Abstract
Keywords
Introduction
In recent years, the development of tight oil reservoirs has aroused great interest in petroleum industry (Rashid et al., 2017; Wang et al., 2014a, 2015, 2017). In general, most of the tight reservoirs are exploited by natural energy; therefore, the reservoir rock is in equilibrium state due to a combined action of overburden pressure, pore fluid pressure and matrix stress. However, with the exploitation of the reservoir, the pore fluid pressure decreases, resulting in a gradual increase in the effective stress of the rock matrix and thereby a gradual change in the pore structure and volume. This variation of rock matrix with effective stress is the so-called stress sensitivity, which is also known as pressure sensitivity. The change in pore structure and volume on the other hand will significantly affect the porosity and permeability of the reservoir, and ultimately, it will affect the fluid flow and the production performance of the reservoir (Liu et al., 2017). Especially, a large number of studies have proved that the stress sensitivity of permeability is much significant than the stress sensitivity of porosity. Therefore, most studies in the literature only focus on the stress sensitivity of permeability (Gao et al., 2005; Yu et al., 2007).
The research on the stress sensitivity of permeability for tight oil reservoir has attracted attentions in laboratory studies (Guo et al., 2007; He et al., 2012; Jones, 1975; Li, 2006; Li and Li, 2013; Worthington, 2008; Zhu et al., 2012; Zhu et al., 2011). It is found, however, that most measurements on rock stress sensitivity are based on an individual method, i.e. variable confining pressure (VCP) or variable pore pressure (VPP). Meanwhile, the studies in the literature are limited to conventional reservoirs (Guo et al., 2008; Jiao et al., 2011; Kilmer et al., 1987; Li et al., 2006; Liu et al., 2008; Ren et al., 2012; Wang et al., 2014; Xiao et al., 2010; Zhou and Bai, 2012), while there are only a few studies investigating the stress sensitivity of unconventional reservoirs (Aybar et al., 2015; Kang et al., 2006; Song and Zheng, 2006; Yang et al., 2017, 2013). To shed more light on the stress sensitivity of unconventional oil reservoirs and fill the gaps in the literature, a systematic study on the stress sensitivity of permeability was carried out in this study using both tight sandstone and limestone rock samples. In particular, both VCP and VPP methods were used to determine the stress sensitivity of permeability in tight sandstone and limestone reservoirs at reservoir conditions. In addition, the pore structure of tight sandstone and limestone was analyzed using casting thin section imaging and scanning electron microscopy (SEM), respectively, to reveal the influential factors of stress sensitivity of permeability. To the end, the performance of oil production for stress-sensitive tight reservoirs was analyzed to elucidate the production characteristics of tight reservoirs, and meanwhile, several suggestions on the development strategy of tight reservoirs were also provided to improve the oil production of tight reservoirs.
Experimental methods and procedures
The experiment method used in this study is in reference to SY/T 5358-2010 “Formation damage evaluation by flow test”. A Quizix Q5000 pump (piston pump, which can operate at high precision and ultra-low speed) and a pressure sensor (TRAFAG 8251) were used in the experiments (Figure 1). The key parameters in the experiments are listed as follows: the maximum pressure is 10,000 psi, the maximum flow rate is 15 ml/min and the experimental temperature is 60°0 which is the average temperature of the tight reservoirs. The effective stress is 2–35 MPa in these experiments, which covers the range of the effective stress changes in the reservoirs.

Main experimental devices. (a) Confining pressure variation equipment. (b) Pore pressure variation equipment. (c) Quizix Q5000 pump. (d) Core holder.
Preparation of core samples
In this study, nine tight sandstone cores and nine tight limestone cores in Sichuan Basin were used in the stress sensitivity tests of permeability (Figure 2). Prior to the tests, the experimental core samples were prepared according to the following procedures: first, several piston-like core samples, with a diameter of 2.5 cm, were extracted from the original large core samples; second, these core samples were then cleaned by solvents (e.g. alcohol and benzene); third, the core samples were dried at 65°C in a vacuum oven to a constant weight, and finally the length and the diameter of the dry samples were measured. The basic parameters of the core samples are shown in Table 1.

