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CHAPTER 4
Risk Assessment of Basin Analysis Results for an Offshore
North-South Seismic Section in the South Caspian Basin*
Abstract Probability and sensitivity analyses are applied to the
results of 2D basin modeling of the South Caspian Basin. A 150 km
length, 6-second deep, seismic line across the basin was used as a
basis for constructing quantitative dynami-cal, thermal and
hydrocarbon evolution patterns along the profile. The cross-section
extends into the deep-water part of the basin, where the absence of
in-formation because no wells have been drilled in this zone, a
great thickness (up to 30 km) of sedimentary cover, a complex
tectonical structure, and the proc-esses of mud diapirism and
volcanism, all cause a high degree of uncertainty in the input used
for model processes.Because of uncertainty in the depths and ages
of boundaries between stratigraphic units, and in lithology,
paleothermal conditions, organic matter content, and in parameters
related to dynamical processes, the simulation results also have
ranges of uncertainty. Attention is focused on the behavior of
excess pressure, temperature, porosity and hydrocarbon
accumulations. Based on the results of runs with the GEOPETII code
(the program used for 2D basin modeling), the logarithmic standard
deviations are computed for present-day values at each basinal
loca-tion and mapped. The relative sensitivity of the uncertainty
in each specific out-put to each input uncertainty is examined. The
global relative importance of in-put uncertainties to output
variabilities is also looked at. For each of the specific output
parameters, 2D probability plots were constructed indicating values
that will not be exceeded with fractional probabilities of 0.9, 0.6
and 0.3. In addition, plots of cumulative probabilities for
different values of specific outputs were con-structed. The upshot
is to provide an idea of which ranges of input variables are
causing the greatest contributions to uncertainties in estimates of
present-day hydrocarbon accumulation amounts and locations, to
thermal conditions, and to excess pressure determinations.
* E. Bagirov and I. Lerche
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I. Introduction
At the present time the deep water section of the South Caspian
Sea, where no wells have yet been drilled, is a prime focus for oil
company explora-tion. Accordingly, assessments of potential oil and
gas accumulations are of major interest in planning economic
strategies in the area. Such assessments are necessarily uncertain
due to the lack of control data from wells; and it is of importance
to determine not only the degree of uncertainty of any particular
as-sessment made but also which factors used in the assessment are
contributing the most to the assessment uncertainty. In this way it
becomes clear where at-tention must be directed in order to narrow
the attendant uncertainty of the as-sessment. Quantitative basin
modeling procedures provide a compendium of pow-erful devices to
aid with solution to the problem of assessing likely hydrocarbon
accumulation amounts and locations, but results of such procedures
are not unassailable. The point is that in constructing a
quantitative model, precise nu-merical values are used for input
information. The resulting hydrocarbon as-sessments depend, to
greater or lesser extents, on the exact specification of these
input values. And yet the absence of drilled wells in the deep
water part of the South Caspian Basin precludes definitive
statements from being made con-cerning formation ages (or even
seismic horizon ages), lithology, organic carbon content and type,
porosity, sub-surface temperature, etc.; and the ranges of
un-certainties on these quantities in the past are even less
well-controlled. Accordingly, a probabilistic assessment is made of
hydrocarbon accu-mulations, and is used to delineate the relative
importance of variability in indi-vidual factors in relation to
their impact on hydrocarbon accumulation uncertain-ties. The
quantitative procedure utilized is the recently developed RISK2D
code (Bagirov and Lerche, 1996), which is tied directly to the 2-D
quantitative basin modeling code, GEOPETII (developed at the
University of South Carolina). The essence of the procedure
involves running the GEOPETII code twice, once with all input
parameters set to their maximum values, and once with all minimum
values. Each output of declared interest from the basin modeling
code is then recorded at each grid node and for each time-step.
Then, using the values so recorded, an assessment is made of the
logarithmic variance, de-noted by µ
2, of the equivalent log normal probability distribution for
each output
of interest at each grid node and for each time-step. In
addition, one generates the mean value for each output, together
with both the cumulative probability of occurrence and the Relative
Importance, RI, of uncertainty in each input pa-rameter in
contributing to the uncertainty of each output, also at each
grid-node and for each time-step. One also computes the Global
Relative Importance, GRI, for the contribution of each input
parameter to the uncertainty of each out-put, no matter where it is
important or when, so that one can immediately evalu-ate quickly
which factors are controlling uncertainty in which output. The
quanti-tative method for providing these assessments in both
one-and two-dimensional basin modeling problems has been detailed
elsewhere (Cao, Abbott and Lerche (1995) for one-dimensional
problems; Bagirov and Lerche (1996) for two-dimensional problems)
and need not be repeated here, where the concern is
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more directed to application of the methods to the deep-water
section of the South Caspian Basin. II. Geological Background and
Input Parameter Ranges A 6-second regional cross-section, which
transits the western side of the South Caspian Basin from north to
south-west, was taken as a basis. The surfaces for the
stratigraphic units for the deeper part of the cross-section have
been chosen by extrapolation from an east-west 12-sec
two-way-travel time (TWT) cross-section which the 6-second seismic
section intersects (Gambarov, 1993). Ascription of horizon ages on
the 6-sec seismic line is based on con-tinuation to on-shore
outcrops (as is lithology ascription), as well as to extrapola-tion
of information from shallow-water offshore wells, as detailed in
Bagirov et al. (1996). The absence of any drilled wells in the
deep-water region does not allow one to be precise about lithology,
ages of seismic stratigraphic horizons, TOC content of each
formation, overpressure development with depth; nor does one have
any thermal indicators which could be used to bracket possible
paleoheat flux variations. Indeed, even the present-day heat flux,
and its possible spatial variation along the line, are uncertain.
Based on the best current estimates, the 6-sec seismic
cross-section has been interpreted to provide a present-day
geo-logic cross-section as given in figure 1; although one must
bear in mind the un-certainty associated with the interpretation,
which is based both on extrapola-tions from on-shore outcrops and
on seismic stratigraphic extrapolation from shallower offshore
regions, where seismic stratigraphy is controlled by borehole
measurements (Nadirov et al., 1996; Tagiyev et al., 1996). Because
of the great thickness of sedimentary cover and the absence of well
measurements across the line of the cross-section, some uncertainty
is present of ages of the seismic-stratigraphic surfaces. Where the
boundaries of the seismic-stratigraphic units are traced on the
profile, the uncertainties of the depths of the surfaces are
relatively small compared with the uncertainties of their ages.
Therefore we keep the depths of formations fixed and vary only the
ages. The principles for the definition of the estimated mean
formation ages are described in Nadirov et al. (1996). Here, we
just bracket the uncertainty of these values. The age of the
basement is defined as 170-200 My, with a most likely value of 180
My. The age of the base of the Jurassic formation is estimated as
160-180 My, with a most likely value of 173 My. The bases of the
Cretaceous, Paleogene, Neogene and Quaternary complexes are taken
in the ranges: 145±10, 65±5, 23±2, and 1.3±0.2 My, respectively.
The duration of the Produc-tive Sequence (Middle Pliocene) is
estimated as from 5.0±0.5 to 2.5±0.3 My. The uncertainty of the
ages of sub-formations of these complexes (there are 27 in total)
are defined in proportion to the total formation thickness. The
thickness of sedimentary cover is large, up to 28 km in some
places. One can obtain an idea of the depths and thicknesses from
Fig. 1. Lithologically the section is represented mainly by shales,
with interspersed sandy and carbonate sublayers, and crystalline
formations in the lower part of the section. Therefore, attention
is confined here to the uncertainty of only the shale fraction.
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The lithologies of the Jurassic and Lower Cretaceous formations
vary along the cross-section, defined by different tectonic
conditions. In the zone of the accretionary prism we take a mix of
different lithological units. The range of shale fraction is taken
to be 0.2-0.5 with a most likely value of 0.3. The other volumetric
fractions of rock consist of sand, carbonate, dolomite and
crystalline rocks in equal proportions. The lower part of the
Jurassic formation in the abys-sal zone is more shaley (90±10% of
shale) with a small fraction of sands and carbonates. In the upper
part of the Jurassic and in the Cretaceous formations the carbonate
content increases. The range of shale content varies from 60% to
80% (with a most likely value of 70%).
Figure 1. 2-D section used in the modeling. The shale content of
the Lower Paleocene formation varies from 20% to 40% (in the north
of the basin up to 50%) with a most likely value of 30%. About
10-20% of the sediment fill is sandstones, the remainder consists
of carbonates and dolomite. The Upper Paleocene is both more shaley
and more sandy, with the shale content being 50% ± 10%, and the
sandstone fraction at 20-30%. Lithologically the Eocene formation
was divided into three sub-layers: a lower part with 50% ± 10%
shale, 20-30% sand, and the remainder being carbonates and
dolomite; a middle part with 80% ± 10% shale, 10-20% sand, and
0-10% carbonate; and an upper part with 70± 10% shale, 10%
carbonate, and 20 ±10% sand. The Oligocene-Lower Miocene complex,
called the Maikopian formation, is the most shaley, with the shale
content of the lower part of this complex vary-ing between 90% and
100% (with a most likely value of 95%), the small remain-der
(0-10%) is taken as sand. In the upper part of the complex the
shale con-tent is between 80% and 100%, with a most likely value of
90%. The rest of the Miocene complex can be divided into two layers
- a lower layer, which is more sandy, with a shale content of 40% ±
10% and a sand content of 60 ± 10%; and an upper, more shaley,
layer, with a shale content of 80 ± 10% and a sand con-tent of 20 ±
10%. The Lower Pliocene (Pontian) formation is mostly shaley. The
minimum shale content is taken as 80%, with 10% sand, and 10%
carbonate. The most likely lithology mix is 90% shale, and 10%
sand; while 100% shale is taken as the maximum value of the shale
content.
