3 THE R1 RECORDS

The information supplied by the R1 records consists of time-independent data, all of which is read within subroutine READ1. This data specifies some of the physical properties of the global system including its geometry, boundary conditions, and initial conditions on pressure and temperature. The I data of Chapter 5 then refines the pressure initialization for the natural-flow field and provides initialization on the concentrations. The R1 records also contain a partial statement of the wellbore source/sink parameters and a definition of the discretization of the global system. The general procedure for input of the spatially dependent parameters is to specify large homogeneous regions followed by modification records to insert inhomogeneities.


3.1 PHYSICAL PROPERTIES

READ R1-1 (5E10.0) Physical Constants.
 

CW Compressibility of the reservoir fluid, psi-1 (Pa-1).
CR Compressibility of the pore structure or rock compressibility, psi-1 (Pa-1). [For multiple entries, see R1-1.5 or R1-2.5]
CTW Coefficient of thermal expansion of the reservoir fluid, EF-1 (EC-1).
CPW Fluid heat capacity, Btu/lb-EF (J/kg-EC).
CPR Rock heat capacity per unit volume of solid, Btu/ft3-EF (J/m3-EC). [For multiple entries, see R1-21 or R1-23]
If CR < 0, (READ R1-1), READ R1-1.5, otherwise, skip to R1-2.

READ R1-1.5 (List 1:(I5); List 2:(2E10.0)) Time dependent rock compressibility.
 

NPDST Number of entries in time-compressibility table.
 
LIST 2: TIMTDST(I), CRTDST(I), I=1, NPTDST
  TIMTDST Time, d(s).
CRTDST Rock compressibility of pore structure, psi-1 (Pa-1).
 
READ R1-2 (7E10.0) Physical Constants. LIST: UKTX, UKTY, UKTZ, CONV, ALPHL, ALPHT, DMEFF
  UKTX Thermal conductivity of the fluid-saturated porous medium in the x direction, Btu/ft-d-EF (J/m-s-EC) (see CONV). [For multiple entries, see R1-2.5]

UKTY Thermal conductivity of the porous medium in the y direction.

UKTZ Thermal conductivity of the porous medium in the z direction.

CONV Conversion factor for the thermal conductivities. The entered values of the thermal conductivities are multiplied by CONV to obtain units of Btu/ft-d-EF (J/m-s-EC). If entered as zero, thermal conductivities should be read in Btu/ft-d-EF (J/m-s-EC).

ALPHL Longitudinal dispersivity factor, ft (m). [For multiple entries, see R1-2.5]

  ALPHT Transverse dispersivity factor, ft (m). [For multiple entries, see R1-2.5]   DMEFF Molecular diffusivity in the porous medium, includes porosity and tortuosity effects (porosity * fluid molecular diffusivity * tortuosity), ft2/d (m2/s). [For multiple entries, see R1-2.5]

Skip the following read if NRT = 1, and proceed to READ R1-3. Otherwise enter sequentially one group (List 1 and List 2) for each rock type.
To specify block locations for different rock types, see Record R1A-1.
 

READ R1-2.5 (LIST 1: 4E10.0; LIST 2: 4E10.0) Rock-Dependent Properties.
  UTCX Thermal conductivity of the fluid-saturated media in the x direction for rock type I, Btu/ft-d-EF (J/m-s-EC).

UTCY Thermal conductivity in the y direction.

UTCZ Thermal conductivity in the z direction.

CONV Conversion factor for thermal conductivities to obtain units of Btu/ft-d-EF (J/m-s-EC).
 

LIST 2: ALPHAL(I), ALPHAT(I), DMEFFR(I), CRR(I)
  ALPHAL Longitudinal dispersivity factor for rock-type I, ft (m).   ALPHAT Transverse dispersivity factor, ft (m).   DMEFFR Molecular diffusion coefficient for rock-type I, includes porosity and tortuosity effects, ft2/d (m2/s).   CRR Rock compressibility for rock-type I, psi-1 (Pa-1).

The fluid densities are entered here for brine concentrations C = 0 (natural aquifer fluid) and concentration C = 1 (contaminated fluid). Both densities must be entered at the same reference temperature and pressure.
 

READ R1-3 (5E10.0) Reference Densities.

Reference: Reeves et al. [1986a], Section 3.1.
 

