A New Method to Investigate Rheology of Zechstein Salt at Rest Through Inverting the Sinking of Stringer Fragments

SHIYUAN LI et.al: A NEW METHOD TO INVESTIGATE RHEOLOGY OF ZECHTEIN SALT AT REST THROUGH …

A New Method to Investigate Rheology of Zechstein Salt at Rest through Inverting the Sinking of Stringer Fragments

Shiyuan Li*, Yuekun Xing

School of Petroleum engineering, China University of Petroleum, Beijing, 102249, P.R. China

Abstract - There is a heated debate about the long-term rheology of salt at rest. As many researches show, pressure solution creep and dislocation creep mechanisms dominate mechanical behavior of salt. We summarize the database of researches of salt rheology for the first time. A new method is used to evaluate salt rheology through inverting the gravitational sinking of anhydrite inclusions (also called ‘stringers’) embedded in Zechstein salt at rest during the Tertiary. Seismic data can be used to compare with numerical model of sinking stringer. Results show that under the control of dislocation creep, the fragments has almost no movement but under the control of pressure solution creep, the fragments will sink obviously through the salt section during a few Ma (some fragments can sink hundreds of meters and touch the presalt). In conclusion, through inverting the sinking of stringer fragments the long-term Zechstein salt rheology can be investigated and dislocation creep dominates its deformation during Tertiary.

Keywords - long-term rheology, pressure solution creep, dislocation creep, gravitational sinking of stringer, Zechstein salt.

E-mail: [email protected] I. INTRODUCTION of the salt, A is a material dependent parameter, Q is the 0 specific activation energy while R is the gas constant Rocksalt and salt structure have strong relationship with (R=8.314Jmol-1k-1) and T is the temperature. Moreover, petro-geology and petroleum engineering. Since 1980s in solution-precipitation creep (pressure solution) is also an last century, a lot of geologists have studied on salt important deformation mechanism in rocksalt and it is structure due to oil and gas exploration. Many geologists, shown in the previous researches [4, 28-29].The mechanism researchers of rock mechanics and petroleum or mining solution-precipitation creep is described following as a engineers concentrated on the studies of creep property of Newtonian flow law: rocksalt. Chinese researchers have widely applied the  achievement of the study on creep deformation and damage nnQ 13 PS BB()  exp()(  ) (2) on the establishment of salt carven and drilling engineering 0 RT TDm of salt-gypsum layer. In this paper, we first build the and the strain rate is dependent on the strain size D, Δσ = database of salt rheology mechanism through the methods σ1-σ3 is the differential stress and B= B0 exp(-Q/RT)/TDm of laboratory experiment, microstructure observation and is the viscosity of the salt, B0 is a material dependent displacement analysis in active salt tectonics. We parameter, Q is the specific activation energy while R is the summarized two dominant deformation mechanisms. gas constant (R=8.314Jmol-1k-1) and T is the temperature. The order m influences the strain rate dependence on the In the last 30 years, some researches have been grain size. Finally, the total strain rate are the sum of the operated on the deformation mechanism of rocksalt at a two strain rates: range of temperatures (20-200°C). Dislocation creep    [1-17] mechanisms are widely investigated . In the salt mining    DC   PS  industry, salt deformation is controlled by dislocation creep mechanism which is shown laboratory experiments [18-27]. It is clearly demonstrated in Figure. (1) that relation The steady-state strain rate follows power-law creep (non- between strain rate and differential stress in these Newtonian) equation: experiments are controlled by power-law equation with the  power order 5 which is relevant to dislocation creep when nnQ   DC AA() 013 exp()()    the salt deforms at 30°C to 200°C [26, 30-34]. At each RT temperature value, the strain rate can increase 2 or 3 orders has been used where έDC is the strain rate, Δσ =σ1-σ3 is the of magnitude at the same differential stress. The data in differential stress and A=A0exp(-Q/RT) is the viscosity Figure 2 shows that the salt rheology is dependent on three important factors for wet halite deformation, the grain size, *Address correspondence to this author at the School of Petroleum water content and temperature. engineering, China University of Petroleum, Beijing, 102249, P.R. China; Tel: +86 10 89739073; Fax: +86 10 89734150;

