258

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

259

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

260

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.

261

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.

262

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

263

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-

264

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

265

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

266

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%.

267

Figure 7.Plot for excess pressure values corresponding to a cumulative probability of 0.9.

268

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.

269

Figure 10. Cumulative probability plot for excess pressure.

270

Figure 11. Logarithmic standard deviation plot of temperature.

Figure 12. Relative Importance of the Input and Assumption variables for temperature.

271

Figure 13. Relative Importance of the Input variables for temperature.

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.

273

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.

274

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.

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.

276

Figure 20. Plot of oil accumulation values corresponding to a cumulative probability value of 0.9.

277

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.

278

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.

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.

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.

281

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.

282

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.

283

References

Bagirov, E. and Lerche, I., 1996, Probability and Sensitivity Analysis of 2-D Ba-sin Modeling Results, Chapter 7 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.

Cao, S., Abbott, A.E. and Lerche, I., 1994, Risk and Probability in Resource Assessment as Functions of Parameter Uncertainty in Basin Analysis Exploration Models in Quantification and Prediction of Hydrocarbon Resources (ed. A. Doré). Norwegian Petroleum Society, Elsevier Pub-lishing Co., The Netherlands (in press).

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.

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

285

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

286

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

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.

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;

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

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

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)

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)

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.

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-

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.

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.

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.

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.

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).

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.

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.

302

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.

303

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.

304

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

305

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-

306

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?

307

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

308

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.

309

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-

310

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.

311

312

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.

313

Figure. 7 Sensitivity analysis results for the shape-determining parameters for the left side of the diapir.

314

315

316

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.

317

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-

318

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.

319

320

321

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-

322

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