TCA's MULTIFLOOD Flood Simulator has been designed to reproduce the effects of the major mass transfer and phase transport phenomena known to be associated with miscible flooding processes with particular emphasis on CO2 enhanced oil recovery (see Ref 1). For immiscible conditions, phase equilibria may be input to the simulator so as to represent enhanced oil recovery mechanisms of oil phase swelling with condensed solvent and vaporization (or extraction) of hydrocarbon fractions into the solvent-rich phase. Multi-contact miscible (MCM) displacement may be represented explicitly with the program by inputting appropriate phase equilibrium data. However, the philosophy of the modeling technique employed in the program is to maintain segregated solvent-rich and oil-rich regions. By controlling the degree of segregation of these regions through the mixing parameter approach (Ref 2), the important phenomenon of viscous fingering, characteristic of highly unfavorable mobility ratio displacements, may be represented without describing the detailed structure of the unstable frontal advance. Local "miscibility" is determined by comparing computed pressure with a "miscibility pressure" input to the program as a function of composition. Here, again, the philosophy is to represent miscible displacement and miscible-immiscible transition without describing the detailed compositional path required for explicitly representing MCM.
The motivation, both for using the mixing parameter model for representing unstable frontal advance and the miscibility-pressure approach for representing MCM, is to allow predictions of field performances with realistic reservoir descriptions using reasonable numbers of grid blocks. In fact, a numerical grid fine enough to accurately describe waterflooding performance will in most cases be adequate for predicting solvent flood perform ance with this simulator. A completely compositional approach to representing these phenomena, on the other hand, might require grid systems (with attendant storage requirements and run-time costs) ten to a hundred times larger than that required here.
Other phenomena characteristic of solvent displacement processes that are represented by the simulator are 1) CO2 loss through solubility in the aqueous phase, 2) water blocking of oil from contact by the invading solvent, 3) asphaltene drop-out and concomitant reduction in phase transmisibilities, and 4) a residual oil saturation to solvent at "miscible" conditions.
Although the simulator has been designed primarily for CO2 displacements, the model can be applied for other high pressure gas and LPG-dry gas displacements as well.
The simulator treats seven components which may partition among three phases. The three phases are 1) a liquid hydrocarbon phase, 2) a gas or solvent rich phase and 3) an aqueous phase. The seven components may partition among the three phases as follows:
Component Liquid hydro- CO2 rich Aqueous
carbon phase or gas phase phase
1. Nitrogen X X
2. Methane X X
3. CO2 X X X
4. Lite (C2-6) X X
5. Medium (C7+) X X
6. Heavy (Asphaltenes) X
7. Water X
Component 6 is allowed to precipitate out according to a user specified saturation relationship input as a tabular function of any three of the concentrations of components 1 thru 6 in the liquid hydrocarbon phase.
The Component designations shown above are only representative. Any desired chemical species or pseudo component can be represented by specifying the appropriate equilibrium and transport data. Partitioning of Components 1 thru 5 is determined by user specified K-value tables. These tables may depend upon from one to three of the following variables: concentration of Component 1, 2, 3, 4, 5, or 6 in the hydrocarbon phase, or pressure.
CO2 solubility in water is input in tabular form as a function of CO2 partial pressure in the gas phase.
Gas phase density data is input in the form of pressure dependent z-factors.
Liquid densities are calculated from concentration and user input partial molar volumes of each component. Total compressibility of the liquid phase is calculated from user input partial molar compressibilities of each component.
Liquid hydrocarbon phase and gas phase viscosities are both concentration and pressure dependent.
Relative permeabilities are input in tabular form as func tions of saturations. Effective phase permeabilities are calculated using the Todd-Longstaff mixing parameter model.
Inaccessibility of oil for mobilization due to water blocking is accounted for by a user input water blocking function which depends upon water saturation. User may also specify a remaining miscible oil saturation. (See Appendix 1 for the expressions actually used in the program to define the phase mobility coefficients.)
The nonlinear coupled partial differential equations describing the conservation of the seven chemical species are spatially discretized using standard finite differences.
Time dating of variables with respect to the interblock flux terms is implicit in pressure and explicit in saturation and concentrations (IMPES). This allows the use of two point up stream weighting of mobilities with attendant second order accuracy in the spatial discretization. The program automatically employs a stabilized Runge-Kutta time discretization to alleviate the usual stability limitations imposed by the IMPES procedure. Up to 49 times the usual stable time step size can be employed for 7 times as much computing work. This yields an overall factor of 7 improvement in work requirement to simulate a given time period when stability is limiting. When truncation error is limiting, the standard time discretization is employed.
To further improve stability, the well model is completely implicit in all variables except when the constant potential rate constraint option is specified by the user. Under this option, the time dependent uniform potential is lagged a time step.
The discretized conservation equations and additional con straint equations are reduced numerically to a single pressure equation which is solved using direct Gaussian elimination with alternate diagonal ordering (D4). Equation formation, reduction and solution are iterated to convergence each time step.
The user may specify either cartesian or cylindrical coordi nates. Any other coordinate system may be "manually" specified by means of individual modifications to grid block pore volumes and interblock transmissibilities. This feature permits maximum flexibility in specifying heterogeneities in rock properties (permeabilities and porosities) and in reservoir configuration (variable thickness layers, variable width cross sections, etc.).
Injection wells and production wells may both be either pressure or rate constrained. If both constraints are given for a well, the simulator will automatically choose that which is limiting at the current time step.
Multiflood saves restart information to Fortran Unit 7, which the user must catalog through appropriate job control language. On a restart run, the user must attach the previously saved restart record as Fortran Unit 8.
To keep restart record size to a minimum, only transient quantities are saved rather than the entire reservoir description. The philosophy is that since the static reservoir description is contained in the original data deck (which is already prepared), this information can be re-read upon restart and then the transient quantities input from the restart record previously saved to tape or disk. This approach also provides the user the additional flexibility of changing normally static information upon restart if desired.
Multiflood has the option of reading input data decks in either free format (list directed Fortran I/O) or the traditional fixed format. In either option, comment cards may be liberally spread throughout the data deck to increase readability.
The default units for mass, length, time, and fluid volumes are the usual English reservoir engineering units of feet, days, STB, MCF, etc. A nonstandard-unit-option allows the user to specify any set of units by inputting new alphameric unit labels and conversion factors from new units to standard units.
a) saturation arrays for each phase and a pressure array,
b) component mole fraction concentration arrays for each phase,
c) material balance summary showing cumulatives injected and produced,
d) cumulatives and current rates for each well.
Combinations and frequency of the above are selected by the user.
Printer plot contour maps of saturatons, pressure and concentration of indiviual components may also be requested as well as ternary diagram contour maps of three phase oil relative permeability.
1. Todd, M.R., "Modeling Requirements for Numerical Simulation of CO2 Recovery Processes", SPE 7998 (1979).
2. Todd, M.R. and Longstaff, W.J., "The Development Testing and Application of a Numerical Simulator for Predicting Miscible Flood Performance", JPT, July (1972).
3. Chase, C.A. and Todd, M.R., "Numerical Simulation of CO2 Flood Performance", SPEJ, December (1984).