DOI 10.5013/IJSSST.a.17.46.38 38.1 ISSN: 1473-804x online, 1473-8031 print SHIYUAN LI et.al: A NEW METHOD TO INVESTIGATE RHEOLOGY OF ZECHTEIN SALT AT REST THROUGH …

Figure 1. The relation between strain rate and differential stress of coarse grain at 20-200°C

Figure 2. The relation between strain rate and differential stress of wet fine and coarse grain at 20-200°C

Due to time scale constraint in the experiment, it is density difference between the salt and anhydrite inclusion, rather difficult to realize the deformation process with the the stringers can sink towards the bottom of the salt bodies. strain rate below 10-9s-1, in figures we put two creep laws as One major issue contributing to the complexity of the not only comparison but also an extrapolation of the data problem are the rheological differences between the salt, the which were observed in the experiments. The rheology of embedded carbonates and the sediments overlaying the salt slow deformation is controversial. body. A few numerical studies about the salt deformation of salt structures has been implemented [35-38]. In salt II. SIMULATION ON METHODS AND MODELS structures, there are carbonate or anhydrite inclusions In nature, large anhydrite inclusions, called stringers, embedded and the movement and displacement of are embedded in salt structure. In our study, a very inclusions are researched [38-42]. Since there is obvious

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Figure 3. (a) East–West seismic profile through the study area with the stringer interpolation surface A (black, dashed line) and the smoothed surface B (white, dashed line) and (b) its interpretation figure. In (b), blue represents the Z2–Z4 salt section between the pre-salt, brown the Basal Zechstein, Rotliegend and Carboniferous and yellow the sedimentary overburden. Note the differences in Z3 stringer geometry west and east of the central salt wall related to structural features of the Top Salt

TABLE I. MATERIAL PARAMETERS FOR ANHYDRITE AND ROCKSALT (FOLLOWING THE TWO DIFFERENT DEFORMATION MECHANISMS AT 50° C (I.E. LOWER LIMIT OF THE MODEL))

Salt A: Pressure solution creep Salt B: dislocation creep (Non- Anhydrite

(Newtonian flow) newtonian flow) blocks

-4 -1 -1 -9 -5 -1 A0 4.70×10 MPa s 1.802×10 MPa s - Q [J/mol] 24530 53920 - R [J/mol] 8.314 8.314 - m,n 3/1 0/ 5 - ρ/density [kg/m3] 2200 2200 2900 E/Youngs Modulus [GPa] 10 10 40 ν/ Poisson's ratio 0.4 0.4 0.3 Reference [28] [26] [46] On average the Zechstein salt thickness above the stringer is important process is anhydrite stringer (or stringer less than fragments) can sink at a certain speed until the bottom of salt body due to the density contract between salt and that below (Figure. (3)), and hence the stringer mostly anhydrite rock. We use commercial software ABAQUS to occurs close to or at the Top Salt. The study area is located build numerical model and we model gravitational sinking in the Dutch offshore (area introduced as ‘western off- of stringer in Zechstein salt with two different dominant shore’[43]) on the Cleaver Bank High. These basins were laws after salt tectonic stopped. The numerical results can inverted in the Cretaceous and Tertiary [44]. All the stringer be used to compare with seismic data. The seismic data we fragments embedded in the Zechstein salt should reach the use is provided [43, 44]. The study by van Gent et al. bottom of salt body if the stringer can sink rapidly due to (2011) has already shown that the on average 40–50 m gravitational loading [43, 44]. thick Z3 stringer has a complex structure dominated by It is an effective method to investigate salt rheology boudinage and folding, frequently offset vertically over through inverting stringer sinking in salt [45]. The results of more than half of the total Zechstein thickness (Figure. (3)). movement and stress around stringer can be compared to

