In contrast to that of previous sections, the R2 data are time-dependent. Two different time regimes are used by the code. The first regime is a set of relatively coarse recurrent time steps. The time-dependent parameters are changed at the beginning of each such step by input from subroutine READ2. The second regime is a relatively finer time grid within each recurrent time step used for numerical integration of the transport equations. The recurrent data consists of control integers, source information, numerical-solution control and output control.
The minimum number of records for one recurrent data set is 3, R2-1 (options), R2-12 (time stepping), and R2-13 (print control). There is no limit to the number of recurrent data sets. A data set is terminated by an additional R2-1 record in which ITHRU=1.
For steady-state analysis, one set
of recurrent data is required. The user can terminate the run or continue
execution in one of two ways. For example, steady-state flow (NCALL = 4,
M-3) completes and sets the solution option to NCALL = 3 (no primary equations).
The run can be terminated and a restart file written (RSTWR = 1, R2-13)
or continued. In either case, the solution control NCALL must be set to
1 or 2 etc. This is accomplished in the recurrent data using ICLL(R2-1)
and NCALL (R2-11.1). Thus the first time change TCHG (R2-12) is zero and
"real" time stepping appears in the second recurrent data set.
8.1 CONTROL INTEGERS
READ R2-1 (11I5)
1 - Read seven well rates per card in READ R2-5.
2 - Read one card per well rate in
READ R2-6.
1 - Read new or altered well data.
1 - Read new or altered method of solution.
1 - Run is to terminate at this point.
No more recurrent data will be read after this card. If no plots are desired,
i.e., if NPLP, NPLT and NPLC are all zero, this should be the last card
in your data deck.
1 - Read new or altered source-rate data (R2-10).
2 - read new or altered waste-leach
data (R2-10.5).
1 - Read new or altered well-head data.
1 - Read new or altered wellbore iteration
data.
1 - Read new or altered iteration data (R2-11).
2 - Read new or altered iteration data
and L2SOR data (R2-11, R2-11.1).
1 - Read new equation solution control,
NCALL.
1 - Read new or altered recharge data.
1 - Read new or altered compressibility
data.
8.2 DIFFERENCING AND MATRIX SOLUTION CONTROL
The following data are entered if IMETH … 0. If it is a new run and IMETH = 0, the program selects METHOD = 1 and WTFAC = 1.0 (direct solution with backward space and time approximations).
2 - Two-line successive-overrelaxation (L2SOR) solution with a backward finite-difference approximation in time (BIT).
-1 - Reduced band-width direct solution with a centered finite-difference approximation in time (CIT).
-2 - Two-line successive-overrelaxation
solution (L2S0R) with a centered finite-difference approximation in time
(CIT).
8.3 SURFACE RECHARGE SPECIFICATION
The following data are entered if IRCH … 0. Read as many records as necessary and follow the last record with a blank record.
READ R2-2.5 (4I5,E10.0)
J1, J2 (Similar definition for the J index).
RCHG Recharge rate, ft/d (m/s).
READ R2-2.6 (LIST 1: 2E10.0; LIST 2: I5, E10.0; LIST 3: I5,4E10.0)
CRD Local rock compressibility (see
R1D-1).
AKSD Local rock hydraulic conductivity (see R1D-2).
PBD Specified boundary pressure (see R1D-3).
TPBD Specified boundary temperature.
SWBD Specified brine concentration.
8.4 WELL DATA
The following data are entered if IOPT > 0 (READ R2-1). If default values are desired, insert a blank record and proceed to READ R2-4. The default values of the parameters are discussed below.
**** THIS FEATURE DOES NOT CONFORM TO QUALITY ASSURANCE STANDARDS. USE OF THIS IS NOT RECOMMENDED.****
READ R2-3 (I5,4E10.0) Wellbore Data.
Reference: Reeves et al. [1986a], Section 4.2.
TOLX The tolerance on the fractional change in pressure over an iteration. If TOLX # 0, the default value of 0.001 is selected.
TOLDP The tolerance on pressure, psi (Pa). The default value is 7000 psi (4.8 x 107 Pa).
