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UBC Theses and Dissertations

Nonlinear temperature and consolidation analysis of gassy soils Vaziri-Zanjani, Hans Hamid


A study is undertaken to formulate and solve the equations governing the time dependent response of gassy soils. The formulations have been implemented into a finite element program capable of analyzing stress state and flow phenomenon under a variety of boundary conditions. The validity of such a program has been verified by comparing its results with closed form solutions. This program has then been applied to simulate the processes involved in depleting oil sand reservoirs in order to give some insight into the mechanism causing fluid flow and sand production. The theory developed couples the effects of both stress and flow. It takes account of the varying permeability and compressibility of the pore fluid, and the nonlinear stress-strain behaviour of the soil. A hyperbolic model is employed to represent the soil's stress-strain characteristics and a distinction in behaviour is made between shear and tensile failures. Various schemes are proposed for transferring loads which violate the yield criterion and in ensuring that a reasonable behaviour is modelled during failure. In order to compute the change in pore pressure in gassy soils, both under undrained and transient states, the concept of a homogenized compressible phase is introduced which is used to treat a multiphase soil system as a two phase material. Such a hypothesis is found to be highly akin to the procedure normally followed in finite element analysis since it replaces the compressibility of fluid and solid phases by one phase which occupies the entire soil volume. Assuming that the gases are present only in the form of bubbles within the liquid phase, the compressibility of the fluid phase is obtained by giving due consideration to the mixture of liquid and gas phases using Boyle's law and Henry's law and taking account of the surface tension effects. Under undrained conditions the pore pressure is computed by invoking volumetric compatibility between the soil skeleton and the compressible phase. Under transient conditions, the pore pressure is calculated by using Biot's theory of consolidation and modifying it to account for a soil with an incremental stress-strain law and a compressible fluid phase. Formulations are derived to compute the change in pore pressure and effective stress as a result of changes in temperature and a methodology is proposed for implementing these effects into finite element analysis. Various numerical techniques are incorporated for increasing the accuracy, efficiency, and stability of the finite element procedure. The computer program based on these formulations is verified by comparing the computational results with known solutions for several problems. Application of the finite element program to analyze the problem of unloading a cavity in oil sand reservoir has revealed that the principal factor leading to fluid production is the compressibility attained by the pore fluid as a result of the gas evolution. It is also demonstrated that large movements develop around uncased wellbores when the internal fluid pressure is reduced below the in-situ pore pressure. The factor which governs the overall stability of the reservoir is the flow rate which is a function of the pore pressure gradient, soil strength properties, permeability, and the volume of evolved gases.

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