Constant Pressure Injection

Abstract

In practical hydraulic fracturing, limited by the operating power of the syringe pump and long transportation of pipelines, it is often difficult to maintain high pum** fluid pressure to crack the reservoir rock in deep formation.

1 Introduction

In practical hydraulic fracturing, limited by the operating power of the syringe pump and long transportation of pipelines, it is often difficult to maintain high pum** fluid pressure to crack the reservoir rock in deep formation. To overcome this difficulty, Ma et al. [1] and Zang et al. [2] tried to use “static fatigue” to break the reservoir rock by maintaining a constant fluid pressure on the rock for a long time, which has been proven to be able to reduce the breakdown pressure of the reservoir. The feasibility of this method has been verified in granite, limestone and sandstone reservoirs [3]. However, relevant technologies have not been applied to shale reservoirs, and the delayed fracturing process of shale lacks reliable laboratory evidence. In addition, few efforts focus on unraveling the mechanisms of fracturing reservoirs by constant pressure injection (delayed breakdown).

The delayed breakdown process of hydraulic fractures induced by constant pressure fluid is essentially the consequence of the long-term action of the extremely high fluid pressure, resulting in the initiation of hydraulic fractures due to fatigue damage. Different from the previous disturbance of pore pressure to the rock fracturing process, under the condition of constant pressure, hydraulic fracturing is dominated by fluid pressure. In terms of pore pressure disturbance, previous studies have focused on analyzing the effect of uniform pore pressure on rock fracture properties. Under the action of constant and uniform pore pressure, the damage to rock tends to be progressive and integral along the minimum principal stress. The nature of instability and damage caused by water inrush, collapse, slip, etc. [4, 5]. At present, there are few related studies on the effect of heterogeneous and asymmetric high pore pressure on the rock fracture process. Lu et al. [6] used the stress intensity factor at the crack tip and analyzed the deflection mechanism of hydraulic fracture propagation caused by non-uniform pore pressure, but failed to clarify the effect of local pore pressure on rock strength, deformation and fracture characteristics.

In this section, the constant pressure fracturing test is carried out based on previous research. The syringe pump is controlled by the constant pressure injection mode using a feedback loop control. The constant pressure injection test scheme has been described in detail in Sect. 3.4.2. The following is an analysis of the delayed breakdown characteristics of hydraulic fractures based on the observation under constant pressure injection tests.

Note that the changes in pum** parameters (P_inj and V_inj) with time and fracture morphology under constant pressure and constant flow conditions were presented and compared, respectively. Specifically, to elaborate the characteristics of these pum** parameters during the fracturing process, four key parameters were defined: the maximum pump pressure (instantaneous or delayed breakdown pressure, P_b), the time (onset) of pressure declining (T_pd), the maximum injection rate (maxV_inj) and the time at which the injection rate reaches the maximum (maxT_inj).

2 Results and Analysis

2.1 Typical Curves of Pump Pressure and Injection Rate Versus Time

Unstable crack propagation leading to a macroscopic failure (a crack reaching the rock surface and splitting the specimen into two parts) is accompanied by a simultaneous drop of fluid pressure in the wellbore [7]. To quantitatively evaluate the relationship between fluid pressure and crack propagation, we introduced the pressure decay rate (v_decay) following Gehne et al. [8].

$$v_{{{\text{decay}}}} = \frac{{P\left( t \right) - P\left( {t + \Delta t} \right)}}{\Delta t}$$

(5.1)

where P(t) is to the wellbore pressure at the time t, and Δt denotes an increment of time. According to Song et al. [9] and Hu et al. [10], when the friction flow of fracturing fluid inside the wellbore is neglected, the wellbore pressure (P(t)) can be considered the pum** pressure (P_inj) which is monitored in real-time by a pressure transducer near the injection hole. Thus, Eq. (5.1) can be rewritten as

$$v_{{{\text{decay}}}} = \frac{{P_{{{\text{inj}}}} \left( t \right) - P_{{{\text{inj}}}} \left( {t + \Delta t} \right)}}{{\Delta t}}$$

(5.2)

In the following part, we presented curves of pum** pressure and injection rate as a function of time under constant pressure injection conditions of P_con = 17, 19, and 21 MPa, respectively.

