Simplified Composite Model Research Articles

Oxidation Effects on Short-Term Creep Response in Air of Commercially Pure Titanium (CP-2 Ti)

The creep response in the air of commercially pure titanium was investigated at 550, 600, and 650 °C to assess the effect of oxidation on the mechanical response. Experiments demonstrated that prolonged exposures at high temperatures produced a marked reduction in the minimum creep rate under a given applied stress. Microhardness measurements showed that a hardened zone formed in proximity to the surface due to oxygen penetration into the metal. A simplified composite model was then used to describe the creep response. In this model, the sample consisted of two zones, the hard case that was enriched in oxygen and the soft pure-titanium core, both creeping with similar strain rates. Calculations led to an estimation of the dependence of the minimum creep rate on stress and temperature for the hard high-oxygen zone. The simplified composite model presented here provided a good description of the experimental creep data for pure titanium, tested in its air, and a reliable picture of the effect of oxidation on complex Ti alloys.

Pressure and rate transient analysis of composite shale gas reservoirs considering multiple mechanisms

Based on multiple mechanisms, including adsorption/desorption, viscous flow, diffusive flow in shale matrix and stress sensitivity of natural fractures, a new semi-analytical composite model is presented for multi-stage fractured horizontal well (MFHW) in shale gas reservoirs. The simplified composite model of an actual gas reservoir is composed of an inner and an outer region. Inner region represents stimulated reservoir volume (SRV) and contains natural fractures and matrix. Matrix-natural fracture transfer flow is assumed to be pseudo-steady state (PSS) or transient state (TS) which are described by the Warren & Root and the De Swan models respectively. Outer region is un-stimulated reservoir volume (USRV), which is described by single porosity medium model. First, transient flow model for continuous line source in composite shale gas reservoir is established. Perturbation method is applied to linearize the model. Then the line source solution is solved by Laplace transformation. Pressure responses of multi-stage fractured horizontal well is obtained using principle of superposition. The model is verified with the available field data from the Barnett Shale. In addition, transient pressure and production rate of MFHW in shale gas reservoirs with consideration of multiple mechanisms and SRV are analyzed and five typical regimes are identified: radial flow in SRV, interporosity flow, region pseudo-steady flow, diffusive flow and late pseudo-radial flow. In PSS transfer model, type curve has two cavities: the early one is caused by pseudo-steady interporosity flow between natural fractures and matrix and the late one is caused by diffusive flow in the matrix. But in TS transfer model, there is no obvious cavity in interporosity flow period due to subtle pressure fluctuation. The effects of relevant parameters on transient pressure and production rate are analyzed, including SRV radius, stress sensitivity coefficient, adsorption index, storability ratio, interporosity coefficient and diffusivity coefficient. The results demonstrate that larger SRV can reduce formation energy depletion and improve production rate. Stress sensitivity causes more pressure depletion, while desorption and diffusion can compensate for the pressure loss in the formation. The production rate increases as adsorption index σ rises. Storability ratio of natural fractures ωf and interporosity coefficient λ1 mainly affect interporosity flow period while storability ratio of matrix ωm and diffusivity coefficient λ2 mainly have effects on diffusive flow period. The larger the value of these four parameters, the larger the production rate in corresponding periods.

Analysis of effective diffusivity of cement based materials by multi-scale modelling

This paper presents a simplified composite model, which considers the contribution of each phase participating to the transport within OPC pastes and concretes. At the micrometer scale, the phases considered hereafter are capillary porosity (macro-porosity) and the Low Density and the High Density C–S–H both containing gel pores (nano-porosity). Predicted values of tritiated water (HTO) diffusivity in OPC pastes with various (w/c) ratios are confronted to experimental results with a good agreement. The approach is then extended to mortars and concretes scale where microstructure is described by a three-phase composite sphere assemblage. Here, elementary phase distribution is assumed to change as a function of distance from aggregate surface. Model results about HTO diffusivities of mortars and concretes are presented with some experimental values. The competition between the more diffusing ITZ zone and the less diffusing bulk matrix is investigated from a sensitive analysis. The dominance of the ITZ control is confirmed.

Modeling of the link between microstructure and effective diffusivity of cement pastes using a simplified composite model

The knowledge of the relationship between porosity and transport properties of concrete is a point of major importance to run properly the models coupling chemistry, transport and mechanics in order to simulate the engineered barrier degradations in the context of the nuclear waste deep repository. The present work proposes a simplified composite model aiming at linking microstructure and effective diffusivity of cement pastes. The proposed analytical method allows the estimation of the evolution of effective diffusivity of such materials submitted to porosity opening or plugging, at the scale of the Representative Elementary Volume (REV). The method is then applied to Ordinary Portland Cement (OPC) pastes. The porosity–diffusion evolutions determined from the composite model for various OPC pastes are implemented into simplified chemo-transport simulations aiming at describing the leaching of cementitious materials. Using these evolutions, OPC paste leaching simulations are in good agreement with the available experimental data, indicating a good reliability of the simplified composite model.