on the accuracy of modelling hydrocarbon generation and migration: the egersund basin oil find,...

AdvBeu in Organic G e o ¢ ~ 1969 Org. Geochem. Vol. 16, Nos 1-3, pp. 389-399, 1990 Printed in Great Britain. All rights reserved

0146-6380/90 $3.00 + 0.00 Copyright © 1990 Pergamon Press pie

On the accuracy of modelling hydrocarbon generation and migration: The Egersund Basin oil find, Norway

C. HERMANRUD, S. EGGEN, T. JACOBSEN, E. M. CARLSEN and S. PALLESEN Statoil, P.O. Box 300 Forus, 4001 Stavanger, Norway

(Received 11 October 1989; accepted 18 February 1990)

Abstract--Quantitative estimates of kerogen transformation and hydrocarbon charge to the y-structure of Block 9/2, Norwegian North Sea, were obtained by integrated basin modelling. A probability distribution was assigned to each input parameter, and the sensitivity to these parameters was investigated by subsequently varying each parameter within the assigned ranges. The inaccuracy in the modelling results were mainly due to imprecise knowledge of hydrocarbon generation kinetics, depth conversion and present day virgin rock temperature (kerogen transformation modelling), and source rock richness/ thickness/areal extent (volumetric charge calculations). Monte Carlo/latin hypercube sampfing based on the probability distribution of each parameter was performed, giving a 40% probability for a dry structure, a mean value of 10.7.106 Sm 3 recoverable oil, and a considerable high side potential (4% probability for more than 50.106 Sm 3.

Key words--Egersund Sub-basin, basin modelling, sensitivity analysis, volumetric calculations, modelling accuracy

INTRODUCTION

Murris (1984) described how organic geochemistry has become a widely accepted tool in oil and gas exploration within the past two decades, and also clearly showed that organic geochemistry has improved the ability to forecast the presence of oil and gas accumulations. The improved forecasting ability is to a large extent due to the improved knowledge of the physical processes responsible for the formation of oil and gas accumulations. This improved knowledge of subsurface physics, combined with the improvements in computer facilities, has allowed numerical simulation of the processes leading to petroleum formation and occurrence. Such simulations are frequently termed "basin modelling", even when only one-dimensional simulations on structural highs are performed. Since the pioneering work of Yiikler et al. (1978), numerical basin modelling has become widely used in hydrocarbon exploration. Several basin modelling studies have been carried out in the Norwegian North Sea within the last five years (Ungerer et al., 1984, 1985; Dahl et al., 1987; Doligez et al., 1986a, b; Cao and Lerche, 1987; Ritter et al., 1987, Ritter, 1988; Hermanrud et al., 1990).

Whereas the physical rules responsible for the distribution of thermal energy in a sedimentary basin are fairly well known, considerable controversy exists concerning the processes responsible for the generation and migration of hydrocarbons in the subsurface. Modelling of these processes may thus be unwarranted. As a result, several methods for volumetric calculations of hydrocarbon accumulations which do not simulate the physical processes, but

rather rely on empirical relationships, have been proposed (Cooles et al., 1986; Heum et al., 1986).

The sensitivity of the results of the modelling exercise to variations in the input parameters was not made clear in many of the early basin modelling studies. Application of sensitivity analysis in basin modelling has been undertaken by Ritter et ai. (1987), Ritter (1988) and also by Cao and Lerche (1990a, b). These studies are confined mainly to the modelling of heat transport and hydrocarbon generation, and do not discuss all the factors affecting the volumetric calculations of accumulated hydrocarbons.

This paper describes a basin modelling study which was performed as a part of an evaluation of the 9/2 ?-structure (drilled by Well 9/2-1) in the Egersund Sub-basin, Norwegian North Sea. The study aimed to find a probability distribution for the volume of recoverable hydrocarbons in the 9/2 ?-structure, and to reveal which parameters contribute significantly to the uncertainty. The evaluation presented in this paper is entirely based on data that were available prior to the drilling of Well 9/2-1, so the results from Well 9/2-1 can be used to evaluate the modelling results.

The results from this study are to some extent universal, in that they point to key parameters which are crucial to modelling results in a large variety of geological settings. However, both the accuracy of the parameters and their impact on the final modelling results are intimately linked to the actual geological situation. The results obtained in the study presented here may nevertheless give an indication as to what accuracy can be expected from modelling in other areas.