BROCK Rock density (solid particle), lb/ft3 (kg/m3).   PBWR Reference pressure at which the densities are to be entered, psi (Pa).   TBWR Reference temperature at which the densities are to be entered, EF (EC).   BWRN Density of the natural reservoir fluid (C = 0) at PBWR and TBWR, (lb/ft3).   BWRI Density of the contaminated fluid (C = 1) at PBWR and TBWR, lb/ft3 (kg/m3).   Note: BWRN and BWRI define the end member of fluid density. This is related to specific gravity as discussed in Section 12.4.
 

3.2 WELLBORE DATA

If ISURF = 0, omit READ R1-4 and READ R1-5 and proceed to READ R1-6.

Reference: Reeves et al. [1986a], Section 4.2

 

READ R1-4 (I5) Output Control.
 

NOUT Output control parameter for the wellbore calculations.
  0 - No output is activated.

1 - An iteration summary, including the number of outer iterations, the flow rate and the bottom-hole pressure, is printed for each well.

2 - The well pressure and temperature, at the surface for an injection well and at the bottom-hole for a production well, and the flow rate are printed every time the wellbore subroutine, WELLB, is called.

3 - The pressure and temperature in the well are printed for each vertical increment (see DELPW in READ R1-5).
 

READ R1-5 (3E10.0) Wellbore Constants. PBASE Atmospheric or reference pressure at the well-head, psi (Pa). This is used to convert absolute pressure to gauge pressure.

DELPW Incremental value of pressure over which wellbore calculations are to be performed, psi (Pa).

The pressure and temperature calculations in the wellbore proceed in increments. The length increments corresponding to DELPW are calculated, and the temperature change over each increment is simulated. TDIS Thermal diffusivity of the rock surrounding the wellbore, ft2/d (m2/s).
 

3.3 VISCOSITY AND TEMPERATURE INITIALIZATION

The input data described in this section defines both the viscosity function and the initial-temperature definition. The latter is self evident since it consists of a simple interpolation table. The former, however, requires some explanation. Section 3.2 of Reeves et al. [1986a] provides a detailed description of the data necessary to generate the viscosity function. Thus, only a summary is given here.

Figure 3-1 presents a useful visual aid. The minimum data necessary to specify the function shown consists of the two points VISRR = m (C =0,T=TRR) and VISIR = m (C=1,T=TIR) (READ R1-7). The remainder of the function is then generated from the generalized curve of Lewis and Squires (for the dependence on temperature) and from interpolation (for the dependence on brine concentration). As discussed in the above reference, the generalized curves may introduce as much as an 18 percent error in the temperature dependence of the viscosity function. It is therefore desirable to supply additional data whenever possible. Temperature data for C = 0 may be included by using arrays TR(I) and VISR(I) (READ R1-9) with control parameter NTVR. Temperature data for C = 1 may be included by using arrays TI(I) and VISI(I) (READ R1-10) with control parameter NTVI. Concentration data for T = TRR may be included by using arrays SC(I) and VCC(I) (READ R1-8) with control parameter NCV. In order to define a constant value of viscosity for C = 0 (or C=1), it is necessary to specify the same value for two different temperatures. For example, a constant function m (C = 0,T) = 1 cp is determined by specifying NTVR = 1 and VISRR = VISR = 1.0 with TRR … TR.
 
 

Figure 3-1. Fluid Viscosity as a Function of Temperature and Pressure.
 
 
 

Fig 3-1

The numbers called for immediately below (except for NDT) refer to the viscosity values to be entered in addition to the reference viscosities.

READ R1-6  (4I5) Control Parameters.
 

NCV Number of entries in the concentration-viscosity table. This table is for viscosities other than the reference values entered for C = 0 and C = 1. This index refers to data points along curve c in Figure 3-1, exclusive of the end points. If only the two end-point, pure-fluid viscosities are available, enter zero and read in the viscosities of the pure fluids as reference viscosities.

NTVR Number of entries in the temperature-viscosity table for C = 0. This index refers to data points on curve r of Figure 3-1, exclusive of the end points.

NTVI Number of entries in the temperature-viscosity table for C = 1. This index refers to data points on curve i of Figure 3-1, exclusive of the end points.

NDT Number of entries in the depth-versus-temperature table.

READ R1-7 (4E10.0) Reference Viscosity Values.
  TRR Reference temperature for the resident-fluid viscosity, EF (EC).

VISRR Viscosity of the resident fluid at the reference temperature, TRR, cp (Pa-s).