DAMPX Damping factor in estimating the next value of the pressure (at the surface for an injection well and at the bottom-hole for a production well). If the frictional pressure drop in the well is high, a linear extrapolation may lead to oscillations around the right value. The default value is 2.0.
EPS The tolerance on calculating temperature from given values of enthalpy and pressure. The fluid temperatures in the wellbore are calculated over each pressure increment as specified in READ R1-3. The default value is 0.001.
READ R2-4 (I5) Rate Specifications.
Enter the following data only if INDQ = 1.
READ R2-5 (7E10.0) Rate Specifications.
READ R2-6 (I5, E10.0) Rate Specifications.
QWELL Production rate, ft3/d (m3/s). Enter negative values for injection rates. Enter only the well rates which are to be changed from an earlier recurrent data set.
The following data are entered for IWELL = 1. Read one set of data for each well, and follow the last record with a blank record.
READ R2-7 (LIST 1: (6I5); LIST 2: (4E10.0); LIST 3: (8E10.0); LIST 4: (7E10.0)) Definition of Well Options.
IIW I index of the grid cell containing the well.
IJW J index of the grid cell containing the well.
IIC1 Uppermost layer in which the well is completed.
IIC2 Lowermost layer in which the well is completed.
IINDW1 Well specification option.
2 - Layer allocation via mobility and pressure drop between wellbore and grid block. Rate control only.
3 - Layer allocation via mobility and pressure drop between wellbore and grid block. Variable rate-pressure control.
2,3 - Explicit implementation.
-2,-3 - Semi-implicit implementation.
-4 - Steady-state pressure-limited
Specifically, the point of application of the bottom-hole pressure. Figure 8-1 shows a well completed into three layers. As indicated there, the enforcement position for the specified bottom-hole pressure is the block center of the top layer of the completion zone. Usually this is also the position of the physical pressure measurement.
BHP Bottom-hole pressure, psi (Pa). This must be specified only if IINDW1 = 3 or 4.
TINJ Temperature of the injected fluid, EF (EC). If surface conditions are being specified, TINJ is the temperature at the surface.
CINJ Brine concentration of the injection fluid, dimensionless.
Skip LIST 3 if ISURF = 0 (READ M-2).
DW Inside diameter of the tubing, ft (m).
ED Roughness of the inner surface of the tubing for a smooth pipe, ft (m).
OD Outside diameter of the casing, ft (m).
TTOPW Initial rock temperature at the top-hole, EF (EC).
TBOTW Initial rock temperature at the bottom-hole, EF (EC).
UCOEF Overall heat transfer coefficient between the inner surface of the tubing and the outer surface of the casing, Btu/ft2-EF-d (J/m2-EC-s).
THETA Angle of deviation of the well bore from the vertical direction, degrees.
Skip LIST 4 if the well is completed
in only one layer, i.e., if IIC1 = IIC2.
Skip the following READ if IPR0D =
0 (READ R2-1). However, it is used only for those wells having specification
option IINDW1 = "3.
READ R2-8
(7E10.0) Wellbore Data.
8.5 SINK/SOURCE INFORMATION
If IRSS = 0, skip this section of input and proceed to READ R2-11.
If NREPB > 0, skip to READ R2-10.5.
READ R2-9
(I5) Specified-Rate Data.
Enter one set of data for each source and follow the last set with a blank record.
If IRSS = 1, READ R2-10 and skip R2-10.5.
Enter NSS sets of data.
READ R2-10 (LIST 1: 4I5; LIST 2: 7E10.0) Specified-Rate Data.
IIS I index of the source block.
IJS J index of the source block.
IKS K index of the source
block.
QHH Heat discharge rate, Btu/d (J/s).
QCC Discharge rates of radioactive components, lb/d (kg/s). Omit this parameter if NCP = 0.
Note: be careful not to doubly specify the water flow rate using QWW in this record and also as a well R2-5,6,7. For clarity it is recommended that fluid sources associated with heat or radionuclide input be entered on R2-10 records.
If IRSS = 2, READ R2-10.5.
If NREPB = 0, skip the following READ.
READ R2-10.5 (2E10.0) Waste-Leach Data.
BLCH Lag time from start
of simulation to initiation of waste leaching or heat loading of the repository.
