Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol.30, No.7, pp. 1205-1208, 1993 0148-9062/93 $6.00 + 0.00 Printed in Great Britain Pergamon Press Ltd

Pore Pressure Change and Compaction in North Sea Chalk Hydrocarbon Reservoirs MERVYN JONES" ERIC MA'FHIESEN""

INTRODUCTION

Production of hydrocarbons from reservoirs formed in late-Cretaceous and Danian chalks in the central North Sea graben began in 1971 and has continued until the present. These oil fields (which include the large Ekofisk Field) were highly overpressured with initial overburden effective stresses in the range 5-15 MPa at a nominal depth of 3 km [1]. P roduc t ion has been accompanied by pressure depletion and today the largest of these reservoirs (Ekofisk) is suppor t ing an overburden effective stress of the order of 38 MPa [2]. The chalk is a weak rock with a strength that is primarily dependent upon the extent to which its open coccolith structure has been thrilled with sparry calcite cement [3]. The highest porosity reservoir chalks (40-50% pore space) are barely cemen ted and they exhibit a pronounced transition from dominantly elastic to ductile ( irrecoverable) compaction behaviour at effective stresses only slightly greater than those prevailing at the outset of fluid production. This change in behaviour (yield) is accompanied by very pronounced increases in compressibility [3]. However, chalks of lower porosity are also present within the reservoirs (20-30% pore space) and these should not yet have experienced effective stress increases commensurate with their laboratory determined yield strength [2]. Obviously as reservoir pressures have been reduced chalks of progressively lower porosity will have reached the yield condition [4]. The reduction in pressure associated with production of hydrocarbons has thus led to compaction of the reservoir rocks in a number of these reservoirs which, in the case of Ekofisk, has led to substantial displacements of the sea floor [4].

BACKGROUND

The subsidence problem at Ekofisk was first recognised in 1984 and has been the subject of considerable research activity in subsequent years. This has included evaluating the mechanical behaviour of the chalk [3,5], improved reservoir description and the construction of numerical models to enable predictions of future subsidence to be made [4]. These models have generally followed normal geotechnical practice, using reservoir pressure changes to alter the effective stress

^ I)cpurlmcnl of (/cological Sciences. University College l,~m- don.Gower SII-cl21. | ,ondon W( 'II ! 61~'I'. U.K.

Norwegian Petroleum I)ireclot';ltc. Prof. OI;tv ! lansscnsvci IlL P.(). Ilox 600. N4001 NltlVilllgCl', Norway.

6

1 2"

1975 1985 1995 Year

Fig. 1 Measured and pt~cdictcd sea floor subsidence over thcEkofisk oil field.

acting on the modelled reservoir, thereby simulating compaction. NO attempt has yet been made to simulate the complex, pressure-dependent, behaviour of the reservoir fluids in a coupled manner with the compaction even though in reality, reservoir fluid behaviour, pressure change and compaction will be intimately related. Simulations of the compaction and subsidence at Ekofisk undertaken in the period 1985- 1988 gave results that were in good agreement with the measured subsidence and predicted that subsidence rates would decline appreciably in the period 1988-1992 as the rate of change of reservoir pressure became small (Figure 1) [1]. Unfortunately, and despite the earlier good agreement of the subsidence models, subsidence rates have not declined and the predictions no longer conform with the field behaviour (Figure 1) even though the rate of change of reservoir pressure has declined in the anticipated manner (Figure 2). Thus surface subsidence appears to be accelerating with respect to reservoir pressure change (Figure 3).

60"

~ 5 0 "

30-

2O

Y ~

Iqg. 2 ( 'hungc in lilt;tin rc~,.:l'VOil pl'C~.',,tlft; Ihf()UgJl tdtllC d~a,..: I~'J the rpl'Od~.l,~'lh'~n o f fh~id~, f rom Ihc I:k~f'ink ~il Iwld.

1205

1200 ROCK MECHANICS IN THE 1990s

t 2-

1-

0 ! ! ! ! ! 0 5 10 15 20 25

Fig. 3 Surface subsidence as a function of rese,voir pressure change ifor the lnglewood and F, kofisk oil fields.

