Petroleum Engineers

RESERVOIR SIMULATION 48-5pressure and solution gas (R, , scf/STB). As discussedlater original work in formulations’6m’8 led to a numberof papers ‘9m23 describing black-oil models during the1960’s.The remaining model types discussed here account forsome mobilization mechanisms in addition to the fourbasic recovery mechanisms. The isothermal compositionalmodel represents reservoir fluids by N components, includingwater and N- 1 hydrocarbon components.Generally, but not necessarily, solubilities of water in theoil and gas phases and of hydrocarbon components in thewater phase are considered negligible. For water, then,the concentration in Eqs. 5 is as given in Table 48.1. Thehydrocarbon component I concentration CIJ is P JX IJ, asmentioned earlier, for J=o,g or 2,3. Gas/oil phaseequilibrium and phase densities within each gridblock arecalculated using equilibrium K-values from pressure- andcomposition-dependent correlations or, more recently,from EOS’s. 25-28 Unlike the black-oil model, the compositionalmodel can represent the mobilization of oil byoutright (single-contact) or dynamic (multicontact)miscibility, oil swelling and viscosity reduction by solutionof an injected nonequilibrium gas (e.g., CO,), andstripping or vaporization of an oil’s lighter ends by injectionof a dry gas. With one exception,29 recentpapers 29-33 describing compositional models are based onequilibrium K-values obtained from EOS’s.A thermal simulation model is a set of N conservationequations, similar to Eq. 5, which expresses conservationof mass of H2 0 and N-2 hydrocarbon componentsand conservation of energy. With energy designated as“component” N, the last (I=N) of Eqs. 5 becomes theenergy balance upon addition of terms representing heatconduction and overburden heat loss. An additional requirementis the use of pJHJ for cNJ in the well and interblockflow terms and p J UJ for CNJ in the right sideaccumulation term. HJ and UJ are enthalpy and internalenergy, respectively, energy/mole. If the in-situ combustioncapability is included then the mass conservationequations include source (sink) terms represented by Arrheniusreaction rate expressions for cracking and oxidationof hydrocarbon components and the energy balanceincludes heat of reaction terms. For the same number offluid components, a thermal model has one more (energy)conservation equation than the compositional model andone additional unknown, temperature T.For steam-injection processes, thermal model componentsare typically H 20, heavy (nonvolatile) and light(solution gas or distillable) hydrocarbon components andenergy. For in-situ combustion studies, typical componentsare HzO, heavy-oil component, a lighter(distillable) oil component, solid coke, 02, CO*, N2,and energy. Frequently CO2 and N2 are lumped as onecomponent to reduce computing expense. The steam tablesand/or an EOS are used to calculate liquid Hz0 (waterphase) properties and the Hz0 gas/water phase K-valueas functions of pressure and temperature. In most applications,Hz0 is assumed insoluble in the oil phase. In mostcurrent models, the distribution of other (non-H20) componentsamong all phases is represented by user-providedK-values dependent on only pressure and temperature.Thermal simulators are applied to steam-injection or insitucombustion processes in heavy-oil reservoirs whereoil is mobilized primarily by (1) reduction of oil viscosi-TABLE 48.1-DEFINITIONS OFCONCENTRATIONS C,, FOR THEBLACK-OIL MODELPhaseJ=l J=2 J=3I Component Water- __Oil-Gas1 water bw 0 02 oil 0 bo 03 gas 0 b,Rs b,ty with increased temperature, (2) distillation of intermediatehydrocarbon components from the oil phaseto the more mobile gas phase, and (3) cracking of the oilphase [usually above 500°F (26O”C)l with subsequentdistillation. Thermal models developed from 1965 to198234-40 generally exhibit a trend toward inclusion ofmore dimensions, more components and dual capabilityof steamflood and in-situ combustion.Chemical flood models include polymer, micellar (surfactant),and alkaline (caustic). Polymer waterflooding improvesoil recovery by lowering the oil/water mobilityratio, by reducing the effective permeability to water,and/or by increasing water viscosity. In micellar flooding,surfactants greatly reduce oil/water IFT, thereby solubilizingoil into the micelles and forming an oil bank. 4’ Thesurfactant slug and mobilized oil normally are propelledtoward the production well by a graded bank of polymerthickenedwater. The mechanisms responsible for improvedoil recovery in alkaline flooding are thought toinclude low IFT, wettability alteration, and emulsification.42 Chemical flooding processes involve complicatedfluid/fluid and rock/fluid interactions such as adsorption,ion exchange, viscous shear, and three- (or more) phaseflow. Several recent papers 43-45 describe implementationof these complex chemical flood mechanisms in numericalsimulators.The four types of models described above are definedor distinguished by the recovery process and the natureof the original reservoir fluid. Considering the nature ofthe reservoir formation leads to a fifth, fractured-matrixtype of simulation model. While in theory any recoveryprocess can be implemented in a fractured-matrix reservoir,most simulation work reported to date is concernedwith black oil fracture&matrix models. Three-dimensionalmodels are described by Thomas et a1.“6 for the threephasecase and by Gilman and Kazemi4’ for two-phasewater-oil flow. Their models consider a discontinuous arrayof matrix blocks in a continuous 3D fracture network.Flow throughout the reservoir and to the wells occurs inthe fracture system and the matrix blocks are treated assink/source terms in that system. Their model equationsinclude the set of N conservation Eqs. 6 written for eachgridblock in the fracture system. Each gridblock may containa number of similarly behaving matrix blocks.However, additional terms are added to Eqs. 6, representingmatrix-fracture flow. Also, for each gridblock additionalequations are required to express mass conservationof each component in the matrix blocks included in thegridblock. These additional equations can be eliminatedor combined with the basic N (fracture system) flowequations4”v4’ so that the final model includes only Nequations (per block) possessing interblock flow terms.Blaskovich et a1.48 describe a fractured-matrix model