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the seismic data. We choose typical value of mechanical properties for salt and embedded stringer in Table 1. We built a simplified model of the Zechstein salt section with physically isolated stringer fragments of 50m thickness A initial model and 100, 200, 300m width embedded in a 10km width and 500m thickness salt section similar to Figure. (3) (observed by the research [44]). The model is 2D plane strain.The boundary conditions are zero displacement perpendicular to the boundary at the bottom and at the sides. Here we only model the time period after tectonic setup, the Zechstein B -60Ma salt at rest in Tertiary. Modeling the breakup of stringers is not necessary in the research [38].This post-tectonic setup is simulated about a time span of 60 Ma to simulate the Zechstein salt at rest in the Tertiary. Table 2 summarizes the geometric parameters used for the stringer fragments, the salt section and the time duration of experimental C -30Ma phases.

TABLE II. GEOMETRICAL AND TEMPORAL MODEL SETUP

Width of salt body 16 km Height of salt body 1 km D 0Ma Stringer fragment thicknesses 30, 50, 80 m Stringer fragment widths 100,200, 300 m Figure. 4: Model A shows the position of sinking stringer fragment in salt Amplitude down-building 300 m (n=1). A: initial model setup after salt tectonics; B: Model A after salt Duration salt tectonics 4 Ma tectonics (-60 Ma); C: Model A after salt tectonics (-30 Ma); D: Model A Duration salt at rest 60 Ma after salt tectonics (today)

III. RESULTS A initial model Figure. (4)a and (5)a show the initial model setup with No.1-9 stringer fragments. The gravitational sinking causes a rotation of some of the elongated stringer fragments for the Newtonian salt (Model A; Figure. (4)B-C), while those in the salt with n=5 (Model B; Figure. (5)B-C) remain more B -60Ma or less in place. Figure. (4)D and (5)D show the final results of the model with stringer fragments. Figure. (4)show that the stringer fragments sinks significantly on the left sides, and the velocity of the stringer fragment No.1 (small stringer fragment) is 6m/Ma. The stringer fragment No. 2 rotates and moves downwards from -60Ma to 0Ma and the C -30Ma stringer fragment No. 3 rotates strongly and sinks vertically, finally touch the bottom boundary. The stringer fragment No. 5 and stringer fragment No. 6 have limited distance between each other and the distance constraints the downwards movements. The stringer fragment No. 7, No. 8 and No. 9 are very close to the right boundary, due to the D 0Ma boundary condition the gravitational sinking are also restricted. Fig 5D shows the stringer fragments remain more or less in place, and they have almost no movement.Figure.6 shows that the differential stress around Figure 5: Model B shows the position of sinking stringer fragment in salt the stringer is 0.2MPa and this value occurs after the stress (n=5). A: initial model setup after salt tectonics; B: Model A after salt relaxation when tectonics stops. tectonics (-60 Ma); C: Model A after salt tectonics (-30 Ma); D: Model A after salt tectonics (today)

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evaluate long-term rheology during slow deformation in nature. The long-term rheology of Zechstein salt at rest is controlled by dislocation creep mechanism.

ACKNOWLEDGEMENTS

We thank Heijn van Gent, Frank Strozyk for their previous research of embedded stringers in Zechstein Salt.

