The ease and ability to predict sintering shrinkage and densification with the Skorohod-Olevsky viscous sintering (SOVS) model within a finite-element (FE) code have been improved with the use of an Arrhenius-type viscosity function. The need for a better viscosity function was identified by evaluating SOVS model predictions made using a previously published polynomial viscosity function. Predictions made using the original, polynomial viscosity function do not accurately reflect experimentally observed sintering behavior. To more easily and better predict sintering behavior using FE simulations, a thermally activated viscosity function based on creep theory was used with the SOVS model. In comparison with the polynomial viscosity function, SOVS model predictions made using the Arrhenius-type viscosity function are more representative of experimentally observed viscosity and sintering behavior. Additionally, the effects of changes in heating rate on densification can easily be predicted with the Arrhenius-type viscosity function. Another attribute of the Arrhenius-type viscosity function is that it provides the potential to link different sintering models. For example, the apparent activation energy, Q, for densification used in the construction of the master sintering curve for a low-temperature cofire ceramic dielectric has been used as the apparent activation energy for material flow in the Arrhenius-type viscosity function to predict heating rate-dependent sintering behavior using the SOVS model.

Summary Geologic, and historical well failure, production, and injection data were analyzed to guide development of three-dimensional geomechanical models of the Belridge diatomite field, California. The central premise of the numerical simulations is that spatial gradients in pore pressure induced by production and injection in a low permeability reservoir may perturb the local stresses and cause subsurface deformation sufficient to result in well failure. Time-dependent reservoir pressure fields that were calculated from three-dimensional black oil reservoir simulations were coupled unidirectionally to three-dimensional nonlinear finite element geomechanical simulations. The reservoir models included nearly 100,000 gridblocks (100 to 200 wells), and covered nearly 20 years of production and injection. The geomechanical models were meshed from structure maps and contained more than 300,000 nodal points. Shear strain localization along weak bedding planes that causes casing doglegs in the field was accommodated in the model by contact surfaces located immediately above the reservoir and at two locations in the overburden. The geomechanical simulations are validated by comparison of the predicted surface subsidence with field measurements, and by comparison of predicted deformation with observed casing damage. Additionally, simulations performed for two independently developed areas at South Belridge, Secs. 33 and 29, corroborate their different well failure histories. The simulations suggest the three types of casing damage observed, and show that, although water injection has mitigated surface subsidence, it can, under some circumstances, increase the lateral gradients in effective stress that in turn can accelerate subsurface horizontal motions. Geomechanical simulation is an important reservoir management tool that can be used to identify optimal operating policies to mitigate casing damage for existing field developments, and applied to incorporate the effect of well failure potential in economic analyses of alternative infilling and development options. Introduction Well casing damage induced by formation compaction has occurred in reservoirs in the North Sea, the Gulf of Mexico, California, South America, and Asia.1–4 As production draws down reservoir pressure, the weight of the overlying formations is increasingly supported by the solid rock matrix that compacts in response to the increased stress. The diatomite reservoirs of Kern County, California, are particularly susceptible to depletion-induced compaction because of the high porosity (45 to 70%) and resulting high compressibility of the reservoir rock. At the Belridge diatomite field, located ~45 miles west of Bakersfield, California, nearly 1,000 wells have experienced severe casing damage during the past ~20 years of increased production. The thickness (more than 1,000 feet), high porosity, and moderate oil saturation of the diatomite reservoir translate into huge reserves. Approximately 2 billion bbl of original oil in place (OOIP) are contained in the diatomite reservoir and more than 1 billion bbl additional OOIP is estimated for the overlying Tulare sands. The Tulare is produced using thermal methods and accounts for three-quarters of the more than 1 billion bbl produced to date at Belridge.5 Production from the diatomite reservoir is hampered by the unusually low matrix permeability (typically ranging from 0.1 to several md), and became economical only with the introduction of hydraulic fracturing stimulation techniques in the 1970's.6 However, increased production decreased reservoir pressure, accelerated surface subsidence, and increased the number of costly well failures in the 1980's. Waterflood programs were initiated in the late 1980's to combat the reduced well productivity, accelerated surface subsidence, and subsidence-induced well failure risks. Subsidence rates are now near zero; however, the well failure rate, although lower than that experienced in the 1980's, is still economically significant at 2 to 6% of active wells per year. In 1994 a cooperative research program was undertaken to improve understanding of the geomechanical processes causing well casing damage during production from weak, compactable formations. A comprehensive database, consisting of historical well failure, production, injection, and subsidence data, was compiled to provide a unique, complete picture of the reservoir and overburden behavior.7,8 Analyses of the field-wide database indicated that two-dimensional approximations9–11 could not capture the locally complex production, injection, and subsidence patterns, and motivated large-scale, three-dimensional geomechanical simulations. Intermediary results for Sec. 33 that used preliminary reservoir flow and material models were reported earlier.8 This paper presents results for best-and-final simulations that used improved reservoir flow models, more sophisticated material models, and activated contact surfaces. The simulations were performed for two independently developed areas at South Belridge, Secs. 33 and 29.

