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Physical simulation experiment and numerical inversion of the full life cycle of shale gas well
Petroleum Research 4 (2019) 181e190
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Full Length Article
Physical simulation experiment and numerical inversion of the full life cycle of shale gas well Shusheng Gao a, b, *, Huaxun Liu a, b, Liyou Ye a, b, Zhiming Hu a, b, Weiguo An b a b
Research Institute of Petroleum Exploration & Development, CNPC, Beijing, 100083, China Department of Porous Flow & Fluid Mechanics, Research Institute of Petroleum Exploration & Development, PetroChina, Hebei, Langfang, 065007, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 November 2018 Received in revised form 26 March 2019 Accepted 3 April 2019 Available online 8 May 2019
The ultra-low porosity and permeability, as well as complex occurrence and transport state of shale reservoir make it possess special L-type production characteristic curve and complicated shale gas flow mechanism. To solve the difficulty of collecting complete production data due to short production time and operation discontinuity, a full-diameter core physical simulation experiment on the full lifecycle production process of shale gas well depletion is conducted with the purpose of obtaining many important production data including complete pressure and daily gas output in the simulated production process of shale gas well. The experimental results show the production characteristic from simulation is consistent with those from gas well. Based on the simulation data, the critical desorption pressure (12 MPa) of core, free gas production (3820.8 mL), adsorbed gas production (2151.2 mL), the proportion of the daily gas production between free and absorbed gas under different time and formation pressure, as well as the production time and final recovery rate corresponding to abandoned pressure, can be determined accurately. Numerical inversion is carried out to calculate the production performance curve of shale gas well and predict the development effect of gas well based on well testing and similarity analysis of the dimensionless time between core experiment and gas well production. Finally, the permeability and the fracturing effect (fracture network density) as the keys to the effective development of shale gas reservoirs are proposed. The permeability is the fundamental factor and the fracturing technology is the major means. © 2019 Chinese Petroleum Society. Publishing Services by Elsevier B.V. on behalf of KeAi. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Shale gas well Full lifecycle Physical simulation experiment Numerical inversion Similarity theory Permeability Fracturing effect
1. Introduction In shale gas reservoir, which is different from the conventional gas reservoir, shale is both the source rock generating natural gas and the reservoir and cap layer for accumulating and storing natural gas. Shale gas is primarily trapped in the fissures, pores and other reservoir spaces of black mud shale as a free phase, adhered to the surface of kerogen, clay particles and pores as an adsorbed phase with the proportion ranging from 20% to 80% (Wu et al., 2011, 2017), or as a dissolved phase with very small amount. The accumulation of shale gas is the typical in-situ accumulation mode near the hydrocarbon source rocks (Dong et al., 2016). In recent years, the exploration and development of shale gas in China has achieved important breakthroughs, many national shale gas demonstration
* Corresponding author. Research Institute of Petroleum Exploration & Development, CNPC, Beijing, 100083, China. E-mail address: [email protected] (S. Gao).
zones, such as Fuling, ChangningeWeiyuan and Zhaotong, have been established successively with proven gas reserves of 5441.29 108 m3. The industrial production of shale gas in China had been realized with a production capacity of 65 108 m3/a by the end of 2015 and 85 108 m3/a by the end of 2016 (Wu et al., 2017). There are many types of micro- and nano-scale pores in shale gas reservoir, and most of them are nano-scale pores (Ji et al., 2016). Shale gas reservoir is characterized by complex gas occurrence states, extremely low porosity and permeability, basically free of seepage capability, thus the effective diverting capacity of shale gas is mainly dependent on diffusion and fracture (Carlson and Mercer, 1991; Carlson, 1994; Wen et al., 2014; Su et al., 2016). The effective development of shale gas wells fundamental lies in large-scale integrated multi-stage fracturing. The characteristics and development mode of shale reservoir determine the shale gas production has the characteristics of typical L-shaped production curve with high initial output, fast decline, low and stable production for long time in the later stage.