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The Middle Pliocene (Productive Sequence) is represented
lithologically as an alternation of relatively thin beds of sand,
sandstone and shale. To exhibit this behavior in the model, we
divided the section into five layers, two of which are mostly sandy
(90% sand) and three mostly shaley (90% shale). In this part of the
section no uncertainty range was used. The Agchagyl formation
(Upper Pliocene) consists of 80% ± 10% shale, and 20% ± 10% sand.
In the central part of the basin, the shale content in-creases and
reaches 90% ± 10% for the Apsheron formation (Upper Pliocene), with
a 10% carbonate fraction. For the Pleistocene, the shale fraction
varies be-tween 70 to 90% (with a most likely value of 80%) and a
sand fraction of 10±10%. Top Quaternary formations consist of shale
(80±20%) and a small sand fraction (20±10%). Permeabilities of
faults are taken to be variable, rang-ing from closed faults with
zero permeability up to 500 mD for an open fault. Paleoheat flows
at any pseudo-well location along the section are taken to increase
linearly in the past relative to the present-day value, which is
taken to be 0.75 HFU across the basin except for the north slope
region where the pre-sent-day value is 1.65 HFU. Three extreme
values are used at Jurassic time, 1.0 HFU for the minimum data
file, 1.65 HFU for the most likely data file, and 3.0 HFU for the
maximum data file. Paleosurface temperatures were taken to lie
always in the range 4°C to 12°C, with an average of 9°C. The TOC
content (in weight %), and the fractions of type 1 and type 2
kerogens, were varied across the section for each formation as
shown in Table 1.
Figure 2. Cumulative ranges of uncertainty of input and
assumption parameters for present-day.
Apart from the Input Data File (IDF), containing information
specific to the
particular basin, there are parameters of an Assumption Data
File (ADF), which
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contains information specific to processes used to describe the
evolution of the basin (Bagirov and Lerche, 1996). And, of course,
each assumption parameter also has an allowed range of uncertainty.
Uncertainty in ADF parameters was handled using the ranges given in
Table 2. To demonstrate the relative contribution of each input
variable to the total input uncertainty, we used a measure of
uncertainty of input parameters, a dimensionless value, given by ai
= (X av
(i) - X min(i) ) / (X max
(i) - X min(i) ), where
X min(i) , X max
(i) and X av(i) are, respectively, the minimum, maximum and
most
likely values of the ith parameter (Bagirov and Lerche,
1996).
Figure 3. Cumulative ranges of uncertainty of input parameters
for present-day. Figure 2a presents the input uncertainty
percentage at the present-day, organized by different parameter
groupings, while figure 2b presents the same information organized
in decreasing percentage contributions. Groupings with respect to
ADF and IDF are also possible so that, for instance, all ADF
parame-ters can be grouped together as one for their Relative
Contribution, and the indi-vidual lithologic parameters, paleoheat
flow, and paleo-temperature, etc. can be presented separately, as
shown in Fig. 3. Comparing Fig. 2 and Fig. 3 one can see that the
largest uncertainty of input is caused by organic matter (the
fraction of TOC plus fractions of different kerogen types), with
about 33% contribution at the present-day, and with about 12% due
to the uncertainty of type 1 kerogen, 11% due to the type 2 kerogen
fraction, and the other 10% due to the TOC frac-tion. The next
smaller group of parameters, as determined by the size of their
fractional input uncertainties, are paleothermal conditions (32%),
made up of paleoheat flow (~16%) and paleosurface temperature
(~16%). The third group-ing is lithology (~24% contribution),
caused by contributions due to shale uncer-tainty (7%), sand
uncertainty (6%), carbonate uncertainty (5%), and dolomite
uncertainty (3%); the contribution of uncertainty of the
crystalline rocks is negli-
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gible (about 1%). The ages of formations and all ADF parameters
contribute 7% in total to the IDF uncertainties. The value of
uncertainty in the fault perme-ability is very small and its
contribution to the total uncertainty of inputs is negli-gible. A.
Excess Pressure (i) Uncertainty of output results As a measure of
uncertainty of an output parameter we plot the value of logarithmic
standard deviation, µ, for present-day at each basinal location. As
shown on Fig. 4, the largest uncertainty is in the deep central
zone of the basin and at the edge zones of the section, where µ
> 1.5. The uncertainty is relatively small for Neogene
formations (µ=0-1.0).
Figure 4. Logarithmic standard deviation plot for excess
pressure. (ii) Influence of IDF and ADF Uncertainties on Excess
Pressure Now the question is: which of the input parameters has the
largest ef-fect on the total uncertainty of excess pressure? To
examine the effect on a par-ticular output (here excess pressure)
of all of the different IDF and ADF pa-rameters being varied, we
used the Global Relative Importance introduced in Bagirov and
Lerche (1996). Figures 5 and 6 provide analysis of which particular
input variables (or group of variables) dominate the uncertainty of
excess pres-sure at the present-day. Figure 5a shows the values of
Global Relative Impor-tance for different groups of input variables
to the uncertainty of excess pres-sure. The biggest impact to the
total uncertainty is made by the TOC amount, paleothermal
conditions, and lithology, which itself has a large uncertainty. At
the same time, stratigraphic data and solubility parameters, which
have negligi-ble contributions to the total uncertainty of all IDF
and ADF variations, play a significant role in the uncertainty of
excess pressure. Therefore, for each input variable it is useful to
consider the difference between the relative importance to the
specific output parameter, and the relative contribution to total
uncertainty of all the IDF and ADF variations, which indicates the
relative sensitivity of the spe-cific output parameter to each
input variable. As shown on Fig. 5b, in spite of the
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large importance of uncertainty in TOC amount and paleothermal
conditions on the excess pressure, the sensitivity to variations of
these inputs is small. Ex-cess pressure is more sensitive to the
lithological contents, and very sensitive to the values of
formation ages, and permeabilities of faults. In general,
variations of the other ADF parameters have less significant
influences on the excess pressure.
Figure 5. Relative Importance of Input and Assumption variables
for excess pressure. Figure 6 shows the same uncertainty values,
but now for groupings with respect to IDF parameters, with all the
ADF parameters grouped together. Fig-ure 6 shows that, among
lithological units, the fraction of the crystalline rocks, and sand
have the largest values of relative sensitivity for the excess
pressure; a relative sensitivity to the TOC fraction, rather than
to the kerogen types, is also observed. (iii) 2-D Probability Plots
Using the method given in Bagirov and Lerche (1996) it is possible
to examine the cumulative probability of obtaining a given output
value at any time or location, independently of the underlying
causes of the variation in the specific output parameter. For
instance, at a given instant of time one can ask for a cu-mulative
probability not to exceed a particular percentage and to then plot
the iso-values of a parameter for that cumulative probability.
Figures 7, 8 and 9 show such plots for excess pressure for
cumulative probabilities of 0.9, 0.6, and 0.3, respectively, at
present-day. Because of the high variability of the excess pressure
values across the section, we plotted the isolines on different
scales. Figure 7a shows high values of excess pressure, indicating
that in the Lower Cretaceous formations there is a possibility of
excess pressure of the order of 5,000 KSC (1 KSC =1 kgcm-2≅1
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atmosphere). However, using that scale does not allow us to
trace the behavior of excess pressures of magnitude 500 KSC and
less. Figure 7b shows the vari-ability of excess pressure in the
range 10
2-10
3 KSC in more detail. In the Pro-
ductive Series, the excess pressure will not exceed the value of
500 KSC with a probability of 90% and, in most parts of the Miocene
and Maikop layers, excess pressure will likely (90% certainty) not
exceed 1000 KSC.
Figure 6. Relative Importance of Input variables for excess
pressure. To show the values of excess pressure for shallower parts
of the sec-tion we compressed the scale to between 0-1000 KSC (Fig.
7c), indicating that excess pressure in Quaternary sediments will
not exceed 100 KSC (90% cer-tainty) and, for the Apsheron and
Agchagyl layers, excess pressure is less than 200 KSC, with a
probability of 90%. Comparing Figs. 7a,b,c with Figs. 8 and 9, one
can see that there is no large difference in the values of excess
pressure in the upper parts of the section, as reflected by the low
values of logarithmic stan-dard deviation. For the deeper part of
the section, the highest excess pressure is observed in the zones
of the accretionary prisms (more than 1000 KSC), while the excess
pressure will not exceed about 1000-1200 KSC (60% certainty) for
the Paleogene complex, and there is only a 30% chance the pressure
will not exceed 800 KSC. Equally, for a specified value of excess
pressure (an isobar) we can ask for the cumulative probability
curves of obtaining a value less than or equal to the specified
value. Such plots are shown on Figs. 10a,b,c for the specific
val-ues of 1000, 500 and 250 KSC, respectively. White zones on
figure 10 indicate the values of excess pressure exceed the
specific isobar values with a probabil-ity higher than 90%.
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Figure 7.Plot for excess pressure values corresponding to a
cumulative probability of 0.9.
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Figure 8. Plot for excess pressure values corresponding to a
cumulative probability of 0.6.
