At a given global timestep, the global modelsolution provides accurate boundary conditions to the local near-heater models. These boundary condi-tions account for the global characteristics of the thermal-reactive flow and transport phenomena. In turn,upscaled properties and fine-scale information about the heater responses are derived from the localmodels. These fine-scale flow-based properties correct the thermal-reactive flow and transport responseof the global model either at the given global timestep through a convergent iterative scheme, or at thenext timestep if no iterations are performed. Upon convergence of the iterations (or if timesteps aresufficiently small), global coarse-scale and local fine-scale solutions are compatible with each other.

We demonstrate the significantly improved accuracy and efficiency delivered by the multiscale methodusing a 2-D cross-section pattern-scale ICP test problem. The following conclusions are reached as theresult of the numerical testing work: (1) The multiscale method improves the accuracy of the simulationresults over conventionally upscaled models. The method is particularly effective in correcting the globalcoarse-scale model through the use of the fine-scale information about heater temperature to regulate theheat-injection rate into the formation more accurately. The effective properties computed by the multiscalemethod at every timestep also enhance the accuracy of the ICP simulations, as demonstrated in a dedicatedtest case, where a constant heat-injection rate is enforced for models of all investigated resolutions. (2) Themultiscale method delivers enhanced computational performance out-of-the-box without any specialeffort to optimize the scripted implementation. A 4- to 16-fold speed-up with respect to fine-scale modelshas been achieved in our numerical experiments. (3) Simultaneously with accurate fine-scale near-heatersolutions, the local-global coupled multiscale model provides key commercial ICP performance indicatorsat the pattern-scale (a few hundreds of feet-long spatial scale) such as production functions. The multiscalemethod can alternatively be used to compute ultra-high-resolution solutions in the vicinity of the heatersat a low computational cost. In this set-up, the coarse-scale global model is in fact the normal fine-scalesimulation model, and the local near-well models are at a significantly higher resolution, i.e. usinginch-sized gridblocks. These ultra-fine-scale solutions can be used to better understand the evolution ofthe fluids and solids, e.g., kerogen conversion, coke deposition, etc., in the vicinity of the heaters (withina few feet-long spatial scales).

The implementation of the multiscale method for ICP is performed at a high-level using the built-inscripting language that accompanies the dynamic modeling package. There are multiple options toimprove the method further: for ICP, an obvious extension is to combine this work with the multiscaletreatment of solid-reactions discussed in a separate paper (Li et al. 2015). For more general (alsonon-thermal) applications, one can investigate dynamically generating pseudo-relative permeability (andwhere appropriate) capillary pressure curves, using fine-scale results. Further speed-up can be achievedwith a more efficient implementation of the method as part of the low-level simulation code.

AcknowledgementsThe authors would like to thank Shell International Exploration and Production Inc. for permission topublish this paper.

References1. Alpak, F.O. 2014. Quasiglobal Multiphase Upscaling of Reservoir Models With Nonlocal

Stratigraphic Heterogeneities. SPE Journal, published online. doi: 10.2118/170245-PA2. Alpak, F.O., Pal, M., and Lie, K.-A. 2012. A Multiscale Adaptive Local-Global Method for

Modeling Flow in Stratigraphically Complex Reservoirs. SPE Journal, v. 17, no. 4, p. 10561070. doi: 10.2118/140403-PA

SPE-173218-MS 23

3. Aouizerate, G., Durlofsky, L.J., and Samier, P. 2012. New models for heater wells in subsurfacesimulations, with application to the in situ upgrading of oil shale. Computational Geosciences, v.16, no. 2, p. 519533. doi: 10.1007/s10596-011-9263-1

4. ASTM D3904-90 1984. Test Method for Oil From Oil Shale (Resource Evaluation by the FischerAssay Procedure).

5. Chen, Y. and Durlofsky, L.J. 2006. Adaptive LocalGlobal Upscaling for General Flow Scenariosin Heterogeneous Formations. Transport in Porous Media, v. 62, no. 2, p. 157185. doi:10.1007/s11242-005-0619-7