The data in figure 3 imply is that the reservoir chalk is becoming weaker as it compacts. This contradicts the laboratory determined mechanical behaviour which shows that as the chalk densities through compaction it also hardens . This d icho tomy has led to a re- examination of the mechanical behaviour of the chalk rock mass with the proposition that shear deformation and stress intensification due to shear along existing fractures are increasing compaction [6]. Some shear deformations are undoubtedly occurring within the Ekofisk reservoirs although the extent of this effect is unknown. It is however unlikely that the reservoir as a rock mass is deforming under conditions other than those close one-dlmensional compaction.

The relationship between change in reservoir pressure and surface subsidence (figure 3) is not unique to Ekofisk. Published data for subsidence over the Inglewood Oilfield in California [7] also show an apparent weakening of the deforming system (Figure 3) which is remarkably similar to that exhibited by Ekofisk. It is also commonly the case that almost l inear relationships exist between the net volume of fluids extracted from compacting reservoirs and subsidence (Figure 4) [7,8]. Comparison of the data in Figure 3 with those in Figure 4 indicate that the assumption, that change in reservoir pressure is the cause of the

8000

4000 ~ ' ~

O.OE4 O0 2.0E+ 08 4.0E+ 08 Fluid Extraction (eu. rnetres)

Fig.4 Surface subsidence as a function of the volume olexwacted 11uids for the lnglewood, Wilmington and [:.kofisk oll fields.

compaction strain, as the net fluid volume is reduced may be incorrect.

To investigate this it is necessary to dosely examine the appropriate field data for Ekofisk to more accurately define the physical character of this deforming system, The preliminary status of this investigation is reported in this technical note.

~P~UCTION IN ~ FLUID VOLUME AI~D ~ ~ ~ .

Prior to the onset of sea water injection in 1988, the Ekofisk reservoirs received only limited fluid influx so that hydrocarbon production was accompanied by a net reduction in the quantity of fluid occupying the pore spaces in the reservoir rock. This fluid voidage is compensated in two ways: through expansion of the remaining fluids (which is accompanied by a decrease in pore pressure) and through compaction of the reservoir rock. The change in reservoir pressure is given by integrating a simple relationship of general form:-

^P = - O/{PV* (Cpv+Cfl))

where: ^P is the change in reservoir pressure; Q is the volume of fluid removed; PV is the pore volume of the reservoir; Cpv is the pore volume compressibility of the reservoir rock and Cfl is the compressibility of the reservoir fluid. In the majority of hydrocarbon reservoirs the high compressibil i ty of the hydrocarbon fluids dominates the system so that reservoir compaction is relatively minor. However, the behaviour of the Ekofisk reservoir in recent years suggests that the value of Cvv, mobilised by the compacting field, may substantially exceed the value of Cfl mobilised by the remaining pore fluid.

To further develop an understanding of the problem we have taken two approaches. The first is a qualitative analysis of the dynamics of the deforming reservoir system, in which the energy changes commensurate with production and compaction are simply evaluated and equated. The second uses field data to evaluate the pore volume and fluid compressibilities mobifised by the field. Combining these two approaches provides a qualitative explanat ion of the physics of the compact ion phenomenon.

The dynamics of the Ekofisk system can be simply described in terms of the potential energy increase of the voided fluids as they are lifted to the surface, the decrease overburden potential energy as it moves downwards due to compaction and a change in the volume strain energy of the remaining pore fluid which would be positive if the fluid is compressed or negative if the fluid expands. Thus, if all frictional losses are ignored a simple balance should exist between the change in potent ia l energy of the voided fluids (Epotv_id) and the sum of the changes in overburden poten[lVal energy (Epotob) and fluid strain energy (Estrfl) which will depeffcl primarily on the effective

ROCK MECHANICS IN THE 1990s 1207

compressibilities of the reservoir rock and the pore fluid:-

Epotvoid = -(EpOtob + Estrfl).

Of course this is not entirely correct because the movement of fluids to the surface will involve overcoming fr ict ion in the rock and in the wells• However, although these changes are ignored in the present analysis, the results reveal an important aspect of field behaviour.

8]~4-14

8~+J4

4R+14

ZF.+14

r.~ - 2E-I- 14

- 4 E + 1 4

- 8 R + 1 4

- f lEX14 ~0

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . ~'_ . . . . . . . . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . .

. . . . . . . . . . . . . ;:''" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ ' ~ S . . . . . .