Figure 9. Plot for excess pressure values corresponding to a
cumulative probability of 0.3. B. Temperature Logarithmic standard
deviations of the present-day temperature are characterized with
relatively low values of µ, ranging for most of the section
be-tween 1.0-1.5 (Fig. 11). The high uncertainty in the near
surface part is caused by the high relative uncertainty in surface
temperature (present heat flow is as-sumed to be constant). In the
deeper part of the section the uncertainty is caused by the
uncertainty of thermal conductivity of the rocks. The impact of
different input parameters to the uncertainty of tempera-ture is
approximately the same as for excess pressure (Fig. 12,13).
Comparing 0.9, 0.6 and 0.3 probability plots (Fig. 14a-c) one can
see differences only in the upper part of the section; the lower
part being basically similar for different val-ues of
probability.
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269
Figure 10. Cumulative probability plot for excess pressure.
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270
Figure 11. Logarithmic standard deviation plot of
temperature.
Figure 12. Relative Importance of the Input and Assumption
variables for temperature.
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271
Figure 13. Relative Importance of the Input variables for
temperature.
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272
Figure 14. Plots of the values of temperature corresponding to
specific cumulative
probability values: a) probability = 0.9; b) probability = 0.6;
c) probability = 0.3. C. Porosity The logarithmic standard
deviation of porosity is higher in the accretion-ary prism zone of
the Mesozoic formations, connected directly with the ranges of
lithological content. In most parts of the section, µ-values vary
uniformly be-tween 0.75-1.5 and, in the accretionary complex, µ is
higher - up to 2.0 (Fig. 15). Figures 16a-c show the probability
plots for iso-probabilities values of 0.9, 0.6 and 0.3,
respectively.
Figure 15. Logarithmic standard deviation plot for porosity.
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Figure 16. Plots of the values of porosity corresponding to
specific cumulative probability values: a) probability = 0.9; b)
probability = 0.6; c) probability = 0.3.
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Figure 17. Logarithmic standard deviation plot for oil
accumulation. D. Hydrocarbon Accumulations The uncertainty plots of
oil and gas accumulations for present-day are very different than
for excess pressure, temperature, or porosity patterns of be-havior
(Figs. 17 and 18). For oil accumulations the cross-section is
divided into two zones; a deeper zone (with depths greater than
9-10 km) where the µ-values are very close to zero almost
everywhere (indicating the absence of oil accumulations with
probability almost 100%); and an upper zone (shallower than 9-10
km) with high values of uncertainty, so that oil accumulations
occur along the whole cross-section at depths 9-10 km and
shallower. For gas accumula-tions, the values of uncertainty are
also high, especially in the shallow zone, and uncertainty is
present across almost the whole section.
Figure 18. Logarithmic standard deviation plot for gas
accumulation.
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275
Figure 19. Relative Importance of Input and Assumption
parameters for oil and gas accumulations.
The character of relative importance of different input
variables to the uncertainty of accumulations of oil and gas is
similar (Figs. 19), and the values of relative importance are
almost the same. For example, TOC has 23% contri-bution to the
uncertainty of hydrocarbon accumulations. To decrease the
uncer-tainty in hydrocarbon accumulation assessments, and to make a
connection with risk factors during exploration, it is necessary to
pay attention first to the lithology, TOC, and paleothermal
conditions; also to the ages of stratigraphic units and,
especially, to the nature of faults to which the model is very
sensitive. Probability plots (Figures 20-26) show that the
probability is less than 10% that oil accumulations will exceed 95
mg/g rock at any location of the cross-section (Fig. 20a). But, in
general, with a probability of 90% oil accumulations will not
exceed the values 10-30 mg/g of rock in the Apsheron-Agchagyl-Upper
Produc-tive Series in the section (Fig. 20b). In the lower part of
the Productive Series, oil accumulations will not exceed 10 mg/g of
rock in the Sabayil structure, 5-7 mg/g of rock in the Oguz field,
and are unlikely to exceed 1-2 mg/g of rock in the central part of
the profile at 90% certainty (Fig. 20c). At a 60% chance, oil
ac-cumulations will not exceed 5-15 mg/g rock in the Quaternary and
Apsheron formations and also in the upper part of the Productive
Series (Fig. 21). There is only a 30% chance, almost everywhere,
that oil accumulations will not exceed 5-7 mg/g rock i.e. there is
a 70% chance oil accumulations will exceed 5-7 mg/g of rock (Fig.
22). The probability plots for oil accumulations (Figs. 23-26) show
the zones, and cumulative probability values in these zones, for
oil accumulations of 3, 5, 7 and 10 mg/g rock, respectively. These
zones are predominantly in the Middle and Upper Pliocene, and in
Quaternary formations.
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Figure 20. Plot of oil accumulation values corresponding to a
cumulative probability value of 0.9.
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Figure 21. Plot of oil accumulation values corresponding
to a cumulative probability value of 0.6.
Figure 22. Plot of oil accumulation values corresponding
to a cumulative probability value of 0.3.
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Figure 23. Probability plot for an oil accumulation value of 3
mg/g rock.
Figure 24. Probability plot for an oil accumulation value of 5
mg/g rock.
Figure 25. Probability plot for an oil accumulation value of 7
mg/g rock.
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279
Figure 26. Probability plot for an oil accumulation value of 10
mg/g rock.
The presence of gas accumulations occurs almost everywhere for
the
whole section beginning from Middle Pliocene and deeper
formations (Figures 27-32). With a probability 90%, gas
accumulations are unlikely to exceed 10 mg/g rock, but in some
local zones may reach 20-25 mg/g rock. For example, for the 30%
probability plot, across most of the section the gas accumulation
value which cannot be exceeded is only a modest 6 mg/g rock.
Figure 27. Plot of gas accumulation values corresponding to a
cumulative probability of 0.9.
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280
Figure 28. Plot of gas accumulation values corresponding to a
cumulative probability of 0.6.
Figure 29. Plot of gas accumulation values corresponding to a
cumulative probability of 0.3.
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Figure 30. Probability plot for gas accumulation values of 3
mg/g rock.
Figure 31. Probability plot for gas accumulation values of 5
mg/g rock.
Figure 32. Probability plot for gas accumulation values of 7
mg/g rock.
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IV. Discussion and Conclusion The study area is an unexplored
region. Information about geological structures, lithology, organic
matter content and paleoheat flow is either not available or poorly
known. Therefore, the data used in modeling have large ranges of
uncertainty, which is why the results from dynamical simulations do
not enjoy high confidence levels. Under such conditions a
probability approach to the modeling results provides an assessment
of trustworthiness. The proce-dures for probability and sensitivity
analyses, based on the method of cumulative probabilities, allow
one to estimate the ranges of uncertainty of specific outputs, the
relative importance of different groups of input variables to the
uncertainties of outputs, and the sensitivity of output variables
to different groups of inputs, as well as permitting one to obtain
the cumulative probability distributions for differ-ent output
parameters. The present chapter has considered only excess
pressure, temperature, porosity, and hydrocarbon accumulations
across the profile at present-day. Oil and gas accumulation values
are characterized by high values of uncertainty. For oil
accumulations, high uncertainty values are typical for the upper
part of the section; for oil accumulations deeper than 9-10 km the
low degree of uncer-tainty is caused by the absence of oil in such
deep zones, due either to oil con-verting to gas or migrating to
shallower in the section, or both. As for gas accu-mulations, less
uncertainty is typical for almost all of the section. The
uncertainties of excess pressure, temperature, and porosity are
caused mainly by different fractions of lithological units in the
section. Most im-portant for the uncertainty of all output
parameters are the amount and type of organic matter, paleothermal
conditions, and lithology. Outputs are also sensi-tive to the ages
of formations and to solubility factors. Oil can be accumulated
predominantly in the upper part of the Middle Pliocene, Upper
Pliocene and Quaternary formations. Perhaps the dominant conclusion
is that gas accumula-tions in most of the zones, from Middle
Pliocene and deeper, are unlikely to ex-ceed 10 mg/g rock, but in
some local areas may reach 20-25 mg/g rock. Acknowledgments The
work reported here was supported by the Industrial Associates of
the Basin Modeling Group at USC.
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283
References
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Gambarov, Yu. G., 1993, Structural formation analysis and
seismic-stratigraphical investigations of the sedimentary cover of
the South Caspian Megadepression, Moscow, Nauka, 128 p.
Nadirov, R. Bagirov, E., Tagiyev, M., and Lerche, I., 1996,
Flexural Plate Subsidence, Sedimentation Rates, and Structural
Development of the super-deep South Caspian Basin, Chapter 1 of
Evolution of the South Caspian Basin: Geologic Risks and Probable
Hazards (I. Lerche, E. Bagirov, R. Nadirov, M. Tagiyev, and I.
Guliev). Azerbaijan Academy of Sciences, Baku, 625 p.
Tagiyev, M., Bagirov, E., Nadirov, R., and Lerche, I., 1996,
Predicted Hydro-carbon Accumulations and Pressure Evolution for a
2-D Section of the South Caspian Basin, Chapter 3 of Evolution of
the South Caspian Basin: Geologic Risks and Probable Hazards (I.
Lerche, E. Bagirov, R. Nadirov, M. Tagiyev, and I. Guliev).
Azerbaijan Academy of Sci-ences, Baku, 625 p.
