Influence of stress sensitivity on microscopic pore structure and fluid flow in porous media

Journal of Natural Gas Science and Engineering 36 (2016) 20e31

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Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse

Influence of stress sensitivity on microscopic pore structure and fluid flow in porous media Yongfei Yang a, *, Wenjie Zhang a, Ying Gao b, Yujin Wan c, Yunhe Su c, Senyou An a, Hai Sun a, Lei Zhang a, Jianlin Zhao a, Lei Liu a, Pengfei Liu a, Zhihui Liu a, Aifen Li a, Jun Yao a, ** a b c

School of Petroleum Engineering, China University of Petroleum (East China), Qingdao, Shandong, 266580, China Department of Earth Science and Engineering, Imperial College London, London, SW7 2AZ, UK Langfang Branch, PetroChina Petroleum Exploration and Development Research Institute, Langfang, Hebei, 065007, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 14 April 2016 Received in revised form 22 September 2016 Accepted 23 September 2016 Available online 28 September 2016

At present, large quantities of experiments related to stress sensitivities on the macroscale have been conducted. Pore structure is complicated, especially in unconventional reservoirs of tight sandstone. As a result, stress sensitivity has a great influence on changing the pore space. This is of great significance for enhancing oil recovery to systematically study the stress sensitivity at the pore scale. In this paper, based on CT scanning technology, which can capture the real pore space characteristics of the core samples, and combined with a digital core and pore network model, the relationships between the effective stress and the pore structure are obtained. First, the theory and method of constructing the digital core and extracting the pore network model according to CT scanning are introduced. The 3D core image could be obtained after CT scanning, and the digital core is established after filtering and segmentation. The rock structure characteristics are obtained from analyzing the geometry-topology structure of the extracted pore network model, and the fluid flow analysis is conducted by numerical flow simulation. Second, the stress sensitivity experiments and analysis are conducted. Stress sensitivity experiments are performed in the carbon fiber core holder, and the core is scanned under a series of pressures. Digital cores and pore network models under a series of pressures are obtained, and the corresponding pore structure characteristics and fluid flow laws are analyzed. Last, these methods are employed in middle-high permeability sandstone and tight sandstone. The stress sensitivities of these sandstones are achieved and compared. In this paper, the stress sensitivity evaluation method at pore-scale is developed, which has the practical application of oilfield development. © 2016 Elsevier B.V. All rights reserved.

Keywords: CT scanning Digital core Pore network model Stress sensitivity Tight sandstone

1. Introduction Stress sensitivity is the changing of permeability and pore structure resulting from the changing of the effective pressure, which has a great influence on fluid flow in porous media (Dvorkin et al., 1996). The storage and flow capability of the reservoir are determined by the pore structure of the porous media. Thus, it is necessary to analyze the effect of the stress sensitivity on pore structure and the fluid flow in porous media (Vairogs et al., 1971;

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Y. Yang), [email protected] (J. Yao). http://dx.doi.org/10.1016/j.jngse.2016.09.061 1875-5100/© 2016 Elsevier B.V. All rights reserved.

Warpinski and Teufel, 1992). In this way, we can analyze the reasons that cause the stress sensitivity fundamentally, and reveal its nature. Particularly in tight oil reservoirs, formation pressuresensitivity can affect oil production. Specifically, pressuresensitive permeability affects both the permeability near wells and the production rates of pressure-sensitive reservoir. The permeability of the conglomerate decreases 85%e90% and the sandstone decreases 10%e20%, which means serious damage to the formation (Lei et al., 2007). The changing of the pore structure is an important reason that causes stress sensitivity. The simulation based on digital core can reveal the mechanism of stress sensitivity. In order to understand the mechanism of stress sensitivity better, it is necessary to combine microscopic and macroscopic scale (Yuan et al., 2015a). Rather, we must study this effect at the pore scale.