389

390 C. HERMANRUD et al.

GEOLOGICAL DESCRIPTION OF THE EGERSUND SUB-BASIN

The Egersund Sub-basin is a small extensional basin situated approximately 100km west of the southernmost part of Norway (Fig. 1). The geology of the area has been described by Hamar et al. (1983), Pegrum (1984), D'Heur and de Walque (1987), Ritter et al. (1987) and Ritter et al. (1988) and the general geological evolution of the Northern North Sea by Pegrum and Spencer (1990) and references therein. The reader is referred to these works for an in-depth discussion of the geological evolution of the area.

As the Egersund Sub-basin is not part of the main extensional zone of the Central and Viking Grabens, it was less affected by the heating related to the late Jurassic stretching, and thus experienced less thermal subsidence in Tertiary times than the graben areas further to the west. The source rocks are thus buried to a comparatively shallow depth in the Egersund Sub-basin, and are only marginally mature or immature in most of the basin.

Several different formations (Ula, Sandnes, Bryne, Tau, Egersund, Sauda) have been mentioned as possible source rocks in the Egersund Sub-basin by Ritter et al. (1987), who claimed that the Upper Jurassic Tau Formation ("hot shale") only contributes with about 10--15% to the total hydrocarbon generation. However, primary migration is likely to be more efficient from the rich Tau Formation than for the other formations (HI = 800 vs 100--450 mg HC/ g org.C in well 9/4-4, 350 vs 150-250 mg HC/g org.C in well 18/10-1; Ritter et al., 1987).

The reservoir rocks (and carrier beds) are the Middle Jurassic sandstones of the Sandnes For- mation, which are separated from the Tau Formation by the comparatively leaner shales of the Egersund Formation. This separation may be an obstacle to migration from the Tau source rocks to the Sandnes reservoirs. This obstacle is partly overcome by a north-south normal fault which juxtaposes the Tau and Sandnes formations (Fig. 2). As long distance migration is not required in this area, calculated loss during secondary migration is expected to be moderate. The areal extent of the drainage area is unclear to us because of a lack of data on the faults just south of the 9/2 7"structure.

Seismic evidence suggests that the eastern parts of the Egersund Sub-basin may have been moderately uplifted in Tertiary times. Later subsidence has nevertheless reburied the source rocks, which are presently at their maximum depth of burial. How- ever, the source rock temperatures may not be at their maximum values at present (Ritter et al., 1987). The source rock temperatures seem to be somewhat reduced due to the dramatic reduction of surface temperatures in Late Cenozoic times, combined with moderate subsidence and probably reduced heat flow in this time period. Modelling of hydrocarbon generation in the Egersund basin will thus be more affected by paleo heat flow than in areas where

the Tertiary and Quaternary subsidence has been more pronounced, such as in the Haltenbanken area offshore mid-Norway.

Of the 11 wells drilled in or near the Egersund Sub-basin prior to Well 9/2-1, three (17/12-1, 17/12-2, 18/10-1) encountered minor amounts of oil, all in structures which were not filled to their spill points. The Well 9/2-1 made a small hydrocarbon discovery, and it is presently not clear whether this structure is filled to its spill point. The total (recoverable) resources in the 9/2 ~,-structure have been estimated to 24.106Sm 3 oil and 1.109Sm 3 gas (Norwegian Petroleum Directorate Annual Report, 1988).

MODELLING STRATEGY

The in-house Statoil basin modelling program Geosim was used for the basin modelling of the Egersund Sub-basin. Geosim is a fully integrated basin modelling program for the simulation of compaction, porosity, permeability, heat and fluid flow, fluid pressure and temperature. The Geosim program has been described by Hermanrud et al. (1990). Only the one-dimensional version of the program was applied, as previous studies (Hermanrud, 1989) showed that two-dimensional effects only give minor focusing or defocusing of heat to the kitchen sourcing the 9/2 ~-structure.