• (1) Constant fluid pressure (specimen P-17)

Figure 5.1 depicts the curves of injection rate, pump pressure, and pressure decay rate with the increase of time for Specimen P-17. Overall, the pressurization of the wellbore was steadily maintained at a pump pressure of 17 MPa with no fluid leak-off into the sample (V_inj = 0). Even after this state (constant pressure stage) lasted for nearly 370 min, the change in the curves was still hardly identified, indicating that there was probably no fluid exchange between the wellbore and the hydraulic fracturing system. Thus, the whole rock and fluid injection system were in static equilibrium, which means no fracture initiation or fluid infiltration occurred over the entire pressurization process. In this regard, the 17 MPa pump pressure is insufficient to break up the shale strength on the timeframe of 370 min. A much more extended period or higher pump pressure value is necessary to initiate a progressive (delayed) breakdown for fracture behavior evaluation.

Fig. 5.1

Curves of pump pressure and injection rate versus time for Specimen P-17 (P_con = 17 MPa)

Additionally, we outlined a local zoom of a time zone (Fig. 5.1b) when increasing the fluid pressure from zero to its target value (P_con = 17 MPa). The fluid injection rate and pressure decay rate were respectively recorded and calculated during the loading process, whose absolute values, unlike the increasing trend of pump pressure, increased first and then decreased to zero once the fluid pressure reached the preset pressure. Note that the minus sign of the pressure decay rate corresponds to the case that the fluid pressure is continuously increasing. Practically, the variations of injection rate and fluid pressure are associated with the initial fluid flow in the pipeline and wellbore, where the air is evacuated or compressed into smaller volumes with the accumulation of the injected fluid [11]. In this case, the initial variation of pum** parameters (fluid pressure or injection rate) may only reflect a primary change and adjustment in the stress state of the wellbore rather than a direct response of fracture behaviors. Therefore, this loading phase will not be analyzed when evaluating the relationship between fracture characteristics and pum** parameters in the following sections.

• (2) Local pressure drop (specimen P-19)

The fracturing results for Specimen P-19 are presented in terms of pump pressure, injection rate, and pressure decay rate over time, as seen in Fig. 5.2. A similar constant change in pump pressure (constant pressure stage) is visible at P_con = 19 MPa compared with the sample pressurized at P_con = 17 MPa in Fig. 5.2a. We can see that within the first 400 min of hydrofracturing (excluding the initial loading stage), the pump pressure gradually stabilized at a level of 19 MPa, with the injection rate fluctuating around an average value of 0.1 mL/min. This fluctuation feature of the injection rate is different from the no fluid leakage phenomenon (V_inj = 0) under 17 MPa pump pressure, which implies that the static equilibrium previously observed at P_con = 17 MPa breaks as the pump pressure increases to 19 MPa. Instead, there is a stable leakage stage with constant pressure (19 MPa) and a roughly stable injection rate (0.1 mL/min), indicating that the sample-fluid (injection) system reaches a new dynamic equilibrium where a constant fluid leakage was maintained by the constant pump pressure (i.e., inflow equals outflow). This circumstance is possibly attributed to the occurrence of a local crack that connects the wellbore with the rock surface and provides a flow channel for the injected fluid, as later confirmed in Sect. 5.2.2. As a result, the internal fluid will continually spill out of the wellbore via an oriented crack channel, which further holds back the closure of the crack. Nevertheless, due to the actual compactivity of fracturing fluid, the outflow is not strictly stable, which appears to be an indirect reflection of the fluctuation of the injection flow [12]. On the other hand, these results indicate that the currently pumped 19 MPa fluid pressure can only initiate local cracks (or partly activated bedding planes) in the shale specimen with a constant aperture (opening) rather than further promote crack growth.

Fig. 5.2

Curves of pump pressure and injection rate as a function of time for Specimen P-19 (P_con = 19 MPa)

It is noteworthy that after T_inj = 403 min, the pump pressure started to decline, and the injection rate suddenly dropped to zero (Fig. 5.2a). These variations of the curves were caused by the stop** pum** operation when the fracturing fluid in the pump chamber was exhausted and the fluid injection was passively terminated, signifying the end of the hydraulic fracturing experiment.

