Abstract:Light olefins are the main building blocks used in the petrochemical and chemical industries for the production of different components such as polymers, synthetic fibers, rubbers, and plastic materials. Currently, steam cracking of hydrocarbons is the main technology for the production of light olefins. In steam cracking, the pyrolysis of feedstocks occurs in the cracking furnace, where hydrocarbon feed and steam are first mixed and preheated in the convection section and then enter the furnace radiation section to crack to the desired products. This paper summarizes olefin production via the steam cracking process; and the reaction mechanism and cracking furnace are also discussed. The effect of different operating parameters, including temperature, residence time, feedstock composition, and the steam-to-hydrocarbon ratio, are also reviewed.Keywords: olefin production; steam cracking; cracking furnace; ethylene; propylene; butenes; reaction parameters
A fracture-mechanics-based crack-growth simulator, rather than a purely stochastic method, was used to generate fracture networks with realistic clustering, spacing, and fracture lengths dependent on Young's modulus, the subcritical crack index, the bed thickness, and the tectonic strain. Coupled fracture-matrix fluid-flow simulations of the resulting fracture patterns were performed with a finite-difference simulator to obtain equivalent permeabilities that can be used in a coarse-scale flow simulation. The effects of diagenetic cements completely filling smaller aperture fractures and partially filling larger aperture fractures were also studied.
Brittleness, which is generally viewed as a property (or ability) of solid material that ruptures with little appreciable permanent deformation, has long been considered approximately equivalent to fracability, because it shows empirical relevance to the possibility of crack propagation: reservoir comprising brittle rocks usually responds well to stimulation, whereas preexisting and hydraulic fractures tend to heal rather than to propagate in a less brittle reservoir. This is probably attributed to less energy consumed by the ductile deformation of brittle rock materials .
In summary, many brittleness indices currently popular in fracability evaluation for reservoir lacks mechanical relevance to the rock cracking process. On the other hand, the evaluation indices used in other areas (e.g., those used to estimate rock cuttability ) are usually inapplicable for reservoir fracability evaluation owing to the essential differences of physical meaning between brittleness and fracability. Thus far, few evaluation indices of rock fracability meet the following requirements :
To address this issue, we propose a new evaluation index for rock fracability that we call the crack tolerance. See Section 2 for its definition. Section 3 and Section 4 show the experimental measurement of this new index and the corresponding numerical simulation results, respectively, to demonstrate the rationality of the index. Based on these analyses, the effects of several characteristics of the rock materials on the crack tolerance are discussed in Section 5.
Crack propagation in tensile mode is most common in hydraulic fracturing because the effect of hydraulic pressure imposed on the crack surface approximates remote tensile stress in nature; additionally, rocks have a much lower tensile strength than compressive and shear strengths. Thus, cracks easily propagate driven by an injected fluid. The principal stresses at a tensile crack tip can be described as 
where σ1 and σ2 are maximum and intermediate principal stresses, KI is tensile stress intensity factor, r and θ are polar radius and polar angle for polar coordinate system from the tip. Note that the minimum principal stress not listed here equals to zero. The range of FPZ (i.e., its size) is calculated based on the hypothesis that nonlinear deformation occurs within a region around crack tip when the local stress state satisfies a certain criterion (e.g., tensile strength criterion for rock materials, von Mises criterion for metal materials). The tensile cracks are assumed to propagate parallel to their own plane (i.e., θ = 0) when the σ1 reaches the tensile strength of the rock (σt), because the critical state of crack propagation is attained, which corresponds to the maximum size of the FPZ:
A large rc would indicate that micro-cracks are distributed within a large FPZ in front of a preexisting crack tip. It would also suggest a considerable number of micro-cracks within the FPZ because a preexisting crack will not propagate until the micro-crack density is high enough to reach a critical level . Therefore, rc may characterize the maximum number of micro-cracks generated in the preparation stage for macroscopic crack propagation. In other words, rc can be used to indicate the ability of a rock to tolerate micro-cracks before crack unstable propagation. For this reason, we refer to rc as the crack tolerance. The crack morphology may also depend on the crack tolerance because a large rc would indicate an extensive distribution of micro-cracks, which would likely result in irregular and branch cracks.