REFERENCES

[1] Carter, N. L. and Hansen, F. D. 1983. Creep of rocksalt. Tectonophysics, 92(4), 275-333. [2] Carter, N. L., Horseman, S. T., Russell, J. E. and Handin, J. 1993. Rheology of rocksalt. Journal of Structural Geology, 15(9-10), 1257- 1271. Figure 6: Close up of stringer fragments No. 1 (the left stringer) after salt [3] Rutter, E. H. 1983. Pressure solution in nature, theory and relaxation (-50Ma). experiment, J.Geol. Soc., 140, 725-740. [4] Urai, J. L., Spiers, C.J., Zwart, H. J. and Lister, G. S. 1986. Weakening of rock salt by water during long-term creep. Nature, 324, 554 - 557. IV. DISCUSSTION [5] Wawersik, W. R. and Zeuch, D. H. 1986. Modeling and mechanistic interpretation of creep of rock salt below 200°C. Tectonophysics, 121(2-4), 125-152. [6] Heard, H. C. and Ryerson, F. J. 1986. Effect of cation impurities on It is obviously shown that the value of differential steady-state flow of salt: B.E. Hobbs and H.C. Heard, Editors, stress around stringer fragments embedded in salt at rest is Mineral and Rock Deformation: Laboratory Studies, AGU very low (around 0.1-0.2MPa). The sinking velocities Geophysical Monograph Series, 36, 99-115. linearly changes for the case of the Newtonian flow, and [7] Senseny, P. E., Hansen, F. D., Russell, J. E., Carter, N. L. and Handin, J. W. 1992. Mechanical behaviour of rock salt: nonlinearly changes for the case of non-Newtonian flow. Phenomenology and micromechanisms. International Journal of The results show that the stringer fragments in the salt Rock Mechanics and Mining Sciences and Geomechanics Abstracts, following pressure solution creep (Newtonian law and n=1) 29(4), 363-378 sink significantly and ground the salt section within [8] Van Keken, P. E., Spiers, C. J., Van den Berg, A. P. and Muyzent, E. Tertiary. In contrast, stringer fragments embedded in the J. 1993. The effective viscosity of rocksalt: implementation of steady-state creep laws in numerical models of salt diapirism. salt following dislocation creep (non-Newtonian law and Tectonophysics, 225(4), 457-476. n=5) remain the place without obvious sink displacement [9] Franssen, R. C. M. W. 1994. The rheology of synthetic rocksalt in after tectonics. Comparing the model results to the seismic uniaxial compression. Tectono- physics, 233(1-2), 1-40. data of the Dutch Zechstein (Figure. 3), we can see all the [10] Peach, C. J. and Spiers, C. J. 1996. Influence of crystal plastic stringer fragments remains in the upper or mid part of the deformation on dilatancy and permeability development in synthetic salt rock. Tectonophysics, 256(1-4), 101-128. salt. This situation is similar to the results as the model with [11] Weidinger, P., Hampel, A., Blum, W. and Hunsche, U. 1997. Creep dislocation creep law following n=5 shows. behaviour of natural rock salt and its description with the composite model. Materials Science and Engineering, 234, 646-648. [12] De Meer, S., Spiers, C. J., and Peach, C. J. 1997. Pressure solution creep in gypsum: Evidence for precipitation reaction control. Physics V. CONCLUSIONS and Chemistry of The Earth, 22(1-2), 33-37. [13] Hampel, A. 1998. Description of the creep of rock salt with the composite model - II. Steady state creep. Aubertin, M., Hardy Jr., H. We have modeled the gravitational sinking of Z3-4 R. (Eds.), The Mechanical Behavior of Salt IV; Proc. of the 4th stringer fragment in salt after tectonics. Results show that Conf., (MECASALT IV), Montreal 1996. Trans Tech Publications, the sinking velocities of anhydrite inclusions in salt at rest Clausthal: 287-299. are strongly dependent on the rheology of the surrounding [14] Brouard, B. and Bérest, P. 1999. A tentative classification of salts according to their creep properti-es. Laboratory of solid mechanics salt. Results also show that the stringer fragments have in Ecole Polytechnique obvious movement and rotation in the salt controlled by [15] Bérest, B., Blumb, P. A., Charpentiera, J. P., Gharbia, H and Valesa, dislocation and pressure solution creep. Some stringers F. 2005. Very slow creep tests on rock samples. International Journal have reached the base of the salt section during the time of Rock Mechanics and Mining Sciences, 42, 569-576 [16] Ter Heege, J. H., De Bresser, J. H. P. and Spiers, C. J. 2005a. span. However, the stringer fragments embedded the salt Dynamic recrystallization of wet synthetic polycrystalline halite: following dislocation creep has minor sinking during the dependence of grain size distribution on flow stress, temperature and time span due to the very low differential stresses (0.1- strain. Tectonophysics, 396(1-2), 35-57. 0.2MPa) around the fragments. It can be concluded that the [17] Ter Heege, J. H., De Bresser, J.H.P. and Spiers, C. J. 2005b. Rheological behaviour of synthetic rocksalt: the interplay between modeling of gravitational loading of Z3 stringer (anhydrite water, dynamic recrystallization and deformation mechanisms. blocks) based on the simplification from seismic data can Journal of Structural Geology, 27(6), 948-963