Thermal histories for different parts of the kitchen were modelled in "pseudo wells" in the kitchen area selected from seismic lines. The modelled thermal histories at different locations (and thus at different depths) turned out to be almost identical to the thermal histories at corresponding depths at pseudo well x [see Fig. l(b)]. The modelled transformation ratios vs depth in pseudo well x could thus be applied in the entire kitchen area. The modelled thermal histories were used as input to a module which simulates hydrocarbon generation by a series of first order kinetic reactions. The transformation ratios predicted by this modelling were subsequently applied in volumetric calculations following the principles of Cooles et al. (1986).

Modelling the hydrocarbon potential of the Egersund Sub-basin was carried out in two phases. The first consisted of a sensitivity analysis. Each of the 22 key input parameters to the calculations were assigned a probability distribution, and the effect of "extreme" values of the input parameters were examined by varying only one parameter at a time, keeping the other parameters fixed at their best value. Tectonic heat flow vs. time was adjusted (with equal amounts at all times) to fit the calibration temperature in the pseudo well in each simulation. The determination of the probability distribution for each parameter (including the extreme values used for the sensitivity analysis) is discussed in the appendix.

A random number generator was then used to draw a value for each parameter, according to the probability distribution specified for that parameter.

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Some of the parameters were assigned (partial) dependence on other parameters. A large number of input files was created by this procedure. Each file was then modelled by Geosim, and statistical analysis could be applied to the modelling results. The final

outcome of this kind of modelling gives a cumulative probability distribution of the calculated volumes of hydrocarbons generated, migrated and charged to the 9/2 ~,-structure, as opposed to single numbers describing these volumes.

Modelling hydrocarbon generation and migration 393

Z~ Transformation r a t i o

o o .o o o .~

Porosity vs depth, chalk , ~

Porosity vs aepth. ~ ,

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Fig. 3. The sensitivity of changes (A) in transformation ratio to variations within "extreme" ranges of some input par-

ameters.

M O D E L L I N G R E S U L T S / D I S C U S S I O N

Sensitivity analysis

Figure 3 displays the results of the sensitivity analysis for the transformation of kerogen. The parameters which contribute most to errors in the transformation ratio are activation energies, virgin rock temperature (for the calibration of heat flow) and depth conversion, even though the estimated standard deviations for both depth conversion and virgin rock temperature are moderate compared to what may be encountered in other areas. Each of these three parameters may cause the modelled transformation ratio to vary with +0.3 or more, which will have serious implications for the volumetric calculations.

The accuracy of the calculated transformation ratio can only be significantly improved if all of these three parameters can be better constrained. The presence of temperature data from deep drill stem tests will increase the accuracy of the estimated virgin rock temperature significantly (Hermanrud et al., 1990). Continuing research on conversion of kerogen to hydrocarbons is aimed at reducing the inaccuracy of modelled kerogen degradation. This research is still in its infancy (as demonstrated by Dahl and Yukler, 1990) but is progressing rapidly. The accuracy of depth conversion of sparsely drilled areas is limited by the accuracy of interval velocities picked from seismic stacking velocities. The determination of interval velocities is an area of current research among geophysists.

One interesting result was that assessment of the paleo heat flow turned out to be a significant, but not a major source of error. As the source rocks are not presently at their maximum temperature, determination of paleo heat flow will influence the modelled maximum temperature of the source rocks. The modelled paleo temperatures are, however, more dependent on the virgin rock temperature used for calibration of the heat flow and the errors in the depth conversion than on the choice of stretching model and on the input parameters to these models. It is also of interest to note the significant influence of paleo seabed temperatures, which, as a rule, are not regarded as a major source of error.

The modelled transformation ratio turned out to be rather insensitive to changes in porosity and thermal conductivity. This moderate sensitivity results from the fact that the modelled heat flow in each simulation was required to match the virgin rock temperatures at a depth of 3550 m, which is only 200 m shallower than the depth to which the figures of Fig. 3 are referred. This relationship is demonstrated by Fig. 4, which shows transformation ratio vs. depth for simulations with high and low thermal conductivity.

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Fig. 4. Transformation ratio vs depth for two different sets of thermal conductivity.

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394 C. H ~ r ~ u o et al.

The sensitivity of the modelled volumes of generated hydrocarbons are displayed on Fig. 5. The mean value for the modelled quantity of generated hydrocarbons (to be discussed later) is 139. 106Sm3; the difference between the high and low estimates for each set of input parameters is divided by this number to derive the values at the y-axis at Fig. 5. Changes in only one of the parameters (initial hydrocarbon potential, source rock area, transformation ratio and source rock thickness) can result in the calculated, generated quantities changing by about 100%. These results testify that volumetric calculations of generated hydrocarbons should be treated with caution.