https://doi.org/10.1016/j.ptlrs.2018.04.001 2096-2495/© 2019 Chinese Petroleum Society. Publishing Services by Elsevier B.V. on behalf of KeAi. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
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Some studies suggested that the reservoir characteristics of low porosity and extremely low permeability in shale matrix could be described by double-porosity model (Javadpour et al., 2007; Javadpour, 2009; Ji et al., 2016). The flow of shale gas could be described as a process that free gas generated in the fracture, pressure difference produced between fracture and matrix, adsorbed gas flowed to wellbore along fractures after desorbing from matrix surface, and gas in matrix diffused to surface under concentration difference. The flow of gas in shale matrix followed the molecule diffusion principle, which could be described by Darcy's law when gas flowed from fractures to wellbore and by Langmuir equation during gas desorption. Schepers et al. (2009) and Civan et al. (2011) proposed the triple-porosity and dual-permeability model and believed that flow of gas in both fractures and matrix should follow Darcy's law, shale matrix could play not only the source of gas desorption but also a dominant role in seepage compared with diffusion. Swami and Settari (2012), Swami et al. (2013) put forward the four-porosity gas flow model with considering the free gas in the micro-cracks, the free gas in the nanopores, the adsorbed gas on the pore walls and the kerogen solution gas, established the flow equation of shale nano-pores and solved the numerical solution, considered that Knudsen diffusion, Langmuir gas desorption, gas slippage and diffusion of solution gas should be taken into account during shale production prediction and numerical simulation. Alharthy et al. (2012) proposed the double- and triple-porosity model containing convection, diffusion and slip flow, completed the numerical calculation and believed that the triple-porosity model could better simulate the gas flow in shale gas reservoir and the flow channel of desorption gas would not be affected by the mesoporous. Duan et al. (2011) proposed the mathematical model of macroscopic seepage involving adsorbed gas, free gas and solution gas for dual medium shale gas reservoir fracturing wells and calculated the unstable productivity of shale gas well. Li and Li (2012) considered the nano-pore gas desorption and diffusion and argued that gas desorption could induce shale matrix contraction and increase gas seepage channel and permeability when the formation pressure was lower than the gas critical desorption pressure. If the proportion of gas molecules with free path larger than pore diameter (D) was set to be a and the proportion of molecules with free path smaller than D was set as 1-a, the gas seepage and diffusion equation could be established. Wang et al. (2015) proposed an adsorption model at high-temperature and high-pressure for shale. Guo et al. (2016) established the dual-media gas-water two-phase seepage model with considering the desorption-adsorption, diffusion, slippage and stress sensitivity. Zhu et al. (2016) studied the propagation law of pressure disturbance in the shale matrix reservoir by using the steady state replacement algorithm and analyzed the production decline law of shale gas wells by numerical calculation. According to literature survey, most results of productivity calculation and performance prediction for shale gas well are from the theoretical research, lacking practical basis and having obvious defects. Firstly, all calculation or prediction models are founded on some assumptions that will not happen in most cases; secondly, most of the key parameters used in calculation cannot be accurately obtained; thirdly, it is difficult to accurately determine the amount of free gas and adsorbed gas in production while the analytical gas amount determined according to the Langmuir model has a large error (Wang et al., 2015). In view of the above reasons, through the current productivity calculation and performance prediction, it is difficult to reasonably explain the special production curve for shale gas well, so that it cannot be used to guide the effective development of shale gas wells. Focused on the full lifecycle production performance of shale gas well in this study, full-diameter shale core was used to simulate
the entire production process for the first time in keeping with the gas well. As a result, the production curve obtained from simulation was highly consistent with that from the gas well. The production curve of gas well would be effectively explained as long as that of simulation was reasonably understood. Moreover, the complete production data and key parameters required in the full lifecycle productivity of shale gas well could be obtained through the physical simulation experiment of full-diameter core, so as to solve the current difficulties in shale gas well productivity calculation and performance prediction. 2. Physical simulation experiment of the full lifecycle of gas well 2.1. Experimental scheme and process The full-diameter shale core (with a diameter of 10 cm and a length of 15 cm) is sampled from Longmaxi Formation in Zhaotong area of South Sichuan. In order to maintain the original characteristics of the core, the first time sampling is carried out with the pressure-retained coring device on the drilling site. After simply cleaning the core, we quickly put it into the pressure-retained coring device with saturated natural gas up to 10 MPa, close the valves at both ends of the coring device, and transport it to the lab for standby application. The experimental equipment is a set of physical simulation device for the desorption-diffusion-seepage coupling of shale gas, independently developed by Department of Porous Flow & Fluid Mechanics, PetroChina Research Institute of Petroleum Exploration and Development. The experimental process is shown in Fig. 1. The experimental pressure sensor has the measuring range of 40 MPa and the precision of 0.3%, which meet the measurement requirements of experimental pressure. The specific experimental process is shown as follows: (1) The task includes taking out the full-diameter core holder from the pressure-retained coring device, putting it into a laboratory with constant temperature of 25 C and connecting it with the simulation experiment device, pressurizing the natural gas in the high-pressure vessels with highpressure pumps to maintain the pressure at 28 MPa, opening the regulating valve 1 and 2, charging methane (considering methane accounting for 99% of the natural gas component in the reservoir) from the both ends of the core holder, then carrying out a secondary saturation pressurization until the pressure in the vessels reach the simulated formation pressure of 28 MPa, increasing the confining pressure to 50 MPa synchronously. Since the shale is extremely tight and possesses special adsorption characteristics, it takes a long time to completely restore the shale to the formation state and the saturation pressurization needs to last for 200 days until the pressure of high-pressure vessels at the outlet and inlet of the core holder no longer decreases. Under this condition, the shale gas will be almost completely restored to its original reservoir state. Then we can close the inlet regulating valve 1 and the outlet regulating valve 2, remove the highpressure air source, and get ready for the full lifecycle production simulation experiment.