TIR Reference temperature for the contaminated-fluid viscosity, EF (EC).

VISIR Viscosity of the contaminated fluid at TIR, cp (Pa-s).

If NCV = 0, omit READ R1-8.

 

READ R1-8 (7E10.0) Concentration-Dependent Viscosity Values.
 

SC Concentration, mass fraction.

VCC Viscosity of fluid mixture at concentration SC and temperature TRR, cp (Pa-s).

If NTVR = 0, skip READ R1-9 and proceed to READ R1-10.

 

READ R1-9 (7E10.0) Temperature-Dependent Viscosity Values.
 

TR Temperature, EF (EC).

VISR Viscosity of the resident fluid at the temperature TR, cp (Pa-s). Do not re-enter the reference viscosity at TRR (READ R1-7).

If NTVI = 0, skip READ R1-10 and proceed to READ R1-11.

 

READ R1-10 (7E10.0) Temperature-Dependent Viscosity Values.
 

TI Temperature, EF (EC).

VISI Viscosity of the contaminated fluid at the temperature TI, cp (Pa-s). Do not re-enter the reference viscosity at TIR (READ R1-7).

Initial temperatures in the aquifer and the over/underburden blocks are to be entered here. The initial temperature is assumed to be a function of depth only.

Reference: Reeves et al. [1986a], Section 5.1.2.
 

READ R1-11 (2E10.0) Initial Temperatures.
 

ZT Depth relative to reference plane, ft (m).

TD Temperature, EF (EC).
 


3.4 OVER/UNDERBURDEN PARAMETERS

As described in Reeves et al. [1986a], Section 5.4, heat transport between the reservoir and the overburden and/or underburden is accounted for in the SWIFT code by means of a fully coupled, completely implicit heat-transport calculation within these neighboring regions. Boundary temperatures for the top of the overburden and the bottom of the underburden are obtained from the temperature-versus-depth table (READ R1-11). Initial conditions are also obtained from this table. Except for the assumptions of no lateral transport and no fluid flow within these external zones, the calculations there are completely general. The data defined in READ R1-12 through READ R1-15 gives the information necessary to discretize the over/underburden region and to define the heat-transport parameters therein.

Reference: Reeves et al. [1986a], Section 5.4.

If NZ = 1, the underburden heat loss is assumed to be equal to the overburden heat loss, and only the parameters of the overburden are utilized.

 

READ R1-12 (2I5) Number of Over/Underburden Grid Blocks.
 
 

NZOB Number of overburden blocks. If NZOB # 2, overburden heat-loss calculations are not performed.

NZUB Number of underburden blocks. If NZUB # 2, the underburden heat-loss calculations are not performed.

 

Skip to R1-16 if both NZOB = 0 and NZUB = 0.

READ R1-13 (4E10.0) Physical Parameters.
 

KOB, KUB Vertical thermal conductivities of the overburden and the underburden blocks, respectively, Btu/ft-d-EF (J/m-s-EC). CPOB, CPUB Heat capacities of the overburden and underburden blocks, respectively, Btu/ft3-EF (J/m3-EC). Skip the following READ if NZOB = 0.

 

READ R1-14 (7E10.0) Discretization of the Overburden.

LIST: DZOB(K), K=1,NZOB DZOB Thickness of each overburden block, ft (m). The first overburden block is at the upper edge of the reservoir. The overburden block numbers increase moving away from the reservoir. Skip the following READ if NZUB = 0.

 

READ R1-15 (7E10.0) Discretization of the Underburden.

LIST: DZUB(K), K=1,NZUB DZUB Thickness of each underburden block, ft (m). The block numbers increase moving away from the reservoir.
 

3.5 REFERENCE DATA AND PRESSURE INITIALIZATION

Reference: Reeves et al. [1986a], Section 5.1.1.

 

READ R1-16 (4E10.0) Reference Data.

LIST: TO, PINIT, HINIT, HDATUM TO Reference temperature for both hydraulic conductivities and densities, EF (EC).

PINIT Initial pressure, pI, at the depth HINIT, psi (Pa). Also used as the reference pressure PO = PINIT. See Figure 3-2.