Pictures of core samples. (a) Tight sandstone. (b) Tight limestone.
Basic parameters of the core samples.
Experiment procedures
Prior to the stress sensitive experiments, the gas permeabilities of tight sandstone and limestone samples were first measured. In fact, the permeability of rock measured with a flow media of gas (not liquid) is usually termed to as the Klinkenberg permeability in petroleum industry. More specifically, the gas permeability for each core sample was measured with five different pressures and flow rates using the nitrogen gas. The Klinkenberg permeability was obtained by a linear regression method, namely, fitting the five experimental points (the permeabilities and the pressure derivatives) with a straight line, and the intersection of the line and its ordinate is the Klinkenberg (1941) permeability. Second, the porosities of the core samples were measured by: vacuuming the core samples for more than 24 h, saturating the core samples with synthetic formation water under 10 MPa and then weighing these wet core samples to calculate the porosity. Finally, the stress sensitivity tests were carried out with VCP and VPP methods, separately. In the VCP method, the outlet of the core sample was connected to the atmosphere. The inlet pressure of the core was kept constant during the experiment, while the effective stress of the core was varied by changing the confining pressure (CP). In the VPP method, a variable back pressure was exerted to the outlet of the core sample; however, the original back pressure remained to be the same as the original reservoir pressure. Meanwhile, the CP was kept constant to simulate a constant overburden pressure (Gong and Xie, 1989; Wu et al., 1999). The effective stress of the core was varied by changing the back pressure. The stress sensitivity of permeability was tested by the following procedures: (a) the initial effective stress was used as the starting point, then the effective stress was increased slowly, with an interval of 4 MPa, until a maximum value was reached. (b) At each pre-set effective stress point, the permeability was measured when the gas flow stabilized. (c) The effective stress was gradually reduced to the initial effective stress, with an interval of 4 MPa, after reaching the maximum value. At each pre-set effective stress point, the permeability was measured when the gas flow stabilized. A schematic diagram of the experimental setup is shown in Figure 3.

Flow chart of the experiment.
Analysis of results
In this paper, the stress sensitivity of the permeability for tight sandstone and limestone samples was tested by two methods VCP and VPP. In the VCP method, the CP increases first followed by a decrease, by which the effective stress increases first and then it decreases. In the VPP method, the pore pressure decreases first followed by an increase; therefore, the effective stress changes in the same way as the former method. The stress sensitivity of permeability can be estimated by three formulas (SY/T 5358-2010)
Stress sensitivity experiments of the tight sandstone
Figures 4(a) and 5(a) show the experimental results of permeability for the tight sandstone measured by the VCP method. It can be seen that the permeability of the core sample decreases with an increase in the effective stress, showing a significant stress sensitivity in the permeability of tight sandstones. In addition, the decrease in permeability is found to be very quick with an effective stress of 10–20 MPa, while the decrease in permeability slows down when the effective stress increases from 20 MPa to 33.3 MPa (Yang et al., 2017). To the end, the

Stress sensitivity curve of the tight sandstone and limestone. (a) VCP (sandstone). (b) VPP (sandstone). (c) VCP (limestone). (d) VPP (limestone).

The stress sensitivity of permeability for the (a) tight sandstone and (b) tight limestone.
Figures 4(b) and 5(a) show the experimental results of permeability for the tight sandstone measured by the VPP method. The permeability of the core sample also decreases with the increase in the effective stress, and the
Stress sensitivity experiments of the tight limestone
Figures 4(c) and 5(b) show the experimental results of permeability for the tight limestone measured by the VCP method. The permeability of the core sample is found to drop rapidly with the increase of the effective stress from 10 MPa to 20 MPa, and then it decreases slowly with a further increase in the effective stress from 20 MPa to 35 MPa. In consequence, the
Figures 4(d) and 5(b) show the experimental results of permeability for the tight limestone measured by the VPP method. The permeability of the core sample decreases with an increase in the effective stress, and the
From the above experiment results, it can be concluded that the loss in permeability by increasing effective stress is very high (e.g.
Comparison on the stress sensitivity between different core samples
The relationship between

The relationship between
The difference in the stress sensitivity of permeability between the tight sandstone and the tight limestone can be attributed to the differences in their mineral compositions and types of pore structure. The Jurassic tight sandstone in the Sichuan tight oil reservoir is primarily comprised of sand grains cemented by mud. The pores are mainly composed of isolated intergranular pores and intergranular dissolved pores. Figure 7(a) shows a casting thin section of the tight sandstone, which suggests that the pores are connected by narrow throats. In direct contrast, the Jurassic tight limestone in the Sichuan tight oil reservoir is composed by bivalve bioclastic particles with calcite crystals distributed between these particles. Figure 7(b) shows an SEM image of the tight limestone, which suggests that the bivalve particles present in the form of strips, and meanwhile, both micro- and nanoscale fractures are found to develop on these interstitial materials.