DOI 10.5013/IJSSST.a.17.46.38 38.5 ISSN: 1473-804x online, 1473-8031 print SHIYUAN LI et.al: A NEW METHOD TO INVESTIGATE RHEOLOGY OF ZECHTEIN SALT AT REST THROUGH …

[18] Ottosen, N. S. 1986. Viscoelastic-viscoplastic formulas for analysis [33] DeVries, K. L. 1988. Viscoplastic Laws for Avery Island Salt. Report of cavities in rock salt. Inter- national Journal of Rock Mechanics for Stone Webster, RSI-0333, RE/SPEC, Inc., Rapid City, S.D. and Mining Sciences and Geomechanics Abstracts, 23(3), 201-212 [34] Hunsche, U., Schulze, O., Walter, F. and Plischke, I. 2003. Projekt [19] Haupt, M. and Schweiger, H. F. 1989. Development of a constitutive Gorleben: Thermomechanisches Verhalten von Salzgestein model for rock salt based on creep and relaxation tests. Computers [35] Schultz-Ela, D. D. and Jackson, M. P. A. 1993. Evolution of and Geotechnics, 7(4), 346-346 extensional fault systems linked with salt diapirism modeled with [20] Aubertin, M., Gill, D. E. and Ladanyi, B. 1991. An Internal variable finite elements. AAPG Bulletin, 77, 179 model for the creep of rocksalt, Rock Mechanics and Rock [36] Van Keken, P. E. 1993. Numerical modeling of thermochemically Engineering, 24(2), 81-97 driven fluid flow with non-Newtonian rheology: applied to the [21] Cristescu, N. D. 1993. A general constitutive equation for transient Earth's lithosphere and mantle. Faculty of Geosciences. Utrecht, and stationary creep of rock salt. International Journal of Rock Utrecht University. PhD. Mechanics and Mining Sciences and Geomechanics Abstracts, [37] Koyi, H. 1996. Salt flow by aggrading and prograding overburdens. 30(2), 125-140 In: I.Alsop, D. Blundell and I. Davison (eds.), Salt Tectonics. [22] Munson, D. E. 1979. Constitutive model for the low temperature Geological Society Special Publication, 100: 43-258 creep of salt (with application to WIPP). Technical Report, [38] Li, S., Abe, S., Reuning, L., Becker, S., Urai J.L. and Kukla, P.A. SAND79-1853, Sandia National Laboratories, Albuquerque, NM 2012a. Numerical modeling of the displacement and deformation of [23] Munson, D. E. 1997. Constitutive model of creep in rock salt applied embedded rock bodies during salt tectonics - a case study from the to underground room closure. International Journal of Rock South Oman Salt Basin, in: Alsop, I. (eds), Salt tectonics, sediments Mechanics and Mining Sciences, 34(2), 233-247 and prospectivity. Geological Society Special Publication, 363: 503- [24] Jin, J. and Cristescu, N. D. 1998. An elastic/viscoplastic model for 520 transient creep of rock salt. International Journal of Plasticity,14(1- [39] Van der Bogert, V. D. 1998. In-situ stress assessment of intra-salt 3), 85-107. stringers. Society of Petroleum Engineers. The SPE/ISRM Eurock [25] Hampel, A. 2007. The Composite Dilatancy Model: A constitutive ’98 in Trondheim Norway model for the mechanical behavior of rock salt, in: Proceeding of 6th [40] Chemia, Z., Koyi, H. and Schmeling, H. 2008. Numerical modelling Conference of the Mechanical Behavior