Permeabilities are determined assuming that the input conductivities are referenced to temperature TO. Densities are related internally to this temperature and to the pressure PINIT in that only changes from the density at TO and PO = PINIT (and C = 0) are calculated. HINIT An arbitrary depth, hI, for setting up initial conditions measured relative to the reference plane, ft (m). HINIT can be any depth within the reservoir. HINIT is used only to set up initial pressures in the reservoir. See Figure 3-2. Quantities HINIT, HDATUM, DEPTH (READ R1-20) and UH (READ R1- 21) are all measured from the reference plane shown in Figure 3-2. HDATUM Datum depth, hD, measured relative to the reference plane, ft (m). See Figure 3-2. Quantity HDATUM is used only for the printing of the dynamic pressures or pressure at datum (p-rgh/gc). The pressure at block centroid depth, h, relative to the reference plane is converted to the datum plane using the reference density. Figure 3-2. Specification of the Geometry and the Initial Pressure in a Cartesian System.
 

Fig 3-2


3.6 DISCRETIZATION FOR A CARTESIAN GEOMETRY

If HTG = 3 (radial geometry), skip to READ R1-22.

 
READ R1-17 (List Directed) Grid-Block Definition.
 

DELX Length of each row of blocks in the x direction, ft (m). READ R1-18 (List Directed)1 Grid-Block Definition. LIST: DELY(J), J=1,NY
  DELY Length of each row of blocks in the y direction, ft (m).
READ R1-19 (List Directed)1 Grid-Block Definition. LIST: DELZ(K), K=1,NZ
  DELZ Thickness of each vertical layer, starting with the top-most, ft (m). Note: To flag the stair-case grid option below, enter a negative value for DELZ(1)
READ R1-19.1 (List Directed)1 Stair-cased Grid Definition. LIST: HTOP, (DELZ(K),K=1,NZ) HTOP Distance below datum to top of upper-most block in column (i,j) where i refers to x-direction and j refers to y-direction, ft (m).

DELZ(K) Block thickness, starting with top-most block, ft (m).

Note: The list is read for all columns in the system. The code starts with the (1,1) columns, increments first on j (y-direction) and then i (x-direction). A total of NX * NY list are required to complete the grid definition.
 

3.7 RESERVOIR DATA FOR A CARTESIAN GEOMETRY

The following data are read only if HTG = 1 or 2, and by themselves describe a homogeneous reservoir. Heterogeneity may be introduced by using READ R1-21 and/or regional modifications in READ R1-26, in addition to READ R1-20.
 

READ R1-20 (7E10.0) Homogeneous Reservoir Information.

LIST: KX, KY, KZ, PHI, SINX, SINY, DEPTH KX Hydraulic conductivity in x direction, ft/d (m/s).

KY Hydraulic conductivity in y direction, ft/d (m/s).

KZ Hydraulic conductivity in z direction, ft/d (m/s).

PHI Porosity (fraction).

SINX Sine of the reservoir dip angle along the x-axis (positive down). See Figure 3-2.

SINY Sine of the reservoir dip angle along the y-axis (positive down). See Figure 3-2.

DEPTH Depth, hO, to the center of grid block (1,1,1) measured from the reference plane (positive downward). See Figure 3-2.
The following data are read only if HTG = 2. Enter as many sets of data as required. Follow the data with a blank record.

 

READ R1-21 (List 1: 6I5; List 2: 7E10.0) Heterogeneous Reservoir Information.

LIST 1: I1, I2, J1, J2, K1, K2 I1, I2 Lower and upper limits inclusive, on the I index of the region to be described.*

J1, J2 (Similar definition for the J index).

K1, K2 (Similar definition for the K index).
 

LIST 2: KX, KY, KZ, PHI, UH, UTH, UCPR KX x-direction hydraulic conductivity, ft/d (m/s).

KY y-direction hydraulic conductivity, ft/d (m/s).

KZ z-direction hydraulic conductivity, ft/d (m/s).

PHI Porosity, fraction.

UH Depth in ft (m) measured positive downward from reference plane to center of the cell. See Figure 3-2. If entered as zero, the depth is unaltered from the value calculated for a homogeneous aquifer.

UTH Grid-block thickness in the vertical direction, ft (m). If the layer thickness is equal to DELZ(K) (READ R1-19), UTH may be entered as zero.

UCPR Heat capacity of the rock, Btu/ft3-EF (J/m3-EC). If the rock heat capacity is equal to CPR (READ R1-1), UCPR may be entered as zero.

 

*A negative value for I1 indicates that a separate binary file will be used instead. The program will pause and request the file name. See Section 10.7 for further details.


