In the numerical studies above, the interface surfaces between the sandstone and mudstone layer are assumed to be strong enough to prevent any other fracture initiation on the interface, i.e.
, the top and bottom rock layers are perfectly bonded. However, the assumption of perfectly bonded interfaces is often incorrect for geological interfaces, since most interfaces have limited strength. As a fracture propagates toward an interface, tensile stresses develop across the interface. Debonding and subsequent opening of the interface may occur when the interface normal tensile stresses exceed the prescribed interface tensile strength. Geological discontinuities such as natural joints, faults and flaws, as well as bedding planes, in reservoir rocks and in ore bodies may contribute to the deflections and branching of hydraulic fractures [5
]. In this section, we attempt to highlight the fracturing process developed in layered rocks, and to use these concepts for a better understanding of the demonstration models established from the field observations in beach-bar sandstone reservoirs in Shengli Oilfield. Basically, there are three points that are crucial in fracturing across interfaces: (1) confining stresses, representing the effect of the in
stresses; (2) strength of the interfaces; and (3) material properties of the layers on either side of the interface.
3.2.1. The Influence of Confining Stress on Hydro-Fracture Propagation
The success or failure of hydraulic fracturing technology is largely dependent on the design of fracture configurations and the optimisation of treatments compatible with the in-situ
conditions of a given reservoir. To make a detailed investigation on the influence of in
stresses on hydraulic fracture propagation in a model with a bedding plane (referred to as an interface), a 2D numerical model, as shown in Figure 9
, is first employed.
The model has geometry of 400 mm × 400 mm, and has been discretised into a 40,000 element mesh. The bottom layer, hosting the hydro-fracture, is sandstone, while the top layer is mudstone. Totally three cases are simulated to illustrate the influence of the far-field stresses on the hydraulic fracturing behaviour. The applied constant confining stresses, which represent the effect of the far-field stresses, are listed in Table 4
The mechanical parameters for the three cases are kept constant at the values listed in Table 3
. The hydraulic pressure applied along the boundary of the wellbore is an increasing fluid pressure with an increment of 0.05 MPa per loading step. The diameter of the wellbore is 8 mm. In this model, an interface is embedded between the sandstone and mudstone. In RFPA, a specified type of material is then used to represent the interface between different rock matrixes [58
The interface is assumed to consist of ‘‘weak material’’ with a lower strength and stiffness compared to the sandstone and mudstone. Because it’s hard to evaluate the accurate strength data for interfaces in beach-bar sandstone reservoirs, an interface is simulated with mechanical properties of E
= 500 MPa, v
= 0.4, c
= 3.0 MPa, and ft
= 1.0 MPa, referring to the previous studies [60
]. In this model, the interface is referred to as the moderate-strength interface.
Abrupt changes in mechanical properties between horizontal layers can also significantly affect the opening up of discontinuities ahead of a propagating hydrofracture. For example, a layer with a low Young’s modulus (a soft layer) tends to suppress, whereas a layer with high modulus (a stiff layer) tends to magnify, the tensile stresses around the hydrofracture tip [11
]. Before reporting the results of the simulations in progressive fracture, the stress distribution that governs the model’s behaviour was first focused on. Figure 10
a shows the fluid pressure distribution when the applied pressure in the wellbore is 25.0 MPa. One of the most widely used techniques to visualize stress fields is the technique of photoelasticity. The numerical photoelasticity in Figure 10
b provides the contours of difference in principal stresses. Because the stresses adjacent to interface are the main concern, we just show a small portion of the model in a big box. The fringes in general appear as broad bands, the thickness of the fringe is indicative of the gradient of the stress variable. The fringes are very broad when the gradient is small, and vice versa
. The zone of high density of fringes indicates a zone of stress concentration. It is shown that the interface acts as a barrier for the stress to transfer, which induces evident stress concentration within the region adjacent to the fracture tip and interface. However, in reality, the rock formation in the field is usually heterogeneous. In order to demonstrate the difference in stress fields between models with and without considering the rock heterogeneity, the numerical photoelasticity for the heterogeneous case is further presented in Figure 10
c. These two computed fringe patterns clearly show that the heterogeneity has a strong influence on the stress fields in the model. Since it is not possible to obtain the fringe patterns in heterogeneous materials, the numerical results are of significance to improve our understanding of the stress field in such a layered and heterogeneous model.