of Salt - Understanding of of rise and fall of a dense layer in salt diapirs. Geophysical Journal THMC Processes in Salt: 99-107. International, 172(2), 798-816 [26] Hunsche, U. and Hampel, A. 1999. Rock salt - the mechanical [41] Chemia, Z. and Koyi, H. 2008. The control of sat supply on properties of the host rock material for a radioactive waste entrainment of an anhydrite layer within a salt diapir, Journal of repository. Engineering Geology, 52(3-4), 271-291. Structural Geology, 30(9): 1192-1200 [27] Peach, C. J., Spiers, C.J. and Trimby, P. W. 2001. Effect of confining [42] Chemia, Z. and Schmeling, H. 2009. The effect of the salt viscosity pressure on dilatation, recrystallization, and flow of rock salt at on future evolution of the Gorleben salt diapir, Germany, 150°C. Journal of Geophysical Research, 106, 315-328. Tectonophysics, 473(3-4): 446-456 [28] Spiers, C. J., Schutjens, P. M. T. M., Brzesowsky, R. H., Peach, C. J., [43] Van Gent, H., Urai, J. L. and De Keijzer, M. 2011. The internal Liezenberg, J. L.and Zwart, H. J. 1990. Experimental determination geometry of salt structures - a first look using 3D seismic data from of constitutive parameters governing creep of rocksalt by pressure the Zechstein of the Netherlands. Journal of Structural Geology, 33, solution, in: Knipe, R.J., Rutter, E.H. (Eds.), Deformation 292-311 Mechanisms, Rheology and Tectonics. Geol. Soc. London, Spec. [44] Strozyk, F., van Gent, H., Urai, J. L. and Kukla, P. A. 2012. 3D Publ., 54, 215-227. seismic study of complex intra-salt deformation: an example from [29] Martin, B., Röller, K. and Stoeckhert, B. 1999. Low-stress pressure the Zechstein 3 stringer in the western Dutch offshore, in: Alsop, I. solution experiments on halite single-crystals. Tectonophysics, (eds), Salt tectonics, sediments and prospectivity. Geological Society 308(3), 299-310 Special Publication, 363: 489-502. [30] Heard, H. C. 1972. Steady-state flow in polycrystalline halite at [45] Li, S., Strozyk, F., Abe, S., Van Gent, H., Kukla, P. and Urai, J. L. pressure of 2 kilobars: H.C. Heard, I.Y. Borg, N.L. Carter and C.B. 2012b. A method to evaluate long-term rheology of Zechstein salt in Raleigh, Editors, Flow and Fracture of Rocks. AGU Geophysical the Tertiary. In: Proc. 7th Conference on the Mechanical Behavior of Monograph Series, 16, 191-210. Salt (Bérest, Ghoreychi, Hadj-Hassen and Tijani), 215-220. [31] Wawersik, W. R. and Hannum, D. W. 1980. Mechanical Behavior of [46] Sayers, C. M. 2008. The elastic properties of carbonates, Leading New Mexico Rock Salt in Triaxial Compression Up to 200°C. Edge, Schlumberger, Houston, TX, United States. Society of Journal of Geophysical Research, 85, 891-900. Exploration Geophysicists, Tulsa, 27(8):.1020-1024. [32] Hansen, F. D. and Carter, N. L. 1984. Creep of Avery Island rocksalt, in: Proceedings of the First Conference on Mechanical Behavior of Salt. Clausthal-Zellerfeld, Germany. Trans Tech Publications: 53-69.

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