3.8 RESERVOIR DATA FOR A CYLINDRICAL GEOMETRY

The following three records are read for a radial geometry with a well located at the center of the system. The user has the option of generating the grid block centers using an equal Dlog(r) basis, (i.e., ri/ri-1 is constant) or entering the radius of each grid-block center.

Skip to READ R1-26 if HTG … 3.
 

READ R1-22 (4E10.0) Geometrical Data.

Reference: Reeves et al. [1986a], Section 7.1.2.

LIST: RWW, R1, RE, DEPTH RWW Well radius, ft (m). See Figure 3-3.

R1 For mesh generation on an equal Dlog(r) basis, R1 > 0 represents the center of the first grid block. See Figure 3-3. For direct specification, R1 = 0 should be used.

RE External radius of the reservoir, ft (m). See Figure 3-3.

DEPTH Depth, hO, from the reference plane (positive downward) to the center of the first layer of blocks, ft (m). See Figure 3-2.
 
 

Figure 3-3. Schematic of the Radial Mesh Including Grid-Block Centers, ri, and Grid-Block Boundaries, i.
Fig 3-3 READ R1-23 (5E10.0) Reservoir Parameters. LIST: DELZ(K), KYY(K), KZZ(K), POROS(K), CPR1(K), K=1,NZ One record should be entered for each vertical layer. DELZ Layer thickness in the vertical direction, ft (m).

KYY Horizontal hydraulic conductivity, ft/d (m/s).

KZZ Vertical hydraulic conductivity, ft/d (m/s).

POROS Porosity, fraction. CPR1 Rock heat capacity, Btu/ft3-EF (J/m3-EC). If the rock heat capacity in the layer is equal to CPR (READ R1-1), CPR1 may be entered as zero.
Skip to READ R1-26 if R1 … 0.

READ R1-24 (7E10.0) Radial Grid-Block Centers.

LIST: RR(I), I=1,NX RR Radial grid-block centers, ft (m). See Figure 3-3.
 

3.9 RESERVOIR DESCRIPTION MODIFICATIONS

Read as many sets of the following data as necessary to describe all the reservoir description modifications which are desired. Follow the last set with a blank record, which the program recognizes as the end of this data set. Even if no regional modifications are desired, the blank record must be included.

 
READ R1-26 (LIST 1: 6I5; LIST 2: 7E10.0; LIST 3: 3E10.0)

LIST 1: I1, I2, J1, J2, K1, K2 I1, I2 Lower and upper limits, inclusive, on the I index of the region to be modified.

J1, J2 (Similar definition for J index).

K1, K2 (Similar definition for K index).

The x transmissibility indexed as (I,J,K) refers to the transmissibility at the boundary separating grid blocks (I-1,J,K) and (I,J,K). Similarly the y transmissibility indexed as (I,J,K) refers to the transmissibility at the boundary separating grid blocks (I,J-1,K) and (I,J,K). LIST 2: FTX, FTY, FTZ, FPV, FPHI, HADD, THADD FTX If positive or zero, this is the factor by which the x-direction transmissibilities within the defined region are to be multiplied. If negative, the absolute value of FTX will be used for the x-direction transmissibilities within the region to be modified.

FTY This has the same function of FTX, but applies to the y-direction transmissibilities.

FTZ This has the same function of FTX, but applies to the vertical transmissibilities.

FPV This has the same function of FTX, but applies to pore volumes. Set FPV to zero to make the block inactive. This will remove the block from the matrix solution and avoid printing and mapping of output with efficient storage and no loss of accuracy. Wells cannot be placed in zero pore volume blocks.

FPHI If positive, this is the factor by which the values of porosity used in the heat storage calculation within the defined region are to be multiplied. If negative, the absolute value of FPHI will be used. A zero or unit value has no effect.

HADD This is an increment that will be added to the depths within the defined region, ft (m). A positive value moves the designated cells deeper, and a negative value brings them closer to the surface. See Figure 3-2.

THADD This is an increment that will be added to the thickness values within the defined region, ft (m). A positive value makes the cell thicker, and a negative value makes it thinner. Pore volumes are implicitly modified with thickness changes.
 

LIST 3: FTUX, FTUY, FTUZ FTUX If positive, this is the factor by which the x-direction Darcy velocities within the region defined are to be multiplied. The modified velocities are used in the heat and solute dispersion coefficients. A zero or unit value has no effect.

FTUY This has the same function of FTUX, but applies to the y-direction Darcy velocities.