For a quantitative evaluation of the heterogeneity and in
stress effect, we have shown in Figure 11
the minimum principal stress along the top of the interface (the mudstone side of the interface). In Figure 11
, the smooth curves are the results for the homogeneous cases, while the fluctuant ones are the results for heterogeneous cases. It is shown that the changes in confining stress configuration between horizontal and vertical stress can significantly affect the opening up of discontinuities ahead of a propagating hydro-fracture. Under conditions of higher deviatoric confining stress, a more evident high tensile stress becomes concentrated near the region of interface so that it would normally be easy for the hydro-fracture tip to enter, and propagate through the top layer. Again, the influences of material heterogeneity on the stress distribution are illustrated very clearly. We find that the maximum fluctuations of minimum principal stress are 50% of the mean stress for this heterogeneous case. It is obvious that ignoring these stress fluctuations may result in wrong conclusions if fracturing process is conducted.
To clearly show the hydraulic fracturing process, the case with σv
= 20.0 MPa and σh
= 13.0 MPa (i.e.
, the deviatoric confining stress is 7 MPa) is focused on. Figure 12
a illustrates the development and formation of the hydraulic fractures in detail, with the relative magnitude of the elastic modulus of the mesoscopic elements indicated by the grey scale. A brighter shade of grey corresponds to a higher Young’s modulus. In Figure 12
, the dark elements represent the nucleated flaw. Fractures form through the connection of flaws. Figure 12
b shows the evolution of the fracture and stress field (the minimum principal stress) during the hydraulic fracturing process. The grey scale indicates the relative magnitude of the stress within the elements. The elements with lighter shade of grey have relatively higher stresses. As the hydraulic pressure increases, the average maximum tensile stress increases along the boundary of the wellbore and fracture, particularly fracture tips display remarkable stress concentrations.
The hydraulic fracture deterministically selects the path of least resistance through the material based on its statistical features, and the random locations of the local heterogeneities result in an irregular hydraulic fracture trajectory. As shown in Figure 12
, the fracturing paths on the top and bottom sides of the wellbore are different from one another. On the top side, as the fracture propagating, the fracture “senses” the interface before coming in contact with it. The interface material provides stress transfer fluctuation between the sandstone and mudstone. Before the fracture approaches the interface, there is a large area of stress concentration between the fracture tip and the interface.
As the fracture approaches and penetrates the interface, a maximum tensional stress is observed in mudstone layer. However, the fracture does not grow at this location and fully penetrate through the interface (Figure 12
(a2)). Instead, the fracture is blunted and propagates near the interface, because the strength of the mudstone layer is relatively strong and the fracture needs more energy to keep propagating forward. After the accumulated fluid pressure is reached to a certain level, an offset fracture is initiated from the blunted fracture (Figure 12
(a3)). Once the fracture resumes its forward propagation, the stress concentration near the interface begins to decrease and the stress concentration is transferred to the fracture tip. Once the fracture passes the interface, it continues to propagate within the mudstone along the orientation of the maximum principal stress. On the bottom side of the wellbore, the fracture keeps propagating forward with the increasing fluid pressure, although the fracture path is flexural (rather than straight).
The simulations in this study account for any previously failed neighbouring elements. Following the first redistribution of stress, additional elements may fail owing to the stress increment. Therefore, in each loading step, the stress redistribution procedure is repeated until all of the elements for which the strength criteria are met and are stress-free, the released stresses are distributed between the intact neighbours, and global equilibrium of the sample is achieved. The next loading step is then performed. The broken elements form clusters that grow and coalesce as the load increases. Finally, the macroscopic failure zone, i.e., a fracture, is formed with the mutual connection of a plurality of such clusters. The final result of the micro-damage accumulation is a brittle fracture initiation and propagation rather than a single event.
The variation of the fracture pattern is highly sensitive to the interaction between the isolated fractures and the local disorder features of the rock matrix in the highly stressed field. In practice, the rock formation in field is usually heterogeneous. As a result, the fracture path is rough, and mixed-mode fracture propagation further affects the non-planar fracture growth in the non-preferred direction. In reality, there are two types of failure, high-stress failure and low-strength failure, for different materials. In a homogeneous material, failure begins at the high-stress site, whereas in a heterogeneous material (e.g., rock), failure may start at the weaker locations because of the presence of pores, microfractures, and grain boundaries. This observation led Fairhurst [63
] to introduce the notion of ‘‘stress severity’’, which represents the ratio of the theoretical stress at the moment of failure to the stress that would theoretically be necessary for failure at any given point. Therefore, maximum tension stress is not the only consideration for fracture initiation. Fractures typically initiate at local concentrations of tensile stress around flaws, such as fossils [57
]. Since flaws produce greater stress concentrations, the location of fracture initiation depends on the distribution of the flaws as well as the magnitude of maximum principal tension stress [64
is the numerical results for the case with a higher deviatoric confining stress (σv
= 20:8). It is shown that the fracture penetrates straight through the interface and keeps propagating in the mudstone layer. While for the case with a lower deviatoric confining stress (σv
= 20:18) (Figure 14
), the fracture is fully blunted and stops at the interface. Finally a T-shaped fracturing mode is formed.