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284
Table 1. Uncertainty of Weight % TOC for Kerogen Fraction Type
1/Type 2 TOC (%) Type 1/Type 2 Kerogen (%)
Formations Minimum Average Maximum Minimum Average Maximum
Q 1 1.5 2 0/100 0/100 10/90 Ap 1 1.5 2 0/100 0/100 10/90 Akch. 1
1.5 2 0/100 0/100 10/90 PS5 1 1.5 2 0/100 0/100 10/90 PS4(sand) 0.2
0.3 0.5 0/100 0/100 10/90 PS3 1 1.5 2 0/100 0/100 10/90 PS2(sand)
0.2 0.3 0.5 0/100 0/100 10/90 PS1 1 1.5 2 0/100 0/100 10/90 Pont 1
1.5 2 0/80 10/90 20/80 Mi3 1 1.5 2 20/80 30/50 50/50 Mi2 1 1.5 2
10/80 30/70 30/70 Mi1 2 3 4 10/80 20/80 20/80 Ol 3.5 4.5 5.5 10/80
20/80 20/80 Eo3 0.5 0.6 0.8 0/100 0/100 10/90 Eo2 0.5 0.6 0.8 0/100
0/100 10/90 Eo1 0.5 0.6 0.8 0/100 0/100 10/90 Pal2 0.5 0.6 0.8
0/100 0/100 10/90 Pal1 0.2 0.3 0.5 0/100 0/100 10/90 K2 0.5 0.6 0.8
0/100 0/100 10/90 K1 0.5 0.6 0.8 0/100 0/100 10/90 T3 0.5 0.6 0.8
0/100 0/100 10/90 T2 2 3 4 0/100 0/100 10/90
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Table 2. Uncertainty of ADF Parameters Parameter Minimal Average
Maximal
1. Exponential coefficient for shale in void ratio calculation
(dimensionless)
-0.4
-0.333
-0.3
2. Surface void ratio for shale (dimensionless)
2.5
3.0
3.5
3. Scaling frame pressure (dyncm-2)
68948
80000
90000
4. Density of oil at surface (gcm-3)
0.75
0.8
0.85
5. Surface permeability for shale (cm2)
1.0 x 10-10
5.0 x 10-10
1.0 x 10-9
6. Permeability coefficient for shale in permeability
calculation (dimensionless)
3.00
4.00
5.00
7. Surficial thermal conductivity for shale (cal/°C/cm/sec)
0.004
0.0049
0.006
8. Coefficient for shale thermal conductivity calculations
(dimensionless)
0.06
0.064
0.07
9. Anisotropy of thermal conductivity (dimensionless)
0.7
0.73
0.75
10. Interfacial tension of gas to water (dyncm-1)
25
30
35
11. Critical number for fracturing calculation
(dimensionless)
0.8
0.85
0.9
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CHAPTER 5
Dynamic Modeling of Mud Flows for Offshore Mud Volcanoes*
Abstract The eruptions of mud volcanoes, occurring in many areas of
the world, are accompanied by the ejection of thousands, and
sometimes millions, of cubic meters of mud breccia. Mud flowing
downhill along the slopes of a volcano can destroy exploration and
production equipment in its flow path, such as platforms,
pipelines, and other operational equipment. Therefore, predictions
of possible tracer paths of mud flows, and of maximum lengths of
mud flows, are of great importance. A 3-D mud flow model, called
MOSED3D, has been used to examine the mud flow problem. The method
is based on the concept that a mud current moves along a
three-dimensional surface according to the balance between gravity
(driving force) and friction (resistance force) in the fluid media,
supported against topographic facies resistance. Modeling of mud
flow and deposition is accomplished by taking quanta of mud,
released at a suspected eruptive center, and allowing the mass of
mud breccia to flow, constrained by the existing topography of the
mud volcano slope and by previously deposited mud flows of earlier
eruptions. Each quantum of released mud is transported downslope
and deposited when its flow energy drops below a critical value.
The mud flow can also cause erosion of the basal sediments and of
previous mud flow deposits on the slopes of the volcano; the total
mass of the mud current then follows the transport rules. Each
quantum of mud can be composed of variable fractions of different
lithologic types, ranging from very fine-grained to coarse-grained
material. Deposition at a given location takes place according to
the distribution of fractions that reached that location:
coarse-grained material is deposited first and fine-grained
material last. The Chirag oil field area in the Caspian Sea has
been chosen to dem-onstrate application of the method. A map of the
sea bottom in the area sur-rounding a mud volcano was digitized,
and mud flows from possible eruptive centers (and with variable
volumes) modelled, indicating amounts, directions, and thicknesses
of potential flows - of concern in rig siting in the offshore South
Caspian waters.
* E. Bagirov and I. Lerche
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287
I. Introduction
Mud volcanism occurs in many areas of the world and can pose a
sig-nificant drilling hazard to rigs sited in volcanic mud areas.
One of the reasons is that mud volcanoes are known to erupt and
spread massive amounts of breccia over a scale of tens of
kilometers, both as airborne ejecta and as mud flows. During
eruptions over several hours or days, massive amounts of brec-cia
and large volumes of gas are ejected. Breccia flows, several meters
thick, spread over hundreds of meters (occasionally several
kilometers) in length. Flowing mud can destroy all platforms and
other operational equipment, be-cause mud volcanoes are usually
associated with oil and gas fields. Therefore, it is important to
know the potential lengths and possible di-rections of mud flows
for each volcano to plan safe locations of future platforms. The
length of a mud flow, as well as its thickness and direction,
depend on: 1) volume of mud erupted; 2) the morphology of a mud
volcano and the position of each eruptive center on the volcano; 3)
the transport medium in which the erup-tion occurs (offshore versus
onshore; air versus water). The volume of mud erupted by any
volcano in a given basin can be de-scribed by a random process
variable. The distribution of such variables for the South Caspian
Basin is estimated by Bagirov, Nadirov and Lerche (1996a) from
historical records. Analysis of the linear characteristics of mud
flows observed on land has shown that they are mostly associated
with surface topography. If an eruptive center lies in a flat area,
then the mud volcano flows are isometric in form and cover
approximately circular areas. If there is a topographic slope, the
mud flows tend to be directed towards the maximum slope angle and
acquire an elongate form. The same may also be true with submarine
flows, because mud flow in an aqueous medium acquires an elongate
linear shape, even with rela-tively gentle angles of slope, due to
its lower viscosity (Garde and Ranga Raju, 1978). Therefore the
form and morphology of a volcano is very important for the
estimation of mud flow. Morphologically mud volcanoes occur as
hills and raised areas, some-times reaching upwards of 400 m in
height, and with volumes of up to several x 10
7 m
3. Externally, mud volcanoes are similar to magmatic volcanoes,
often dis-
playing a dome-like structure. The products of mud-volcano
activity are carried to the surface along exit channels, leading to
craters at the surface. The crater field is most commonly circular
to oval in outline and is surrounded by one or more concentric
crater ramparts. The crater forms an area of subsidence, and varies
in form from gently convex to a deep caldera. The area of the
crater pla-teau can reach 10 km
2, and the crater rampart may rise 5-25 m above the cen-
ter of the crater. The morphology of mud volcano breccia flows
depends mainly on the topography and on the breccia composition.
Volcanoes lying offshore differ morphologically from those on land,
forming islands (7 such islands occur in the Caspian Sea) or
submarine banks. At the time of an eruption some volcanoes form new
islands, which are often eroded within several days.
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288
The kinematic and dynamic characteristics of flows differ
depending on the medium in which the flows erupt and move. For
onshore volcanoes, where the flow erupts onto the earth's surface
in air, mud flows possess high viscosity and density, and have a
low rate of movement. The form of the flow, and its ve-locity, then
depend on the topography (angle of slope) of the surface and,
par-ticularly, on the moisture content of the erupting mass which
controls the viscos-ity. The flow speed is also influenced by
rainfall and season of the year. The results of measurements of
flow rates show that mud flow velocities increase after rain
(Bagirov et al., 1996b). The duration of the flow movement may vary
from several days to several months, and depends on how quickly the
mud dries. The period of flow movement until complete stoppage is
affected by cli-matic factors. Air at high temperatures, and also
wind, lead to the drying of mud flows and a slowing of their rates
of movement. Low air temperatures (frost) also slow the rate of
flow movement due to mud freezing, with subsequent restora-tion of
the movement after a period of warming. Mud flows on land differ
from those in the marine environment primarily because the
boundaries of the media (mud and air) are clearly defined on land
but are blurred in marine conditions (mud with sea water). Onshore
the leading edge of the mud flow becomes more viscous in the
process of moving forward and drying out, and acts as a braking
mechanism, resulting in the mud flow be-ing unbroken and
continuous. In marine conditions the mud flow from the eruptive
center is more dense and viscous than lower down the slope or in
the near-surface parts of the flow. A fraction of the mud, together
with bubbles of emitted gas, creates a pe-numbra of turbid
mud/water, which moves downslope with the mud flow. The aim of this
chapter is to show the track of a mud flow of given vol-ume,
erupted on a volcano with known morphological structure. The
quantitative method and associated program (MOSED3D) described in
Cao and Lerche (1994) have been used to address this problem. The
method assumes a "slump" deposition of mud on the surface, with the
release of "quanta" of mud being triggered by internal catastrophic
failure (much as a snow avalanche). The consequent development of
turbidite sequences is but one instance where episodic and
catastrophic "pulsing" of sediment models is required. The
com-puter model MOSED3D simulates the flow of sediment in three
dimensions as a result of a sudden release of a quantum of
sediment. The basic outline of the problem to be modeled is
sketched in figure 1. A quantum of sediment or mud is released over
a given volume centered at a location with higher potential energy
on a basin slope. The ejected mud mixes with fluid (water, air,
etc.), forming a gravity-driven current flowing downslope. The mud
will then be transported and deposited; slope sediments can also be
eroded when the mud current is strong enough. In order to simulate
the transport, deposition and erosion of mud and sediment during
such a mud current, the following assumptions and conditions are
used: # Failure of the slope (mud ejection) is autochthonous (no
external en-ergy is provided) and instantaneous; # Mud current is
constrained by the existing topography of the slope;
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289
# Basin is filled with fluid (water, air, etc.), which is
initially completely still (no eddy currents); # Mud is not
cemented and all grains are free to move independently; # Slope
sediments can have a different lithology than the quantum of
erupted mud, but with coarser grain sizes at the bottom and finer
grain sizes at the top of the sediment column; # Porosity for the
slope sediments is unchanged during the simulation; # Porosity for
a given mud current is unchanged during the flow, and different
currents may have different porosity values; # Only thicknesses of
the slope sediments and the height of the mud currents are changed
when deposition and erosion occur; # Topography of the slope is
updated after a given sediment current ends; # All grain sizes have
the same grain density; # Series flows are allowed.