The modelled volumes of recoverable hydrocarbons from the 9/2 v-structure are even more sensitive to changes in input parameters than was the case for modelling of the generated hydrocarbons (Fig. 6). The values on the y-axis of Fig. 6 were established in the same manner as for Fig. 5, using 10.7.106 Sm 3 as the mean value for recoverable hydrocarbons. The parameters which were most critical in the calculations of hydrocarbon generation are also the most critical to the calculation of recoverable hydrocarbons. As the additional uncertainties which are introduced when hydrocarbon migration is modelled are secondary compared to the uncertainties due to parameters involved in the calculation of hydrocarbon generation, the quantification of hydrocarbon generation in the Egersund Sub-basin seems more uncertain than the quantification of loss of hydrocarbons by migration.

The huge impact of variations in the presumed initial source rock potential on the volumes of recoverable hydrocarbons should be noted. The sensitivity to this parameter is large because a modelled

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Fig. 5. The sensitivity of changes (A) in generated hydrocarbons to variations within "extreme" ranges of some input

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Fig. 6. The sensitivity of changes (A) in recoverable hydrocarbons to variations within "extreme" ranges of some input

parameters.

improvement in source rock quality does not imply extra modelled loss of hydrocarbons (given that hydrocarbons do reach the structure), and so all of the extra potential will result in a modelled extra charge to the structure. Increases in modelled source rock area and thickness do, on the other hand, not only result in a larger modelled supply of hydrocarbons, but also imply that a larger rock volume must be saturated with hydrocarbons before the structure is reached. The modelled recoverable hydrocarbons in the 9/2 7-structure were 26.10 6 and 0.8.10 6 S m 3

using the high and low values for initial source rock potential.

Stochastic modelling

The 40 input files prepared for the thermal modelling gave the frequency distributions as shown in Fig. 7(a) (temperature) and Fig. 7(b) (present day heat flow). The temperature distribution is mainly due to variations of the input values for depth conversion and virgin rock temperature, with minor influence from the variation of thermal conductivity. Note that the present day heat flow values are determined by calibration of the modelled temperatures to the virgin rock temperature. The heat flow (Q) is dominantly governed by Fourier's law (Q =-2~T/~z) . As the overall thermal gradient (AT/Az) only varies by +8% due to variations of virgin rock temperatures needed for heat flow calibration, while the thermal conductivities (2) are varied by 50% in the input files, the present day heat flows of Fig. 7(b) mainly reflect changes in thermal conductivity. As these variations in thermal conductivity have only a minor influence on the modelled transformation ratios (Fig. 3), the large spread of present day heat flow shown by Fig. 7(b)

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has indeed a limited impact on the modelled hydrocarbon generation.

The transformation ratio for each of the 40 input files were plotted vs depth [Fig. 8(a)]. The outcomes of Fig. 8(a) show a slight bimodality, with relatively few calculated values in the transformation ratio range of 0.25--0.75. Such a bimodality was expected, as the conversion of kerogen to hydrocarbons takes place over a relatively narrow temperature range (i.e. they are in most cases either immature with a low transformation ratio, or nearly exhausted with a high transformation ratio). The transformation

ratios of Fig. 8(a) were grouped in four different depth intervals [Fig. 8(b)], for the purpose of being used as input parameters to the volumetric calculations (together with the other input parameters required for the volumetric calculations (see the Appendix)). The volumetric calculations were performed by latin hypercube sampling over 500 itera- tions. The results of these simulations are displayed in Figs 9(a)-9(d).

The cumulative probability distributions for generated and primary migrated hydrocarbons, as well as those for hydrocarbon charge to the structure and

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396 C. HERMANRI.rD et al.