It is clear that the large difference between the vertical and the horizontal in situ
stresses, can give rise to higher interaction stresses and more difficulty for fracture propagation along the interface. Fracture termination is more likely under conditions of lower deviatoric confining stress. A larger vertical stress can suppress the small and localized interface opening that acts to terminate fractures and promote either step-over fractures or fracture propagation through interfaces. The trend of fracture growth from numerical result here is consistent with the experimental results that increased interface normal compression can encourage fracture propagation through the interface [65
shows the variation of fracture length in vertical direction with the increasing hydraulic pressure. For the case with a higher deviatoric confining stress, the fractures on the top and bottom sides of the wellbore are generally symmetric. While for the other two cases, the growth of the top and bottom fractures is evidently asymmetric, particularly for the case with a lower deviatoric confining stress. Once branches and offsets appear during the hydraulic fracturing process, the fractures that develop such offsets in their path require higher fluid pressure to sustain fracture growth, as was suggested by previous studies [15
]. In the practical engineering of hydraulic fracturing of beach-bar sandstone reservoirs in Shengli Oilfield, unusual high pressures are often recorded [67
]. The peak values of the pressure recorded in beach-bar sandstone reservoirs in Shengli Oilfield is 20%–30% higher than that recorded in conventional reservoirs [4
]. Numerical results show that the fracturing behavior of branches and offsets between the sandstone and mudstone layers is one of the sources of high treating pressures and reduced fracture volume.
3.2.2. The Influence of Interface Strength on Hydro-Fracture Propagation
Clearly, besides in
stresses, fracture propagation across interface depends on many other factors, in which the interface properties play a key role in the interaction of the hydraulic fracture with the interface. To make a detailed investigation on the influence of interface properties on hydraulic fracture propagation, varying the interface properties while holding all of other material parameters and boundary conditions constant, another two cases (referred to as weak interface case and strong interface case) are considered. The properties for weak interface are E
= 100 MPa, v
= 0.45, c
= 1.0 MPa and ft
= 0.1 MPa, while the properties for strong interface are E
= 1000 MPa, v
= 0.35, c
= 5.0 MPa and ft
= 2.0 MPa. The other mechanical parameters are the same as those listed in Table 3
. The applied constant confining stresses are σh
= 13 MPa and σv
= 20 MPa.
The numerical results for the two cases are presented in Figure 16
. As a comparison, the numerical results of the case with moderate-strength interface are also listed in Figure 16
. The overall fracturing patterns are similar to those in Figure 12
, Figure 13
and Figure 14
; the profiles of the hydraulic fracture are characterized by numerous deflections, branchings, and terminations or step-over. Upon intersecting the interface, a fluid-driven fracture can grow along it in either direction or in both directions by overcoming the higher vertical stress and the extra compressive stress from the interaction between the interface and fractures.
For the case with a weak interface, as a fracture propagates toward the interface, weak interface can open easily under interface tension. Debonding and subsequent opening of the interface occur when interface normal tensile stresses exceed the prescribed interface tensile strength, then fracture propagates forward along the interface. Finally the fracture is blunted and fully arrested in sandstone layer. While for the case with strong interface, since these strong interfaces neither open nor slide within the model, the interfaces are likely to be bonded or welded. As a fracture propagates toward an interface, tensile stresses smoothly develop across the interface. The high interface stiffness minimize elastic deformation along the interface so that the resulting behavior is limited to keeping close due to stresses that meet the prescribed interface opening criteria. As a result, the fracture directly propagates through the interface, although the fracture path is rough.