Figure 1. Schematic representation of the problem to be modeled.
In MOSED3D, a discrete method, similar to Tetzlaff (1990), is used
to simulate the transport, deposition and erosion of sediments
during a mud flow in three dimensions. The advantages of such a
discrete method are that less CPU time is required and there is
more flexibility to control the simulation. The disad-vantage is
that the simulation is not explicitly time dependent, as in the
determi-nistic methods of 3D simulation of mud flow (Blitzer and
Pflug, 1989). As a con-sequence, not all potential energy in the
mud flow is necessarily fully converted before the sediment hits
the numerical "boundary wall" for a spatially small simu-lation.
Care must be taken to ensure that the simulation volume is large
enough so that boundary wall effects are far removed from the
domain of interest. II. Mathematical Formulation
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290
MOSED3D is based on the concept that a mud current moves along a
three dimensional surface according to the balance between gravity
(driving force) and friction (resistance force). Changes in the
velocity of the current cause changes in the transport capacity
which, in large, controls the deposition and erosion of mud and
sediments. The rates of deposition and erosion also depend on the
basin slope and on the sediment type being carried by the cur-rent.
The basic equations governing the current flow, as well as the
transport, deposition and erosion of sediment and mud, are taken
from Allen (1985). Some modifications are made to the equations in
order to fit the needs of MOSED3D. A. Gravity current flow.
Consider a flow element as a section of the flow of unit width and
fixed streamwise length. The driving force per unit width is the
downslope component of the immersed weight of the element. The
driving force will increase with the thickness and excess density
of the current, and with the angle of the slope. The resisting
force comes from friction between (i) the current and the bed, and
(ii) the current and the medium. From Allen (1985) the mean flow
velocity of the current is given as
Va =8 2 1
2
12sin
)( )β ρ ρ
ρ(f f0 1+−⎡
⎣⎢
⎤
⎦⎥ ms-1 (1)
where Va is the mean flow velocity of the current, h the
thickness of the flow element, r1 and r2 the densities of the
ambient medium (fluid) and the current respectively, g the
acceleration due to gravity, b the slope angle, and f0 and f1
the Darcy-Weisbach friction coefficients for the bed and the
medium respec-tively. Values of f0 usually vary from about ~0.006
to ~0.06 for rivers, and val-ues of f1 are usually less than 0.01
(Middleton, 1966).
B. Mud transport. The theoretical sediment load which a current
can carry is (Allen, 1985)
Mt = Mb + Ms =JV
JV
b
b
s
s+ kgm
-2 (2)
where Mt is the total theoretical mud load, Mb and Ms are the
theoretical bed load and suspended load respectively, Jb and Js are
the mass transport rates for bedload and suspended load
respectively, and Vb and Vs are the respective transport velocities
(usually Vb ≅ 0.2 Va and Vs ≅ Va). Equation (2) shows that the
total transport load consists of two compo-nents, bed load and
suspended load. According to Bagnold's (1966) semi-empirical
formulae, we have
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291
Jt = Jb + Js = ( )ρ
ρ ρρ
−+
⎛⎝⎜
⎞⎠⎟
120148 0 01 8g
V foV
a
f. . (Va)3 kgm-1s-1 (3)
and Js/Jb = 0.068VV
a
f (4)
where Jt is the total-load transport rate, ρ1 the density of the
ambient medium, ρ the grain density, Vf the terminal fall velocity
of the mud particles in the current. The terminal fall velocity Vf
is defined as (Allen, 1985)
Vf = ( )1
181ρ ρ
η−
gD2 ms-1 (5)
where ρ and ρ1 are the density of grain and fluid, h the fluid
viscosity, and D the
grain diameter. The power factor 3 in equation (3) is set as a
user-defined con-stant (CON_T) in MOSED3D so that users can better
control the transport ca-pacity calculation. C. Mud deposition
Whether deposition will actually occur, with consequent losses of
ex-cess density and possibly thickness, depends on the balance
between the mud load actually present in the gravity current and
the mud load that can be theo-retically supported by the forces due
to the motion of the current. The mud can be deposited only if it
is present in excess of the theoretical maximum transport-able load
(Mt). Hence no mud deposition will be expected if the actual load
at all times is equal to or less than the theoretical value Mt
(Allen, 1985). The actual load Ma can be defined as
Ma = ρ2 h kgm-2
(6) where ρ2 is the density of the current and h the height or
thickness of the cur-rent. If Ma > Mt, mud deposition occurs and
the amount of mud deposited in mass will be Ma-Mt. The coarser
grain-size material will deposit first and the finer grain-size mud
later. In MOSED3D the deposited amount of mass is converted to
thickness and a fractional constant (HHGO), ranging from 0.0 to
1.0, is introduced to con-trol the actual thickness to be
deposited, with HHGO = 1.0 being the total thick-ness. D. Erosion
Two criteria are used to examine whether erosion will occur for the
slope sediments. The first criterion is that the total theoretical
load must be greater than the actual load, i.e. Mt > Ma, and the
second criterion is that the shear stress (t) of the current on the
slope sediments must be greater than the critical shear stress (tc)
for the sediments to be eroded, i.e. t > tc. The shear stress t
is defined as (Allen, 1985)
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292
t = fo8
ρ2 Va
2
Nm-2
(7)
In MOSED3D, the power factor of 2 in equation (7) is set as a
user-defined con-stant (CON_E) for more control on the erosion
capacity. The critical shear stress tc is defined as
τc = θ (ρ - ρ1) gD Nm-2
(8) when q is the dimensionless threshold shear stress, ρ and ρ1
the density of grain particles and fluid, respectively, and D the
grain diameter (Allen, 1985). As in the case of deposition, the
eroded amount is converted from mass to thickness with the factor
HHGO. The dimensionless threshold shear stress, θ, has different
values for different grain sizes. In MOSED3D, ten grain sizes are
allowed and the corresponding q values are taken from Allen (1985,
Fig. 44, p. 58) as given in Table 1. III. Test Case As a test case
the Chirag area in the offshore Caspian Sea has been chosen. The
South Caspian basin is a classical zone of mud diapirism and
vol-canism development. Most of the anticline structures are
accompanied by mud volcanoes on their crests. Thus, in planning a
safe exploration and exploitation program in this region, one
always has to keep in mind the possibility of mud eruption. Chirag
is an area of a prime focus for oil companies, and both
explo-ration and development currently are underway. Figure 2a
shows the bathymet-ric map of the area with a structural dome,
corresponding to the location of a mud volcano. The broken line
indicates a zone of possible eruptive centers. Figures 2b shows the
same surface mapped onto a computer after digitizing. The
lithological content of mud, as well as of the sediments on the
slopes of the volcano, is taken to consist of clay (70%); fine
sand, very fine sand, coarse silt and fine silt (5% each); and from
medium sand up to pebbles (2% of each fraction). Default values of
eleven modeling parameters are used for the first run. These
default values are as follows: PSB = 70% (porosity of the basin
slope sediments) PGC = 70% (porosity of the sediment current) DG =
2650 kg/m3 (density of the sediment matrix) DF = 1025 kg/m3
(density of the fluid) VF = 0.0009 N s/m2 (viscosity of the fluid)
DWF0 = 0.008 (Darcy-Weisbach friction coefficient for bed) DWF1 =
0.01 (Darcy-Weisbach friction coefficient for fluid) CON_T = 2.50
(constant in calculation of transport capacity) CON_E = 1.20
(constant in calculation of shear stress for erosion) HHGO = 0.50
(Erosion/deposition coefficient)
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293
ELEFT = 0.70 (Residual energy fraction in the mud flow due to
energy loss during deposition (erosion))
Figure 2. (a) Sea-bed topography (bathymetry contours in meters)
over lateral and vertical scales of 10 km in the Chirag region of
the offshore South Caspian Basin. The mud volcano is shown centered
at coordinates 5 km laterally, and 10 km vertically; (b) digitized
map of the information from figure 2a.
The eruption center was first put very close to the steepest
slope, which causes a long mud tongue to develop. Figure 3 shows
the track of the mud cur-rent movement when a mud volume of 200 m
(length) x 200 m (width) x 10m (height) (= 400,000 m
3) was released. This volume is on the same order as the
average volume of mud breccia ejected during the eruptions of
observed mud volcanoes. The mud was released from the southwest
region of the diapir so that the steepest topographic slope was
encountered by the mud. The mud flow has a maximal extent of about
4 km but the bulk of the mud is deposited within about 2 km of the
source as can be seen by the distribution of the number of tracks.