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In this paper, based on real core samples and the microscopic research method, the mechanism of the stress sensitivity influencing the fluid flow laws and the pore structure are studied (Yuan et al., 2015b). Generally speaking, there are two methods to study stress sensitivity (Holt et al., 2005). The first is to use conventional experiments. Using physical experiments, the effective pressure influencing on the porosity and permeability of different types of reservoirs can be obtained (Li et al., 2013; Ruistuen et al., 1996); the other method is modeling and numerical simulation. In this method, coupled models of rock matrix deformation and fluid flow in porous media are developed (Cappa and Rutqvist, 2011; Rutqvist and Stephansson, 2003). In the 1920s, some studies addressed how permeability changes with confining pressure. For elastic porous media, Terzaghi studied fluid flow in a deformable saturated medium (Terzaghi, 1925). Terzaghi proposed the one-dimensional consolidation theory, which considered saturated fluid flow consolidation, and obtained the effective stress formula. However, this formula is limited in real engineering applications due to its assumptions incompressible soil particles and fluid in the soil pores. After 1941, Biot developed the three-dimensional consolidation theory and extended it to apply to anisotropic porous media, motive power, stress analysis of dam foundation, soil consolidation, and so on (Biot, 1941, 1956). Some researchers developed their methods and mentioned that Biot's coefficient or fracture porosity would strongly affect the value of stress-sensitivity index (Zhu, 2013). Based on Boit's theory, Noorishad surmised that the stress field should be considered when we analyze flow in porous media, and the equations should be developed into constitutive relations with nonlinear deformation (Noorishad et al., 1982). He studied the relationship between stress and flow in porous media based on the developed equations. Bruno and Nakagawa studied the effect of pore pressure on rocks (Bruno and Nakagawa, 1991). Chen extended the conventional flow equation coupling of stress-strain, which can be used to calculate complicated reservoirs, such as fractured reservoirs (Chen et al., 1995). The porosity and permeability change with stress, but their changing rates are different. Compared with permeability, porosity has a smaller variation range. There are many conclusions based on the results of these experiments: with increasing confining pressure, porosity and permeability decrease. And, some other factors will influence permeability, including temperature, pore fluid pressure and stress loading methods. Generally speaking, porosity and permeability both displayed classic stress sensitivity behavior (Lei et al., 2015). Each property followed a fairly rapid initial decrease at the beginning of the stress increasing process. Thereafter the property decline followed a slower decline with increasing stress. Porosity is a less stress sensitivity property than permeability (Farquhar et al., 1993). The reason is that the degree of formation compaction is greater in the low permeability reservoir, which means that with increasing effective stress, porosity will decrease slightly, but permeability will change substantially because of the deformation of the throats in porous media (Lei et al., 2007; McLatchie et al., 1958; Zhu, 2013). Micro flow simulation is a type of technology based on the real digital core. The main work is that digital core can be reconstructed by physical experiments and numerical algorithms. Micro flow simulations can be conducted in the reconstructed digital rock. This is a new research method to study the influence of the stress sensitivity on microscopic pore structure and fluid flow in porous media. Some research have been conducted on microscopic structures of porous media under different effective stress conditions, however, these research are few and limited in application. At present, there are still some problems involved in stress sensitivity experiments: (1) Most stress sensitivity research is conducted on

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the macroscale, with few studies at the pore scale (An et al., 2016; Blunt, 2001). Because the pore structure change is an important source of stress sensitivity, it is necessary to study microstructure deformation, which results from changes in stress at the pore scale. This study can provide a better way to understand stress sensitivity at the microscopic scale. (2) The research equipment and process of pore structure change are imperfect. At present, most pore structure evolution research employ CT or SEM of samples removed from a pressure vessel, which cannot obtain the real pore structure in terms of confining pressure. We modify this experimental method, and attempt to obtain the real pore structure of core samples under different stress conditions. With the development of this technology and method, micro stress sensitivity research will be gradually improved based on digital rocks. During the development of the reservoir, the formation is unavoidably influenced by stress, which deforms the pore structure. As a result, the physical properties of the reservoir are greatly influenced. Thus, the relationship between micro and macro characteristics can be obtained by studying the microscopic structure change in micro-scale experiments. The main content and procedure of this paper are as follows: (1) Reconstruct the digital core based on CT scanning; (2) Establish an evaluation method of stress sensitivity based on CT scanning images; (3) Analyze the stress influence on pore structure and flow ability; (4) Compare the stress influence degree on the middle-high permeability reservoir and low permeability reservoir.

2. The experimental process to study stress sensitivity The diameter of the core sample is 10 mm, and the length of the core sample is approximately 15 mme30 mm. A conventional core holder is usually made of stainless steel, but the core needs to be scanned by a CT scanner in this experiment, so the material that used to make core holder can be carbon fiber, PEEK material and other material that will allow X-ray through. In this study, we choose carbon fiber (tensile strength is greater than 73 MPa, density is 1.26e1.34 g/cm3, and Brinell hardness is greater than 10) to make it. The core holder is specially made for this study and is shown in Fig. 1. The CT scanner is MicroXCT-400 which is produced by Zeiss. The experimental procedures of stress sensitivity based on CT scanning are as follows: (1) Put the core into the core holder. Scan it at the condition without confining pressure. Adjust the x-ray resource, detector and sample to obtain three-dimensional core images without confining pressure. (2) Assemble the instruments: connect the hand pump, six-way valve and core holder together according to Fig. 2. It is more convenient and easier to use six-way valve compared with

Fig. 1. Core holder made of carbon fiber.

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ordinary valve, which can connect more pipes. In order to make the changing of the pore structure clearly and do not miss any data, the confining pressure is evaluated in the following order: 2.0 MPa, 4.0 MPa, 6.0 MPa, 8.0 MPa, 10.0 MPa and 12.0 MPa. And this pressure interval data is also suggested by the standard of oil and gas industry of China. (3) The sample is scanned after equilibrium by maintaining at constant pressures in step (2) for more than 30 min to make sure that the changing caused by the pressure is finished. Other operations and parameters are the same as step (1). For each experiment, we might spent 0.5 h to wait for the change of pore space to become stable and 4 h to scan the sample (about 27 h totally for all the confining pressures). (4) Decrease the confining pressure slowly in the following order: 12.0 MPa, 10.0 MPa, 8.0 MPa, 6.0 MPa, 4.0 MPa, 2.0 MPa, and 0 MPa (about 27 h totally for all the confining pressures). (5) After maintaining every confining pressure for one hour, the sample is CT scanned. The reason why the waiting time becomes longer in this step is that the sample needs more time to recover. The other parameters are the same as step (1).

