Interbed Storage Package (IBS)

Last modified on Wednesday, January 31, 1996 - 5:58:19 PM

Skip forward to Input instructions for the Interbed Storage Package.

The original instructions for the Interbed Storage Package are on pages 16 to 18 of Leake and Prudic (1991).

Introduction: The Interbed Storage Package is used to simulate subsidence and release of water by the elastic and inelastic compaction of interbeds. If both elastic and inelastic compaction occur within a single time step, the total compaction is automatically allocated between them. Interbeds are assumed to be thin, low permeability units of small lateral extent. They are not included in the model as separate layers. Instead, their properties are incorporated into the properties of the aquifers which contain them. Compaction of thicker or more continuous beds can also be simulated. However, they may need to be represented by several layers.

If an aquifer cell has several interbeds the average elastic and inelastic specific storage values for the cell would be the weighted mean arithmetic specific storage values of the interbeds.
S(system) = {Sum(S(i)b(i)]}/{Sum[b(i)]}
Where

S(system) = the average elastic or inelastic specific storage of the aquifer cell,
S(i) = the elastic or inelastic specific storage of the i'th interbed, and
b(i) = the thickness of i'th interbed.

The specific storage must be multiplied by the total interbed thickness to obtain the dimensionless specific storage factor. The dimensionless storage factor is thus

Sum(S(i)b(i)]

This formula is used for both Sfe and Sfv.

Assumptions and Limitations:

Changes in effective stress due to changes in geostatic pressure are ignored. Only the effects of changes in head are considered. This can lead to errors in the compaction of unconfined aquifers. Such changes are likely to be small if the total thickness of the interbeds is less than 300 m. If they exceed 300 m in thickness, problems can be minimized by modeling the unconfined aquifer as more than one layer. In a confined aquifer overlain by an unconfined aquifer, effective stress will be overestimated if the water table in the unconfined aquifer declines and underestimate it if it increases.

The interbeds must have time to relieve excess pore pressure through the release of stored water during each time step of the model. The time (t) required to relieve 93% of the excess pore pressure by inelastic compression in a bed being drained from both sides is
t = [S(b/2)^2]/K
Where

t = the time required to relieve 93% of the excess pore pressure by inelastic compaction,
S = inelastic skeletal specific storage constant,
b = interbed thickness, and
K = hydraulic conductivity of the interbed.

Compaction is assumed to be proportional to change in effective stress rather than change in the logarithm of effective stress as experiments suggest. The percent error associated with this is
error (%) = 100*{[0.434*(Delta{p})]/[p(0)*(Delta{p}] -1} Where

Delta{p} = the change in effective stress, and
p(0) = the initial effective stress

Errors can be minimized by selecting the inelastic skeletal specific storage constant on the center of the range of stress change rather than its extremes. In addition, the simulation period can be broken into several parts each of which would have different specific storage constant. Each part would be run as a separate model but using the final heads from the previous model as starting heads.

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Input Instructions

All input parameters should be right justified.

Line 1
- Spaces 1-10, IIBSCB, Integer, If >0, unit number for cell-by-cell flow terms
- Spaces 11-20, IIBSOC, Integer, If >0, printing and saving of subsidence, compaction and preconsolidation heads will be as specified by Output Control on Lines 8+, otherwise subsidence will be printed at the end of every stress period.
Lines 2+, One line if there are 40 or fewer layers, 2 lines for 41-80 layers.
- IBQ(NLAY) array entered in 40I2 format, >0 if the layer has interbed storage
Lines 3+, One copy for each layer in which IBQ>0, complete Lines 3+ to 6+ for each layer before entering data for the next layer
- HC(NCOL,NROW) array entered with U2DREL, preconsolidation head (minimum previous head)
Lines 4+, One copy for each layer in which IBQ>0, complete Lines 3+ to 6+ for each layer before entering data for the next layer
- Sfe(NCOL,NROW) array entered with U2DREL, dimensionless elastic storage factor
Lines 5+, One copy for each layer in which IBQ>0, complete Lines 3+ to 6+ for each layer before entering data for the next layer
- Sfv(NCOL,NROW) array entered with U2DREL, dimensionless inelastic storage factor
Lines 6+, One copy for each layer in which IBQ>0, complete Lines 3+ to 6+ for each layer before entering data for the next layer
- Com(NCOL,NROW) array entered with U2DREL, The starting compaction, All 0's for a new simulation
Line 7
- Spaces 1-10, ISUBFM, Integer, Code for the format in which subsidence will be printed
- Spaces 11-20, ICOMFM, Integer, Code for the format in which compaction will be printed
- Spaces 21-30, IHCFM, Integer, Code for the format in which preconsolidation head will be printed
- Spaces 31-40, ISUBUN, Integer, Unit number on which subsidence values will be saved (if they are saved)
- Spaces 41-50, ICOMUN, Integer, Unit number on which compaction values will be saved (if they are saved)
- Spaces 51-60, IHCUN, Integer, Unit number on which preconsolidation heads will be saved (if they are saved)
Lines 8+, One copy for each time step in which IIBSOC>0
- Spaces 1-10, ISUBPR, Integer, if ISUBPR>0 subsidence is printed
- Spaces 11-20, ICOMPR, Integer, if ICOMPR>0 compaction is printed for each layer with interbed storage
- Spaces 21-30, IHCPR, Integer, if IHCPR>0 preconsolidation head is printed for each layer with interbed storage
- Spaces 31-40, ISUBSV, Integer, if ISUBSV>0 subsidence is saved
- Spaces 41-50, ICOMSV, Integer, if ICOMSV>0 compaction is saved for each layer with interbed storage
- Spaces 51-60, IHCSV, Integer, if IHCSV>0 preconsolidation head is saved for each layer with interbed storage

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Line 1, Spaces 1-10, IIBSCB, Integer

IRIVCB is used to tell whether cell-by-cell flow terms should be printed, saved to disk or neither. You must also set ICBCFL in the Output Control option to print or save cell-by-cell flow terms.

if IIBSCB > 0, unit number for cell-by-cell flow terms;
if IIBSCB <= 0, cell-by-cell flow terms will not be printed or saved;