The corresponding width of the mud flow is only about 300 m for the
bulk of the flow, and less than 100 m at the distal part (4 km) of
the flow. On the other hand, from the hazard point of view it is of
greater interest to evaluate mud eruptions of maximal strength.
Figure 4 shows the mud current movement when 200m (length) x 200m
(width) x 50m (height) (= 2MMm
3) of mud was released.
This volume of mud is observed during some eruptions of onshore
mud volca-noes; while the probability is only 10
-7 that ejected mud volume during a new
eruption will exceed 2MMm3 (Bagirov, Nadirov and Lerche, 1996),
nevertheless
this situation likely represents a worst case hazard. On figure
4 one can see that in such a case it is probable that two mud
tongues of very large extent will be produced. Again the mud is
released from the southwest region of the diapir, so that the
maximum topographic slope is encountered. In this case note that
both of the separated mud tongues are about 4 km in total length
with about 500 m spacing between the tongues, each of which is
about 200-400 m wide.
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294
Figure 3. Mud current movement tracks when a moderate (0.4MMm3)
mud release
occurs on the southwest side of the mud volcano for the default
friction parameter HHGO set to 0.5, over a narrow area of 200 x 200
m
2.
Figure 4. As for figure 3 but with a mud volume release of
2MMm3.
More interestingly, a different picture emerges when the same
volume of mud is released from a broader area. Then the width of
mud flow is larger, corresponding more to the majority of observed
cases, but not to the extreme worst case. Figures 5a,b,c show mud
flow tracks for a 2MMm
3 release with dif-
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295
ferent modeling parameters (Fig. 5a for HHGO=0.5; Fig. 5b for
HHGO=0.1; and Fig. 5c for HHGO=0.9). One can see that the higher
the value of HHGO, the shorter and wider is the mud flow tongue.
The point here is that the distribution of tracks from the wider
region of mud release encounter different topographic gradients
and, in addition, the larger the value of HHGO the faster the mud
is brought to a halt. Thus, relative to the default case of
HHGO=0.5 (shown in fig-ure 5a), the low value of HHGO=0.1, depicted
in figure 5b, indicates a more uni-form filling of mud across the
width of the flow to about 1 km lateral scale. By way of
comparison, the high value of HHGO=0.9, depicted in figure 5c,
indicates little lateral mud flow, but a concentrated core of mud
flowing at the center of the turbidite. While figure 5b shows a
more uniform mud flow extending out to about 4 km length, the
central core flow of figure 5c is limited to around 2 km length for
the bulk of the released mud. For the default value of HHGO=0.5,
the topography of the sea-bed prior to mud release is shown on
figure 6a; while the corresponding topography after release of
2MMm3 of mud is shown on figure 6b, indicating the production of a
broad, flat region near the diapir and a slight flattening along
the mud flow. Along the cross-section marked on figure 5a by a bold
line terminated by stubs at each end, one can also plot the change
in thickness of the sediment surface (denoted by S-surface on
figures 7a and 7b) both before and after the mud flow. Figure 7a
shows the cross-section before the eruption, Fig. 7b after
eruption, and Fig. 7c shows the mud flow overlain on the original
sediment surface (hatchured area). From figure 7c one can see that
the mud flow thickness has reached 20-25 m in some places. On the
other hand, in spite of the very long track of the mud - up to 4 km
(Fig. 5a) - the thickness of the flow after 2 km from the release
position is negligible (Fig. 7c). When the position of the eruptive
center is moved to the east side of the mud volcano, then the mud
flow tongue is wider, shorter and thinner (Fig. 8a,b) than for the
default case. The reason for this shift in mud shape is that the
east-ern side topography is considerably flatter than the southwest
side, so that there is not as much opportunity for mud to reach a
high slope region before deposi-tion terminates the flow. The
corresponding cross-section (marked by a bold line terminated by
stubs on figure 8 a) after mud deposition is shown on figure 8b by
the hatchured area overlain on the pre-release topography,
indicating deposition only to about 1 km from the release position.
As the position of the eruptive center is moved around the diapir
the overall patterns of flow change because of the topographic
variations around the diapir onto which the mud flows are released.
Figures 9a-g show eight such pat-terns, each for a released mud
volume of 2MMm
3 and a value of 0.5 for HHGO.
In general, releases from the western and southern flanks of the
mud volcano travel furthest and are widest because steeper
topographies are encountered by the flowing mud. Releases from the
northern and eastern flanks of the mud vol-cano tend to encounter
flatter topographic regions so that the mud flows tend to pool
locally within about a kilometer or so of their release positions,
with widths comparable to their lengths, representing broad, but
short, flows as compared to the longer, but narrower, flows
occurring to the south and west.
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296
Figure 5. Mud current movement tracks when a 2MMm3 mud flow
volume is released
on the southwest side of the mud volcano over a broad area of
400 x 400 m2 for differ-
ent values of the friction parameter, HHGO: (a) HHGO=0.5; (b)
HHGO=0.1; (c) HHGO=0.9.
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297
Figure 6. Topographic changes brought about by release of
2MMm
3 of mud over a
broad area of 400 x 400 m2: (a) topography prior to the mud
release; (b) topography
after the mud flow ceases.
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298
Figure 7. Topographic variation of the sediment surface along
the cross-section marked on figure 5a by the stub-ended bold line:
(a) topography along the section prior to mud release; (b)
topography after mud flow ceases; (c) superposed topography of the
mud flow thickness (hatchured region) on the original sediment
surface.
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299
Figure 8. Mud flow release of 2MMm
3 occurs on the eastern side of the mud volcano
over a broad release area of 400 x 400 m2: (a) patterns of mud
flow tracks; (b) varia-
tion of topography along the cross-section (marked on figure 8a
by a stub-ended bold line) caused by the mud flow (hatchured
region).
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300
Figure 9. Different locations of release of a fixed mud volume
(2MMm3) show different patterns of
mud flow depending on surrounding topographic gradients. Figures
9a-d show, respectively, how the flow is altered for a southern
area of release as the area is moved systematically across the mud
volcano from west to east; while figures 9e-h show, respectively,
the different flow patterns as a northern area of mud release is
moved systematically across the mud volcano from east to west.
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301
Because one does not know ahead of time where a mud release will
occur on a mud volcano, we have taken the results of each fixed
volume mud flow, released with a volume of 2MMm
3 with a value of 0.5 for HHGO, and su-
perposed the mud flow tracks for different release positions on
the mud volcano. The result was then divided by the number of
release cases run to provide a region around a mud volcano where
there is a significant hazard of mud flow. Shown on figure 10a is
the overall pattern of likely hazard area around the mud volcano in
the Chirag area for a mud flow thickness of 5 m or greater. Note
the prevalence of the southwest region, as expected given the
higher topographic slope in that area. If attention is restricted
to mud flows producing a thickness of 10 m or greater, then the
area of hazard around the mud volcano shrinks as shown in figure
10b, but there is still a south-west "tongue" due to the higher
topographic slope.
Figure 10. Area of maximal hazard for a mud flow release of
2MMm
3 from anywhere on
the mud volcano. The hatchured regions correspond to a final mud
accumulation of greater than 5 m (figure 10a) and 10 m (figure
10b), respectively. IV. Discussion and Conclusions The purpose of
these calculations has been to provide an assessment of likely
hazards that could influence operational equipment in the Chirag
region of the offshore South Caspian due to potential mud volcano
releases of material. The argument for considering a worst case
assessment, based on the historical record of mud flows recorded
for land-based mud volcanoes, is that one should plan for a worst
case hazard even if the probability of occurrence is low. One can,
presumably, then accommodate for higher probability, but lower
risk, haz-ards.
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The use of a mud flow code to investigate such hazards then
enables identification of not only the most likely directions of
hazard for operational equipment, but also the likely mud-flow
distances from the diapir (length and width) at which significant
hazards could occur. The criterion of concern is where on a mud
volcano a mud release will occur. Because one does not have prior
knowledge of such locations, and be-cause land-based statistics do
not indicate any distinguishable preferences for different sides of
volcanoes as release conditions, it is appropriate to put to-gether
a suite of potential release sites and then consider the average as
a haz-ard domain around a mud diapir. Depending on the mud
thickness that one can gear equipment to stand up against, then one
has a hazard position statement at different criteria of strength
of release and frictional deposition of mud. In this way high risk
and low risk regions for siting rigs, platforms, pipe-lines and
allied infrastructure equipment can be identified prior to a
potential mud flow, which could otherwise be disastrous rather than
just inconvenient. And that is the purpose for the calculations
reported here. Acknowledgments The work reported here was supported
by the Industrial Associates of the Basin Modeling Group at
USC.
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References Allen, J.R.L., 1985, Principles of Physical
Sedimentology, George Allen and
Unwin, London, 272 p. Bagirov, E.B., Nadirov, R.S. and Lerche,
I., 1996a, Flaming Eruptions and
Ejections from Mud Volcanoes in Azerbaijan: Statistical Risk
Assess-ment from the Historical Record. Energy Explor. Exploit. (in
press).
Bagirov, E.B., Nadirov, R.S., and Lerche, I., 1996b, Chapter 4
of Evolution of the South Caspian Basin: Geologic Risks and
Probable Hazards, Azerbaijan Academy of Sciences, Baku, 625 p.
Bagnold, R.A., 1966, An approach to the sediment transport
problem from gen-eral physics, Professional Paper, U.S. Geological
Survey, No. 422-I.