In a partially enlarged view of the local cracking stage (Fig. 5.2b), a rapid change in fluid pressure was recorded, accompanied by an increase in the injection rate, which is consistent well with the previous reports [12,13,14]. By integrating the P_inj data, the pressure decay rate became evident, which helped classify the curves into three key stages. First, the constant pressure stage (1.5–120 s) was maintained at v_decay = 0 MPa/s and V_inj = 0 mL/min as the wellbore was subject to a constant pressure of 19 MPa. These variations of curves for Specimen P-19 look like those of Specimen P-17, demonstrating that Specimen P-19 is also in static equilibrium during this period. Afterward, the curves entered the second (typical) stage of local cracking at T_pd = 120 s, when the pump pressure started to decline. Shortly after a period of 15 s, the pump pressure dropped to the lowest (18.805 MPa) and then rebounded to an approximately stable level. This typical process was named P_inj oscillation, which was caused by the fracture tip locally outpacing the driving fluid and then catching up to further extend the crack, according to Gehne et al. [8].

During the P_inj oscillation, the pressure decay rate changed significantly in response to a slight drop-off in the pump pressure. Meanwhile, a noticeable change in the curve of injection rate was recorded with the maximum value (maxV_inj) of 0.82 mL/min at maxT_inj = 126 s. Considering the fact that a slight decline in the pump pressure always coincides with a sharp increase in the injection rate, we may ulteriorly correlate the fluctuation of pressure decay rate with the evolution of the injection rate. The variation of the injection rate allows the wellbore to be compensated with an appropriate amount of fluid so as to maintain a constant pressure output (P_con = 19 MPa) under feedback loop control. Hence, the attenuation rate of wellbore pressure should correspond to the compensation rate of the injected fluid. The maximum v_decay (237.6 MPa/s) occurred at T_inj = 125 s, which is 1 s earlier than the maximum injection rate. This distinction illustrates that the variation of injection rate lags the fluid pressure decay rate. From this point of view, the fluctuating injection rate can be considered the result of fluid pressure oscillation in the wellbore under constant pressure output. As the fluid pressure gradually stabilized around 19 MPa (v_decay → 0), the injection rate decreased accordingly, approximating a constant rate (V_inj = 0.1 mL/min), which heralds the beginning of the stable leakage stage. This stage is in dynamic equilibrium where fluid inflow is equal to fluid outflow, as expounded above. However, it is noteworthy that the pressure oscillation accompanied by flow compensation can still be observed, particularly during the preliminary leakage. Unlike the previous stage, curve oscillations during the leakage stage are mainly reflected in the injection and pressure decay rates: each increase in pressure decay rate was associated with an increase in the injection rate. By contrast, the fluid pressure changes are almost indistinguishable. In this sense, the pressure decay rate (v_decay) behaves more sensitively to the changes in fracture initiation, which demonstrates the feasibility of employing this pressure gradient (v_decay) to evaluate fracture initiation.

• (3) Continuous pressure drop (specimen P-21)

Figure 5.3 shows the hydraulic fracturing data under the constant pressure of 21 MPa. Some characteristics of the curves for P-21 are similar to previous examples (P-17 and P-19): a constant pressure stage (7.5–1560 s) was first observed after the pump pressure reached its target value. Then, a local cracking stage emerged, followed by a more evident fluid pressure oscillation compared to the Specimen P-19. However, the pump pressure did not return to a constant value like recorded in Fig. 5.2. Instead, it remained an approximately steady downward trend accompanied by a uniformly varying injection rate (Fig. 5.3a). This process continued for 618 s until T_inj = 2178 s when significant changes in the pump pressure curve were observed alongside a stepwise increase of injection rate. These variations indicate that the curves stepped into a new stage (unstable cracking) completely different from other stages in previous examples. During this unstable cracking stage (Fig. 5.3a), the fluid pressure in the wellbore kept decreasing until encountering a transient plateau (2234–2429 s) after a sudden pressure reduction and recovery. Shortly afterward (57 s), the pressure dropped remarkably, with the injection rate rising to the maximum (maxV_inj = 106.62 mL/min). This significant drop-off in fluid pressure means that the current stress conditions and the sample deformation are no longer sufficient to create an extra barrier to maintain the wellbore’s constant pressurization for a long duration. Following these changes, yellow-green fracturing fluid was seen leaking from new cracks on the sample surface, which finally resulted in the loss of specimen integrity. The hydraulic fracturing pump was manually shut down as soon as the fluid pressure declined to zero for the sake of protecting the experimental setup from liquid shocks. This operation causes a plummet in injection rate at the end of the experiment (T_inj = 2495 s), as recorded in Fig. 5.3a.

