Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

OUTPU T 29 OUTPU T 30 OUTPU T 31 OUTPU T 32 OUTPU T 25 OUTPU T 26 OUTPU T 27 OUTPU T 28 OUTPU T 21 OUTPU T 22 OUTPU T 23 OUTPU T 24 OUTPU T 17 OUTPU T 18 OUTPU T 19 OUTPU T 20 OUTPU T 13 OUTPU T 14 OUTPU T 15 OUTPU T 16 OUTPU T 9 OUTPU T 10 OUTPU T 11 OUTPU T 12 OUTPU T 5 OUTPU T 6 OUTPU T 7 OUTPU T 8 OUTPU T 1 OUTPU T 2 OUTPU T 3 OUTPU T 4 29 30 31 32 25 26 27 28 21 22 23 24 17 18 19 20 13 14 15 16 9

A User’s Guide

The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

/pdf/validity-of-cubic-law-for-fluid-flow-in-a-deformable-rock-2ynq4id3hq.pdf

VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

The flow of homogeneous fluids through porous media: analogies with other physical problems

The present invention relates to engineered multivalent and multispecific binding proteins, methods of making, and specifically to their uses in the prevention, diagnosis, and/or treatment of disease.

Dual variable domain immunoglobulins and uses thereof

Drilling through salt sections requires that the particular properties of salt, its creep behaviour and high solubility, be recognized and incorporated in the drilling plan Salt is a viscous material and creeps under differential stress; the creep rate is a strong function of both temperature and stress difference (actually underbalance between the mud pressure and the vertical stress) A simple model approach to account for these effects in a reasonably quantitative manner is described Problems encountered in drilling through salt include hole closure leading to stuck tools, differential dissolution of beds of carnallite, bischofite and other halides, encountering stiff and non-viscous stringers in salt strata, and exiting salt into non-salt rocks, always a challenging phase of the drilling Strategies for successful salt drilling involve recognizing salt closure behavior, stresses, and adjusting drilling fluid density and temperature to minimize problems Casing design issues in salt are also discussed Figure 1 shows cases ranging from shallow bedded salt to deep diapiric structures In salt tongues (sheets) and bedded salt cases, well trajectory choice is limited, but with diapiric structures, a wide range of drilling trajectory choices exists, including paths which avoid salt altogether, and other paths designed to pass through as much salt as possible Which is chosen depends on the geomechanical state of the rocks surrounding the salt, the depth (T, σ) and creep rate of the salt, and other factors, some experiential, some gleaned from analysis Assuming that salt dissolution issues in the drilling fluid are properly managed, the two major concerns are borehole closure through creep, and borehole instability when exiting salt or in cases of sharp lithology contrasts (eg anhydrite/salt interfaces) Casing point choices must account properly for stresses so that drilling can proceed at low blowout and lost circulation risk To manage drilling risks, it is necessary to: • Determine the in situ conditions, T(z), σ(z) • Choose a suitable constitutive law for creep • Calculate borehole closure rates as functions of depth and activating stress (σv – pb) • Assess the risks and if necessary execute thermal (cooling and heating) calculations • Choose the best mud weight program for the casing program and trajectory • Monitor hole performance and be prepared to modify the program appropriately • Be prepared to act decisively when exiting thick salt structures Figure 1 (Left and Below): Some Conditions Encountered in Drilling Salt 2 IN SITU CONDITIONS 21 Stresses and Temperatures Figure 2 shows a profile of a thick salt tongue in the GoM The temperature is ~0°C at the sea floor, and ~80°C at 55 km subsea In the cases sketched in Fig 1, the geothermal gradient is on the order of 2025°C/km, typical values for sedimentary basins, but there is a lower geothermal gradient, on the order of 15°C/km in the GoM deep offshore area These low T gradients facilitate salt drilling, compared to North Sea cases where gradients within salt approaching 38°C/km have been found Because salt rocks are viscous and flow slowly at all non-zero shear stress states, one may assume that σv = σHMAX = σhmin = z ⋅ γ , where γ is the mean overburden bulk density Careful measurements in mines and LOT or FIT values obtained during salt drilling all tend to confirm this condition Isotropic stresses are only found in viscous rocks and very Z km