6. Chen, Y., Durlofsky, L.J., Gerritsen, M., and Wen, X.H. 2003. A coupled local-global upscalingapproach for simulating flow in highly heterogeneous formations. Advances in Water Resources,v. 26, no. 10, p. 10411060. doi: 10.1016/S0309-1708(03)00101-5

7. Chen, Y. and Li, Y. 2009. Local-Global Two-Phase Upscaling of Flow and Transport inHeterogeneous Formations. SIAM Multiscale Modeling and Simulation, v. 8, no. 1, p. 125153.doi: 10.1137/090750949

8. Fan, Y., Durlofsky, L.A., and Tchelepi, H.A. 2010. Numerical Simulation of the In-Situ Upgrad-ing of Oil Shale. SPE Journal, v. 15, n. 2, p. 368381. doi: 10.2118/118958-PA

9. Farmer, C.L. 2002. Upscaling: a review. International Journal for Numerical Methods in Fluids,v. 40, n. 1-2, p. 6378. doi: 10.1002/fld.267

10. Fowler, T.D. and Vinegar, H.J. 2009. Oil Shale ICP ? Colorado Field Pilots. Paper SPE 121164,presented at the SPE Western Regional Meeting, 24-26 March, San Jose, California, USA. doi:10.2118/121164-MS

11. Li, H., Vink, J.C., and Alpak, F.O. 2014. An Efficient Multiscale Method for the Simulation ofIn-situ Conversion Processes. SPE Journal, published online. doi: 10.2118/172498-PA

12. Li, H., Vink, J.C., and Alpak, F.O. 2015. A Multipoint Multiscale Modeling Method forSolid-based Thermal Reactive Flow, with Application to the In-situ Conversion Process. PaperSPE 173248, presented at the SPE Reservoir Simulation Symposium, 23-25 February, Houston,Texas, USA.

13. Por, G.J., Boerrigter, P., Maas, J.G., and de Vries, A. 1989. A Fractured Reservoir SimulatorCapable of Modeling Block-Block Interaction. Paper SPE 19807, presented at the SPE AnnualTechnical Conference and Exhibition, 8-11 October, San Antonio, Texas, USA. doi: 10.2118/19807-MS

14. Romeu, R.K. and Noetinger, B. 1995. Calculation of Internodal Transmissivities in FiniteDifference Models of Flow in Heterogeneous Porous Media. Water Resources Research, v. 31,no. 4, p. 943959. doi: 10.1029/94WR02422.

15. Shen, C. 2009. Reservoir Simulation Study of an In-situ Conversion Pilot of Green-River OilShale. Paper SPE 123142, presented at the SPE Rocky Mountain Petroleum Technology Con-ference, 14-16 April, Denver, Colorado, USA. doi: 10.2118/123142-MS

16. Shen, C., McKinzie, B., and Arbabi, S. 2010. A Reservoir Simulation Model for Ground FreezingProcess. Paper SPE 132418, presented at the SPE Annual Conference and Exhibition, 19-22September, Florence, Italy. doi: 10.2118/132418-MS

17. White, C.D. and Horne, R.N. 1987. Computing Absolute Transmissibility in the Presence ofFine-Scale Heterogeneity. Paper SPE 16011, presented at the SPE Symposium on ReservoirSimulation, 1-4 February, San Antonio, Texas, USA. doi: 10.2118/16011-MS

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Adaptive Local-global Multiscale Simulation of the In-situ Conversion ProcessIntroductionMathematical Model for ICPGoverning EquationsChemical Reaction ModelPermeability Development Model

Multiscale Model for ICPGlobal Coarse-scale Model via Flow-based UpscalingLocal Fine-scale ModelsMultiscale Algorithm

Numerical ExperimentsFine-scale ModelMultiscale ModelResults of the Proof-of-concept Test CaseAccuracy of the Multiscale ModelThe Effect of Multiple Fixed-point IterationsComputational PerformanceThe Effect of Enlarging the Near-heater ZoneEvaluating the Impact of Effective Properties

Conclusions

AcknowledgementsReferences