Fig. 5.3

Curves of pump pressure and injection rate versus time for Specimen P-21 (P_con = 21 MPa)

In order to elaborate the variation characteristics of the pump pressure and injection rate for Specimen P-21, the graphs of local cracking and unstable cracking stages were separately amplified in Fig. 5.3b and c. Similar to Specimen P-19, the pump pressure experienced a pressure (P_inj) oscillation (v_decay = 170.18 MPa/s) at the beginning of the local cracking stage and then jumped into a transient and stable leakage state with a constant injection rate of 0.12 mL/min from T_inj = 1630 to 1666 s as marked in grey shadow in Fig. 5.3b. These similarities suggest approximate fracture behavior of Specimen P-19 and Specimen P-21 during the initial fracturing process, where the inflowing fluid equally compensates the outflowing fluid. Within 303 s after the leakage state, P_inj decreased gradually and uniformly with the increase of V_inj. The fluctuation of the pressure decay rate also corresponds to the variation of the injection rate. Subsequently, the pump pressure met a new P_inj oscillation at T_inj = 1976s with a pressure decay rate of 208.88 MPa/s. The new P_inj oscillation is relatively weaker than the previous oscillation at T_inj = 1578 s. In addition, a higher injection rate (V_inj = 1.685 mL/min) at T_inj = 1979s was observed in the second fluid oscillation compared to the maximum injection rate (V_inj = 1.3 mL/min) at T_inj = 1583 s in the first fluid oscillation.

By contrasting the pressure curve of carbonate rocks with AE events under constant pressure injection conditions, Lu et al. [14] reported that the precursor pressure oscillation was indicative of new fracture initiation and growth. This fracture initiation may provide more leakage paths for internal fluid. Thus, new fracture initiation or propagation could be responsible for the oscillation cases portrayed in Fig. 5.3b. On this basis, different oscillation degrees of the injection rate and the pressure decay rate should have a correlation with the fracture behavior and final morphology, which will be further analyzed and discussed in Sect. 5.2.2. It is also interesting to note that the changes in injection rate (V_inj) always lag the changes in pressure decay rate (v_decay) in the leakage stages of Specimen P-19 and Specimen P-21. Through comparison, we can speculate that this lag effect is caused by the pump’s feedback control loop, which works by tracking pressure changes and adjusting the flow rate in an effort to regain constant pressure output. Under different pressure conditions, the lag time (hereafter refers to the time interval between the variations of v_decay and V_inj under the same P_inj oscillation) is different. For example, the lag time decreases from 5 s under ΔP_inj = 0.52 MPa (first oscillation) to 3 s under ΔP_inj = 0.2 MPa (new oscillation). For the P_inj oscillation of Specimen P-19 with ΔP_inj = 0.164 MPa, the lag time becomes even shorter (1 s). These indicate that the lag time increases with the increase of the pump pressure decrement (ΔP_inj) at the oscillation point. More significant pressure decrements usually correspond to more extended fractures [15]. Therefore, the variation of lag time can reflect the cracking degree (fracture length and width) of hydraulic fractures in the specimen.

As Fig. 5.3c shows, the unstable cracking stage is relatively unique compared to the previously observed stages. A sudden pump pressure drop followed an initial gentle decay of pump pressure (2160–2223 s). Each decrease in pump pressure corresponds to the next jump of injection rate and a significant fluctuation of the pressure decay rate. Then, the pump pressure entered a plateau (P_inj ≈17.77 MPa) when the injection rate still maintained a growing trend. Integrating the injection rate over time, we noted that the injected fluid volume is essentially equal to the sum of the leakage fluid amount and the crack volume inside the specimen. In the case of a constant leakage from a crack with a specified length (or width) at a certain P_inj, the increasing trend of injection rate broadly reflects the increase of the crack length (or width) per unit time inside the specimen. In this case, the sample was in the progressive failure stage, where crack opening and length increased gradually [16]. However, the continuously rising injection rate can only represent an increase in the fracture size (width and length) but cannot locate the specific crack coordinates. In other words, the increasing injection rate is a composite response of the crack volume change inside the rock, independent of crack location. At T_inj = 2428 s, the pump pressure started to drop rapidly. The maximum pressure decay rate (229.5 MPa/s) occurred at T_inj = 2484 s, and 1 s later, the injection rate reached its maximum maxV_inj = 106.82 mL/min. In addition, the period of rapid pressure decay suggests that the output of 21 MPa fluid pressure cannot consistently maintain a constant fluid leakage like observed in P-19. Instead, the 21 MPa fluid pressure will finally induce the initiation of new cracks.

