1. Introduction
The development of conventional petroleum reservoirs has been unable to keep pace with the increasing global energy demand, which has shifted industrial attention to low permeability or tight reservoirs [
1]. Rapid development of horizontal wells and multi-stage hydraulic fracturing technology enables unconventional tight reservoirs to be exploited [
2,
3]. In the process of stimulation, hydraulic fractures may connect and reactivate the already existing natural fractures or generate new induced fractures near the wellbore. Well productivity could be substantially increased if complex fracture networks are created by hydraulic fracturing [
4,
5].
Different from conventional fracturing, slickwater is the most commonly used fracturing fluid in unconventional reservoirs. Slickwater has a relatively low cost and low viscosity, which may help to create complex fracture networks [
5,
6,
7]. Horizontal wells that undergo multi-stage fracturing operations often require a large amount of water injected into the formation to create a large stimulated reservoir volume. After hydraulic fracturing is completed, the flowback treatment of fracturing fluid should be carried out, followed by long-term production [
8,
9,
10]. However, field data show that the recovery efficiency of tight oil or gas wells is generally low, and a remarkable fraction of fracturing fluid remains in the reservoir even after long-term production [
11,
12,
13,
14]. Scholars have carried out some work to clarify the problems arising after hydraulic fracturing and to help improve the clean-up operation in low permeability formations [
15,
16].
If hydraulic fracturing fluid is trapped in the formation, then it must be in the rock matrix or fracture systems [
17]. An analytical model was presented for spontaneous imbibition of capillary force, which explained the fracturing fluid was imbibed into the shale matrix by strong capillary forces [
18]. However, Dutta et al. [
19] showed that water-loss rate of low-permeability sands was far lower than that of high-permeability sands. Although the tight sands had strong capillary force, the low permeability of the formation also limited water imbibition. Similarly, experimental data showed that the water imbibition capacity of tight shale was very low, even for hydrophilic rock samples [
20]. Furthermore, it was difficult to explain the reason for low water recovery efficiency when the spontaneous capillary forces were absent in oil-wet tight rocks [
21,
22] or the wells were immediately cleaned up without shut-in. By analyzing the pressure transient data, natural fractures that re-opened during fracturing were apparently closed in subsequent production processes [
23]. In the process of fracture reopening and closing, water entering natural fractures continues to be imbibed into matrix, and only part of the water can flow back to the wellbore in the end. McClure [
24] focused on the impact of fracture network complexity on water recovery efficiency. The results of his simulations indicated that the closure of unpropped fractures within fracture networks resulted in low water recovery. Fu et al. [
25] collated and processed the early flowback data of seven multi-fractured horizontal wells in tight reservoirs. Data analysis suggested that most of the facture systems were un-propped after stimulation and held most of the fracturing water.
Whether the fracturing fluid remains in the matrix or fractures, it will affect the productivity of tight oil wells. Spontaneous imbibition of fracturing water into the matrix was considered as a possible mechanism to improve oil production [
26,
27]. Extensive experimental and mathematical studies were devoted to explaining the oil displacement efficiency by water imbibition with various rock wettabilities, physical parameters, pore size distribution, and fracture characteristics [
28,
29,
30]. The results showed that water imbibition could drive oil out of the matrix pore, and the displacement effect would be better when the tight rocks contained fractures [
29]. However, Wang and Leung [
31,
32] established a series of numerical models to investigate the water-loss mechanisms during flowback operations. They reported that although prolonging shut-in time could enhance water imbibition into the matrix and increase initial oil rate, there was no benefit for long-term production. Low recovery efficiency means that a large amount of water remains in secondary fractures, which reduced oil mobility and had a negative impact on long-term production. Similar negative impacts were also found in studies of tight shale [
33,
34,
35], where water retention might cause water blocking or damage to hydrocarbon phase relative permeability. Moreover, for tight formations, the invasion of fracturing fluid into the matrix did not require much depth to cause enough damage [
15,
16].