2.2. Experimental results The full lifecycle depletion simulation experiment of fulldiameter shale core for gas well lasted 1631 days. According to the similarity of dimensionless time, the petrophysical parameters
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Fig. 1. Physical simulation experimental process of the full lifecycle production for gas well. (2) The task includes opening the outlet regulating valve 2 and starting the experiment. In order to control the excessive initial gas flow, the outlet should maintain a reasonable back pressure. When the flow rate dropped to a proper range, the back pressure should be adjusted to atmospheric pressure and then the dynamic simulation of the full lifecycle production of shale gas well could be started. (3) The inlet pressure, outlet pressure and outlet flow rate were measured by the pressure sensor 1 at the inlet, the pressure sensor 2 and the gas flowmeter at the outlet respectively. The whole simulation experimental process was recorded continuously in real time by the computer data acquisition software.
of shale core and the geological parameters of Longmaxi Formation, the production time calculated in shale core simulation was equivalent to 4.5e550 years in shale gas well under different permeability and fracturing conditions, which achieved the purpose of simulating the full lifecycle production of shale gas well. Considering that there was 1 mL dead volume at the outlet of core holder and the early gas production mainly from the dead volume part could not reflect the gas flow in shale core, the early outliers in experimental data should be deleted during the analysis. According to the dead volume, initial pressure, back pressure at outlet and high-pressure physical parameters of gas, the early gas mainly from the dead volume accounted for 260 mL. After eliminating some uncertainty experimental data arising from the defects of experimental process, the daily gas production curve in the simulation experiment was almost identical to that in the shale gas well (Fig. 2a). The simulation results showed that the gas production in the former 40 days dropped rapidly from 135.9 mL/d on the first day to below 9 mL/d, with the cumulative gas production increasing rapidly to 1038.6 mL and the recovery rate of about 17.4%. After that, the decline of daily gas production and the rise of cumulative gas production slowed down simultaneously, the gas
production dropped to 3 mL/d when the production time reached l00 days. Followed by about 1500 days of a low production stage, the gas production slowly dropped from 3 mL/d to about l mL/d, and the cumulative gas production was up to 1909.5 mL when the production time was up to 444 days with the recovery rate of 32%. The gas production increased from 1 mL/d to about 2 mL/d in an obvious recovery process, began to decrease slowly to about l mL/ d after a stable period, and then reached the current cumulative gas production of 3634 mL with the recovery rate of 60.8%. The simulated production curve of shale core is totally different from that of tight sandstone core, which shows that daily gas production and apparent formation pressure are in a continuous decline process with short production time. According to the pressure curve of shale gas production, it is possible to judge that the adsorbed gas in the core begins desorption in large quantities and the desorption increases continuously with the decrease of formation pressure when the apparent formation pressure reaches 14.7 MPa (with the formation pressure of 12 MPa) (Fig. 2b), which can be proved by the curve characteristics that both apparent formation pressure and daily gas production gently decrease after a slight rise.
Fig. 2. Relationships of daily gas production, cumulative gas production and apparent formation pressure of core with time.