3. Reconstruct the digital core and pore network model There are two main methods to build the digital core, including numerical reconstruction and physical experiments (Blunt et al., 2013; Yang et al., 2015b). The numerical reconstruction methods will reconstruct 3D pore space randomly based on 2D images information and they can only give geometrical and topological equivalently pore space. However, the digital core obtained by physical experiments, eg. CT scanning with high resolution, can accurately reflect the real pore structure. In this paper, we will use digital cores obtained by CT scanning to analyze the stress sensitivity. CT technology has many applications in oil development, including studying the microscopic pore structure of cores, the distribution of oil and water after water flooding experiments, the distribution of the remaining oil and the pore and fracture distributions in cores. The CT scanning procedure is conducted as follows: (1) Fasten the core on the sample holder. (2) Shut the CT door and open the x-ray source. (3) Adjust the x-ray source position according to the size of the core sample. In this stage, check the positions of the x-ray source, sample and detector to ensure that they will not collide. (4) Set up the scanning parameter in the control computer software, and after this, conduct the experiment. The detector will capture and save the remaining x-ray. The sample

Fig. 2. The experimental flow chart to measure stress sensitivity.

will be rotated on its axis for an angle to obtain different x-ray images. When the turning angle gets to 360
, the experiment is over. The x-ray will have various degrees of attenuation under different angles. Based on this information, the raw three-dimensional core images can be reconstructed. The equipment used in this paper is a MicroXCT-400 CT machine produced by Zeiss. The x-ray should be measured from 0
to 360
to obtain full x-ray images. The three-dimensional data can be obtained by reconstructing the images. This machine always has high contrast for all types of materials. The raw three-dimensional images obtained from the CT scanning cannot be used directly (Fig. 3). Further treatments should be performed to obtain digital core. In this paper, the images are treated using Avizo software (Avizo Fire 7.0). The main procedures include filtering and segmentation. Noise is usually chosen as a standard to judge whether the CT images are effective. Some noise in the images requires removal by filtering. There are some types of filtering, for example, anisotropic diffusing filtering, Gaussian filtering, nonlocal average filtering, and median filtering, which are effective for removing noise. (Guo et al., 2011). According to the experiment, Gaussian filtration and median filtering are not effective at removing salt and pepper noise, and nonlocal average filtering and anisotropic diffusing filtering perform well in addressing segmentation of two phases. Considering these properties, nonlocal average filtering is chosen for the further segmentation in this paper (Buades et al., 2005). Segmentation is an important step in image processing, and the most important step of segmentation is to determine the threshold. There are three common methods using for the image segmentation. The watershed segmentation is significantly more robust and it is a most widely used method on digital core (Leu et al., 2014). So we choose watershed segmentation method for the segmentation treatment. It is a method based on the topological theory to simulate the procedure of immersion (Vincent and Soille, 1991). In this procedure, the local minimum expands its affected area gradually, and creates the watershed at the junction of two reception basins. The digital core is a specific and professional word, which is a series of 0 & 1 data including the three-dimensional information of a real core sample. This information can reflect the space structure of a real core (Fig. 4). There are two methods for the calculation of the pore space flow ability. The first method is to calculate the permeability by the lattice Boltzmann method using the digital core directly (Ramstad et al., 2010; Zhang et al., 2015). Because of the huge calculation cost, it is difficult to apply this method in largescale calculations. The other method is to extract the pore network model after simplifying the pore space in the digital core using regular shapes. This method is suitable for flow controlled by

Fig. 3. Extracted 3D raw image.

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capillary force and simulating multi-phase flow in porous media (Piri and Blunt, 2005). Fatt firstly proposed the concept of pore network model and built a model for the first time (Fatt, 1956). From then on, pore network models have become increasingly more complicated and practical. They can currently be used to simulate irregular lattices, boundary layer flow, two- or three-phase flow with arbitrary wettability, and some complicated physical phenomena, such as phase exchange, non-Newtonian flow, non-Darcy flow, reacting flow, and so on (Blunt, 2001; Zhao et al., 2010). When extracting the pore network models, narrow space is defined as throats, greater space is defined as pores, and pores are connected by throats. The pore network model is composed of pores and throats with simple cross section shapes, such as squares, triangles, and circles. Some effective physical parameters can be calculated by pores and throats in the network model, such as volume, inscribed ball (for capillary calculation), and pore shape. The connection information between pores and throats are also recorded in the model files (Dong and Blunt, 2009). The pore network is extracted by the medial axis method (Lee et al., 1994; Lindquist et al., 1996). The central position of the pore space needs to be found first, followed by connecting the corresponding pore voxels to obtain the medial axis lines. This method can effectively maintain the real topological structure of porous media (Yang et al., 2015b). The main steps of extracting the pore network models are as follows. (1) the isolated pore and rock skeleton from image segmentation errors are removed. (2) the pore space's medial axis system is established. (3) the pore center is positioned, and the pore throat is determined. (4) the geometric parameters of the pores and throats are calculated, including the volume, the radius of the inscribed circle, the length, and the shape factor, etc.

the distribution of the shapes of pores and throats. The main parameters include the shape factor, throat length, radii and number of pores and throats, and tortuosity. In the process of extracting the pore network model, the largest inscribed sphere can be used to define the pore element, and the radius of which is obtained by the equal diameter sphere expansion method. The locations of the sphere centers are defined by medial axis thinning algorithm. So the initial locations of sphere centers are the intersection points of medial axes. The radius of the inscribed sphere is the radius of the pore element. The volume of the pore element can be obtained by counting the total number of the voxels of the pore elements. Elements that connect pores are throats, so it is easy to identify throats after recognizing the pores. The volume of throats can be determined using the volume of the total space minus the volume of the pores. Similarly, the volume of the throat can be also calculated by the number of throat voxels. The shape factor is a parameter used to describe the shape characteristics of elements (pores and throats) in the network model, and it is defined as (Mason and Morrow, 1991; Patzek and Silin, 2001):

4. The method to evaluate structure and flow parameters

where V and S are pore volume and surface area respectively, m3, m2. The shape factor distribution of all the pores and throats can be obtained by calculating every cross section of pores and throats using equations (1) and (2). The shape factor can actually describe the size and shape of the pore and throat elements, and it is an important parameter to show the geometrical characteristics of the pore space.

