Donald E. Cormack

Calculation of vertical fracture containment in layered formations

An analytic procedure for calculating vertical fracture extent in symmetrical trilayered formations was extended to multilayered, asymmetrical formations using a semianalytic technique. The fracture extends computed by this method were compared with those calculated with the finite-element method. It was found that even for modulus variations between layers as large as a factor of 5, the semianalytic procedure gave exactly the same results as the finite-element solution in a fraction of the computation time and with significantly less manual data manipulation. It is recommended that the analytic and numerical procedures be used in a complementary manner to calculate fracture-width profiles in layered formations.

Effect of low-temperature oxidation on the composition of Athabasca bitumen

The effect of low temperature oxidation on the composition of Athabasca bitumen was examined. Oxidation temperatures in the range 125–135 °C and extents of oxidation up to 100mg O2g bitumen were investigated. The aromatics concentration was observed to decline steadily and the concentration of asphaltenes to increase, during oxidation. The saturates were unaffected by low-temperature oxidation. The resins concentration displayed a strange behaviour, first dropping and then increasing to a maximum and again dropping as oxidation proceeded.

Predicting Carbon Dioxide Corrosion of Bare Steel under an Aqueous Boundary Layer

Abstract The corrosion of bare steel under an aqueous boundary layer with dissolved carbon dioxide (CO2) was modeled to investigate the effect of CO2. The model incorporated the coupled effect of CO2 diffusion, hydration, local ionic equilibria, ferrous carbonate (FeCO3) precipitation, and steel corrosion. The model was verified against published experimental data under both FeCO3-saturated and unsaturated boundary layers. Good agreement was shown under a variety of conditions. For saturated boundary layers, the results show that the corrosion rate in carbonic acid (H2CO3) is greater than in hydrochloric acid (HCl)for a given pH and that H2CO3 reduction is the cause for the increase of corrosion rate in H2CO3. Increasing temperature was found to increase corrosion rate substantially. This work provides further understanding of the CO2 corrosion mechanism and is a reliable, convenient, and practical tool for predicting the rate of CO2 corrosion.

Green's functions for the biharmonic equation: bonded elastic media

A comprehensive formulation of Green’s functions for biharmonic equations with respect to perfectly bonded, bimaterial, linear, isotropic, elastic media is presented. This is accomplished by extending Mindlin’s nuclei of strain method, which employs the method of images. The analysis involves properly scaling the nuclei, grouping the nuclei into different classes and introducing a matrix structure for each class. The strength vectors of the nuclei, required at the object and image points to represent the solution, are obtained by matrix-vector multiplications involving two invariant matrices, the “reflection matrix” and the “transmission matrix.” Algebraic expressions for the elements of the reflection and transmission matrices, which depend on the elastic properties of the materials, are presented.

Steel Corrosion under a Disbonded Coating with a Holiday—Part 1: The Model and Validation

Abstract A model was developed to investigate the corrosion of a coated pipeline surface in a thin, narrow channel crevice formed between the pipe surface and the coating. Such crevices are often found on natural gas pipelines when the coating is high-density polyethylene (HDPE). Imposed cathodic protection current passage through the holiday and oxygen diffusion through both the holiday and the coating were included in the model. The effect of the corrosion product, ferrous hydroxide (Fe[OH]2), on the transport of oxygen and ionic species in the crevice solution was neglected because it is porous. Mass balance for oxygen pressure and Laplaces equation for the steel potential in the crevice solution were used to derive the model equations. For a crevice solution with uniform pH and uniform resistivity, the model equations were solved using a collocation technique programmed in MATLAB. This new model was validated with published experimental data and model results—good agreement was found.

Steel corrosion under a disbonded coating with a holiday-Part 2: Corrosion behavior

Abstract Corrosion of a pipe surface in a channel crevice has been modeled assuming oxygen diffusion through a holiday in a permeable coating. The crevice was thin and narrow with a finite length. ...

An invariant imbedding method for singular integral evaluation on finite domains

The “invariant imbedding” technique is used to develop versatile and powerful integration formulae for the evaluation of singular integrals on finite domains encountered in continuum problems in engineering and applied science. This method is considerably simpler than the several ad hoc integral evaluation methods presented in the recent literature. Moreover, the method provides new insight into the central role played by the residue in the evaluation of principal value integrals. This relationship is embodied as a “gauge condition.” The main emphasis of the paper is on developing a general approach from which specific cases follow. Several examples chosen from different areas of engineering computation are provided in order to show the advantage of this approach.

The continuation approach: a general framework for the analysis and evaluation of singular and near-singular integrals

The continuation approach, presented in this paper, is a simple and unified framework for analyzing and computing a large class of singular and near-singular integrals such as those that arise in the boundary element method. The analysis formulates singular and near-singular integrals consistently as instances of a single phenomenon, with all types of algebraic singularities treated in a similar way for domains of arbitrary dimension. Singular integrals are viewed merely as “continuations” of nonsingular (but perhaps near-singular) ones, by placing the singularity of the integrand outside the integration domain, and taking the limit as it approaches the domain.The technique exploits the functional homogeneity shared by the Green’s functions of many physical problems. For flat surfaces, this allows the integral to be mapped to the contour of the integration domain. Curved surfaces are handled by projecting the integration domain to a tangent hyperplane, where the singular components of the integral can be ...

A new concept in near-singular integral evaluation: the continuation approach

The functional homogeneity of Green functions is exploited in the derivation of continuation formulae for the accurate evaluation of near singular integrals. These formulae provide a means of systematically continuing such unconventional integrals as the principal value and finite part integrals of singular functions to conventional integrals of nonsingular functions. A new concept, the notion of continuum integral, which is applicable to singular as well as to nonsingular integrals, is introduced as a generalization of principal value and finite part integrals. Numerical examples are provided that illustrate the computational advantages of the continuation method and give a new perspective on the subtleties of singular and near-singular integrals.

Nuclei of strain for bi-material elastic media with sliding interface

The nuclei of strain method, which was previously developed for a perfectly bonded bi-material elastic medium, is modified to obtain the fundamental solutions for the elastic state of a bi-material, isotropic elastic medium with sliding interface. The solutions are conveniently expressed in terms of strength vectors at object and image points which are related by the transmission and reflection matrices given in the paper.