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Hydraulic fracture geometry (i.e., critical results of length and proppant placement) is driven by four major in situ parameters: Fracture Height (H), Modulus (E), Fluid Loss (C), and "Apparent" Fracture Toughness (KI c-app ). In many (even most) cases, "Height" is the most important of these parameters – due to the need for some height confinement to achieve long fractures, or the need for height growth to insure good pay coverage. Due to this importance, industry research effort and most field measuring techniques concentrate on "Height." In particular, the growing use of seismic imaging is offering a tool to measure height growth away from the wellbore. Results from such diagnostics have often shown, as one expects, that in situ stress variations control height. However, results have also shown situations where this is apparently not the case. This paper examines another in situ parameter, "Layered Modulus," which also affects height. In addition, by controlling the "local" width of a fracture, layered modulus (i.e., layered formations with different layers having significantly different modulus) can have a critical effect on final proppant placement. The importance of layered modulus in directly controlling fracture height is illustrated in this paper, and this is compared with published solutions. In general, it is found that, just as concluded in the past, modulus contrast is probably not an important parameter in terms of direct control of fracture height. The greater importance lies in the effects on local fracture width. These local width changes can have a significant influence on controlling proppant placement – and this can be critical for low net pressure cases such as "water fracs" or fracturing in "soft" formations. It is also noted that layered modulus significantly impacts the average width of a fracture, and thus impacts the critical material balance aspects of fracture modeling if not properly accounted for. Finally, some of the theoretical solution problems created by "Layered Modulus" formations for fracture modeling are discussed and compared. This is done by comparing with 3–D Finite Element (static) solutions, and shows how some common industry "approximations" for layered modulus give incorrect results. Based on this, examples with a fracture propagation model using a finite element-generated stiffness matrix are used to define types of cases where a simple "average" modulus is acceptable, versus cases where more complex calculations are needed. Introduction Six major variables control hydraulic fracturing, fracture geometry, proppant placement, etc. Two of these are the "controllable" variables of fluid viscosity, µ, and pump rate, Q. The remaining four variables are "natural" variables and include:Height. Fracture height (or more generally fracture geometry) is possibly the most important unknown for fracture design and post-frac production success. Generally, it is recognized that in situ stress differences (the in situ stress profile) is the major controlling factor for this behavior. [1] At a minimum, in situ stress differences control the maximum fracture height, i.e., if the net pressure is not available to grow through high stress shale layers, then fracture height must be contained. The importance of fracture height/geometry is clear, and there are many research efforts and technical publications addressing this issue. [1–6]Fluid Loss. Fluid loss is typically characterized for hydraulic fracturing by a fluid loss coefficient, C, which characterizes linear flow fluid loss out of the fracture. This gives the familiar C/ (t-t) form of fluid loss behavior. Again, this variable has been exhaustively discussed in the literature including wall building characteristics of specific fluid systems, effects of natural fractures, behavior of fluid loss additives, etc. [7–16]

A detailed 3D finite element model (FEM) of the sheep thorax was developed to predict heterogeneous and volumetric lung injury due to blast. A shared node mesh of the sheep thorax was constructed from a computed tomography (CT) scan of a sheep cadaver, and while most material properties were taken from literature, an elastic-plastic material model was used for the ribs based on three-point bending experiments performed on sheep rib specimens. Anesthetized sheep were blasted in an enclosure, and blast overpressure data were collected using the blast test device (BTD), while surface lung injury was quantified during necropsy. Matching blasts were simulated using the sheep thorax FEM. Surface lung injury in the FEM was matched to pathology reports by setting a threshold value of the scalar output termed the strain product (maximum value of the dot product of strain and strain-rate vectors over all simulation time) in the surface elements. Volumetric lung injury was quantified by applying the threshold value to all elements in the model lungs, and a correlation was found between predicted volumetric injury and measured postblast lung weights. All predictions are made for the left and right lungs separately. This work represents a significant step toward the prediction of localized and heterogeneous blast lung injury, as well as volumetric injury, which was not recorded during field testing for sheep.

This work demonstrates the feasibility of using a composite blast shield for hardening an overhead bin compartment of a commercial aircraft. If a small amount of explosive escapes detection and is brought onboard and stowed in an overhead bin compartment of a passenger aircraft, the current bins provide no protection against a blast inside the compartment. A blast from the overhead bin will certainly damage the fuselage and likely lead to catastrophic inflight structural failure. The feasibility of using an inner blast shield to harden the overhead bin compartment of a Boeing 737 aircraft to protect the fuselage skin in such a threat scenario has been demonstrated using field tests. The blast shield was constructed with composite material based on the unibody concept. The design was carried out using LS-DYNA finite element model simulations. Material panels were first designed to pass the FAA shock holing and fire tests. The finite element model included the full coupling of the overhead bin with the fuselage structure accounting for all the different structural connections. A large number of iterative simulations were carried out to optimize the fiber stacking sequence and shield thickness to minimize weight and achieve the design criterion. Three designs, the basic, thick, and thin shields, were field-tested using a frontal fuselage section of the Boeing 737–100 aircraft. The basic and thick shields protected the integrity of the fuselage skin with no skin crack. This work provides very encouraging results and useful data for optimization implementation of the blast shield design for hardening overhead compartments against the threat of small explosives.