4.1. Structure characteristics analysis Simplification of the digital core to represent the pore network involves changing the irregular pores and throats into regular elements. For example, the cross section can be square, circular or triangular. The analysis of the geometrical and topological structure of regular elements can be used to evaluate the pore network structure, which is the main function of the pore network model (PNM) (Yang et al., 2015a). (1) Geometrical structure analysis The geometrical structure is an important standard to evaluate the pore space using the pore network model, which can describe

. G ¼ A P2

where A is the area of the elements cross section, m2; P is the perimeter of the elements cross section, m. Shape factor for 3D geometry is defined as (Prodanovic et al., 2007):

. G3D ¼ V S1:5

(2)

(2) Topological structure analysis The connection relationship between pores and throats is described by topological structures of the pore network model. The parameters include the network connectivity function and coordination number. The network connectivity function is used to describe the topological structures of all elements in a pore network model. It is represented using a specific Euler number. The specific Euler number is defined by Vogel and Roth (2001):

cðrÞ ¼

Fig. 4. Grain distribution image after segmentation.

(1)

NN ðrÞ  NB ðrÞ V

(3)

where NN(r) is the number of pores with a radius larger than r; NB(r) is the number of throats with a radius larger than r; V is the volume of the model. The Euler critical radius, i.e., the radius at which the value of the Euler number is zero, is an important parameter to evaluate the topological structure. The other parameter to evaluate the pore space connectivity is the coordination number. The coordination number z is the number of throats that connect with a pore. It represents the connection relationship between pores and throats to evaluate the connectivity

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degree of the pore space. 4.2. Flow properties analysis Flow simulation in porous media using a pore network can provide insight into some macro properties, such as the relationship between saturation and capillary force, saturation and relative permeability, etc. The study of the multiphase flow mechanism is feasible in the pore network model. Some parameters that are difficult to obtain by the conventional experiments can be obtained by this method, such as relative permeability of shale and tight oil and gas flow (Yao et al., 2013). Flow procedure mainly contains two events: piston-like displacement and filling the pore space. The process of wetting phase water flooding non-wetting phase oil is called imbibition. In this process, in addition to the two displacement events above, snap-off might be another driving mechanisms (Blunt, 1998). In the flow simulation using pore network model, some macro transmission properties can be obtained, including the absolute permeability, relative permeability, capillary pressure, distribution of oil saturation, and so on. The pore pressure of every pore in the model can be obtained with this calculation, which means the flux of every pore can also be obtained. The total flux is obtained by summing up all fluxes of every pore in the exit section. When the model is saturated with a single-phase fluid, giving a driving pressure Dp to the whole model, the absolute permeability can be obtained according to Darcy's formula:

mQL k¼ ADp

(4)

where k is the absolute permeability, mm2; m is the fluid viscosity, mPa$s; Q is the flux when the model is saturated only by one phase, cm3/s; L is the length of the model, cm; A is the area of the cross section, cm2; Dp is the pressure difference between the two ends, 101MPa. 5. Stress sensitivity study of middle-high permeability sandstone and tight sandstone 5.1. The stress sensitivity evaluation of middle-high permeability sandstone The sample of middle-high permeability sandstone in this paper comes from the CQ Oilfield in China. We can achieve a practical change regulation to study the stress sensitivity based on the CT scanning experiment using a real core sample. 5.1.1. Building the digital core and extracting the pore network model The resolution of the CT image is 3.78 mm/voxel. The extracted representative element volume has a size measured by a voxel of 300  300  300. The reason that we choose this number is that when the size is larger than 300 voxels according to the representative elementary volume (REV) study, the properties of this type of samples will be stable (Gao et al., 2014). The corresponding real size is 1134  1134  1134 mm3, which is sufficient to represent the property of the rock. The images of the digital cores in the process of increasing confining pressure are shown in Fig. 5. After the core samples are subjected to the maximal confining pressure (12 MPa in this paper), we decrease the pressure to study the recovery ability of the core sample. The digital cores in the process of decreasing confining pressure are shown in Fig. 6. The pore network models can be extracted using the medial axis method according to the corresponding digital cores (Lee et al.,

1994). The extracted pore network models during the process of increasing confining pressure are shown in Fig. 7. Using the same method, we can obtain the pore network models during the process of decreasing confining pressure. The extracted pore network models under different confining pressures are shown in Fig. 8. It can be qualitatively observed from the digital cores in Fig. 5 that the pore volume represented in purple decreases with increasing effective stress, which suggests that the pore space becomes gradually smaller. Similarly, with decreasing effective stress in the process of decreasing the confining pressure, the pore volume increases (Fig. 6). Analyzing the extracted pore network models, we can only quantitatively observe the change of the number and total volume of pores and throats. In the process of increasing confining pressure, the number and volume both of pores and throats decrease gradually (Fig. 7). On the contrary, in the process of decreasing confining pressure, the number and volume of pores and throats both gradually increase (Fig. 8). The quantification of the degree of change could be represented by porosity in the following figures. According to Fig. 9, formula (5) could be obtained to express the relationship between porosity and confining pressure during the increasing pressure process. Similarly, the other exponential formula (6) matches the curve of the decreasing pressure process.