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' ,~0 ' ~0 ' ~o ' ~o ~" ~ ,go Hydrocarbon charge to structure, 10SSm • Recoverable hydrocarbons, 10eSm a

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Median= 2.8.10eSm a

Fig. 9. Results from stochastic modelling. (a) Generated hydrocarbons; (b) primary migrated hydrocarbons; (c) hydrocarbon charge to the 9/2 y-structure; (d) recoverable hydrocarbons in the 9/2 y-structure

(provided that reservoir capacity is not exceeded).

recoverable hydrocarbons show a significant high side potential, implying that the medians are less than the mean values. Note that the high side potential for recoverable hydrocarbons should not be used in petroleum economic evaluations if it exceeds the trapping capacity of the structure: such a value suggests that hydrocarbons have spilled out of the trap.

The mean value for recoverable hydrocarbons is 10.7.106 Sm 3, while a single simulation using only the most likely value for each parameter gave 6.8' 106Sm 3. Figure 9(c) shows a 40% chance for no hydrocarbons having entered the 9/2-1 y-structure, while the probability of making a discovery of 24.106 Sm 3 (the size postulated after the 9/2-1 discovery) is about 15%. The same set of parameters were subsequently applied to the 9/2-~ structure, giving a 70% chance for no hydrocarbon charge to that structure, with a mean value of 2.106 Sm 3. This structure was drilled by the 9/2-2 well which did not encounter producable hydrocarbons.

C O N C L U S I O N S

A combination of deterministic and stochastic modelling has been applied to the evaluation of the hydrocarbon potential of the Egersund Sub-basin, treating the Tau Formation as the only source rock

which contributes to the charge of the 9/2 y-structure. The modelled frequency distributions of recoverable hydrocarbons in the 9/2 y-structure were not in disagreement with the hydrocarbon accumulation encountered in the 9/2-1 discovery. Although the median value for the modelled recoverable hydrocarbons was minute, the mean value was half of the officially estimated recoverable hydrocarbons, with a 15% chance of finding more than this estimate. On the other hand, the probability of no hydrocarbon charge to the 9/2-2 structure was calculated to be 70%. This structure proved to be dry when drilled by the 9/2-2 well.

The large uncertainties attached to volumetric calculations clearly demonstrate that results from such modelling should be treated with caution, and that one should not rely on volumetric estimates based on the best set of parameters only. The modelling uncertainties reported in this study are probably moderate estimates of the true uncertainties, as the possibilities of wrong geological concepts (e.g. lack of source or reservoir rock) have not been addressed here.

The uncertainties of the modelling results can only be reduced by constraining the parameters to which the modelling results are most sensitive, i.e. source rock properties and extent, mechanisms for primary and secondary migration, determination of chemical


parameters which describe the degradation of kerogen to hydrocarbons, depth conversion of the kitchen areas and virgin rock temperatures used to calibrate the present day heat flow. There is a need for research within all of these fields.

Acknowledgements--We thank Anthony M. Spencer for useful comments and for correcting the English, Brit Sissel Todnem and Thor Oliversen for preparing the figures, and Statoil for allowing us to publish the results of this study.

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Ungerer P., Chiarelli A. and Oudin J. L. (1985) Modelling of petroleum genesis and migration with a bidimensional computer model in the Frigg sector, Viking Graben. In Petroleum Geochemistry in Exploration of the Norwegian Continental Shelf (Edited by Thomas B. M. et al.), pp. 121-130. Graham & Trotman, London.

Yiikler A. M., Cornford C. and Welte D. H. (1978) One- dimensional model to simulate geologic, hydrodynamic and thermodynamic development of a sedimentary basin. Geol. Rundschau 67, 960-979.

A P P E N D I X

Description of Input Parameters and their Uncertainty

The stochastic modelling was based on the determination of probability distributions for several parameters. These distributions were given as percentiles, where the pth percentile P is determined such that p % of the parameter values are smaller than P, and (I00 - p ) % of the parameter values are larger than P. The concept of percentiles was adapted because it can be used for normal as well as non-normal distributions. The 16th and 84th percentiles describe the interval covered by + one standard deviation


97.501 perceriBe

84th percentile

!

2.5~ percentile

Random number

Fig. AI. Work sheet for the determination of parameter values. Numbers (~t) between 0 and 100 are drawn for each parameter by a random number generator, the intersection between the curve and x = at determines the parameter value to be used in the simulation. The generation of one single input file requires the determination of several parameters

by this procedure.

for a normally distributed parameter, and the 2.5th and 97.5th percentiles in this case describe the interval covered by + two standard deviations.