The notched crack of each CCNBD specimen was created by a 1 mm thick circular diamond saw. To ensure cutting accuracy, the expected locations of the circular center and the initial and final chevron notched cracks were marked on each disk. We measured the actual values of the parameters shown in Figure 2a,b and confirmed that the dimensionless parameters α1 and αB of all CCNBD specimens were within the valid range (Figure 2c). The method reported by Fowell et al.  was used to calculate the KIC:
(a) Orthographic and (b) side profiles of a marble CCNBD specimen; (c) valid range for dimensionless parameters α1 and αB (outlined in gray)  and the distribution of parameter values for all of the prepared CCNBD specimens. Geometric parameters: diameter D = 75 mm, radius R = 37.5 mm, thickness B = 30 mm, saw radius Rs = 25 mm, initial chevron notched crack length a0 = 8.45 mm, and final chevron notched crack length a1 = 23.5 mm.
Each CCNBD or BD test (Figure 3a,b) was performed at a constant displacement rate of 0.06 mm/min by an MTS servo-control testing machine (series CMT) with a maximum loading force of 100 kN. This machine is equipped with an SNAS GDS-300 environmental chamber controlled by a WK650 controller (Figure 3c,d). These apparatuses permit environmental temperatures within the chamber up to 200 °C by electrical heaters (Figure 3b). To investigate the effect of temperature, several sandstone specimens were placed in the chamber at 75 or 125 °C for 1 h before the tests began, so that the notched crack propagated within rocks under higher temperatures. Other tests were performed at room temperature (~25 °C). The bedding planes of the shale specimens were set perpendicular (horizontal) or parallel (vertical) to the notched cracks to analyze the effect of the bedding orientation.
Mean tensile strength (brown), tensile fracture toughness (green), and crack tolerance (sienna) of the (a) marble A (diamond) and J (triangle), (b) shale (circle) with horizontal and vertical orientations and (c) sandstone (square).
Crack morphologies of (a,b) marble A and (c,d) J. The red dashed ellipses in (a) denote white patches around the notched crack tips.
The mean crack tolerance of the shale specimens was less with a vertical bedding orientation than with a horizontal orientation (Figure 4b). The tensile strength and fracture toughness displayed similar variation trends with bedding orientation. Similar results can be acquired based on the data from Wang . With a vertical orientation, the main crack of the specimen propagated along the bedding planes (Figure 6a), which generated a smooth rupture surface (Figure 6b). In contrast, with a horizontal orientation, the main crack spanned across bedding planes, and the path with steps was more irregular (Figure 6c,d). This is because the main crack was offset or even bifurcated when it encountered a bedding plane. The branch cracks were captured by bedding planes and then propagated along them, thereby their morphologies were smooth.
The crack tolerance value of the sandstone specimens consistently declined as the environmental temperature rises from 25 °C to 125 °C, while the tensile strength and fracture toughness exhibited V-shaped trends within this temperature range (Figure 4c). It is difficult to identify changes in crack morphology with the rising temperature with the naked eye (Figure 7a,c,e). According to the edge of their rupture surface, we speculated that the main cracks in the specimens at 125 °C may propagate along less curved paths than the specimens at lower temperatures did (Figure 7b,d,f). The variations of the crack tolerance value and crack morphologies imply that high temperatures possibly reduce rock fracability.
Simulated cracking process of marble A CCNBD specimen. (a) Cracking initiation at notched crack tips (~66% Pmax); (b) reaching Pmax; (c) specimen rupture.
Simulated cracking process of marble J CCNBD specimen. (a) Cracking initiation at notched crack tips (~70% Pmax); (b) reaching Pmax; (c) specimen rupture.
As the simulation results (Figure 10b and Figure 11b) showed, the micro-crack density at the vicinity of notched crack tip was especially high in the whole specimen, owing to the nonlinear deformation brought by stress concentration. The FPZ was assumed as a tip-centered circle with radius of rc  that covered the area with high micro-crack density. Therefore, with increasing distance (radius) Rf from the tip and the diminishing intensity of the stress concentration, the deformation transitions from nonlinear inside the FPZ to quasilinear outside the FPZ, and thus the micro-crack density outside the FPZ declined to the background density of the rock . 2b1af7f3a8