(a) Casting thin section of the tight sandstone and (b) SEM image of the tight limestone.
It has been reported that when the pressure of the tight reservoir decreases, the throats are first compressed, instead of the pores, to primarily control the permeability of the tight sandstone (Ruan and Wang, 2002; Xiang et al., 2002). Hence, the size and the shape of the throats are the main factors contributing to the stress sensitivity of the rock permeability (Buchsteiner et al., 1993; Fatt and Davis, 1952). In this study, the connectivity of the tight sandstone is poor because it is mainly determined by narrow throats, as observed from the image of casting thin section. Therefore, the stress sensitivity in the permeability of the tight sandstone is strong. In tight limestone, despite the pore–throat structure, a lot of micro–nano fractures can be observed from the SEM image. These tiny fractures serve as both reservoir space and flow channel. Thus, the connectivity of the tight limestone is better than that of the tight sandstone. As a consequence, the stress sensitivity of the tight limestone is lower than that of the tight sandstone.
Comparison on the stress sensitivity between VPP and VCP methods
In this study, both VPP and VCP methods are used to analyze the stress sensitivity of the permeability. To compare these two methods, the experimental permeability from stress sensitivity tests for limestone is used as an example, and the results are shown in Figure 8. It is observed that the stress sensitivity of permeability measured by the VCP method is greater than that measured by the VPP method. In fact, the overburden pressure (i.e. CP) of the reservoir remains constant with the recovery of oil and gas, while the pore fluid pressure in the reservoir changes dynamically. Hence, the experimental results measured by VPP method can reflect the actual development of the tight reservoir (Tian et al., 2015). On the contrary, the experimental results by the VCP method can overestimate the stress sensitivity of the reservoir due to the variations in the CP. It also can be concluded that the

The relationship between
Development characteristics of the stress-sensitive tight reservoir
The oil production data of two volume fracturing horizontal well A and well B in the tight sandstone reservoir M, and two volume fracturing horizontal well C and well D in the tight limestone reservoir N were analyzed to evaluate the development characteristics of the stress-sensitive tight reservoirs. From the stress sensitivity experiments, we have known that the stress sensitivity of permeability for M (sandstone) and N (limestone) reservoirs are very strong. However, the stress sensitivities of permeability for wells A and B are similar, and those of wells C and D are similar as well. In addition, wells A and C produce by means of amplifying the producing pressure drop, while wells B and D produce by controlling the producing pressure drop.
In Figure 9, it is shown that the oil productions of wells A and C are high at initial stage but the productions decrease rapidly afterwards, and the cumulative productions of well A or C are low. In contrast, the initial oil productions of wells B and D are relatively low, and meanwhile, the productions decrease slowly, and the cumulative productions are relatively high. Therefore, for tight reservoirs with high stress sensitivity, the producing pressure drop can be controlled by selecting a reasonable producing pressure drop to reduce the damage in permeability caused by the stress sensitivity, and thus decreases the decline rate of oil production. To this end, a higher cumulative production from a single well can be achieved due to the maintenance of a much longer stable production period for the single well.

Dynamic production curve of spatial fracturing horizontal wells. (a) Well A and Well B. (b) Well C and Well D.
Conclusions
This paper presents an experimental study of the stress sensitivity of tight sandstone and limestone reservoirs. The main conclusions of this study can be summarized as follows:
In the stress sensitivity experiments by VCP and VPP methods, it is found that both tight sandstone and limestone reservoirs have strong stress sensitivity of permeability, showing that the tight reservoir with a smaller initial permeability has a higher From the above experiment results, it can be concluded that the loss in permeability by increasing effective stress is very high (e.g. From the observation of the casting thin section, it is found that the connectivity in sandstone rocks is primarily determined by narrow throats, introducing strong stress sensitivity of permeability for tight sandstone reservoirs, while plenty of micro–nano fractures can be observed from the SEM image of tight limestone, introducing relatively weak stress sensitivity of permeability for tight limestone reservoirs. VCP method overestimates the stress sensitivity of the reservoir, whereas the VPP method can better reflect the stress sensitivity during the development of the reservoir. However, the results of both methods suggest that the recovery of the permeability for tight sandstone and limestone reservoirs is very low with the backup of pressure, indicating an irreversible effect of stress sensitivity for tight reservoirs. By analyzing the oil productions from several wells in tight reservoirs, it is found that for tight reservoirs with high stress sensitivity, the initial oil production drops quickly, while for tight reservoirs with low stress sensitivity, the oil production can maintain high and stable for a long period of time. Therefore, the oil production of tight reservoirs can be controlled by lowering the pressure drop in order to reduce the damage in permeability caused by the stress sensitivity.