Drilling Through Salt: Constitutive Behavior And Drilling Strategies

Wellbore leakage, the seepage of natural gas through cement channels, casing annuli and behind the outermost casing string, is a problem reported across Canada. Wellbore leakage is a threat to the environment and public safety because of potential groundwater quality deterioration, contributions to greenhouse gas emissions and explosion risks if methane gas accumulates in inadequately ventilated areas. Leakage rates remain poorly quantified and remedial workovers are often challenging. Subsequent costs attributed to remedial workovers are often significant and present an economic strain on the industry as well as lost profit, reduced exploration and production and, therefore, foregone royalties. The purpose of this report has been to (1) identify persistent problems that result in wellbore leakage, (2) discuss potential approaches that appear to reduce the rates and occurrences of wellbore leakage, (3) describe methods for detecting and monitoring for wellbore leakage, and (4) discuss methods that have improved the efficiency of remedial workovers. Our motivation has been to outline the need for a Canadian Road Map for Wellbore Integrity that identifies future research and development (R&D) needs and identifies where the resources for such R&D might be found. Several key processes were identified that lead to the potential development of a leakage problem, working to either prevent the initial creation of an adequate cement seal or compromising the integrity of the cement sheath over time. The pathways produced by these processes include microannuli, channels and fractures due to poor mud removal, invasion by fluids during setting, stresses imposed by operations, cement shrinkage and casing corrosion. Intermediate-depth formations, i.e., non-commercial gas zones, are often found to be the source of the buoyant fugitive gases that migrate up these pathways. ‘Doing it right the first time’ – i.e., creating a robust seal during primary cementation – was uniformly agreed by industry and regulators to be the best approach for reducing leakage development over the operational and post-operational lifetime of a well. Even if an adequately sealed wellbore was achieved during primary cementation, there remains the possibility that a leakage problem may develop due to corrosion or cement shrinkage. Therefore, in addition to ‘doing it right the first time’, new cement formulations, wellbore designs and abandonment approaches are needed. Wellbore monitoring needs to be improved by adopting the use of newer technologies and undergoing more thorough subsurface monitoring. Remedial workovers require advances in source identification (such as enhanced acoustic logging technology and isotopic fingerprinting) and alternative-sealing materials. Wellbore leakage will likely only become worse with time as new wells are completed and old wells are abandoned. We recommend that a Canadian working group be established to develop a Road Map for Wellbore Integrity R&D to improve long-term wellbore integrity. Hydraulic fracturing is perceived as a threat by many in the public, however, we believe that this concern is misplaced. Because of the real issues associated with greenhouse gas emissions and possible groundwater quality deterioration, we believe the more significant issue affecting the social license of the oil and gas industry is long-term wellbore integrity.

/pdf/towards-a-road-map-for-mitigating-the-rates-and-occurrences-43xvf312dp.pdf

Towards a Road Map for Mitigating the Rates and Occurrences of Long-Term Wellbore Leakage

Cold Heavy Oil Production with Sand (CHOPS) has been applied with very good success to enhance heavy oil production in Canada, China, Venezuela, and Kazakhstan. Based on existing laboratory and field information and case histories, the most important physical processes enhancing cold production have been reviewed, summarized, and quantified. Several sanding models are developed, including a new porosity cap model for failure propagation as well as a semianalytical elastoplastic stress model coupled with an unsteady pressure model for foamy oils. The mechanisms for oil rate enhancement by CHOPS, such as porosity and permeability enhancement that arise from sand removal, propagation of the elastoplastic (remolded) zone, increase of oil velocity relative to the matrix, and the effects of foamy oil behavior, are quantitatively described and compared. The proposed model can be applied to predict how much additional oil one might expect for a given amount of produced sand. It might also serve as a tool for optimizing cold heavy oil production while nevertheless keeping the sand flux at a low level, which could reduce operating expenses such as limiting sand disposal costs.

/pdf/how-much-oil-you-can-get-from-chops-kf370l6e1u.pdf

How much oil you can get from CHOPS

The cold, remote, northern regions of Canada constitute a challenging environment for the provision of reliable energy and food supply to communities. A transition from fossil fuels to renewables-based sources of energy is one positive step in reducing the greenhouse gases from the energy supply system, which currently requires long-distance transport of diesel for electricity and heating needs. Geothermal energy can not only displace diesel for part of this energy need, it can provide a base-load source of local energy to support food production and mitigate adverse impacts of food insecurity on communities. In this proof-of-concept study, we highlight some potential benefits of using geothermal energy to serve Canada’s northern communities. Specifically, we focus on food security and evaluate the technical and economic feasibility of producing vegetables in a “controlled environment”, using ground sources of heat for energy requirements at three remote locations—Resolute Bay, Nunavut, as well as Moosonee and Pagwa in Ontario. The system is designed for geothermal district heating combined with efficient use of nutrients, water, and heat to yield a diverse crop of vegetables at an average cost up to 50% lower than the current cost of these vegetables delivered to Resolute Bay. The estimates of thermal energy requirements vary by location (e.g., they are in the range of 41 to 44 kW of thermal energy for a single greenhouse in Resolute Bay). To attain adequate system size to support the operation of such greenhouses, it is expected that up to 15% of the annually recommended servings of vegetables can be provided. Our comparative analysis of geothermal system capital costs shows significantly lower capital costs in Southern Ontario compared to Northern Canada—lower by one-third. Notwithstanding high capital costs, our study demonstrates the technical and economic feasibility of producing vegetables cost-effectively in the cold northern climate. This suggests that geothermal energy systems can supply the heat needed for greenhouse applications in remote northern regions, supplying a reliable and robust source of cost-competitive sustainable energy over the long-term and providing a basis for improved food security and economic empowerment of communities.

https://www.mdpi.com/1996-1073/12/21/4058/pdf

Geothermal Energy for Sustainable Food Production in Canada’s Remote Northern Communities

https://economics.acadiau.ca/tl_files/sites/economics/acea2015/Wheeler%20et%20al.,%202015%20Hydraulic%20fracturing%20etc.pdf

Maurice B. Dusseault

Papers

Drilling Through Salt: Constitutive Behavior And Drilling Strategies

Towards a Road Map for Mitigating the Rates and Occurrences of Long-Term Wellbore Leakage

How much oil you can get from CHOPS

Geothermal Energy for Sustainable Food Production in Canada’s Remote Northern Communities

Hydraulic fracturing – Integrating public participation with an independent review of the risks and benefits