Although the mechanism of fracturing fluid retention underground and its impact on well productivity have been widely studied, there are still many problems to be further explored. Firstly, existing models failed to accurately characterize the distribution of slickwater in matrix and fracture systems during fracturing. These works either directly assign high water saturation value to the fractures or simulate the injection process of fracturing fluid through stress-dependent permeability models [
36,
37]. Although the latter is slightly more reasonable than the former, its mechanism is unrealistic and overestimates the water absorption capacity of the matrix near fractures. The decrease of matrix permeability might be due to compaction, but it was hardly to reasonably increase matrix permeability [
23]. Secondly, after stimulation, secondary fractures and re-opened natural fractures held most of the fracturing water [
38], and fracture depletion was observed during early flowback [
39]. The driving mechanism of fracture-closure is rarely considered in simulation and its impact on water-loss is unclear. Thirdly, the parameters of complex fracture networks are the key factors affecting the distribution of fracturing fluids in formations and subsequent productivity. Numerical studies mainly focus on the density and distribution of natural fractures [
37,
40], while the proppant distribution in complex fracture systems is seldom considered. The stress-dependent porosity and permeability correlations vary because of proppant concentrations, and the effect of proppant embedment on long-term production cannot be neglected [
41,
42]. Finally, the impact of natural fracture heterogeneity on water retention has not been reported.
This paper reports on simulations to better understand water loss and production from complex fracture networks. A triple-porosity model is established by using a numerical reservoir simulator, where matrix and fracture systems are explicitly discretized, so that we can examine imbibition hysteresis and stress-dependent porosity and permeability. The adaptability of a mechanistic model is validated, and the influence of fracture-closure on fracturing water retention is investigated. Next, we quantitatively analyze the effect of uncertain fracture parameters, such as natural fracture density, proppant distribution, and natural fracture heterogeneity. The results of this work can provide a better understanding of the impact of fracture compressibility and uncertainty on water-loss and production performance in tight oil reservoirs.
3. Results and Discussion
Despite the good consistency of the base case results, an ideal historical match with actual flowback data is still difficult to achieve. There are two main reasons: (1) most of the flowback data obtained from the field are daily output, occasionally hourly data, which can hardly reflect the characteristics of early flowback [
31]; and (2) properties of fracture systems are highly uncertain including fracture compressibility, density, and conductivity [
37]. These uncertainties not only make the quantitative validation of simulation results extremely challenging, but also make it difficult to understand the retention mechanism of water and its impact on production. Therefore, a series of models were established to quantify the impact of various factors on water-loss and production performance.
3.1. Impact of Fracture Closure
Extensive analytical models have been used to reveal the fracture depletion process during early flowback. However, these models have some limitations, such as sequential flow and single-phase flow that make it difficult to explain the effect of fracture-closure on two-phase flow in the triple media after oil breakthrough. The flow region of fracture depletion was validated in the previous section, and the impact of fracture-closure on fracturing water retention is modeled here. Three models are built considering different mechanisms: (1) with stress-dependent porosity and permeability (base case), (2) ignoring stress-dependent porosity, and (3) ignoring stress dependence. The simulation result at the end of injection process in basic model is taken as the initial condition to better compare the impacts of three mechanisms on water-loss during flowback. The simulation process is as follows: shut-in for 22 h, then flowback for 10 days, followed by production for half a year.
Figure 10 shows the variation of bottom-hole pressure with time under different mechanisms during flowback. It can be seen from the figure that when considering stress-dependent porosity, the bottom-hole pressure is almost maintained near the fracture-closure pressure for the first half-day, then the pressure drop is gradually accelerated, even lower than the case without considering stress-dependent during the late flowback stage (from the insert figure in
Figure 10). The drive mechanism of fracture-closure can be captured, and this mechanism dominates for nearly five days. The simulation results of production are shown in
Table 3. The oil breakthrough time of the base case is the latest, and the single-phase flow duration is one day longer than that of the other two models, which further reflects the fractured storage effect. Moreover, the water recovery efficiency of the basic case is 55.3%, while ignoring stress-dependent porosity overestimates by 20.8% and ignoring stress dependence overestimates by 26.6%.