Blitzer, K. and Pflug, R., 1990, DEPO3D: A three-dimensional
model for simu-lating clastic sedimentation and isostatic
compensation in sedimentary basins, in Quantitative Dynamic
Stratigraphy, T.A. Cross, ed., Pren-tice Hall, Englewood-Cliffs, p.
335-348.
Cao, S. and Lerche, I., 1994, A Quantitative Model of Dynamical
Sediment Deposition and Erosion in Three Dimensions. Computers and
Geo-science, 20, 635-663.
Garde, R.J., and Ranga Raju, K.G., 1978, Mechanisms of Sediment
Trans-portation and Alluvial Stream Problems, Wiley Eastern
Limited, New Delhi, 483 p.
Middleton, G.V., 1966, Experiments on density and turbidity
currents. II. Uni-form Flow of density currents, Can. J. Earth
Sci., 3, 627-637.
Tetzlaff, D.M., 1990, SEDO: A simple clastic sedimentation
program for use in training and education, in Quantitative Dynamic
Stratigraphy, T.A. Cross, ed., Prentice Hall, Englewood-Cliffs, p.
401-415.
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CHAPTER 6
Evolution of the Abikh Diapir* Abstract Mud diapirism occurs
mostly in zones where the sedimentary section is predominantly
shaley, and is controlled by burial rates of the section and
gen-eration of hydrocarbons. To describe the present-day mud diapir
shape, its motion with time, its effect on the temperature of
surrounding sedimentary formation, and induced stresses and
strains, one can use techniques originally developed to model
quantitative salt diapir motion. As an application of the
procedures, an examina-tion is given of the Abikh mud diapir in the
South Caspian Basin, a classic region of mud diapirism and mud
volcanism development. The Abikh mud volcano is located on a
12-second deep, east-west, seismic profile through the central part
of the basin. It would seem that the rapid deposition of massive
sedimentation from Mid-Pliocene through to the present-day
initiated diapir motion as a conse-quence of buoyancy and gas
generated from deep hydrocarbon production. The rise speed of the
Abikh diapir, post-Pliocene, was of order 5-8 km/My, about two to
three times that of the sediment deposition rate. The corresponding
temperature evolution through both the diapir and its neighboring
sediments indicates a zone of enhanced temperature in the rim
syncline sediments, of benefit in producing hydrocarbons, and a
zone of de-pressed temperature around the apex of the diapir,
extending a few diapir radii laterally, and to around 3-5 km depth
vertically. This cool zone implies that mud diapir gases will
exsolve from connate waters due to the lowering of solubility with
the lowering of temperature, leading to gas expansion and further
adiabatic cooling of the gas. In addition, gas expansion will drive
the unconsolidated mud at the diapir apex to produce gryphons and,
in situations where the gas pressure cannot be released in a steady
manner, to explosive eruption of the diapir. The evolution of
stress and strain in the sediments bordering on the mud diapir
would indicate a deep zone (pre-Middle Pliocene) of sub-horizontal
rock failure, suggesting a deep zone of low seismic velocity caused
by sediment infill of the secondary rim syncline produced by the
diapiric rise. The production of shallow (5-20 km) regions of
subvertical stress and strain in post-Middle Plio-cene sediments
suggests that sediment-induced earthquakes epicenters should occur
mainly within a zone about couple of radii wide around the mud
diapir, with originating centers of 5-20 km depth.
* E. Bagirov and I. Lerche
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Introduction
Mud diapirs play a significant role in the tectonics, structural
formation and mass transportation in the South Caspian Basin. One
such huge structure is the Abikh mud diapir in the central
deep-water part of the South Caspian (Fig. 1). A 12-second two-way
seismic line crosses this structure from east to west (Gambarov et
al., 1993; Lerche et al., 1996). The shape of the diapir on the 2-D
section is very complex (Fig. 2; compare also with Fig. 1 of
Chapter 7).The dia-pir penetrates all sedimentary Meso-Cenozoic
formations present in the section. The roots of the diapir extend
to a depth of 12-seconds on the seismic line, cor-responding to
depths 22-26 km, and the crest of the diapir almost reaches the
sediment surface; the width of the diapir is about 10 km.
Figure 1. Hydrocarbon fields and prospects of the South Caspian
Basin (after Narimanov, 1993).
The right (east) side has a shape like a wall-type diapir, with
a rim-syncline at the base of the diapiric stem; sediment layers
are upturned by the rising diapir. The left (west) side of the
diapir is more complex, with an over-hang near the top and a bulge
on the stem. Sedimentary formations are, corre-spondingly, more
disturbed on this side. The difference between the depths of the
surfaces of the same stratigraphic units on the left and right
sides of the dia-
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pir can be 2-6 km. Without additional geological and geophysical
data it is not clear if that difference is caused only by the
diapir, or if the difference signals some major geological or
tectonic processes.
Figure 2. Interpreted seismic cross-section through the Abikh
mud diapir. To study the evolution of the diapir, and its thermal
and mechanical im-pacts on the sedimentary formations, we used the
method described in Lerche and Petersen (1995) and Lerche et al.
(1996). An inverse procedure, developed for the problems of
modeling both present-day shapes and the evolution of salt and
sediments self-consistently, has been applied to the Abikh mud
diapir. The technique is guided by observational information on the
present-day shapes of mud structures and the geometry of the
surrounding beds, and thus does not rely on having available
information concerning the dynamics of the physical system (Lerche
and Petersen, 1995). In a geologic setting where mud structures
form by dominantly vertical growth, the geometries of the
surrounding sedimen-tary formations provide information on the
different evolutionary stages (Trusheim 1960; Sanneman, 1968; Seni
and Jackson, 1983). This information is not of a dynamic nature,
but rather is geometric. Thickening and thinning of the formations,
as well as existence of unconformities, fault patterns, etc.,
establish the foundation for commonly used section-balancing
models. The inverse pro-cedure is constructed on this basis and
considers the mud shape and sediment horizons as an interlocked
system of geometric shapes that are influencing each other through
time. The questions we address using the quantitative dynamic model
are: 1) What is the geometry of the present-day mud diapir shape?
2) What time did the mud diapir motion begin? 3) How did the mud
structure and associated traps develop through time? 4) What is the
effect of the evolving mud structure on the temperature of
sedimentary rocks surrounding the structure?
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5) What are the stress and strain in surrounding sediments, and
how did they develop with time? The mathematical aspects of the
procedure are somewhat complicated, the reader is referred to
Lerche and Petersen (1995) and Lerche et al. (1996) for details.
II. Present-Day Shape The present-day shape on the scale of the
seismic-section is shown on Fig. 3. Six horizons are mapped, with
decoding of the profile to a physical depth scale the same as in
Chapter 3. To show in more detail the growth of diapir in time the
base of Middle Pliocene was added as an extra horizon.
Figure 3. Mud diapiric shape on the scale of the seismic
cross-section. The quantitative model is able to describe the
present-day shape of four of the basic (traditional) types of
diapir structures: a pillow structure (mound), a vertical mud
diapir (wall), a diapir which has developed an overhang, and a
dia-pir with no or negligible physical connection to the mother
formation (tear-drop). An inverse procedure then permits
determination of parameters in the model most consistent with
observed data of such shapes. The right side of the Abikh diapir
is, most likely, a wall-type diapir while the left side has a
noticeable over-hang. The equations describing the right-hand side
(or left-hand side) shape of a mud structure are based on the
coordinates of five critical points on the diapir surface (see Fig.
4a,b, showing the right and left sides of a diapir shape with
critical points marked). The five critical points on the surface of
a structure are: the position of the top of the diapir (X0, Y0),
the point of maximum lateral extent of the overhang (X1, Y1), the
point of minimum lateral extent of the mud stem (X2, Y2), the
deepest point of the mud in the secondary rim syncline (X3, Y3),
and an arbitrarily chosen position on the mud away from the diapir
(X4, Y4), which serves as a reference point for the geometry of the
mud in the rim syn-cline. Accordingly, a diapir is considered as a
geometric shape with the lateral
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width, x, and height, y, given in parametric form as functions
of arc length along the diapiric surface. The gradients of x and y
along the surface determine the type of shape considered.
Figure4. Present-day mud diapir shape with physical depth with
the critical points shown: a) right side; b) left side.