The stochastic modelling was performed by drawing random numbers • between 0 and I00, and then picking the parameter value corresponding to the ~th percentile. The parameter values for the 2.Sth, 16th, 50th, 84th, and 97.5th percentiles were determined for each parameter, and the parameter values for other percentiles were found by interpolation/extrapolation. The work sheet of Fig. AI was found to be suitable for this interpolation/extrapolation, as the curve of Fig. A- 1 maps the parameter values linearly on the y-axis for normal distributions. This feature of Fig. A1 is specially convenient here, as most of the parameters were assigned nearly normal distributions.

The determination of the probability distributions for the parameters is of unquestionable importance to the modelling results. While some of the parameters have a well defined value with a known uncertainty, such as the virgin rock temperature (Hermanrud, 1988), the probability distributions of other parameters are not precisely known. Some of these parameters were simulated using a triangular probability distribution, while other parameters were assigned percentiles based on insufficient data sets.

The volumetric considerations of this study were based on the method of Cooles e t al. (1986). This method requires that the source rock is saturated with hydrocarbons (given by source rock porosity, hydrocarbon saturation in the pores of the source rock) before expulsion occurs. As this product is supposed to correspond to the S~ value measured in shaly source rocks, this study requires an estimate $1 as an input parameter instead of the product of Cooles e t al. (1986).

The chosen approach of saturating the source rock with a given volume before expulsion occurs, as opposed to retaining a given fraction of the generated hydrocarbons in the source rocks, favours the migration of hydrocarbons from rich source rocks (such as the Tau Formation). This study therefore only considers expulsion from the Tau Formation, despite the results of Ritter e t al. (1987), who claimed that only 10-15% of the generated hydrocarbons in the Egersund Sub-basin are derived from the Tau Formation. This limitation may lead to an underestimation of the hydrocarbon charge to the 9/2 3'-structure.

20.

15. /v~

10-

5.

150 1(~0

gT.~ m

e4th p~eemb

5 0 t h ~

2.Sth ~ /

"time, Ma

Fig, A2. Probability distribution of seabed temperature vs time as input to the stochastic modelling.

The parameters for porosity were based on local experience in the area, with the exception of the extreme values for shale porosity, which were taken from Rieke and Chilingarian (1974) (their Fig. 17). The thermal conductivities were based on the measurements of Bailing e t al. (1981) and measurements performed for Statoil. No overpressure was modelled, and the effects of the moderate fluid overpressure were accounted for while determining the parameters of the porosity equation. Uncertainties concerning paleo-overpressuring were accounted for by increasing the error limits of the paleo heat flow. The rocks overlying the Upper Jurassic are mainly shales and chalks, and only these rock types were modelled. The specific heat and density of the sediment grains were kept constant through- out, as previous experience had demonstrated that the influence to the modelling results of variations of these parameters are minute in the Egersund Sub-basin.

The seabed temperatures (Fig. A2) were taken from Nilsson (1972) and Seyfert and Sirkin (1979), and the deviations from the best values were determined by considering the present day variations of surface temperatures at a given latitude.

The tectonic heat flow vs time curves of Fig. A3 were taken from a McKenzie-type modelling (McKenzie, 1978) of the Egersund Sub-basin. The error bands were determined by varying parameters in the stretching model within reasonable limits and by accounting for the possibility of an incomplete physical description inherent in the stretching model.

Figure A4 shows the contributions from the transient effects of rapid subsidence to the heat flow. The curves were

6 5 -

" % \ | 55 , - m - .

Time, Ma

Fig. A3. Probability distribution of heat flow vs time from tectonic modelling.

0 E

.~ - 2

o -3=

"1~ -4 . g 0 - s -

Modelling hydrocarbon generation and migration

1

97.5th ~ l e

.time, Ma

Fig. A4. Probability distribution of heat flow perturbations due to rapid sediment deposition.

determined by modelling with Geosim; the error bands were derived by varying parameters such as lithospheric thickness, lithospheric heat capacity and radioactive heat production within the crust. The curves of Figs A3 and A4 were treated as independent crustal parameters in this study, although both depend on parameters such as lithe- spheric specific heat. The possible errors due to this treat- ment are minute, however.