In general, different pressure–time curves of the specimens (P-17, P-19, and P-21) have similar constant pressure stages. However, as the predetermined pump pressure increases, the shape of these curves becomes complicated, which indicates the increasing possibility of new fractures. In order to verify this conclusion, it is necessary to evaluate the hydraulic fracture behavior and morphology during the constant pressure fracturing process.

2.2 New Insights from Observing Hydraulic Fracture Morphology

The hydrofracturing characteristics of cylindrical specimens are conventionally described as a scenario that the fracture propagates radially via the shortest stress path, then, once the radial fracture reaches the edge of the sample, continuing vertically and rapidly [17, 18]. During this process, the injected fluid is maintained at a constant flow rate (constant flow injection mode), which continually provides an inner impetus for the extension of hydraulic fracture and finally contributes to sample failure. The hydraulic fracture mainly extended along a relatively straight and smooth path with few bifurcations both in the axial and radial directions. With the increase of the axial stress (V-25 in Fig. 5.4b), the fracture in Specimen V-25 (V_inj = 12 mL/min and σ_v = 25 MPa) became slightly twisted and bent in its strike (or radial) direction. Further, while the confinement of lateral pressure (σ_c = 20 MPa) was axisymmetrically applied on the cylindrical specimen surface in Fig. 5.4c, the fracture bifurcated and formed a more complex shape according to Lin et al. [18]. Knowing how the stress conditions affect the fracture morphology is out of the analytic scope of this study. Here we mainly presented the results to show the morphological similarity under constant flow injection conditions. Overall, the rupture of the shale specimen (bedding planes oriented parallel to the axial loading direction) under constant flow injection mode was either confined to or aligned with a single bedding plane so that the fracture can be preferably described as “simple” with relative homogeneous geometry.

Fig. 5.4

Fracture morphology of Specimen V-5 and Specimen V-25 at different experimental stages

However, when the sample is fractured by a series of constant pump pressures (17, 19, and 21 MPa) rather than a constant flow rate (e.g., 12 mL/min), some apparent distinctions can be discerned in terms of the fracture morphology. To present the hydraulic fracture geometry clearly, we carefully sketched the ultimate fracture path on the specimen surface through macroscopic observation, referring to Ishida et al. [19] and Hou et al. [20]. On this basis, a dimensionless parameter, tortuosity, was introduced to evaluate the hydraulic fracture morphology quantitatively, which can be expressed as [21]

$$\tau = \frac{L}{l}$$

(5.3)

where τ denotes the tortuosity, L is the actual length of the hydraulic fracture, l represents the distance between the two ends of the hydraulic fracture. It should be noted that only the tortuosity of the main hydraulic fractures was calculated based on Eq. (5.3).

As shown in Fig. 5.5, no fluid leakage or macroscopic fractures were observed in the shale Specimen P-17 over the entire fracturing process. Further, the smooth and intact 3D morphology of the Specimen P-17 reconstructed by CT scanning data demonstrates that no micro-crack was ever induced inside this sample. From another point of view, the sample remains in static equilibrium, which corresponds to the constant pressure stage as aforementioned in Sect. 5.1. This steady-state confirms that the applied fluid pressure (17 MPa) is insufficient to crack the shale on a time scale of 350 min.

Fig. 5.5

Fracture morphology of Specimen P-17 at different experimental stages

Figure 5.6 shows the fracture morphology of Specimen P-19 at different experimental stages. A local crevice connecting the wellbore with the sample surface appeared about two minutes after the pump started. This result confirms the previous speculation about local leakage for the decrease in pump pressure and the increase in injection rate in Fig. 5.2b. Then, the phenomenon of fluid continuously spilling out of the local crevice was visible throughout the whole experiment (Fig. 5.6b), which corresponds to the stable leakage stage in Fig. 5.2a. The steady fluid leakage (≈0.1 mL/min) inside the specimen reflects the equivalent fluid exchange process between the inflow and the outflow in the wellbore, indicating the local crevice’s approximate stable state (i.e., a crack with roughly fixed length and width). In addition, macroscopic observation under ultraviolet light (Fig. 5.6c) and 3D reconstruction based on CT data (Fig. 5.6d) after the experiment further demonstrated that there was only one local crack generated near the wellbore. Thus, it is reasonable to correlate this local crack with pump pressure and injection rate variations. Comparing Fig. 5.2 with Fig. 5.6, we can conclude that the initiation of the local crack is characterized by the decline of fluid pressure and subsequent rise of injection rate. So, new cracks should be the fundamental reason for changes in the pump pressure and injection rate curves. On the other hand, the rapid decay of pump pressure and the growth of injection rate serve as two indicators for predicting the initiation and propagation state of the tensile crack.