F ¼ 19:82e0:075seff

(5)

F ¼ 16:345e0:059seff

(6)

In Fig. 9, the FOO is calculated as the porosity value at a certain pressure divided by the highest porosity value at the smallest pressure. So, the y-axis will have value range from 0 to 1. Figures plotted as fraction of origin (FOO) versus the confining pressure can give a relative change degree. From equation (5) and equation (6), we can see that the confining pressure has a great influence on the porosity, and the rate of change follows an exponential relationship. The highest decreased absolute value of porosity is 12.82% during the increasing pressure process, and the highest increased value of porosity is 8.73% during the decreasing pressure process. In the whole process, the unrecoverable porosity is 4.09%. This unrecoverable porosity can be explained by the following reasons. With the increase of the confining pressure, the rock particles will be compacted with each other. When the pressure decreases, these particles cannot recover back totally (Li et al., 2009; Liu et al., 2016; Xiao et al., 2015). So the porosity cannot return back to the original value. 5.1.2. Analysis of structure characteristics under different pressures The characteristic structure curves for the increasing pressure processes are shown in Fig. 10, Fig. 11 and Fig. 12. According to Figs. 10 and 11, the pore radius and throat length curves have greater fluctuation because of the heterogeneity of the real core samples from the CQ reservoir. However, curves under different pressure still follow general laws: with increasing effective stress, the pore space and corresponding pore radius and throat length decrease. From the figures, we can see that the pore radius changes from 8-25 mm to 5e17 mm, and the throat length changes from 40120 mm to 20e80 mm. This is a value range for the main throat length distribution. As the confining pressure increases, the general shape of the curve does not change but they look like to be compressed and their value range become smaller. The change ratio may be large when it comes to short throats, but the long throats will have a small change ratio. According to Fig. 12, network connectivity functions show that with increasing effective stress, the specific Euler number decreases from 13 mm to 9 mm, which shows

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Fig. 5. Digital cores with increasing confining pressures. (The purple color indicates the pore space and the red color is rock skeleton). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

that the connectivity of pores and throats becomes worse. The parameter change curves for the decreasing confining pressure processes are shown in Fig. 13, Fig. 14 and Fig. 15. From Figs. 13 and 14, it can be seen that with the release of effective stress, the pore radius increases more gradually, and the throat length also recovers slowly. The pore radius increases from 5-17 mm to 8e20 mm, and throat length increases from 20-80 mm to 35e100 mm. In Fig. 15, the confining pressure decreases gradually and the effective stress becomes smaller correspondingly. The Euler number can represent the connectivity of pores and throats. The bigger the number is, the better the connectivity is (Jiang et al., 2011; Vogel and Roth, 2001; Wu et al., 2006; Yao et al., 2015). The specific Euler numbers with zero value increase from 9 mm to 12 mm because of the expansion of pores and throats, which suggests that the connectivity of pores and throats gradually improves. 5.1.3. Analysis of flow properties under different confining pressures The absolute permeability at different confining pressures during the increasing and decreasing processes can be obtained from

the flow simulation using the extracted pore network models. The corresponding data are shown in Fig. 16. According to the relationship between confining pressure and permeability in Fig. 16, the exponential formula (7) can be obtained by fitting the increasing confining pressure process; similarly, equation (8) can be obtained by matching with the decreasing confining pressure process.

k ¼ 563:29e0:111seff

(7)

k ¼ 480:51e0:130seff

(8)

It can be observed from the above curves and equations that permeability decreases gradually with increasing effective pressure, and the decreasing rate becomes smaller at higher pressures. The largest decrease of permeability in the increasing pressure process is 394.35  103 mm2. The recovery value in the decreasing pressure process is 339.39  103 mm2. The unrecoverable permeability is approximately 10.29%.

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Fig. 6. Digital cores when decreasing confining pressures (The purple color indicates the pore space and the red color is rock skeleton). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

5.2. Stress sensitivity evaluation of tight sandstone Tight sandstone samples used in this paper are from the CQ gas reservoir. Using the same method for middle-high permeability sandstone in 5.1, digital cores and pore network models under different pressures are built to analyze the relationship between porosity, permeability and stress, and the influence of stress on topological structure. Limited to the length of the paper, only some important data here are shown. The corresponding structure under different pressures obtained from analysis of the pore network model of tight sandstone during pressure increasing process are given in Fig. 17, Fig. 18 and Fig. 19. According to Figs. 17 and 18, it can be seen that pore radius becomes smaller from 4-13 mm to 3e8 mm, and throat length reduces from 10e70 mm to 5e40 mm. It is clear that the pore radius and throat length is smaller compared with middle-high permeability sandstone. As can be seen from Fig. 19, the value of the intersection of the curve with the x-axis reduces from 8 mm to 5 mm with increasing confining pressure, which shows that pore throat connectivity becomes poorer. The porosity and absolute permeability at different confining pressures during the increasing and decreasing processes can be obtained from the digital cores and the extracted pore network models. The corresponding data are shown in Fig. 20 and Fig. 21. From Fig. 20, formula (9) and formula (10) can be obtained to express the exponential relationship between porosity and confining pressure during the increasing and decreasing pressure processes, respectively.