The input parameters and their extreme low and high values are listed in Table AI. The columns for low/high value denote the parameter range where a triangular distribution is applied, the median values for these parameters have been marked with an asterisk. The columns for low/high values otherwise list the 2.Sth and 97.5th percentile respectively for the parameters.

The uncertainty in the depth conversion was derived from the mismatch between a linear time vs depth plot and corresponding time/depth relationships for individual wells. However, although the uncertainties of the depth conversion are a few 100 m in this particular case, depth conversion in kitchen areas are frequently even less accurate. Table A2 shows the depth to eight different kitchens in another area as deduced from four different (independent) seismic interpretation/depth conversion studies. The deviation between the different interpretations are in places of the order of 1 km. Errors of such magnitudes can completely invali- date all results from basin modelling.

The virgin rock temperature used for the heat flow calibration was derived from 8 wells in the area, although most emphasis was put on the deep temperature measurements of Well 17/10-1, where a (bias-corrected) temperature of 125 + 5°C was estimated from well logs.

The values for Sl, porosity of the carrier bed, thickness of the carrier bed, fraction of hydrocarbons migrating from the Tau Formation, thickness of the source rocks, initial S2, source rock density and kitchen area variations were determined from inspection of geological and geochemical data in the area. The values for saturation of carrier beds and hydrocarbon density were taken from England et al. (1987).

The activation energies for hydrocarbon generation were taken from unpublished Statoil work, which predicts a

399

Table AI. Input parameters with uncertainties as applied in this study. C) and C~ are factors in the porosity vs effective stress equation, ;~ is the matrix thermal conductivity, VRT is the virgin rock temperature applied to

calibrate the present day heat flow

Depth conversion, m

VRT at 3500m, "C

C1, shale 10 ?' Pa -1

C1, chalk 107. Pa ~~

C2, shale

C=, chalk

k shale, W/m "C

k chalk, W/m "C

Activation energy (mode) kcal/mol

$1 gHc/g,o¢~ Porosity of carrier bed, %

Saturation of carrier bed, %

Vledlar

125

3.5

1.8

45

5O

1.5

3.3

56

0.006

15"

1"

Thickness of carrier bed, m 150

Migration to carder bed, % 75*

Thickness of source rock, m 45

Initial potential, guclg~o¢~ 0.03*

Hydrocarbon density g/cm s 0.55

Source rock density g/cm 3 2.4

Kitchen area variations, %

Low High value value

- 2 0 0 +200

115 135

2.0 9.8

1.3 2.7

40 50

45 55

0.8 2.2

2.9 3.7

52 6O

0.003 0.009

5 2O

5 10

100 20O

50 100

15 75

0.015 0.05

0.45 0.65

2.2 2.6

- 6 0 +60

Table A2. Depths to different local kitchens in an area as derived from four independent seismic interpretation/depth conversion

studies. See test for further explanation

I~tchen no. 1 2 3 4 5 6 7 8

Study A 48OO 49OO 38OO 42O0 4800 43OO 5OOO 560O

Study B 4800 4700 - - - • 4200 540O 5900

Study C 4600 5100 4100 4500 5600 . - - • 5700 6100

Study D 5300 5700 3700 4400 6200 3500 • 5300 ] - - • I

rather narrow distribution of activation energies with a frequency factor of 5.3. I0 ~4 s -t. The postulated probability distribution reflects analytical uncertainty concerning the derivation of activation energies from laboratory analysis, the fact that the measurements were not performed on the Tau Formation, and that the source rock facies distribution in the kitchen is poorly known. The probability distribution of the activation energies also accommodates the uncertainties concerning the effects of heating rate, mineralogy and fluid pressure on hydrocarbon generation. The frequency factor was kept constant during the simulations, and the probability distribution of the activation energies was designed to compensate for this simplification. Our use of the term "activation energy" does thus not refer to a well defined parameter for a given chemical reaction, but rather to a single number which conveniently describes the total uncertainty attached to the rate of hydrocarbon generation.

The heat flow was not calibrated to maturity parameters in this study, partly because of the imprecise knowledge of the uncertainty of these maturity parameters, and partly because of the calculated moderate influence of paleo heat flow uncertainty on the calculated hydrocarbon volumes.

on the accuracy of modelling hydrocarbon generation and migration: the egersund basin oil find,...

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