SUMMARYThe boundary integral equation method is used for the solution of three-dimensional elastostatic problems in transversely isotropic solids using closed-form fundamental solutions. The previously published point force solutions for such solids were modiÿed and are presented in a convenient form, especially suitable for use in the boundary integral equation method. The new presentations are used as a basis for accurate numerical computations of all Green's functions necessary in the BEM process without inaccuracy and redundant computations. The validity of the new presentation is shown through three numerical examples.

Summary During hydraulic-fracturing operations, conventional pressure-falloff analyses (G-function, square root of time, and other diagnostic plots) are the main methods for estimating fracture-closure pressure. However, there are situations when it is not practical to determine the fracture-closure pressure using these analyses. These conditions occur when closure time is long, such as in mini-fracture tests in very tight formations, or in slurry-waste-injection applications where the injected waste forms impermeable filter cake on the fracture faces that delays fracture closure because of slower liquid leakoff into the formation. In these situations, applying the conventional analyses could require several days of well shut-in to collect enough pressure-falloff data during which the fracture closure can be detected. The objective of the present study is to attempt to correlate the fracture-closure pressure to the early-time falloff data using the field-measured instantaneous shut-in pressure (ISIP) and the petrophysical/mechanical properties of the injection formation. A study of the injection-pressure history of many injection wells with multiple hydraulic fractures in a variety of rock lithologies shows a relationship between the fracture-closure pressure and the ISIP. An empirical equation is proposed in this study to calculate the fracture-closure pressure as a function of the ISIP and the injection-formation rock properties. Such rock properties include formation permeability, formation porosity, initial pore pressure, overburden stress, formation Poisson's ratio, and Young's modulus. The empirical equation was developed using data obtained from geomechanical models and the core analysis of a wide range of injection horizons with different lithology types of sandstone, carbonate, and tight sandstone. The empirical equation was validated using different case studies by comparing the measured fracture-closure-pressure values with those predicted by using the developed empirical equation. In all cases, the new method predicted the fracture-closure pressure with a relative error of less than 6%. The new empirical equation predicts the fracture-closure pressure using a single point of falloff-pressure data, the ISIP, without the need to conduct a conventional fracture-closure analysis. This allows the operator to avoid having to collect pressure data between shut-in and the time when the actual fracture closure occurs, which can take several days in highly damaged and/or very tight formations. Moreover, in operations with multiple-batch injection events into the same interval/perforations, as is often the case in cuttings/slurry-injection operations, the trends in closure-pressure evolution can be tracked even if the fracture is never allowed to close.

The high cost of offshore drilling and the safety aspects of penetrating depleted reservoirs bring borehole stability issues to the forefront of resource development. Drilling in deepwater fields, depleted reservoirs and/or low stress environments requires careful assessment of mud weights. Higher collapse pressures combined with lower fracture gradients limit or eliminate mud weight windows and lead to tight holes or lost circulation. Extended-reach wells require minimization of the number of casing shoes to reach the deeper targets. The need for long, open sections while drilling imposes restrictions on mud windows. Borehole strengthening has become the most effective method to address borehole stability in such circumstances. In this paper, we provide geomechanics insights from the large knowledge base on waterflooding and injector performance to improve the practice of wellbore strengthening. The petroleum industry has morphed over its long history through fewer inventions but a long list of innovations derived from lessons learned from one sector to benefit another. Injector plugging, a nuisance to production/operation engineers, illustrates such an example. The vast amount of knowledge provides the fundamental reasoning and rationale for optimizing wellbore strengthening. Fractured injector geomechanics are extended to improve wellbore strengthening procedures. Strengthening is implemented through creation of plugged minifractures to raise loss circulation pressures. The mud contains particles to mitigate unstable fracture extension created by using higher mud weights. The particles deposit and plug initiated fractures and prevent further propagation. The propagation pressure is raised significantly and lost circulation stops. In the presented model, the stable fracture length and width are related to a given mud weight and rock characteristics. Accordingly, the plugging media (particle) size is optimized based on the fracture geometry and leakage scenarios. The model results are field-verified and demonstrate how the borehole stability problem could be optimized with proper design.

Underground injection of slurry in cycles with shut-in periods allows fracture closure and pressure dissipation which in turn prevents pressure accumulation and injection pressure increase from batch to batch. However, in many cases, the accumulation of solids on the fracture faces slows down the leak off which can delay the fracture closure up to several days. The objective in this study is to develop a new predictive method to monitor the stress increment evolution when well shut-in time between injection batches is not sufficient to allow fracture closure. The new technique predicts the fracture closure pressure from the instantaneous shut-in pressure (ISIP) and the injection formation petrophysical/mechanical properties including porosity, permeability, overburden stress, formation pore pressure, Young's modulus, and Poisson's ratio. Actual injection pressure data from a biosolids injector have been used to validate the new predictive technique. During the early well life, the match between the predicted fracture closure pressure values and those obtained from the G-function analysis was excellent, with an absolute error of less than 1%. In later injection batches, the predicted stress increment profile shows a clear trend consistent with the mechanisms of slurry injection and stress shadow analysis. Furthermore, the work shows that the injection operational parameters such as injection flow rate, injected volume per batch, and the volumetric solids concentration have strong impact on the predicted maximum disposal capacity which is reached when the injection zone in situ stress equalizes the upper barrier stress.

Carbon offset describes the environmental benefit from an initiative that avoids, reduces or removes greenhouse gases (GHGs) from the atmosphere. The Intergovernmental Panel on Climate Change has identified Carbon Dioxide (CO2), Methane (CH4) and Nitrous Oxide (N2O) as major constituent of the GHGs. Wastewater Treatment Facilities (WWTFs) among several other sectors is a neglected source for GHG emission. Considering the risk of rise in GHGs, United States along with other countries signed the Paris Agreement to respond to the global climate change threat in 2016. It is assessing projects to cut GHGs in exchange for emission credits that can be used to comply with goals they set under the United Nations pact. In order to curb the GHG emission by WWTFs, an innovative approach "Bioslurry Injection" (BSI) can be implemented to reduce the emission of the GHGs produced during the course of biological and chemical treatment of wastewater. The technology is inherited from the traditional drill cutting injection and Carbon sequestration technology implemented by the Oil and Gas industry since 1980's. The BSI operation has the ability to accept the feed from different treatment stages after the initial screening process to prepare the injection slurry and help in controlling the GHG emission at respective treatment stage along with managing the intake volume. The slurry can be prepared by mixing the treated biosolids with wastewater and injected into a pre-selected underground earth formation, where biosolids undergo anaerobic digestion and decompose into CO2 and CH4. An injection formation with sufficient capacity to accept the slurry is selected by conducting a detailed geomechanical and fracture simulation analyses. Along with the injection feasibility, the calculations of the amount of Carbon dioxide equivalent (CO2e) sequestrated underground by implementing BSI technique is presented in this paper. The sequestration of decomposed GHGs is an environmentally friendly activity that has proved to be economically beneficial due to its ability to earn carbon offsets. According to the new carbon law in the state of California the amount of CO2e eliminated from the atmosphere can be traded to earn carbon credits. TIRE facility through its ability to sequester and thus eliminate emission of the GHGs from the atmosphere can gain up to $1.5M worth of carbon credits per year providing both environmental and economic benefit. Also, low capital and operating cost for the BSI facility due to its compact surface requirement is an additional advantage along with reduced risk of spillage hazard when BSI facility is incorporated within the WWTF boundaries.