~ . a a_ ~ . . . . . ~ / , \ I ,

................ :-~, ....... ..:-~- .... 7 . ~ - -->r ........ I

",, .." \./' -" I ............ J ........ II~-- --- I ........ ~d- ..... . ............... | I

8 0 90 Year

7--~ Epol .vo id -~- k- 'peLob ~ g s t r d l u i d I

Fig. 5 A n n u a l c n c l ' g y c h a n g e s d u e to l h c IlcI f lu id v o i d a g c at l{kofisk.

If the reservoir fluid is incompressible then for any given voidage, the relationship would reduce to:-

Epotvoid = _ EpOtob

where Epotvoid = maSSvoid 2hvoid* g; EpOtob = massob* hob* g; g 9.81 m/sec ; and h = displacement which is positive for upward movements.

These two equations can be solved simply using available field data and changes in the energy terms are recorded both annually and cumulatively against time in figures 5 and 6. The calculated changes in EpOtob can be regarded as representative because they are derived from the mean overburden displacement which is a direct consequence of compaction in the reservoir due to voidage. In achieving this displacement the overburden mass has already overcome its own frictional resistances and the displacement is therefore a direct response to the compression of the reservoir. Conversely the increase in Epotvoid must be regarded is a minimum value for the work required to lift the voided fluids to the surface. Thus, although the energy of the voided fluids will increase by this amount, rather more work will be required of the reservoir f l u i d / o v e r b u r d e n compaction system to move the voided fluids to the surface because of the frictional resistance encountered along the flow path(s). Nonetheless, the difference between Epotvoid and -EpOtob can be regarded as a

v

reasonable estimation of the minimum change in strain energy experienced by the remaining pore fluid. These curves (figures 5 and 6) are interesting because they show that although in early years the strain energy of the fluid is decreasing as it decompresses, indicating that it is doing work to facilitate the voidage, this contribution is seen to decline from 1978 onwards as the mass of the overburden in motion increases. In 1986, this change in fluid strain energy becomes positive for the first time which indicates that the fluid is now recompressing. After 1986, the work done by the moving overburden mass is not only entirely responsible for the increase in Epot in the voided fluids but also for an increase in Estr in the remaining pore fluid•

The volume change experienced by the reservoir thus exceeds the production voidage by an amount equivalent to the recompression of the remaining fluids. This serves to maintain reservoir pressure at an almost constant value and the overburden effective stress remains nominally constant• These effects are also seen when the pore volume and fluid compressibilities, mobilised by the reservoir are determined•

0E+16

6 E + 1 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . > . . . . . . . . . . . . . . .

4 E + 1 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . . /.1¢"

7~1~+ 1,5 . . . . . . . . . . . . . . . . . . . . . . . . - - - ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-4E+15 ~--=~4~_ , ~ . t

"tO 90 8 0

Year [-.,- ~ o t . , o i d - E~,ot.oU --- E~.~J~i--~

Fig. 6 A c c u m u l a t e d e n e r g y c h a n g c s d u e to the net f luid v o i d a g e a t 1 !kof isk .

The pore volume compressibility mobilised by the reservoir can be de te rmined if the conservat ive assumption is made that the compaction volume is equal to the subsidence volume:-

Cpv = (SubSvol/PV)/"P

where: Subsvo 1 is the incremental increase in subsidence bowl volume which accompanies the incremental reduction in reservoir pressure "P. Similarly the compressibility of the entire pore volume/fluid system (C . . . . ) can be obtained by substituting Q (the t.pv + il) void'age) in place of Subsvo 1 in the above equation. The difference between C v and C, v+fl~ is the fluid

• . . P . . P , compresslbdlty actually mobxhsed ~y the reservoir fluid. The annual incrementa l pore volume and fluid compressibilities for Ekofisk are plotted in figure 7. Even though there is considerable scatter in the data for the more recent years (due possibly to changes in

1208 ROCK MECHANICS IN THE 1990s

r e se rvo i r p r o d u c t i o n scenar io ) , the po re vo lume compressibility mobilised by the reservoir has a general tendency to increase through time and is now very large, whilst the mobilised pore fluid compressibility increased until 1982 and then progressively declined in the past five years.