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Based on the physical simulation experiment of full-diameter shale core, the depletion process of shale gas development can be divided into three main stages: the high-speed development stage in which the gas production decreases rapidly in the first 40 days; the medium-speed development stage in which gas production slows down from the 40th to 440th day; the long-term low-speed steady production stage in which gas production is stable and decreasing extremely slowly. As shown in Fig. 3, the apparent formation pressure greater than 20 MPa changes little in the first 40 days and the gas production is mainly from free gas; the apparent formation pressure decreases significantly with the increase of cumulative gas production in the following 400 days, showing a linear relationship with the fitting slope value as 0.0068 MPa/mL, and decreases to 14.78 MPa with a small contribution of gas production from desorbed gas; the apparent formation pressure decreases slowly with the increase of the cumulative gas production from the 440th to 1631th day, showing a general linear relationship with the fitting slope value as 0.0038 MPa/mL, and decreases to 9 MPa with an increasing proportion of desorbed gas in gas production. It can be seen that the production performance in the full lifecycle physical simulation experiment of shale core is basically consistent with that in gas well. Therefore, the production performance of shale gas well can be reasonably and effectively explained and predicted by the result of physical simulation experiment. 3. Analysis of experimental data During the 1631 days physical simulation experiment of fulldiameter shale core related to full lifecycle of gas well, all experimental data over time, including confining pressure, inlet pressure and outlet flow, were automatically collected by the computer. By analyzing and processing, it is easy to observe the change of cumulative and daily gas production with the decrease of formation pressure. Combined with the basic theory of gas reservoir engineering, the important parameters such as free gas production, adsorbed gas production, porosity and generalized permeability in the gas production process of the core can be calculated. 3.1. Calculation of the amount of free and adsorbed gas Fig. 3 shows the relationship between apparent formation pressure and cumulative gas production in the full lifecycle gas well production through the full-diameter shale core simulation. For a closed gas reservoir, according to the material balance equation, the apparent formation pressure decreases linearly with the increase of cumulative gas production. Due to the limitation of gas well
development or experimental conditions, however, the initial production data often do not conform to the linear relationship of theoretical calculation. Therefore, to analyze the production performance, the production or experimental data after a period of production are generally used. Unfortunately, that is obviously not applicable to explain the middle and later segments of the development curve from depletion simulation experiment of core in Fig. 3. The linear relationship exists in Fig. 3 when the apparent formation pressure is more than 14.7 MPa (with the formation pressure of 12 MPa), but when the apparent formation pressure is less than 14.7 MPa, the decrease of the apparent formation pressure tends to slow down and the linear relationship starts to deviate. The lower the apparent formation pressure is, the greater the deviation will be. The critical desorption pressure of the adsorbed gas in the shale core at room temperature is 12 MPa, which is consistent with the results obtained in the high-pressure adsorption experimental test (Wang et al., 2015). In case of the formation pressure lower than the critical desorption pressure, a large amount of adsorbed gas will be desorbed, and the cumulative gas production will be higher than the material balance calculation amount. The lower the formation pressure is, the larger the difference in the cumulative gas production will be. In other words, the proportion of desorbed gas production increases with the decrease of formation pressure. At the low-speed steady production stage, the cumulative gas production also has a linear relationship with the apparent formation pressure except that the fitting slope is smaller than that at the medium-speed development stage with more obvious desorption of adsorbed gas, which is the main reason for the long-term steady production of shale gas well at the later low production stage. To sum up, the experimental process of core depletion simulation can be divided into three stages: high-speed development and stable high-pressure stage affected by experimental conditions; the medium-speed development stage with linear decline of apparent formation pressure; the low-speed development stage with linear decline of apparent formation pressure. The last two stages can be used to analyze the production performance of gas well. The red dotted line in Fig. 3 is the material balance curve of free gas in enclosed gas reservoir, calculated on the basis of the known core porosity of 1.03% (parallel sample test result) and the principle of material balance. It represents the production performance of free gas in the shale core, which can be used as benchmark data to distinguish free and adsorbed gas production at different formation pressures: y ¼ 0.0076 x þ 29
(1)
In Eq. (1), the cumulative gas production under different formation pressures is from free gas; the gas production corresponding to the measured point is the sum of free and adsorbed gas; the difference between them is the adsorbed gas production in the gas producing process of core. The curve fitting function of the relationship between cumulative gas production and apparent formation pressure at the medium-speed development stage is: y ¼ 0.0068 x þ 28.46
(2)
The curve fitting function of the relationship between cumulative gas production and apparent formation pressure at the lowspeed steady production stage is shown as follows: Fig. 3. Relationship between apparent formation pressure and cumulative gas production in the full lifecycle of shale core.