Fig. 5.6

Fracture morphology of Specimen P-19 at different experimental stages

We then focus on the fracture morphology of Specimen P-19 after the fracturing process. The trajectory of the local crevice is outlined by combining the surface photograph and the CT scanning data, as shown in Fig. 5.6c and d. The local crevice is not strictly aligned with the direction of the bedding plane like those cracks induced by constant flow rate (V-5 and V-25), but across a vertical stratification group and restricted in vertical length. The deviation from the bedding direction could be attributed to the simultaneous initiation and the subsequent merge of multiple near-wellbore micro-cracks, eventually forming the visible local crack on the specimen surface. In this case, the macroscopic crack morphology will be dominated by the initial locations of the micro-crack initiation points around the wellbore and may not be consistent with the bedding planes. This phenomenon (i.e., crack initiation at multiple points) has a great propensity to occur when a constant fluid pressure (less than the instantaneous breakdown pressure) is maintained for a period to induce static fatigue damage inside the specimen in line with Bunger and Lu [22] and Zeng et al. [12]. In addition, although the local crack has not yet wholly fractured the rock matrix, some noticeable differences can still be identified in the fracture morphology between the two injection conditions. The local crack path is relatively tortuous (τ = 1.026) compared to those fractures obtained under the constant flow injection mode (τ = 1.001 for V-5 and τ = 1.024 for V-25). This discrepancy is essentially due to different degrees of fluid diffusion in the rock matrix. Under the constant flow case, the wellbore is likely in a “fast” (nonfluid-penetrating) pressurization regime [7], while during the constant pressure fracturing (static fatigue) process, more fluid can permeate the rock, which effectively reduces rock breakdown pressure and forms complex and undulated fractures [23].

As the wellbore pressurization remains at 21 MPa, the hydraulic fracture appears to be somewhat more complex. Figure 5.7a shows the specimen observed before the experiment. The surface is relatively homogeneous, with notable bedding planes parallel to the sample axis. During the experiment (Fig. 5.7b), the emergence of crack 1# was first recorded by photography at T_inj = 27 min. This crack caused the first P_inj oscillation in the local cracking stage of Fig. 5.3b. After about 7 min, another crack 2# appeared on the left side of the sample, which precisely corresponds to the new P_inj oscillation in the local cracking stage. The leaking fluorescent fracturing fluid perfectly exhibited the position and propagation state of the local cracks. As the experiment progressed, crack 1# started to propagate vertically, which should be related to the non-uniform decline in fluid pressure during the unstable cracking stage in Fig. 5.3c. The flow trajectory of the leaked yellow-green liquid roughly depicts the geometry of the hydraulic fractures. Figure 5.7c displays the resulting fracture morphology obtained by direct observation (under UV light), sketch, and 3D reconstruction after the experiment. The twisted and tortuous fractures indicate that both the tensile and shear stresses are responsible for crack propagation [5.3b), Specimen P-21 experienced two evident P_inj oscillations, which correspond to the two cracks (1# and 2#) on the specimen surface, respectively. For the first P_inj oscillation, the maximum decrement of P_inj, v_decay, and V_inj during the oscillation is 0.52 MPa, 287.63 MPa/s, –1.3 mL/min, respectively, more significant than that (ΔP_inj = 0.2 MPa, Δv_decay = 249.66 MPa/s, and ΔV_inj = -–0.715 mL/min) of the second P_inj oscillation. The P_inj oscillation in Specimen P-19 shows that the decrements of these parameters are 0.16 MPa, 237.6 MPa/s, and 0.57 mL/min, respectively. Combining the fracture leakage situation that followed these P_inj oscillations in Figs. 5.6b and 5.7b, we can infer that higher pressure decrement (or injection rate increase) corresponds to more significant fluid leakage as well as more extended fractures. This phenomenon becomes particularly evident at the end of the unstable cracking stage (Fig. 5.3(c)), where a sudden drop of fluid pressure (7.17 MPa) accompanied by a relatively intact vertical hydraulic fracture (1#) emerged (Fig. 5.7b–iii), with the maxV = 106.82 mL/min and the maximum v_decay = 13,770 MPa/s. This result presents a possible explanation for the (positive) correlation between the lag time and the pump pressure changes. It is likely to be the case that the relatively high P_inj oscillation promotes longer cracks such that more time is required for fluid injection to maintain a constant pressure.