F ¼ 17:277e0:09seff

(9)

F ¼ 13:379e0:073seff

(10)

The largest decrease of porosity during the increasing pressure process is 12.21%. The recovery value of porosity during the decreasing pressure process is 8.59%. Hysteresis of stress sensitivity exists, and the unrecoverable porosity is 3.62%. Similarly, from Fig. 21 formula (11) and formula (12) can be obtained to express the exponential relationship between permeability and confining pressure during the increasing and decreasing pressure processes, respectively.

k ¼ 112:32e0:443seff

(11)

k ¼ 75:655e0:46seff

(12)

It can be observed that with increasing confining pressure, permeability decreases sharply, especially at the beginning of this process (Fig. 21). Because of the hysteresis of stress sensitivity, they cannot return to the original states. The decrease of permeability in the increasing pressure process is 68.13  103 mm2. The recovery of permeability during the decreasing pressure process is 46.95  103 mm2, with permeability loss of approximately 31%. 5.3. Comparison of stress sensitivity between middle-high and tight sandstones The middle-high and tight sandstone in the experiments both come from the oil field. To some extent, they can represent the stress sensitivity of the corresponding formation layers. Some general conclusions can be reached by analyzing the stress sensitivity of two types of core samples between middle-high and tight sandstones. (1) Comparison of porosity and permeability parameters Firstly, changes in porosity are compared. According to the above data, the unrecoverable porosity to middle-high and tight

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Fig. 7. Pore network models with increasing confining pressures.

sandstone are 4.09% and 3.62%. We can conclude that stress sensitivity has influence on the porosity of both core samples and the unrecoverable porosity are both less than 5%. Next, we compare the permeability change of the two types of core samples. For middle-high sandstone, permeability reduces by 394.35  103 mm2 with increasing pressure, i.e., 73.8% of the original permeability. For tight sandstone, the permeability decreases by 68.13  103 mm2 with increasing pressure, i.e., 99.69% of the original permeability. With decreasing pressure, it increases 46.95  103 mm2, i.e., 68.70% of the original permeability value of the tight sample. In the oilfield, for some cases, after depressure too much, the original production well will decrease a lot, even stop production. This data can provide a very good evidence for this phenomena. For the tight reservoirs, if wrong operation (such as depressure too much) is carried out, it will become very difficult to produce more oil or gas (Bin Tajul Amar et al., 1995; Lei et al., 2007; Raghavan and Chin, 2004; Tabatabaie et al., 2016). By comparing the permeability variability, it can be concluded that the tight sandstone changes considerably more under the

same pressure difference. Pressure has a greater influence on permeability of tight sandstone. (2) Comparison of geometric properties By analyzing the distributions of the pore radius, throat length and their changing laws as pressure changes, their geometrical structure properties can be compared. The change trends of the pore radius during the increasing pressure process are first compared. It can be found that the radius of middle-high sandstone changes from 8-25 mm to 5e17 mm, and tight sandstone changes from 4-13 mm to 3e8 mm, as shown in Figs. 10 and 17. It is clear that the radius of tight sandstone is smaller compared with middle-high sandstone. For the pore radius variation, the changing range between the highest pressure curve and the zero pressure curve of the middle-high sandstone is greater than that of tight sandstone. This suggests that the pore radius will change greatly in middle-high sandstone. This can be attributed to the high porosity and loose rock particles of middle-high sandstone, allowing for easy

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Fig. 8. Pore network models with decreasing confining pressures.

0.18 p_confining=12MPa p_confining=10MPa p_confining=8MPa p_confining=6MPa p_confining=4MPa p_confining=2MPa p_confining=0MPa

0.16 0.14

Frequency/%

0.12 0.10 0.08 0.06 0.04 0.02 0.00

0

10

20

30

40

50

60

Pore radius/μm Fig. 9. Relationship between porosity and confining pressure during processes of increasing and decreasing pressure.

compaction. In contrast, the particles of tight sandstone are located much closer. The absolute compressible pore space is smaller when pressure increases. However, its changing percentage is higher than that of middle-high sandstone. The change trends of the pore radius is similar during the decreasing pressure process. The change trends of throat length during the increasing pressure process are shown in Figs. 11 and 18. The throat length of middle-high sandstone changes from 40-120 mm to 20e80 mm, and the tight sandstone changes from 10e70 mm to 5e40 mm. The range of throat length of tight sandstone is narrower, and their throats are shorter. This suggests that the connected throats are not welldeveloped. The change trends of throat length are similar during

Fig. 10. Pore radius distribution with increasing confining pressure.

the decreasing pressure process. (3) Comparison of topological properties Pore structure connectivity of rocks can be represented by their topological structure. As shown in Fig. 12, for middle-high sandstone, the connectivity function curve and x-axis intersect at approximately 10 mm, which indicates the specific Euler number is approximately 10 mm. As for tight sandstone, they intersect at approximately 7 mm. The greater the intersection value is, the better the connectivity will be. Thus, it can be concluded that the connectivity of tight sandstone is worse, which also gives further supporting evidence of the low permeability in tight sandstones.