y ¼ - 0.0038 x þ 22.43
(3)
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In order to correct the deviation of test data caused by the experimental errors, the linear fitting functions at the mediumspeed development stage [Eq. (2)] and the low-speed steady production stage [Eq. (3)] are used to calculate the cumulative gas production under the corresponding apparent formation pressure. Then subtracting the free gas production under the same apparent formation pressure, which is calculated with the material balance equation [Eq. (1)] for closed gas reservoir, the cumulative adsorbed gas production can be obtained (Fig. 4a). The daily gas production (Fig. 4b) can be obtained by differentiating the cumulative adsorbed and free gas production with respect to time. The calculated results are almost completely consistent with the measured results. The elimination of measured outliers caused by the experiment error and the smoothing of curve have no influence on the final experimental results, so that the accurate separation of adsorbed and free gas in the gas production of full-diameter shale cores can be achieved. The initial free gas production of the core calculated with the porosity of the full-diameter shale core is 3820.8 mL and the adsorbed gas production calculated with the fitting curve at lowspeed steady production stage is 2151.2 mL. Therefore, the total gas production of shale core in the initial state is about 5972 mL. The adsorbed gas production accounts for about 36% of the total gas production, with the ratio of adsorbed gas to free gas being about 1:2, equivalent to 2.8 m3/t gas production of shale reservoir rocks, which is basically consistent with the gas production test in the studied area and relatively low in the total gas production (Zhong et al., 2016).
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3.2. Porosity In the developing shale gas well, if reservoir porosity and permeability parameters are absent, it is feasible to use the gas well production data to calculate the reservoir porosity. In terms of the desorption characteristics of shale gas (Wang et al., 2015), the produced gas in shale under high pressure is mainly free gas. According to the material balance equation for closed gas reservoir, the cumulative gas production has linear relationship with the apparent formation pressure:
Zp Gp1 ¼ G1 1 i Zpi
(4)
Eq. (4) shows that the cumulative gas production of shale in the early stage has linear relationship with the apparent formation pressure, with a slope of G1zi/pi and an intercept of the total free gas production G1. The total production of free gas G1 and the pore volume Vp1 and porosity 4 occupied by free gas can be determined on the basis of the curve slope of the early-stage cumulative gas production and the apparent formation pressure: Vp1 ¼ G1Bgi
(5)
4 ¼ Vp1/V
(6)
The linear segment of the relationship between the cumulative gas production and the apparent formation pressure at the medium-speed development stage is selected for analysis (Fig. 3).
Fig. 4. Dynamic characteristic of cumulative and daily gas production for free and adsorbed gas in the depletion process of shale core simulation.
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The linear slope is given as 144.9 mL/MPa. The calculated free gas production is 4191.7 mL, slightly greater than that calculated according to the core porosity. By introducing high-pressure physical properties (Wang et al., 2015) and shape parameters of rock sample, using Eq. (5) and Eq. (6), the calculated pore volume is 13.18 mL and the porosity is about 1.13%, which is slightly larger than the porosity of parallel rock samples in that some of the produced gas came from the adsorbed gas and a small amount of adsorbed gas desorbed at the medium-speed development stage. Although the shale porosity determined according to the cumulative gas production curve at the medium-speed development stage is slightly large, the detection method is feasible due to the relatively small desorbed gas production and deviation at that stage.
3.3. Generalized permeability Shale pore throats are fine, mostly at the nanometer level and contain multiple forms of complex flows, such as continuous flow, slippage flow, transition flow or molecular free flow. Due to the lack of effective technical means to characterize the shale gas flow at present, the equivalent generalized permeability K is usually used to characterize the strength and weakness of flow capacity (Sakhaee-pour and Bryant, 2012; Wang et al., 2013), with the same calculation equation as that of conventional gas.