As is indicated above, the fractures may either become arrested or offset at the interface between two layers. Because for most cases, the interface is relatively weak comparing the properties of its adjacent layers, the stress barriers, resulted from the strongly contrasting stiffness, are very effective at hydro-fracture arrest. If there are (laminated) multilayers, most fractures either become arrested or offset at the layer interfaces, indicating that it is normally more difficult for fractures to propagate through such multilayers simultaneously. The mechanism of this phenomenon is same to that in many composite materials [69
]. The only difference is that the sliding along interface is not considered in this study, because in fracture propagation driven by hydraulic pressure, the local interface opening, rather than sliding, is primarily responsible for the termination and step-over of fractures [1
], although the hydro-fractures from and along frictional interfaces also have been investigated by some researchers [15
shows the variation of fracture length with the increasing hydraulic pressure. For the case with a strong interface, the fractures on the top and bottom sides of the wellbore are generally symmetric. While for the other two cases, the growth of the top and bottom fractures shows is evidently asymmetric, particular for the case with a weak interface. To achieve the same fracture length, the higher fluid pressures are needed in latter two cases.
We investigated the potential for fracture propagation across, termination at, or step-over at a bedding interface by examining the fracturing process and associated stress evolution as the fracture approaches the interface. In general, there are four types of interaction between a fluid-driven fracture and a bedding interface within layered sedimentary rocks. Fractures can penetrate through the interface without any division of the fracture path. This type of crossing is what is implicitly assumed to occur by all current hydraulic fracture design models (the case with a higher deviatoric confining stress or the case with strong interface). In the opposite extreme case, the hydraulic fracture may be arrested or blunted at the interface (the case with a lower deviatoric confining stress or the case with weak interface). Between these above two extremes, a potential intermediate state is that the fracture is deflected into the interface plane and is divided into two branches (the case with a particular moderate deviatoric confining stress or the case with moderate-strength interface). If the interface is free of flaws, the fluid will invade it in the same way as an opening-mode hydraulic fracture growing along the horizontal interface, so that the vertical fracture eventually terminates at the interface, becoming a T-shaped fracture. Moreover, if there are flaws on the interface, potential re-initiation of a new fracture from one flaw will leave a step-over at the interface [1
]. The numerical results are consistent with the conceptual modes of hydraulic fractures approaching interfaces, as sketched in Figure 18
3.2.3. The Influence of Top Layer Strength on Hydro-Fracture Propagation
Complex morphology of hydro-fractures is caused by stress barrier, while the initiation and propagation hydro-fractures not only depend on the stress magnitude but also depend on the strength properties of the adjacent layers of the interface. To investigate the effect of the rock strata properties on the fracturing mode, another two cases (referred to as case with lower-strength top layer and the case with higher-strength top layer) were considered. In case with lower-strength top layer, the strength properties of the mudstone layer are assumed to be reduced by 50%, compared with those of the case shown in Figure 12
(the model shown in Figure 12
is referred to as the case with moderate-strength top layer), while in case with higher-strength top layer, the strength properties of the mudstone layer are increased by 50%. The other parameters were kept constant at the values listed in Table 3
. The applied constant confining stresses are σh
= 13 MPa and σv
= 20 MPa.
shows the fracturing modes for these two cases. In case with lower-strength top layer, the fluid-driven fractures clearly propagate across the interfaces from the mudstone layer to mudstone layers and continue to propagate. By overcoming the higher vertical stress and the extra compressive stress generated from the interaction between the fractures, each fracture is initiated in a non-preferred direction, turns and twists during propagation, and tends to align itself with the preferred direction and plane.
In case with higher-strength top layer, the fluid-driven fractures are clearly blunted by the mudstone layer, although debonding and subsequent opening of the interface occurs. The strength of the mudstone layer is high enough that fractures only keep propagating along the interface and any new fractures along the mudstone side of the interface cannot initiate, then a T-shaped fracture is finally formed. In this case, because the interface in the model is an ideal interface, the fractures keep propagating along the interface. If the fractures stop propagating along the interface due to local heterogeneity of interface or some particular blocking measures in practical engineering, the fluid flow is then prevented from escaping along the interface and an either fracture step-over or fracture propagation across the interface may occur.
shows the variation of fracture length with the increasing hydraulic pressure. For the case with lower-strength mudstone layer, the fractures on the top and bottom sides of the wellbore are generally symmetric. While for the other two cases, the growth of the top and bottom fractures is evidently asymmetric, particular for the case with a higher-strength mudstone layer. The stronger top rock with higher toughness is found to efficiently resist fracture escaping, correspondingly, the higher fluid pressures are needed in the case.