Y. Yang et al. / Journal of Natural Gas Science and Engineering 36 (2016) 20e31

0.30

0.20

p_confining=12MPa p_confining=10MPa p_confining=8MPa p_confining=6MPa p_confining=4MPa p_confining=2MPa p_confining=0MPa

0.20 0.15

p_confining=12MPa

0.18

Frequency/%

0.25

Frequency/%

29

0.10

p_confining=10MPa

0.16

p_confining=8MPa

0.14

p_confining=6MPa p_confining=4MPa

0.12

p_confining=2MPa

0.10

p_confining=0MPa

0.08 0.06 0.04

0.05

0.02

0.00

0.00

0

100

200

Throat length/μm

200

100

100

Specific Euler number / mm-3

10

20

30

40

50

60

70

Minimal pore radius / μm

-100 -200

p_confining=12MPa p_confining=10MPa

-300

p_confining=8MPa

-400

p_confining=6MPa p_confining=4MPa

-500

Specific Euler number / mm-3

200

0

0 -100

500

600

p_confining=0MPa

Fig. 12. Connectivity function curve with increasing pressure.

0

10

20

30

40

50

60

70

Minimal pore radius / μm p_confining=12MPa

-200

p_confining=10MPa p_confining=8MPa

-300

p_confining=6MPa p_confining=4MPa

-400

p_confining=2MPa

-600

400

Fig. 14. Throat length distribution with decreasing confining pressure.

Fig. 11. Throat length distribution with increasing pressure.

0

300

Throat length/μm

p_confining=2MPa p_confining=0MPa

-500 Fig. 15. Connectivity function curves with decreasing confining pressure.

0.18 p_confining=12MPa

0.16

p_confing=10MPa

0.14

p_confing=8MPa p_confing=6MPa

Frequency/%

0.12

p_confing=4MPa p_confing=2MPa

0.10

p_confing=0MPa

0.08 0.06 0.04 0.02 0.00

0

10

20

30

40

50

Pore radius/μm Fig. 13. Pore radius distribution with decreasing confining pressure.

Fig. 16. Absolute permeability at different confining pressures during the increasing and decreasing processes.

6. Conclusions (1) We presented a method to build a digital core and extract a pore network model based on CT scanning technology. 3D images of the real core can be obtained based on CT scanning,

and digital cores can be reconstructed after filtering and segmentation. Then, we can analyze the core structure and flow properties using the pore network models extracted from the digital cores.

30

Y. Yang et al. / Journal of Natural Gas Science and Engineering 36 (2016) 20e31

0.45 p_confining=0MPa

Frequency /%

0.40

p_confining=2.5MPa

0.35

p_confining=5MPa

0.30

p_confining=7.5MPa p_confining=10MPa

0.25

p_confining=12MPa

0.20

0.15 0.10 0.05 0.00 0

10

20

30

40

50

60

Pore radius / μm Fig. 17. Probability distribution of pore radius distribution when increasing pressure for tight sandstone.

Fig. 20. Relationship between porosity and confining pressure during processes of increasing and decreasing pressure for tight sandstone.

0.35 p_confining=0MPa 0.30

p_confining=2.5MPa p_confining=5MPa

Frequency / %

0.25

p_confining=7.5MPa p_confining=10MPa

0.20

p_confining=12MPa 0.15 0.10 0.05 0.00 0

50

100

150

200

250

300

350

400

Throat length / μm Fig. 18. Throat length distribution with increasing pressure for tight sandstone.

1,000

Specific Euler number /mm-3

500 0 -500

Minimal pore radius / μm

-1,000

p_confining=0MPa

-1,500

p_confining=2.5MPa

-2,000

p_confining=5MPa p_confining=7.5MPa

-2,500 -3,000

p_confining=10MPa p_confining=12MPa

-3,500 Fig. 19. Connectivity function curves when increasing pressure for tight sandstone.

(2) We proposed an experimental method to study stress sensitivity based on CT scanning. Digital cores under different stress can be obtained after a series of experiments based on CT scanning technology. Pore network models are

Fig. 21. Absolute permeabilities at different confining pressures during the increasing and decreasing processes for tight sandstone.

extracted from digital cores, and then, the geometrical and topological structures are analyzed to determine the changing laws of the core structure under different confining pressures. Flow capacity changing laws can be also obtained by analyzing the absolute permeability. (3) Based on proposed method of analyzing stress sensitivity, we analyzed and compared stress sensitivity of middle-high and tight sandstones from an oilfield. Some conclusions can be obtained by analyzing data of structure and flow properties. Both porosity and permeability have exponential relationships with stress. Middle-high sandstone has a larger radius and longer throats than tight sandstone. The numerical values of radius and throats of middle-high sandstone have a larger range, but their changing percentage is smaller under the same pressure difference. Thus, the stress sensitivity of tight sandstone is more obvious. Stress sensitivity has different influences on the permeability of different types of rocks. Compared with middle-high sandstone, permeability of tight sandstone is more sensitive to the stress changes. Acknowledgements We would like to express appreciation to the following financial