The reasons for these differences are illustrated in
Figure 11: (1) the S
w near HF (0.04 m to the fracture surface) in base case remains above 50% during early flowback, and Sw in the deeper matrix also substantially increased. While in the other two models, the S
w near HF has been reduced to 43% and almost no water leaks far away; and (2) the equilibrium point S
w = 0.4 shown in
Figure 3a. The S
w near HF is much higher than 0.4 at the end of fracturing, so the hysteresis results in a capillary force that is resistant to water imbibition. With the decrease of water in HF during flowback, if the fracture-closure is ignored, the water near a fracture will flow back into the fracture, which leads to an increase in water recovery efficiency. On the contrary, when fracture compressibility is considered, the reduced water volume in fractures will be equal to the volume of fracture-closure, which provides an opportunity for water near fractures to infiltrate into the deeper matrix.
From
Figure 11, it can be found that the oil phase appears in NF after one day of flowback, when stress-dependent porosity is absent. This is also a good explanation for why the oil breakthrough time in the base case is delayed. By contrast, the cumulative oil production is the lowest for the basic case. Relatively high water saturation reduces the oil permeability because more water leaks into the matrix. The S
w within NF is relatively high (17%) for the base case, which limits the flow of oil in NF. However, the oil production gap between three models is not large because tight reservoirs do not require very high fracture conductivity, and proppant that is evenly distributed within a fracture should be more important for well productivity [
64].
3.2. Impact of Natural Fracture Density
Extensive studies of natural fracture density have been carried out [
21,
24,
37], but the relationship between fracture complexity and fracture width has not been considered. Zou et al. [
65] reported that the average width of the fracture network decreased as the complexity of a fracture system increased. If this relationship is neglected, the total volume of a complex fracture network should be overestimated with the increase of natural fracture density, which will inevitably interfere with the simulation of water injection and the flowback process. Here, a fracture complexity index (FCI) is introduced to quantitatively evaluate natural fracture density, as shown in Equation (13) [
66]:
where FCI is fracture complexity index; V
nf is volume of natural fractures; and V
hf is volume of hydraulic fractures. The value of FCI increases with the augment of fracture complexity.
A series of models are set up as follows: (1) considering that the half-length of HF is constant for all cases, increasing the number of natural fractures increases the value of FCI; and (2) by adjusting the width of HF and NF, the initial volume of fracture system in each case is equal, as shown in
Table 4, and the width of un-propped NF is assigned less than 2.5 mm [
17]. The simulation process is as follows: (1) water injection for two hours and well shut-in for 22 h [
32], then (2) clean-up at a constant rate for 10 days (in the field the choke size is gradually increasing reported by Clarkson [
62], which is simplified here for simulation and analysis), followed by (3) production at constant pressure for one year.
As can be seen from
Table 4, with the increase of natural fracture density, the contact area between fracture and reservoir increases, which reduces the fluid efficiency during injection and more fracturing fluid leaks into the matrix.
Figure 12a shows that oil breakthrough occurs in all cases during flowback, and the oil rate increases with the increase of NF density. On the first day of converting to constant pressure production, the oil rate of case 5 reached 47.5 m
3/d, which was 4.5 times higher than that of case 1. However,
Figure 12a illustrates that oil production rate decreases with the increase of NF density after half a year of production. The reasons for this phenomenon may be: (1) as the fractures become more complex, more water is imbibed into the deeper matrix, which reduces the oil permeability and interferes the long-term production; (2) due to stress-sensitivity in fractures, the longer production time is related to greater failure of un-propped NF conductivity; and (3) the simulated NFs here are completely connected, so the pressure response quickly reaches the matrix boundary, which limits the oil drainage area. As can be seen from
Table 5, the cumulative oil of case 5 is 64% higher than that of case 1 in half a year of production, and the gap narrows to 40% after one year.
Figure 12b shows that with the increase of NF density, the oil breakthrough time is gradually shortened, and the water recovery efficiency decreases accordingly. For case 1, a single-phase flow lasts for five days under the drive mechanism of fracture closure, and more than 90% of water is recovered after long-term production. This is because of limited contact area between HF and the matrix, the effect of imbibition hysteresis, and high HF conductivity. With the increase of FCI, the drive of HF closure is limited, and transient linear flow in the matrix appears in advance, so the oil breakthrough time is advanced. In addition, even in the production process, spontaneous imbibition is continuing, especially for un-propped NFs with low fracture conductivity. For Case 5, although there is no long-term shut-in, the flowback rate is still less than 50%.