8.6 ITERATION AND L2SOR DIRECTIONAL CONTROL
The following data are entered if INDT … 0 (READ R2-1). If default values are desired, enter INDT = 0 and skip to READ R2-11.5.
READ R2-11 (3I5)
MAXITN Maximum number of outer (nonlinear-property due to density variation or water table) interactions in subroutine ITER and ITERS. The default value is 2. For constant density use 1.
Note: For many variable-density or transient water table simulations, a value of 3 is adequate for MAXITN. Under steady-state water table conditions 5 to 15 iterations are recommended.
READ R2-11.1 (2I5, 2E10.0) L2SOR solution data.
1 - Override to force sweep in x-direction.
2 - Override to force sweep in y-direction.
3 - Override to force sweep
in z-direction.
TBUD Convergence (not normalized) criteria for iterations. The default value is 1 x 10-5 units. Be careful not to simply use the default. For example, 10-5 psi may be too small causing an excessive number of iterations. A default of 10-5 mass fraction is too large when simulating concentrations at 10-3 or less.
TPARAM Over or under-relaxation parameter (if IXYZ < 0). A value greater than 1.0 accelerates the solution and less than 1.0 dampens or under-relaxes the iterations. Generally 1.8 - 1.95 is used. Occasionally a coupled pressure-brine simulation will require an under relaxation of 0.85 - 0.99.
8.7 EQUATION CONTROL
This section of input is frequently used for computational efficiency in the transient coupled solution of the primary and radionuclide equations. In such solution, the primary transport processes frequently reach steady-state. The radionuclide processes, however, due to the usual time dependence of the decay/production processes and of the source strength, frequently never reach steady-state. The ICLL option allows one to "turn-off" the primary solution after steady-state has been reached so that the major computational effort may then be devoted to the radionuclide solution.
Skip this READ if ICLL = 0 (READ R2-1).
READ R2-11.5 (I5) Equation solution control.
8.8 RECURRENT TIME AND TIME-STEP SPECIFICATION
READ R2-12 (8E10.0) Time values.
0 - Automatic time stepping to be used for transient analysis or zero for steady-state analysis.
The following six parameters are used only if the automatic time-step feature is selected, i.e., if DT = 0. If this feature is selected, the program will automatically vary the time-step as it seeks a value such that the maximum changes in the concentration, pressure and temperature are less than or equal to the specified values.
DSMX Maximum change desired per time step for the brine concentration. The default value is 0.25 (Col. 31-40).
DPMX Maximum change desired per time step for the pressure, psi (Pa). The default value is 50 psi (350,000 Pa) (Col. 41-50).
DTPMX Maximum change desired per time step for the temperature, EF (EC). The default value is 9EF (5EC) (Col. 51-60).
DTMAX Maximum time step allowed, d (s). The default value is 30 d (2.6 x 106 s) (Col. 61-70).
DTMIN Minimum time step required, d (s). The default value is 1.0 d (8.64 x 104 s) (Col. 71-80).
Note: Column identified in cols. 71-80
cannot be used on this record. use beyond col. 81 to label this record
if desired.
8.9 OUTPUT CONTROL
READ R2-13 (14I5) Output Control.
I02 Control parameter for the frequency of the well summary. For each well this summary gives production and injection rates of fluid, heat and brine, cumulative production and injection, well-head and bottom-hole pressures, well-head and bottom-hole temperatures and the grid-block pressure in which the bottom-hole of the well is located. This summary also gives the total production and injection rates and the total cumulative production and injection (Col. 6-10).
I03 Frequency control for listing the grid-block values of concentration, temperature and pressure for the global system and the local subsystems (Col. 11-15).
I04 Control parameter for printing the injection/ production rates in each layer for each well (Col. 16-20).
I05 Control parameter for listing the grid-block values of radionuclide concentrations for the global system (Col. 21-25).
I06 Control parameter for
listing of aquifer-influence and boundary rates (Col. 26-30).
0 - Print at the end of each time step.
1 - Print only at time TCHG.
n(>1) - Print at the end of every n-th
time step and at the time TCHG.
