Restricted SR.15.11335 Induced seismicity in the Groningen field - statistical assessment of tremors along faults in a compacting reservoir by H.M. Wentinck This document is classified as Restricted. Access is allowed to Shell personnel, designated Associate Companies and Contractors working on Shell projects who have signed a confidentiality agreement with a Shell Group Company. ‘Shell Personnel’ includes all staff with a personal contract with a Shell Group Company. Issuance of this document is restrictedto staff employed by a Shell Group Company. Neither the whole nor any part of this document may be disclosed to Non-Shell Personnel without the prior written consent of the copyright owners. Copyright Shell Global Solutions International, B.V., 2015. Shell Global Solutions International B.V., Rijswijk Further electronic copies can be obtained from the Global Information Centre. SR.15.11335 - I - Restricted Executive Summary In this report, we present a statistical model to understand and predict the tremor rates and magnitudes from trends in the past at a local scale following from oil/gas producing reservoirs. The local scale can be a small gas field or a region of several square kilometers of a large field, such as the Groningen field. The state-driven model supposes that the tremors are generated along the faults in the region of interest. These faults become critically stressed during the compaction of the reservoir in which the reservoir pressure drops. Herewith, the state which triggers the tremors is the mean stress-state along the faults in this region. The model is executed as a Monte Carlo simulation and uses stochastic variables which are related to probabilities that a tremor occurs and that it has a certain magnitude. The relative likelihood of a seismic fault failure depends on the Weibull distribution func- tion. The tremor rates are normalised to the observed tremor rates using the Poisson probability distribution function. The seismic moments of the tremors follow from a Pareto distribution function, as is commonly done when analysing of natural and man- made induced seismicity. The model includes that the tremors reduce the mean stress on the faults in proportion to the seismic moment released. The model does not differentiate between a-seismic and seismic fault slip based on field or fault attributes. This could be seen as a shortcoming but we have no clue what this could be, so far. The model has been applied to 6 relatively small regions in the Groningen field and in the Annerveen and Eleveld fields south of the Groningen field. The model fit parameters have been derived from these regions by comparing the modelled and observed tremors. A sensitivity study has been done and the predictive potential of the model has been explored. The fit parameters of the model, τfail and cM0 have values which can be understood and constrained from geomechanical calculations. τfail is a typical mean shear stress along the faults for which the relative likelihood for seismic fault failure substantially increases. cM0 relates the mean stress reduction along the faults by the tremors generated by uniaxial compaction. Remarkable is the high value of the Weibull shape parameter kW in relation to variations in parameters for rock properties and fault geometry which determine the onset of shear- type fault failure. The Weibull shape parameter determines the period of the transition from no tremors to a constant tremor rate in the case of a constant compaction rate. It’s high value may indicate that the tremors are predominantly determined by only a few of these parameters or by another mechanism that differs from a-seismic slip. The present model cannot reproduce the drastic reduction in the tremor rate in the Eleveld field by a mean field stress relaxation process. This could point to a shortcoming SR.15.11335 - II - Restricted in the submodel for the stress relaxation or to a shortcoming in the submodel for the generation of the tremors. The latter submodel is driven by the Poisson process and the Weibull distribution probability distribution function for the relative likelihood of a tremor. Presumably, the Poisson process expression which normalises the number of tremors should include a term related to the rate of compaction. With reservations, we illustrate that the model has some predictive power about tremor rates in a certain region, using the observed tremors in this region in the previous period. In essence, the state-driven model consistently reproduces the gradual onset of the tremor rate followed by a more or less constant tremor rate. Taking a constant and uniform pres- sure drop over the Groningen field, it must be noted that the model does not capture a small but significant increase in the tremor rate over the last