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The conditions that must be met are the following: (1) the
Y1-coordinate must be smaller than the Y0-coordinate; (2) the
Y2-coordinate must be larger than the Y3-coordinate; (3) the
X2-coordinate must be smaller than the X3-coordinate; (4) the Y4-
and X4-coordinates must be larger than the Y3- and X3-coordinates,
respectively. The critical points determine the turning points
along the diapir surface where the predicted mud diapir curve is
forced to change the sign of the gradient in x at y = Y1, Y2, and
the sign of the gradient in y at x = X3. In the case of a wall
structure the points (X1, Y1) and (X2, Y2) are identical. Together
with seven shape-determining parameters, the five critical points
enable the procedure to calculate any shape in the four shape
categories when supplied with additional observational data from
seismic sections and/or wells (See Lerche et al., 1996 for the
construction of static (present-day) diapir shapes, evolving
structures, and the iteration scheme used to determine the model
parameters most consistent with observations). The G-parameter
deter-mines the overall scale of the shape, i.e. the relation
between the x- and y-coordinates. The speed with which the gradient
in y increases traveling along the curve from y = Y0 is determined
by the b-parameter. As the curve turns at y = Y1, for an overhang
or tear-drop structure, the m-parameter controls the gra-dient in y
as x decreases. As the curve approaches and passes the minimum
diapir stem position at (X2, Y2), the m-parameter controls the
overall speed of change of the gradient in y, while the S-parameter
determines the curvature as y approaches Y3. The shape of the curve
between the points (X3, Y3) and (X4, Y4) is controlled by the
a-parameter. The arc length Ds (i.e. the step length be-tween the
calculated points describing the shape) can be chosen either by the
user or can be allowed to vary as a "free" parameter. A free
parameter implies that the inverse procedure determines the value
of that parameter such that, together with the other parameters, a
best fit to the input data is obtained. The width of the stem for a
structure (i.e. for x = X2 or x = X1) is often difficult to assess
based on conventional 2-D seismic information alone. The location
of the depth of this point, Y2 (Y1), can also be difficult to
determine. One, or both, of these coordinates can also be chosen to
be free parameters. The ranges within which the coordinates may
vary are specified by the user based upon available seismic and/or
downhole information. In order to calculate a diapir shape
consistent with observational data, an iteration scheme must be
chosen in order to determine the values of the pa-rameters. The
ranges of the dynamical parameters are not well-determined
ini-tially. Therefore the iteration scheme is provided with an
initial estimate of each parameter value and a broad allowed search
range. As the initial estimates of the parameter values may be far
from the values providing the best fit to the ob-served data, many
iterations may be necessary. The iteration scheme is there-fore
required to be numerically rapid and remain stable throughout the
calcula-tions. The sensitivity of the system to the various
parameters implies that the procedure may be unable to resolve one
or a set of parameters within the cho-sen range. Thus the scheme
must be able to sort out insensitive from sensitive parameters.
Such a non-linear iteration scheme is described in detail in Lerche
(1991). The iteration scheme varies the shape-determining
parameters, each of which is allowed to vary within an assigned
range. The iteration scheme is guar-anteed to find a set of
parameter values which provide a local least squares best fit to
observations. As described above, the degree of fit is measured by
calcu-
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lating the mean square residual (MSR) of predicted versus
observed positions of the diapir surface. A linear search is
performed on each parameter in turn. A parameter combination
providing a better numerical fit to the data may thus be obtained.
The iteration scheme used in the model is only guaranteed to find a
local minimum with the parameters retained within initial preset
boundaries. The sensitivities of the parameters are important when
interpreting the modeled shape, as shown in Fig. 5 for determining
parameters β, µ, m, S, Γ, and a for the right side of the Abikh
diapir.
Figure 5. Sensitivity analysis results for the shape-determining
parameters for the right side of the diapir.
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Clearly defined minima (i.e. the values of the parameters
providing the best least squares fit to the input data) allow one
to describe accurately the pre-sent-day shape of the right side of
the Abikh mud structure (Fig. 6). The same operations have been
done with the left side of the diapir. Minimal values of MSR (Fig.
7) for the shape-determined parameters allowed a fit to the
present-day shape of the diapir within the measurement error limits
(Fig. 8). The best values of present-day shape-determined
parameters are pre-sented in Table 1. Shown on Fig. 9 is the
present-day shape of the Abikh diapir described by the geometric
model with the parameters given in Table 1.
Figure 6. Comparison of the predicted numerical and visual fits
to observations for the present-day shape of the right side of the
diapir.
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Figure. 7 Sensitivity analysis results for the shape-determining
parameters for the left side of the diapir.
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Figure 8. Comparison of the predicted numerical and visual fits
to observations for the present-day shape of the left side of the
diapir.
Figure 9. Predicted present-day diapiric shape.
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III. Combined evolution of the Abikh diapir and surrounding
sediments The present-day bed configuration provides clues to the
probable evolu-tion of the mud structure, in particular during the
diapiric stage, which is recog-nized as the phase where primarily
vertical flow of mud took place associated with breakthrough and
penetration of the then overlying sediments. The source of mud is
mainly from the area close to the structure. The mud thickness
below the secondary rim syncline decreases, and the sediment load
increases, thus amplifying the pressure gradient on the mud. In
turn this gradient may enhance the flow of mud into the evolving
structure. This self-amplifying process may eventually deplete the
mud interval of its mobile constituent. This phase of evo-lution
should be characterized by a thickening of sediments towards the
mud structure during this time period. But the source of the mobile
mud in mud dia-pirs is not only from the formations below the rim
syncline of the diapir, but also from adjoining formations where
sediments are undercompacted. In addition, deep gas generation
creates an enormous overpressure (see earlier chapters). Therefore,
material from these formations also flows as mud to the body of
dia-pir, thereby increasing the rate of mud diapir growth and
decreasing the thick-ness of neighboring sediments towards the mud
structure. The overpressure increases with time, caused by
generated gas and, when the diapiric crest suc-ceeds in reaching
the depth from which gases and mud can penetrate to the surface
through faults and fractures, the growth rate of the diapir
decreases. Gas and mud then penetrate to the surface forming
gryphons; an eruption will occur when the excess pressure decrease
is not rapid enough. The Abikh diapir cuts through sediments up to
at least Middle Pliocene (Fig. 2), with the diapir covered by Upper
Pliocene and Quaternary formations. A crumpled zone above the
diapir is probably caused by paleo-mud flows from previous
eruptions. In modeling the mud diapir-sediment evolution
self-consistently, several assumptions and criteria are used here:
(a) compaction of sediments is not con-sidered. This assumption
implies that the observed present-day thicknesses equal the
thicknesses in the past. If this assumption is wrong the modeled
bed geometries are, in general, positioned too deep. Changes in bed
geometries due to differential compaction will therefore be
ascribed to the evolution of the mud alone; (b) erosion is not
included in the inverse procedure. Had erosion taken place at time
t, the sediment surfaces at time t and earlier should be
posi-tioned at a higher level (increase in decompaction). Erosion
also implies that a modeled diapir shape evolution during the time
of sedimentation and any ero-sion of the now missing beds may be
different because of potential erosion of mud. If the mud structure
is expected not to experience erosion, the modeled evolution will
not be affected because the evolution is guaranteed to be
consis-tent with the observed bed geometries; (c) mud flow in and
out of the section is not accounted for. Depending on the position
of the modeled cross-section with respect to the diapir structure,
mud volume may be lost or gained at different times in the past.
The modeled evolution may require such in- or outflow in order to
properly satisfy the criteria set up for the evolution of the
depositional surface. The changes in mud mass can be caused by mud
flow from surrounding forma-tions and by eruptions of mud
volcanoes, which carry to the surface a truly enormous amount of
mud (see earlier Chapters). The criterion taken as the major
control during the evolution reconstruc-tion was a horizontal
depositional sediment surface at each formation time. The model
assumed that at some time the pillow shape of a diapir evolved to a
wall-
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shape. For the definition of paleo-shapes of the diapir,
coefficients were used which describe the changes of
shape-determining parameters with time (Lerche et al., 1996).
Inverse methods were used to find the best values of these
pa-rameters, most consistent with the imposed horizontal bed
criterion. Best values for the trend coefficients and oscillation
terms fitting the im-posed requirement of horizontal deposition of
each formation have been found for the right side of the Abikh
diapir (see Table 2). The left side of the diapir is very hard to
handle in the available model, first because of the very
complicated shape, second because of strong distortions of the
surrounding beds. All efforts so far have led to very strange
phenomena, for instance in the very early stages of sedimentation,
the bed surfaces "bend down" (Fig. 12). The reasons for these
problems may be a deep fault of large throw, paleo-ridges at the
location of the diapir, or other factors. Without knowledge in the
third dimension we cannot evaluate the geological conditions of
sedimentation and diapiric development. So far we do not know the
true nature of the diapir and its driving forces. Possi-bly,
sediments are entrained in the mud diapir so that the model, which
was constructed originally for salt diapirs, cannot handle such
more complicated mud diapir shapes and their evolution.
Accordingly, evolution of the diapir, even for one side, is very
important, and is reported here for the right side of the Abikh
structure.
Figure 10. Combined evolution of the right side of the mud
diapir and the sediment formation geometries: (a) t=0
(present-day); (b) t=1.6 MYBP; (c) t=2.8 MYBP; (d) t=5.0 MYBP; (e)
t=16.0 MYBP; (f) t=35.4 MYBP; (g) t=65.0 MYBP.
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The results of the dynamical evolution model are presented in
Fig. 10, showing that before Pliocene time there was no diapir.
Diapiric rise began in Middle Pliocene time and, by Quaternary
time, the diapir had achieved its maxi-mum height, close to
present-day values. The timing of motion and uplift of the Abikh
diapir is consistent with estimates made in prior chapters of: (i)
massive sediment supply in the last few million years; (ii) with
the timing, originating depths and amounts of hydrocarbon
generation and particularly gas production; and (iii) with a
physico-chemical model (Guliev, 1996), suggesting that the dominant
behavior of the evolution of the Abikh diapir has been correctly
cap-
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tured by the model procedure. If rise of the diapir started some
3-5 MYBP, and the present-day height of the diapir is around 24 km,
then the average vertical speed of the diapir during this period is
about 5-8 km/My, roughly two to three times as rapid as the
sediment deposition since Middle Pliocene and, if Darcy's law is
appropriate to describe this rise, then the equivalent permeability
is around 10-2mD, making for a very "tight" seal. The dynamics of
evolution of the volume of the mud diapir is given in Fig. 11,
showing that until the beginning of Middle Pliocene time the area
of mud diapir in the 2-D section is very close to constant,
indicating that at the early stages of the diapiric evolution