1 - The grid-block values (pressure at datum or temperature or brine concentration) will not be printed.
2 - Refers to the first digit only.
Neither the pressure nor the pressure at datum will be printed.
RSTWR Restart-record control parameter
(Col. 36-40).
1 - Restart record will be written
on UNIT 8 at time TCHG.
1 - Areal map (x-y) at TCHG.
2 - Vertical cross-sectional map (x-z or r-z).
3 - Vertical cross-sectional map (y-z).
For radionuclides, all components are mapped.
For pressure, either pressure at datum, environmental head or freshwater head in printing depending on the value of LMAPIT (M-2).
The type of map output is controlled on Record R2-14. This includes listable output, matrix and x, y, z formats.
MDAT Control parameter for entering
the mapping specifications (R2-14, R2-14.5, R2-15) (Col. 46-50).
1 - Read new mapping specifications.
If activating the printing of contour maps for the first time during the
current run, MDAT must be entered as one and MAP must be greater than zero.
1 - Darcy velocities will be printed.
2 - Transmissibilities, Peclet and Courant number will be printed in addition to the velocities.
3 - Fluid densities, viscosities, enthalpies
and dispersions will be printed, in addition to the quantities listed above.
IO5D Control parameter for listing the grid-block values of the radionuclide concentrations for the local subsystems, i.e., matrix (Col. 56-60).
IO8D Control parameter for selectively listing the grid-block values of the primary variables for the local subsystems. The listings are printed according to the frequency specified by IO3 (Col. 61-65).
IIPRTD Intermediate print control for
the local sub-systems. This parameter is analogous to the global control
IIPRT. It also has the form 10n + i where n carries the frequency options
used for IO1 through IO6 (see note following IO6) and where i carries the
function control given under IIPRT (Col. 66-70).
8.10 MAPPING CONTROL
Enter the following data in Reads R2-14, R2-14.5, R2-15 only if contour maps are desired, i.e., if MAP … 0000 (READ R2-13) and if MDAT = 1 (READ R2-13).
It is not necessary to enter these
records each time a map is to be printed. One only needs to enter R2-14,
R2-14.5 and R2-15 once, unless mapping specifications are to be changed
with time.
READ R2-14 (6I5) Map Orientation Control.
NORNXZ, maps, respectively.
NORNYZ
1 - First ordinate increases from left to right and second ordinate increases down the computer page. The origin is the upper left hand corner. Use this for cross-sections where depth is positive downward.
-1 - Use this for cross sections where elevation is positive upwards.
KMP10, map output files on Unit 6 (line printer), Unit
KMP13 10 (x,y,z format as specified in Section 10.5) and Unit 13 (matrix grids). See Table 10.1 for file naming.
-1 - No file writing.
XZXL,XZZL The x/r and z map lengths in inches, respectively, for all the vertical (x-z) maps.
YZYL,YZZL The y and z map lengths in inches, respectively, for all the vertical (y-z) maps.
READ R2-15 (6I5, 2E10.0)
Enter one record for each map requested on R2-13 record. For example, if MAP = 0103, areal pressures and vertical brine concentration maps will be generated. Therefore, 2 data records should be entered here for this example. Note that all nuclide components of concentration are mapped. These data are used for all components present in the simulation.
AMAX(I), I=1, Number of MAPS requested.
J1, J2 Lower and upper limits, inclusive, on the J-coordinate of the region to be mapped.
K1, K2 Lower and upper limits, inclusive, on the K-coordinate of the region to be mapped.
AMIN, The minimum and maximum values of the variable
AMAX used to derive the 20 contour intervals. If the variable in any grid block is higher than AMAX, it will be indicated as AMAX. If AMAX is entered as zero, the program will search for the maximum among all the grid block values and use as AMAX. Similarly, a large negative number for AMIN (#-99) will cause the program to search for the minimum and use as AMIN.
8.11 WINDOW CONTROL
Enter the following data if I08 (R2-13)
is less than zero.
READ R2-16
(6I5) Windowing Output Control.
NJ1, NJ2 Lower and upper limits, inclusive of the window in the y-direction.
NK1, NK2 Lower and upper
limits, inclusive of the window in the z-direction.