Y. Yang et al. / Journal of Natural Gas Science and Engineering 36 (2016) 20e31

support: the National Natural Science Foundation of China (No. 51304232, 51674280, 51490654, 51234007, 51274226), Applied basic research projects of Qingdao innovation plan (16-5-1-38-jch), the Fundamental Research Funds for the Central Universities (No. 14CX05026A), PetroChina Deep Oil and Gas Major Projects (2014E3203), Introducing Talents of Discipline to Universities (B08028), and Program for Changjiang Scholars and Innovative Research Team in University (IRT1294). And we would like to express our great appreciation to the reviewer's constructive suggestions for this paper. References An, S., Yao, J., Yang, Y., Zhang, L., Zhao, J., Gao, Y., 2016. Influence of pore structure parameters on flow characteristics based on a digital rock and the pore network model. J. Nat. Gas Sci. Eng. 31, 156e163. Bin Tajul Amar, Z.H., Altunbay, M., Barr, D., 1995. Stress sensitivity in the Dulang Field - how it is related to productivity. In: SPE European Formation Damage Conference. Society of Petroleum Engineers. Biot, M.A., 1956. Theory of deformation of a porous viscoelastic anisotropic solid. J. Appl. Phys. 27 (2), 459e467. Biot, M.A., 1941. General theory of three-dimensional consolidation. J. Appl. Phys. 12 (5), 155e164. Blunt, M.J., 1998. Physically-based network modeling of multiphase flow in intermediate-wet porous media. J. Petroleum Sci. Eng. 20 (3e4), 117e125. Blunt, M.J., 2001. Flow in porous media e pore-network models and multiphase flow. Curr. Opin. Colloid & Interface Sci. 6 (3), 197e207. Blunt, M.J., Bijeljic, B., Dong, H., Gharbi, O., Iglauer, S., Mostaghimi, P., Paluszny, A., Pentland, C., 2013. Pore-scale imaging and modelling. Adv. Water Resour. 51, 197e216. Bruno, M., Nakagawa, F., 1991. Pore pressure influence on tensile fracture propagation in sedimentary rock. Int. J. Rock Mech. Min. 28 (4), 261e273. Buades, A., Coll, B., Morel, J.M., 2005. A review of image denoising algorithms, with a new one. Multiscale Model Sim 4 (2), 490e530. Cappa, F., Rutqvist, J., 2011. Modeling of coupled deformation and permeability evolution during fault reactivation induced by deep underground injection of CO2. Int. J. Greenh. Gas Control 5 (2), 336e346. Chen, H., Teufel, L., Lee, R., 1995. Coupled fluid flow and geomechanics in reservoir study. I. Theory and governing equations. In: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers. Dong, H., Blunt, M.J., 2009. Pore-network extraction from micro-computerizedtomography images. Phys. Rev. E 80 (3), 036307. Dvorkin, J., Nur, A., Chaika, C., 1996. Stress sensitivity of sandstones. Geophysics 61 (2), 444e455. Farquhar, R., Smart, B., Todd, A., Tompkins, D., Tweedie, A., 1993. Stress sensitivity of low-permeability sandstones from the Rotliegendes sandstone. In: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers. Fatt, I., 1956. The network model of porous media I. Capillary pressure characteristics. Petroleum Transactions. AIME 207, 144e159. Gao, Y., Yao, J., Yang, Y., Zhao, J., 2014. REV identification of tight sandstone in Sulige Gas Field in Changqing Oilfield China using CT based digital core technology. In: 2014 International Symposium of the Society of Core Analysts. Society of Core Analysts. Guo, Y., Wang, Y., Hou, T., 2011. Speckle filtering of ultrasonic images using a modified non local-based algorithm. Biomed. Signal Proces. 6 (2), 129e138. Holt, R.M., Bakk, A., Fjær, E., Stenebråten, J.F., 2005. Stress sensitivity of wave velocities in shale. In: 2005 SEG Annual Meeting. Society of Exploration Geophysicists. Jiang, Z., Wu, K., Couples, G.D., Ma, J., 2011. The impact of pore size and pore connectivity on single-phase fluid flow in porous media. Adv. Eng. Mater. 13 (3), 208e215. Lee, T.C., Kashyap, R.L., Chu, C.N., 1994. Building skeleton models via 3-D medial surface axis thinning algorithms. CVGIP Graph. Models Image Process. 56 (6), 462e478. Lei, G., Dong, P., Wu, Z., Mo, S., Gai, S., Zhao, C., Liu, Z.K., 2015. A fractal model for the stress-dependent permeability and relative permeability in tight sandstones. J. Can. Petroleum Technol. 54 (1), 36e48. Lei, Q., Xiong, W., Yuang, J., Cui, Y., Wu, Y.-S., 2007. Analysis of stress sensitivity and its influence on oil production from tight reservoirs. In: SPE Eastern Regional Meeting. Society of Petroleum Engineers. Leu, L., Berg, S., Enzmann, F., Armstrong, R.T., Kersten, M., 2014. Fast X-ray microtomography of multiphase flow in Berea sandstone: a sensitivity study on image processing. Transp. Porous Media 105 (2), 451e469. , Y., Xiao, W.-I., Chen, Z.-Y., Liu, Z.-Q., 2009. Effective pressure law for Li, M., Bernabe permeability of E-bei sandstones. J. Geophys. Res. 114 (B7), B07205. Li, S., Tang, D., Pan, Z., Xu, H., Huang, W., 2013. Characterization of the stress

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