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Geologic, and historical well failure, production, and injection data were analyzed to guide development of three-dimensional geomechanical models of the Belridge Diatomite Field, California. The central premise of the numerical simulations is that spatial gradients in pore pressure induced by production and injection in a low permeability reservoir may perturb the local stresses and cause subsurface deformation sufficient to result in well failure. Time-dependent reservoir pressure fields that were calculated from three-dimensional finite difference reservoir simulations were input into three-dimensional nonlinear finite element geomechanical simulations. The reservoir models included nearly 100,000 gridblocks (100-200 wells), and covered nearly 20 years of production and injection. The geomechanical models were meshed from structure maps and contained more than 300,000 nodal points. Shear strain localization along weak bedding planes that causes casing dog-legs in the field was accommodated in the model by contact surfaces located immediately above the reservoir and at two locations in the overburden. The geomechanical simulations are partially validated by comparison of the predicted surface subsidence with field measurements, and by comparison of predicted deformation with observed casing damage. Further, simulations performed for two independently developed areas at South Belridge, Sections 33 and 29, corroborate their different well failure histories. The simulations suggest the three types of casing damage observed, and show that although water injection has mitigated surface subsidence, it can, under some circumstances, increase the lateral gradients in effective stress, that in turn can accelerate subsurface horizontal motions. Geomechanical simulation is an important reservoir management tool that can be used to identify optimal operating policies to mitigate casing damage for existing field developments, and also applied to incorporate the effect of well failure potential in economic analyses of alternative infilling plans and operating strategies. P. 403

This paper describes an integrated geomechanics analysis of well casing damage induced by compaction of the diatomite reservoir at the Belridge Field, California. Historical data from the five field operators were compiled and analyzed to determine correlations between production, injection, subsidence, and well failures. The results of this analysis were used to develop a three-dimensional geomechanical model of South Belridge, Section 33 to examine the diatomite reservoir and overburden response to production and injection at the interwell scale and to evaluate potential well failure mechanisms. The time-dependent reservoir pressure field was derived from a three-dimensional finite difference reservoir simulation and used as input to three-dimensional non-linear finite element geomechanical simulations. The reservoir simulation included 200 wells and covered 18 years of production and injection. The geomechanical simulation contained 437,100 nodes and 374,130 elements with the overburden and reservoir discretized into 13 layers with independent material properties. The results reveal the evolution of the subsurface stress and displacement fields with production and injection and suggest strategies for reducing the occurrence of well casing damage. Introduction Well casing damage induced by formation compaction has occurred in reservoirs in the North Sea, the Gulf of Mexico, California, and Asia. As production draws down reservoir pressure, the weight of the overlying formations is increasingly supported by the solid rock matrix that compacts in response to the increased stress. The diatomite reservoirs of Kern County, California are particularly susceptible to depletion-induced compaction because of the high porosity (45-70%) and resulting high compressibility of the reservoir rock. The Belridge Field, located about 45 miles west of Bakersfield, California, recently attained billion-barrel status and is currently the fifth most productive field in the US. The thickness (more than 1000 feet), high porosity, and moderate oil saturation of the diatomite reservoir translate into huge reserves, with more than 3 billion bbl of original-oil-in-place estimated for the Belridge Field. However, 75% of production to date has been from the overlying Tulare sands. Production from the diatomite reservoir is hampered by the unusually low matrix permeability (-0.1 mDa or less). Although the Belridge Field was discovered in 1911, production from the diatomite reservoir became economical only with the introduction of hydraulic fracturing stimulation techniques in the mid-1970's. However, increased production decreased reservoir pressure, accelerated surface subsidence, and increased the number of costly well failures in the 1980's. Waterflood programs were initiated in the late 1980's to combat the reduced well productivity, accelerated surface subsidence, and subsidence-induced well failure risks. Subsidence rates are now near zero; however, the well failure rate, although lower than that experienced in the 1980's, is still economically significant at 2-5% of active wells per year. In 1994 a cooperative research program was undertaken to improve understanding of the geomechanical processes leading to well casing damage during production from weak, compactable formations. The study focuses on the Belridge Field and represents a significant extension of earlier work in two regards. First, a comprehensive data base was compiled to provide a unique, complete picture of the reservoir and overburden behavior. Second, the results of the field-wide analysis motivated large-scale three-dimensional numerical simulations. P. 195