After each P_inj oscillation, as observed in Figs. 5.2b and 5.3a, the pump pressure tends to return to a constant level and remain for a few minutes until the next pressure drop-off. The injection rate is gradually leveling off amid this process. These observations are consistent with an interpretation that cracks can be arrested after their initial growth due to the interaction of the initiating fracture with the near-wellbore stress concentration, which has been theoretically verified by Detournay and Carbonell [7] and experimentally illustrated by Lu et al. [14]. Following such crack arrests, there is an unstable cracking stage (Fig. 5.3c) prior to the final loss of specimen integrity, in which a pressure plateau is visible accompanied by an approximately steady increase in the injection rate. Practically, to maintain the steadily increasing injection rate, the crack aperture and length should also change uniformly, which indicates that the pressure plateau corresponds to the stable propagation of hydraulic fractures. Other irregular fluctuations in the unstable cracking stage can be correlated to the process of unstable fracture propagation, which is influenced by the specimen geometry and imposed stress boundaries according to Gehne et al. [8] and Benshion et al. [25].

In summary, under constant pressure injection conditions, the fracture initiation and failure induced by static fatigue can exhibit a time-dependent progressive process like Specimen P-19 and P-21. In contrast to the smooth and straight fractures under constant flow tests, multiple fracture initiations may occur to form an undulated fracture deviating from the bedding direction. In addition, a more tortuous and complex hydraulic fracture is favored in the specimen as the constant output pressure is relatively high. In addition, the crack behaviors, such as initiation, arrest, stable and unstable propagation, are closely related to the relative variations of pump pressure, injection rate, and pressure decay rate. These findings provide a basis for possibly employing the curves of pump pressure and injection rate to predict and evaluate the extension range of hydraulic fracture in practical hydrofracturing engineering.

3 Correlation Between Fracture Behavior and Pum** Parameters Based on Engineering Parameters

Previous field tests can also verify the relationship between the crack behavior and the pum** parameters. Zorn et al. [26] analyzed the characteristics of the microseismic signals in the Marcellus shale formation (Pennsylvania, America) during the horizontal hydraulic fracturing process. Figure 5.9a displays the map view of passive microseismic monitoring results. The injection fluid was stably pumped by a flow rate ranging from 763 to 960 m³ per hour for all treatments. Thus, the flow rate (or volume) controlled injection mode was practically achieved during hydrofracturing, although the injection rate did not remain constant. The b-value and D-value, as delineated in Fig. 5.9b, are indicators, which represent the fractal properties of microseismics. During hydrofracturing, the onset of seismic events fluid pressurization is correlated with the decrease of the pump pressure and injection rate (marked with red dotted boxes in Fig. 5.9b), which implies that the field hydrofracturing characteristics of shale formations can be reflected by the variation of pum** parameters (pump pressure and slurry rate). These apparent correlations between changes in the microseismic events and pump pressure and rate perturbations reveal quantitatively that the fracture state and permeability of rock mass are continuously changing throughout hydraulic fracturing.

Fig. 5.9

Microseismic monitoring results during hydraulic fracturing operations in the Marcellus shale (after Zorn et al. [26]): a map view of microseismic monitoring results for Wells 1 ~ 6; b The recorded seismic and pum** variation in Stage 10 Well 1. Note that the b-value and D-value are indicators evaluating the fractal properties of microseismic according to Zorn et al. [26]