FTUZ This has the same function of FTUX, but applies to the z-direction Darcy velocities.

In regions in which more than one modification has been made to a parameter, the order of the modifications has no effect, and the final net adjustment is simply the algebraic sum of all the additive factors or the product of all the multiplicative factors that apply to the region. The program will accept a zero modifier as a valid parameter. Therefore, if no changes are desired to data that are affected by multi-plicative factors FTX, FTY, FTZ, or FPV, read the corresponding factors as 1.0, not zero. If no changes are desired for FPHI, FTUX, FTUY or FTUZ, read the factor as 1.0 or zero. Zero additive factors (HADD AND THADD) result in no changes to the depth and thickness values.


3.10 AQUIFER-INFLUENCE FUNCTIONS AND BOUNDARY CONDITIONS

Aquifer-influence functions specify the effects of an aquifer upon the reservoir via an analytic submodel of the aquifer. Conceptually reservoir and aquifer are related as shown by Figure 3-4. For the SWIFT model three different aquifer submodels are available. These submodels are implicitly coupled to the reservoir via the influence functions. In general, both pressure and flow vary as a function of time. The application of such functions means that the aquifer itself need not be modeled as a part of the grid system. Boundary conditions, however, are more simple. They derive from specified constants for pressure, temperature and concentration. Hence, they do not implicitly vary with the internal condition of the reservoir as do the aquifer-influence functions.

Reference: Reeves et al. [1986a], Sections 5.2 and 5.3.

If no aquifer-influence functions or boundary conditions are to be specified (no flow across aquifer boundaries), insert a blank record and proceed to READ R1D-1.
 

Figure 3-4. Geometrical Characterization of the Aquifer.
Fig 3-4

READ R1-27 (2I5) Control Parameters.

LIST: IAQ, PRTAB
  IAQ Control parameter for selecting the type of boundary control. 0 - No aquifer-influence or boundary-condition blocks are to be used. Skip to READ I-1.

1 - A pot-aquifer representation will be used. The aquifer is assumed to be at steady-state with a no-flow outer boundary. [Rarely used option]

2 - A steady-state aquifer representation will be used. The aquifer is assumed to be at steady-state with a constant pressure at the outer aquifer boundary. [Rarely used option]

3 - An unsteady-state aquifer representation will be implemented using the Carter-Tracy approximation.

4 - Constant pressure and brine-component boundary conditions will be used. Boundary conditions for heat transport may be either constant-temperature or radiative.
 

PRTAB Print control key for the aquifer-influx coefficient.
  0 - No printing of aquifer-influence coefficients will be activated.

1 - The locations and values of the aquifer- influence coefficients will be printed.
 
 

3.10.1 Steady-State Aquifer-Influence Functions and Boundary Conditions
This data group consists of two records or any number of sets of two records, each set defining a rectangular region and the value of VAB to be assigned that region. Overlapping of regions is permissible. The order of the sets is immaterial except that any overlapping will result in the VAB of the last set read being assigned to the overlapping subregion.

If IAQ = 3 (READ R1-27), skip the following READ and proceed to READ R1-29.

Follow the last record of this data group by a blank record.
 

READ R1-28 (LIST 1: 7I5; LIST 2: 6E10.0) Region Specification.

LIST 1: I1, I2, J1, J2, K1, K2, KAQ I1, I2 Lower and upper limits, inclusive, on the I index of the aquifer-influx region.

J1, J2 (Similar definition for J index).

K1, K2 (Similar definition for K index).

KAQ Control variable for the heat-transport equation used only for IAQ = 4.
 

-1 - Type 3 radiation condition only. In List 2, T1 is not used. T2 and T3 are used.

0 - Type 1 temperature condition only. In List 2, T1 is used. T2 and T3 are not used.

1 - Type 1 temperature condition and Type 3 radiation condition. In List 2, T1, T2 and T3 are all used.
 
 

LIST 2: VAB, P1, T1, C1, T2, T3
VAB Aquifer influence coefficient for each block within the region defined by I1, I2, etc. The units of VAB are ft3/psi (m3/Pa) for a pot-aquifer representation and ft3/psi-d (m3/Pa-s) for a steady-state representation.
P1, T1, C1, T2, and T3 are not used.
  For IAQ = 4, the Boundary-Conditions

VAB Face-type indicator used to assign transmissibility.
 

1.0 - Block is located on an I = 1 edge.

2.0 - Block is located on an I = NX edge.