three to four years in the regions around Ten Boer and Loppersum. We found no correlations between the regional variation of the observed tremor den- sity and the fault dip angle, fault throw and fault azimuth angle in the Groningen field. A remarkable observation is that most tremors with a minimum magnitude of M = 2.5 can be associated with faults with high dip angles of about 70◦ and throws of about 100 m, see Appendix C. These faults could potentially release most of the stored energy from compaction and the imbalance between the field stresses, see Appendix B, B.2. § We recommend to follow the effects of local gas production reductions in the Gronin- gen field to validate and improve this model, especially in relation to the possible effect of stress relaxation by tremors. The present model does not differentiate between seismic and a-seismic fault slip because we do not know yet which field or fault attributes are determining here. If this knowledge becomes available, it could be used to constrain the model parameters further. Table of Contents 1 Introduction 6 2 Model 9 2.1 Assumptionsandequations . 9 2.1.1 Assumptions............................... 9 2.1.2 Stressstate ............................... 10 2.1.3 Therelativelikelihoodofatremor . 11 2.1.4 Frequency-magnitude-relation-of-tremors . ........ 13 2.2 Energy release by tremors and mean stress reduction . ........ 13 2.2.1 Liberatedenergy,slipandstress . 13 2.2.2 Reduction in the mean shear stress along the faults in the region of interestbytremors .. ... .. .. .. .. ... .. .. .. .. ... 17 2.2.3 Relationwithobservations . 18 2.3 Relation between frequency-magnitude relationship and the asperity dis- tribution..................................... 19 2.3.1 Otherb-values ............................. 20 2.4 Pareto, Weibull and Poisson probability distributions ............ 22 2.4.1 Paretodistribution .. ... .. .. .. .. ... .. .. .. .. ... 22 2.4.2 Weibulldistribution . ... .. .. .. .. ... .. .. .. .. ... 23 2.4.3 Poissondistribution. 23 2.5 Application of the Weibull distribution for the probabilityoftremors . 25 3 Application of the model to the seismic activity in the Groningen, Annerveen and Eleveld fields 28 3.1 Fielddata .................................... 28 3.2 Tremordata................................... 29 3.3 Regionsofinterest ............................... 30 3.4 Results...................................... 35 3.5 Theeffectofthesizeoftheregion. 55 3.6 The effect of the stress relaxation parameter cM0 ............... 59 3.6.1 Eleveldfield............................... 59 3.6.2 Otherfields ............................... 61 3.6.3 Loppersumfield............................. 62 III SR.15.11335 - IV - Restricted 3.7 Predictivepotentialofthemodel . 71 4 Discussion 73 5 Acknowledgements 75 APPENDICES 80 A Failure condition for a fault 81 A.1 Stress changes in the reservoir due to isotropic elastic deformation . 81 A.2 Shearcapacityutilisation. 83 A.3 Failurecriterionparameters . 87 B Deformation around typical reservoir offsets 94 B.1 Deformationaftercompaction . 98 B.2 Energyreleaseduetofaultfailure . 112 B.2.1 Theory-elasticmedia . .112 B.2.2 Theory-poro-elasticmedia . 115 B.2.3 Setupofthecalculations . .117 B.2.4 Results..................................121 B.3 Stress relaxation parameter cM0 ........................129 B.3.1 Typical constants for the stress relaxation parameter cM0 . 129 B.3.2 Reductionofthemeanshearstress . 129 C Reservoir and fault data 132 C.1 Groningenfield .................................132 C.2 AnnerveenenEleveldfields . 147 D KNMI data about tremors in the Groningen, Annerveen and Eleveld fields 149 Bibliographic Information and Report Distribution 176 BibliographicInformation . 176 ReportDistribution.. .. .. ... .. .. .. .. ... .. .. .. .. ...177 SR.15.11335 - 1 - Restricted Table 0.0.1 : List of frequently used symbols Symbol Property Unit ............... .......................................................................................................... .................. b b-value of the Gutenberg-Richter frequency-magnitude law - cM0 geometric constant relating seismic moment to stress reduction Pa/J cf geometric constant relating fault length to fault density in field - cσv geometric constant relating vertical stress to mean shear stress Pa −1 Cm uniaxial compaction coefficient Pa d constant in the asperity size-frequency relationship - D mean seismic slip distance m Df mean distance between faults in selected area m E Young modulus of rock Pa ES seismic energy J ET liberated gravitational and elastic energy of the system by slip J Fel strain-energy or free elastic energy J 0 3 Fel strain-energy density or free elastic energy density J/m g constant of gravitation m/s2 hres reservoir thickness m H poro-elastic constant - kW