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.

Analysis of Eigenfrequencies of a Circular Interface Delamination in Elastic Media Based on the Boundary Integral Equation Method

The widespread of composite structures demands efficient numerical methods for the simulation dynamic behaviour of elastic laminates with interface delaminations with interacting faces. An advanced boundary integral equation method employing the Hankel transform of Green’s matrices is proposed for modelling wave scattering and analysis of the eigenfrequencies of interface circular partially closed delaminations between dissimilar media. A more general case of partially closed circular delamination is introduced using the spring boundary conditions with non-uniform spring stiffness distribution. The unknown crack opening displacement is expanded as Fourier series with respect to the angular coordinate and in terms of associated Legendre polynomials of the first kind via the radial coordinate. The problem is decomposed into a system of boundary integral equations and solved using the Bubnov-Galerkin method. The boundary integral equation method is compared with the meshless method and the published works for a homogeneous space with a circular open crack. The results of the numerical analysis showing the efficiency and the convergence of the method are demonstrated. The proposed method might be useful for damage identification employing the information on the eigenfrequencies estimated experimentally. Also, it can be extended for multi-layered composites with imperfect contact between sub-layers and multiple circular delaminations.

Dynamic Modelling and Nonlinear Characteristics of a Cracked Bolt-Disc Combined Rotor System

Different from the crack on the rotating shaft, the crack on the bolt which is a connecting part of the bolt-disc combined rotor is a kind of local defect. The local crack on the bolt under high pretension is always in open state, and it increases the overall vibration of the combined rotor significantly in practice. This paper studies the modelling of the crack on the bolt and nonlinear dynamic behaviors of the cracked bolt-disc rotor system. The circumferential bolts with a transverse open crack are treated as several bar elements under the assumption that each bolt has the same original tensile extension length. The cracked correction coefficient is introduced to describe the decreasing amount of bolt's tension due to crack. After this coefficient is obtained according to finite element method, the stiffness matrix of circumferential bolts with crack is built based on total potential energy. The dynamic model consists of a time-independent stiffness matrix for perfect bolts, a time-variant reductive stiffness and an additional moment. As a result, the crack in bolt reduces rotor's nonlinear stability and leads to greater vibration and fluctuation. In addition, crack depth has much larger influence than crack location on the dynamic behaviors.

Lamb Wave Scattering Analysis for Interface Damage Detection between a Surface-Mounted Block and Elastic Plate

Since stringers are often applied in engineering constructions to improve thin-walled structures’ strength, methods for damage detection at the joints between the stringer and the thin-walled structure are necessary. A 2D mathematical model was employed to simulate Lamb wave excitation and sensing via rectangular piezoelectric-wafer active transducers mounted on the surface of an elastic plate with rectangular surface-bonded obstacles (stiffeners) with interface defects. The results of a 2D simulation using the finite element method and the semi-analytical hybrid approach were validated experimentally using laser Doppler vibrometry for fully bonded and semi-debonded rectangular obstacles. A numerical analysis of fundamental Lamb wave scattering via rectangular stiffeners in different bonding states is presented. Two kinds of interfacial defects between the stiffener and the plate are considered: the partial degradation of the adhesive at the interface and an open crack. Damage indices calculated using the data obtained from a sensor are analyzed numerically. The choice of an input impulse function applied at the piezoelectric actuator is discussed from the perspective of the development of guided-wave-based structural health monitoring techniques for damage detection.

The Effect of AC (alternating current) and DC (direct current) on Bend Testing Results of Low Carbon Steel Welding Joints

The purpose of this study was to determine the effect of alternating current (AC) and direct current (DC) on the bend testing results of low carbon steel welding joints. The results of this study are expected to determine the cracks that occur from the root bend and face bend testings in the AC and DC welding process. This study used experimental method, where the research was done by giving AC and direct polarity DC (DC-) SMAW welding treatments. The material used in this research was low carbon steel plate DIN 17100 Grade ST 44, thickness 10 with E7016 electrode type. The process of welding joints used a single V seam, strong current of 90A, and the welding position of 1G. The testing of welding joints was carried out by bend testing using the standard acceptance of AWS D1.1 root bend and face bend testing results. The results of the bend testing showed that the AC welding root bend test specimen held no cracks while the DC welding root bend test held cracks with incompelete penetration and open crack defects. On the contrary, the AC welding face bend test had open crack defects and in the DC welding face bend test was found a crack. Thus, there was a difference in the crack resistance of the welding joint from the types of current used through the root bend test and face bend test. Therefore, it can be summarized that AC welding is better for root welding and DC welding is good for capping welding.

Scattering on a square lattice from a crack with a damage zone

A semi-infinite crack in an infinite square lattice is subjected to a wave coming from infinity, thereby leading to its scattering by the crack surfaces. A partially damaged zone ahead of the crack tip is modelled by an arbitrarily distributed stiffness of the damaged links. While an open crack, with an atomically sharp crack tip, in the lattice has been solved in closed form with the help of the scalar Wiener–Hopf formulation (Sharma 2015 SIAM J. Appl. Math. , 75 , 1171–1192 ( doi:10.1137/140985093 ); Sharma 2015 SIAM J. Appl. Math. 75 , 1915–1940. ( doi:10.1137/15M1010646 )), the problem considered here becomes very intricate depending on the nature of the damaged links. For instance, in the case of a partially bridged finite zone it involves a 2 × 2 matrix kernel of formidable class. But using an original technique, the problem, including the general case of arbitrarily damaged links, is reduced to a scalar one with the exception that it involves solving an auxiliary linear system of N × N equations, where N defines the length of the damage zone. The proposed method does allow, effectively, the construction of an exact solution. Numerical examples and the asymptotic approximation of the scattered field far away from the crack tip are also presented.