Modeling of Before Closure Zero Slope Pressure Derivative in a Diagnostic Fracture Injection Test DFIT

Recent diagnostic fracture injection test (DFIT) data presented on a Bourdet log-log diagnostic plot showed derivative slope of 0 in the before closure (BC) portion of the DFIT response. Some works qualitatively describe it as radial flow. This behavior has not been quantitatively analyzed, modeled and matched. The present work disagrees with the hypothesis of radial flow and successfully matches the relatively flat trend in the Bourdet derivative with a model dominated by friction dissipation coupled with tip extension. The flat trend in Bourdet derivative occurs shortly after shut-in during the before closure period. Because a flat derivative trend suggests diffusive radial flow, our first approach was to consider the possibility that an open crack at a layer interface stopped the fracture propagation and caused the apparent radial flow behavior observed in falloff data. However, a model that coupled pressure falloff from diffusive flow into a layer interface crack with pressure falloff from closure of a fracture that propagated up to the layer interface failed to reproduce the observed response. Subsequently, we discovered that existing models could match the data without considering the layer interface crack. We found that data processing is very important to what is observed in derivative trends and can mislead the behavior diagnosis. We succeeded to match one field DFIT case showing an obvious early flat trend. The presence and dominance of geomechanics, coupled with diffusive flow, disqualify the description of the flat trend in Bourdet derivative as radial flow. Instead, flow friction coupled with tip extension can completely match the observed behavior. Based on our model, cases with a long flat trend have large magnitude near-wellbore tortuosity friction loss and relatively long tip extension distance. Further, we match the near wellbore tortuosity behavior with rate raised to a power lower than the usually assumed 0.5. The significance of these analyses relates to two key factors. First, large magnitude near wellbore tortuosity friction loss increases the pressure required for fracture propagation during pumping. Second, tip extension is a way to dissipate high pumping pressure when very low formation permeability impedes leakoff. Matching transient behavior subject to the presence of both of these factors requires lowering the near-wellbore tortuosity exponent.

NONLINEAR PROBLEM OF FRACTURE MECHANICS OF AN INTERFACE CRACK SUBJECTED TO SHEAR WAVE

Solution for the problem for an interface crack under the action of a harmonic shear wave in normal direction is presented. The contact of the crack faces is put into consideration. The problem is solved by the boundary integral equations method, the vector components in the boundary integral equations are presented by Fourier series. The unilateral Signorini boundary conditions are involved to prevent the interpenetration of the crack faces and the emergence of tensile forces in the contact zone. Amonton-Coulomb Friction Law included allows to put into consideration relative resting of the crack opposite faces or their relative motion when one crack face is slipping or sliding across another face. The contact boundary restrictions are implemented using the iterative correction algorithm. The mathematical model adequacy is checked by comparing with classical model solution for statics problems that takes into account the crack faces contact. Numerical researches of friction influence on the displacement and contact forces distribution, size of contact zone are carried out. Influence of the faces contact and value of the friction coefficient on the distribution of stress intensity coefficients of normal rupture and transverse shear, which are the parameters of the biomaterial fracture, are presented and analyzed. It is shown that the nature of change in the distribution of the stress intensity coefficients for the conditions of tensile and shear waves is fundamentally different. It is concluded that it is possible to extend the approach proposed to the problems of three-dimensional fracture mechanics for composites with interfacial cracks at arbitrary dynamic loading.

Analysis of the bi-material interface cracks based on configurational forces

In this paper, an innovative interface fracture criterion is proposed based on the concept of configurational forces in material space. In this criterion, the crack tip configurational forces as driving force is introduced to describe the interface crack evolution under mixed mode loading conditions. And it assumes that the interface crack propagates due to the competition of resultant of configurational forces with interface fracture toughness. The analytical expression of the configurational forces are obtained by differentiating the elastic strain energy density and conservative integral for interface cracks. And the relation of interface crack tip configurational forces with classical complex intensity factors are obtained through strict mathematical deduction. The interface crack tip configurational forces are evaluated for a classic interface crack problem covering a wide range of bi-material oscillation index. The configurational forces based interface fracture criterion is validated through series interface fracture experiments. The proposed criterion may provide a novel framework for analysis of interface fracture under complex loading conditions.

Accurate stress intensity factors for kinked interface crack in bonded dissimilar half-plane

In this study, the stress intensity factor (SIF) of an interface kinked crack is analyzed by the singular integral equation of the body force method. The problem can be expressed by distributing the body force doublets of the tension and shear types along all the boundaries of the kinked and interface crack parts. The SIFs can be obtained directly from the densities of the body force doublets at the crack tips. Although the problem has already been calculated using the crack connection model, the accuracy of the analysis has not been clarified. From the analysis results in this study, it can be seen that the SIFs calculated by the crack connection model have a nonnegligible error, and the present method gives more accurate results. The advantage of the present method is that the SIFs of the kinked and the interface crack tips can be obtained at the same time with high accuracy.