3.3. Impact of Proppant Distribution
Although high fracture conductivity is not required for tight reservoirs, open fractures are better than collapsed ones. Proppants with various grain diameters (ranging from 0.104 mm to 0.838 mm) are commonly used to pack fracture systems during fracturing [
67]. As shown in
Figure 6, the fracture-closure trend is related to proppant concentration, so it is necessary to assess the effect of proppant distribution on water and oil production. Moreover, proppant embedment depending on formation mechanical properties has been extensively studied [
42,
68,
69,
70]. The fracture width loss during production is associated with embedment, especially in soft or weakly consolidated formations, which may lead to a reduction of 60% in propped fracture width [
68]. Therefore, the effect of compaction and embedment on fracture conductivity are considered comprehensively in this work. Due to the lithology of Lucaogou Formation in this paper is similar to the core samples used in Chen’s model [
42], we introduce his formulas, Equations (14)–(16), for calculating proppant embedment that allows for modifying the stress-dependent porosity and permeability [
42] with the results shown in
Figure 13.
In Equations (14)–(16), wf0 is fracture width before embedment, m; h is the proppant embedment, m; η = 2.1 × 10−5, λ = 2.8, when the proppant is 20/40-mesh; and η = 1.6 × 10−5, λ = 3.1, when the proppant is 30/60-mesh.
A series of models are established and various proppant distributions are shown in
Table 6.
Figure 14a shows that the flowback rate is substantially increased when HNF is propped, which is 24.8% and 32.8% higher than un-propped. When NNF is propped, there is a slight increase of flowback rate because of the restraint of low conductivity and stress-dependence in NF. Water within HF and HNF is preferred to recover during early flowback, and a considerable portion of water in NNF is imbibed into the matrix. In addition, it can also be seen from the figure that the variation trends of oil production are similar to the results of water recovery, but there is an obvious difference at various proppant concentrations in HF. The oil production decreases by nearly 25% when proppant concentration in HF decreases, while water production decreases by less than 8% because water production is mainly at the flowback stage, which is mainly driven by fracture closure at the beginning. While oil production is mainly at the production stage, and stress dependence plays a significant role with the extension of time.
Figure 14b shows that when the proppant embedding is considered, the impact on flowback is negligible because water recovery mainly occurs in the early stage of production (flowback) when the main mechanism of fracture closure is compaction. Cumulative oil production is lower when the embedment occurs, and smaller proppant size results in greater loss of production. Furthermore, compared with the embedment in HF, there is greater impact of embedment in NF on oil production. Therefore, it is beneficial to use small size proppant to promote the propping of micro-fractures, but it is also necessary to examine its embedment in micro-fractures.
3.4. Impact of Natural Fracture Heterogeneity
Natural fractures opened during fracturing cannot be uniform, and in the subsequent flowback or production process, excessive closure of some positions may be a key mechanism of water retention. As shown in
Figure 15, NF width is generally non-uniform [
7,
50].
In this work, the heterogeneity of NF conductivity is studied using the Yu et al. [
71] approach to describe heterogeneous distribution of matrix permeability. Three variation coefficients of permeability are used to represent weak heterogeneity, medium homogeneity, and strong heterogeneity, as shown in
Figure 16. Other model parameters and simulation processes are the same as the basic case.
Figure 17 illustrates that, after one year of production, the amount of fracturing fluid remaining in reservoirs increases with the increase of heterogeneity of NF permeability.
Figure 18a shows that the flowback rate decreases with the increase of heterogeneity, in which the rate of strong heterogeneity is 11.2% lower than that of homogeneity. For weak homogeneity, the water recovery efficiency is close to that of homogeneous natural fracture.
Figure 18b shows that the closed natural fracture area still maintains high water saturation during production when there is strong heterogeneity. In addition, the heterogeneity of NF conductivity is 0.1%, 1.5%, and 4.1% less effective for oil production, compared with homogeneity. The reason is that high conductivity is not required for natural fractures in tight reservoirs, and apart from over-closed areas, connected fracture networks are still contributing to productivity.