3.0 - J = 1 edge.

4.0 - J = NY edge.

5.0 - K = 1 edge.

6.0 - K = NZ edge.
 

P1, T1, C1:  Constant values of pressure at block-centroid elevation in psi (Pa), temperature in EF (EC) and concentration (fraction) at the block boundary specified according to VAB and KAQ. See Figure 3-5.
Figure 3-5. Positions for the Boundary Conditions.
Fig 3-5
T2 Temperature of surrounding media, EF (EC). T3 Coefficient of surface-heat transfer, Btu/d-ft2-EF (J/s-m2-EC).

 

3.10.2 Unsteady-State Aquifer-Influence Function
If IAQ … 3, omit the following data and proceed to READ R1-33. This section is used to enter data for the Carter-Tracy method of calculating aquifer-influence functions.

 

READ R1-29 (3I5) Control Parameters.

LIST: NCALC, NPT, PRTIF
  NCALC Control parameter for selecting how the Carter- Tracy aquifer coefficients are to be assigned.
  0 - The Carter-Tracy aquifer coefficients (VAB) will be read as input data.   1 - The VAB will be calculated by the program and assigned to each edge (perimeter) block in each areal plane, K=1,2,...,NZ (use with radial grids only).
 
NPT Number of points in the table of influence function versus dimensionless time (P(tD) versus tD). If NPT = 0, then the program will select the infinite-aquifer solution for which the appropriate table is available internally.

PRTIF Print control key for the influence-function table.

0 - Suppress printing.   1 - Print the table of P(tD) versus tD.
Enter the following data only if NCALC = 0. Otherwise, skip to READ R1-31.

Follow the last VAB record of the following data group by a blank record. This READ group consists of two records, or any number of sets of two records, with each set defining a rectangular region and the value of VAB to be assigned within that region. Overlapping of regions is permissible. The order of the sets is immaterial except that any overlapping will result in the VAB of the last set being assigned to the overlapped subregion.

 

READ R1-30 (LIST 1: 6I5; LIST 2: E10.0) Boundary Specification.

LIST 1: I1, I2, J1, J2, K1, K2 I1, I2 Lower and upper limits, inclusive, on the I index of the aquifer-influence region.

J1, J2 (Similar definition for J index).

K1, K2 (Similar definition for K index).
 

LIST 2: VAB VAB Geometrical coefficient for each block within the defined region. The coefficient VAB, for the Carter-Tracy method, is actually the fraction of the total reservoir-aquifer boundary which the block surface comprises. For this reason it is possible to calculate the VAB from input data previously read, and the VAB does not have to be calculated externally.
READ R1-31 (4E10.0) Carter-Tracy Aquifer Properties.
  KH Conductivity-thickness for aquifer, ft2/d (m2/s). An average value of transmissibility along the edges should be used.

PHIH Porosity-thickness for aquifer, ft (m).

RAQ Equivalent aquifer radius, ft (m). The approximate method of Carter and Tracy is valid for circular aquifers. However, it may be used, nevertheless, to approximate the effect of an infinite aquifer upon a rectangular system.

THETAQ Angle of influence, degrees. This angle should indicate the portion of the aquifer covered by the aquifer-influence boundary. If mass flow is permitted across all the boundaries, enter 360E.

The following data are entered if NPT … 0 (READ R1-29). If NPT = 0, the program will select the aquifer-influence functions for an infinite aquifer and the influence-function data need not be entered. If NPT = 0, omit this READ and proceed to READ R1-33.

 

READ R1-32 (2E10.0) Terminal-Rate Function.
 

TD Dimensionless time, kt/mf (cwcR)re2.

PTD Terminal-rate function.
 
 

3.10.3 Geometrical-Coefficient Modification
These data allow the user to modify the coefficient VAB by the relation VAB(I,J,K) = VAB(I,J,K) * FAB. This is useful when a reservoir may experience no or limited water influx across one boundary. In this case, in the region where influx is limited, the FAB may be used to reduce the VAB along that boundary.

Follow the following data with one blank record. If no modifications are desired, one blank record is still required.

 

READ R1-33 (LIST 1: 6I5; LIST 2: E10.0)
 

I1, I2 Lower and upper limits, inclusive, on the I index of the VAB to be modified.

J1, J2 (Similar definition for the J index).

K1, K2 (Similar definition for the K index).

LIST 2: FAB

FAB Factor by which the VAB will be modified in the defined region.