If combining the laboratory observations in Figs. 5.3 and 5.10, we can further conclude that whether under constant pressure or constant flow mode, the initiation of a new crack corresponds to the decline of the pump pressure. However, the fracturing mechanism under the two injection modes differs in the variation of the pump pressure. For the constant pressure mode, the injected fluid pressure remains constant, and only when the pressurization lasts for enough period can rupture occur. In this case, the constantly controlled pressure servers as the fundamental driving force for the rupture of the shale specimens and thus controls the whole fracturing process. As aforementioned in Sect. 5.2, the initiation of a new crack (crack 1# or crack 2# in Fig. 5.7) was followed by a first decay in fluid pressure and a subsequent increase in injection rate, which indicates a phenomenon that the variation of injection rate lags pump pressure for the constant pressure mode. In the constant flow mode, the increase of pump pressure is unceasingly sustained by the equal inflow of fracturing fluid, ultimately resulting in the breakdown of shale blocks. This rupture of the shale samples under this injection mode is usually characterized by the first increasing and then decreasing pump pressure and the invariable injection rate at the laboratory scale [18, 27]. However, during the field treatment, the stable injection of fracturing fluid can hardly be maintained due to the need to pump proppant materials (e.g., sand, ceramsite). An example illustrating the variation of fluid pressure and injection rate in the field setting can be found in the work of Vulgamore et al. [28], who applied fracture diagnostics in the Woodford shale. The overall variation trend of the treatment pump pressure is similar to the constant flow tests (V-5 and V-25) during the fracturing stage. However, before the pump pressure reached the breakdown value, the injection rate peaked at the time T₁. After the second shutdown of the pump, the decline of the pressure also lagged the injection rate. These results are contrary to the observation under constant pressure mode (i.e., V_inj lagging P_inj), indicating that the different injection modes will change the pump pressure and injection rate variation. In actuality, the different injection modes correspond to different cases of fluid diffusion in the rock matrix, which can change the effective stress around the wellbore and ultimately result in differences in specimen failure [29]. According to Vulgamore et al. [28], more microseismic events and more significant pressure fluctuation were found in the breakdown and sanding process, which ulteriorly demonstrates the correlation between the crack initiation and the variation of pump pressure.

Fig. 5.10

Schematic diagram of variations of pum** parameters resulting from a constant flow condition, and b–d constant pressure condition: a instantaneous failure; b constant pressure (case (i)); c stable leakage (case (ii)); d continuous propagation process (case (iii))

4 Characterization of the Relationship Between Fracture Propagation and Pum** Parameters

The tensile hydraulic fracture is known to be induced via a complex crack-tip fracture process zone constituted by a zone of cohesive and high shear stress [30]. This zone is physically described as a lag with an unknown length between the fluid front and the fracture tip, full of the inviscid vapors from the fracturing fluid and the compressed air [31]. The presence of this crack-tip cavity, to a certain extent, removes the crack-tip singularity in the fluid pressure, according to Detournay [32]. In this case, the initiation of a new crack will merely require the fluid pressure to reach a critical value sufficient for overcoming the tensile strength of the rock matrix (or bedding planes). For the volume-controlled (or constant flow) tests, as mentioned in Sect. 5.2, the wellbore pressurization is probably in a fast nonfluid-penetrating regime, which results in a relatively high instantaneous breakdown pressure in line with Detournay and Carbonell [7]. Figure 5.10a roughly describes the pump pressure and injection rate variations during this instantaneous process. Under the constant pressure injection mode, a target pump pressure lower than the instantaneous breakdown pressure was applied and held constant for an extended period. Despite the low permeability of shale, constant pressurization and fluid diffusion can still be synchronously achieved as the loading duration is long enough. With the increase of this duration, the diffusion area of the pore pressure in the rock also increases, which significantly reduces the near-wellbore effective stress and increases the possibility of specimen failure.

Combining the experimental results (P-17, P-19, and P-21), we can see that there are three prominent failure cases under the constant pressure conditions: (i) If the target pressure is relatively low, no crack is induced inside the specimen, which corresponds to a long constant pressure stage as Fig. 5.10b depicts. Once a tensile notch appears, the constant pressure feedback loop control pushes excess fracturing fluid into the defects, resulting in a subsequent decrease in pump pressure and increased fluid flow (i.e., local cracking stage). The fluid is continuously injected into the specimen until a balance is reached between the notch space and fluid flow. (ii) If the fracture (notch) growth is arrested and the fracturing fluid can leak out via the notch, a stable leakage state (Fig. 5.10c) may be observed throughout the entire experiment, like Specimen P-19. (iii) Otherwise, a new crack near the notch appears accompanied by another decrease in fluid pressure and buildup in injection rate. Afterward, the pressure within the crack will be ramped up, followed by a decrease in the fluid flow, and then gradually approach a new balance between the power of the squeezed fluid and the strength of the shale block (or bedding planes). Another crack initiation near the last crack will break the new balance again and result in similar parameter changes. Therefore, the continuous propagation of hydraulic fractures is likely characterized by the cyclical variation of pum** parameters: the increases in injection rate and pump pressure occur alternately, as shown in Fig. 5.10d.