K¼
200qmg Zpsc L A p22 p21
(7)
The generalized permeability of core under different formation pressure is calculated according to the inlet pressure, outlet pressure and flow rate of core holder in physical simulation (Fig. 5). It can be observed that the generalized permeability of the experimental shale core is very low, about 109 mD in order of magnitude. When excluding a few abnormal points at the high-pressure stage, the generalized permeability of shale core under different formation pressures is basically the same, which implies that the gas flow capacity is basically the same in the whole process of core depletion development experiment. Although the mechanism of gas production in different stages may be different, the daily gas production at the macro level is the same. Therefore, it is feasible to introduce equivalent generalized permeability of shale and calculate the gas well productivity through Darcy's flow model.
Fig. 5. Generalized permeability changes of shale cores under different formation pressures.
4. Similarity analysis and numerical inversion 4.1. Numerical inversion method for physical simulation experiment According to the discrete fracture network (DFN) model proposed by Meyer and Bazan (2011) on the basis of self-similarity principle and dual medium model, the body of volume fracturing stimulation is an ellipsoid structure, containing one primary fracture and several secondary fractures. The main fracture is perpendicular to the direction of minimum principal stress; secondary fractures and primary fracture cut shale matrix into regular cube units (Fig. 6). The fracture network conductivity of shale gas reservoir after volume fracturing stimulation is at the level of 100 mD$m (Cheng et al., 2013), so that the fracture network can be considered to be composed of the infinite conductivity fractures. In other words, the productivity of shale gas well is determined by the gas supply capacity of bedrock to fractures. According to the dimensionless theory in well testing (Kong, 2010), the production time of gas reservoir in core physical simulation can be converted into that of gas well in real gas reservoir through dimensionless time tD, where the calculation of tD is:
tD ¼
Kt
mg fCg L2e
(8)
Since there is gas leakage on all six sides of bedrock block in shale gas reservoir, according to literature (Zhu et al., 2010), the relationship between characteristic length Le and side length a of bedrock block can be described as follows:
Le ¼
pffiffiffi 3 a 6 b
(9)
By converting the production time of gas reservoir in core physical simulation, the production time of gas well in the real gas reservoir can be obtained as:
tt ¼
mt;g ft Ct;g a2b Km tm 12mm;g fm Cm;g L2e Kt
(10)
Fig. 7 shows the relation curves of similarity between the production time in gas well calculated according to Eq. (10) and the gas production time from core physical simulation; the five curves indicate the corresponding similarity relationship under different volume fracturing effects (i.e., fracture network densities, represented by the side lengths of equivalent cube matrix rock with the value ranges from 0.55 m to 30 m). When the side length of bedrock is 0.55 m, the gas production time in core physical simulation is equal to that in gas well. That means, for the shale gas reservoir with extremely low porosity and permeability, good development effects can also be achieved if the fracturing scale is large enough. As the side lengths of bedrock increases, the production time of gas well starts to be greater than that of the core, and the larger the side length of bedrock is, the greater the difference will be. When the side length reaches 10 m, the production time of gas well is about 300 times higher than that of the core simulation. When the side length reaches 30 m, the production time of gas well is about 3000 times higher than that of the core simulation. Therefore, for the shale gas reservoir with extremely low seepage capacity, the volume fracturing directly determines the development effect of the gas reservoir. Fig. 7a shows the similarity relationship of corresponding production time between gas well and core physical simulation under different permeability conditions (permeability distribution from
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Fig. 6. Three-dimension and plane top view of DFN geometric model.
Fig. 7. The similarity relationship of corresponding production time between shale core physical simulation and gas well.