[--- ?uid - ~VGe-volu-rne|

70 80 ~0 Year

Fig. 7 Effective pore volume and fluid compressibilities back-calcu- lated from field data for the Lrkofisk oil field.

D I S C U S S I O N A N D ~ Y CONCLUSIONS.

The simple energy calculations provide a reasonably satisfactory, if qualitative, explanation for the continuing subsidence. Pr ior to 1986 voidage was ba lanced by a c o m b i n a t i o n of f lu id e x p a n s i o n and r e s e r v o i r compaction. But after 1978, the energy from the growing mass of moving rock in the ove rburden increasingly dominated the situation allowing compaction to become the m a j o r v o i d a g e c o m p e n s a t i o n m e c h a n i s m by restricting the expansion of the pore fluid. By 1986 this effect had become sufficiently pronounced that all fluid e x p a n s i o n was s u p p r e s s e d and the p r e v i o u s l y decompressed fluids started to recompress to maintain an appropriate effective stress equilibrium between the reservoir and the overburden. Since that time voidage has b e e n a c c o m p a n i e d by add i t iona l c o m p a c t i o n allowing continuing recompress ion of the remaining fluids so that today the r e se rvo i r rock exhibi ts an anomalously high effective pore volume compressibility which is still increas ing , whilst r e s e rvo i r p r e s su re remains almost constant . Conversely, the fluid is no longer decompressing to compensate voidage so that its effective compressibility now appears to be very low.

Subsidence is thus a direct consequence of voidage and continues in the face of minimal pressure changes. Under such circumstances conventional effective stress based n u m e r i c a l m o d e l s and i n d e e d , l a b o r a t o r y determined rock compressibility data, cannot be u s e d di rec t ly to make p r ed i c t i ons of fu tu re subs idence magnitudes. This is because the reservoir pressure is now maintained through a dynamic interaction with the d i s p l a c e m e n t s in the o v e r b u r d e n a s i t u a t i o n not implemented in the conventional numerical codes used in geotechnical or reservoir modelling.

T h e ana lys i s p r e s e n t e d above is a s i m p l e approximation of a complex system which has revealed previous ly u n r e c o g n i s e d aspects of weak r e se rvo i r behaviour. It shows that in weak rock reservoirs the fluid characteristics and mechanical behaviour are intimately linked. Quantitative modelling and simulation should therefore utilise a fully coupled approach that allows for overburden loading of both the reservoir rock and the pore fluid.

Acknowledgements - The authors wish to thank the Norwegian Petroleum Directorate for permission to publish this article. The views expressed are, however, those of the authors alone.

R E F E R E N C E S

1 Berget O. P., Dretvik 0., Tonstad K. and Mathiesen E. Production of oil and gas from chalk reservoirs in the Norwegian part of the North Sea. In: Proceedings of the International Chalk Symposium. 645-649. Thomas Telford, London (1990).

2 Jones M. E., Leddra M. J. and Potts D. Ground motions due to hydrocarbon production from the chalk~ In: Proceedings of the International Chalk Symposium. 341-347. Thomas Telford, London (1990),

Leddra M. J., Jones M. E. and Goldsmith A. S. Laboratory investigations of the compaction of chalk under conditions of increasing effective stress. In: Proceedings of the Third North Sea Chalk Symposium, June 1990. Session 3, paper 4, 36 pages. NPD, Stavanger (1990).

Potts D, Jones M. E. and Berget O.E Subsidence above the F_,kofisk oil reservoirs. In: Proceedings of the International Conference on the Behaviour of Offshore Structures, 1. (Geotechnics). 113-127. Tapir, Trondheim (1988).

Andersen M. A., Foged N. and Pedersen H. E The rate-type compaction of a weak North Sea chalk. In: Rock Mechanics, 253-262. Balkema, Rotterdam (1992L

Chin L., Boade R., Prevost J. and Landa G. (This Volmne) Numerical simulation of shear-induced compaction in the Ekofisk reservoir. In press.

Castle R.O., Yerkes R. F. and Riley E S. A linear relationship between liquid production and oil field subsidence, In: Land Subsidence, Proceedings of the Tokyo Symposium, ! (1969).

Mayuga M.N. and Allen D.R. Subsidence in the Wilmington oil field, Long Beach, California, U;SA. in: Land Subsidence, Proceedings of the Tokyo Symposium, 1, (1969).