1 103 mD to 1 107 mD) based on the side length of 30 m of equivalent bedrock and porosity of 2.5% controlled by fractured network. When the core permeability reaches 1 103 mD, the production time in gas well is about 0.006 times of that in core simulation, far less than the latter. Although the side length of bedrock is up to 30 m, the gas reservoir has a good development effect due to the high permeability and large drainage area. The production time in gas well begins to increase as the permeability decreases. When the permeability drops to 1 105 mD, the production time in gas well is about 0.6 times of that in core simulation. When the permeability drops to 1 107 mD, the production time in gas well is about 60 times of that in core simulation. It is observed that permeability and volume fracturing effect (fracture network density) are the two most important parameters determining the development effect of shale gas reservoir. If the permeability is greater than 1 105 mD, the fracturing effect on the gas reservoir development is not very obvious; if the permeability is less than 1 107 mD, the gas reservoir development depends on the fracture network density. A good combination of both is the premise for the effective development of shale gas reservoir. When the gas reservoir in core physical simulation is consistent with the shale gas reservoir in the field in terms of the initial pressure and temperature (a consistent initial state), as well as the boundary conditions (closed boundaries in both), according to the
theories of seepage mechanics and similarity, the recovery rate of gas well in gas reservoir shall be consistent with that in core physical simulation at the same dimensionless time tD. In other words, the gas reservoir state both in the physical simulation and in the field shall be constantly consistent:
Gt;p Gm;p ¼ Gt Gm
(11)
Where
Gt ¼ V rGc =Z
(12)
The cumulative gas production of real gas reservoir can be obtained by converting Eq. (11) as below:
Gt;p ¼
Gm;p Gt Gm
(13)
Therefore, when the physical property parameters of real gas reservoir are known, the relation or relation curve between cumulative gas production and time can be obtained according to Eq. (10). Eq. (13) and the physical simulation experiment, and the corresponding daily gas production of gas well is as follows:
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vGt;p qt ¼ vtt
(14)
4.2. Numerical inversion and analysis of the production performance curve of gas well Taking the core from gas reservoir of Longmaxi Formation in Zhaotong area of South Sichuan as an example, the production performance of gas well is analyzed. The original formation pressure of reservoir is 28 MPa; the permeability is 2 109 mD; the porosity is 1.03%; and the gas production is 2.8 m3/t. The production performance analysis is carried out on the assumption that the pore volume of SRV region is 10 106 m3, the geological reserve is 0.44 108 m3, and the equivalent side lengths of the bedrock are 0.55 m and 10 m respectively for two different fracturing scales. Fig. 8a shows the production performance curves of gas well under the condition that the reservoir permeability is 2 109 mD and the side length of bedrock is 0.55 m. As shown in Fig. 7, the production time ratio of gas well to core physical simulation under that condition is 1:1, and at the same recovery rate, the development time of both is completely identical. The production performance curve in Fig. 8a shows that the reservoir permeability is extremely low, if the fracturing scale (fracture network density) is sufficiently large and possessing sufficiently good efficiency, better development effect can be achieved. It is indicated that the initial gas production capacity is up to 100 104 m3/d, and then rapidly decreases to 3 104 m3/d, lasting for a period of 100 days, and the cumulative gas production reaches 10 106 m3, mainly the free gas, followed by a small amount of desorbed gas of about 26 104 m3. At the medium-speed development stage lasting for about 1 year,
the gas production is about 2 104 m3/d, and the cumulative gas production is about 13 106 m3, while the desorbed gas is only about 85 104 m3. Finally, at the long-term low-speed steady production stage lasting for more than 3 years, the gas production is about 1 104 m3/d, the cumulative gas production reaches 26.46 106 m3, and the desorbed gas production is up to about 700 104 m3, accounting for about 25% of the cumulative gas production. That proves the desorption of adsorbed gas is the main gas supply source for the long-term low-speed steady production in the later development period of shale gas reservoir. The final recovery rate is consistent with the physical simulation, up to 60%. Obviously, despite of extremely low seepage capacity, the reservoir can be developed efficiently as long as the development fracturing technology meets the requirement, the volume fracturing effect is good and the fracture network density is large enough. Fig. 8b shows the production performance curves of gas well under the condition that reservoir permeability is 2 109 mD and side length of bedrock is 10 m. The production time ratio of gas well to core physical simulation is 300:1, the development time difference between the two is huge under the same recovery rate, completely different from the production performance above mentioned. It can be found that under that production condition, the gas well needs to produce nearly 550 years before satisfying the current recovery rate in the physical simulation experiment. In the initial stage, the maximum gas production is only 0.3 104 m3/d so that it requires about 114 years for the cumulative gas production of 10 106 m3. The gas production at the later long-term steady stage is only about 0.002 104 m3/d, which obviously has no industrial production value. The permeability and the volume fracturing effect (fracture network density) of shale gas reservoir are the keys to determine whether the gas reservoir can be effectively developed. As the
Fig. 8. Numerical inversion of daily and cumulative gas production at different fracture scale.
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fundament, the higher the permeability, the lower the requirement on volume fracturing will be, namely the density of fracture network can be appropriately small. The cognition is basically consistent with that in literature (Gao et al., 2017), further demonstrating the reliability of conversion result of physical simulation experiment in this study. However, if the permeability is very low, the premise for effective development is only to improve the effects of volume fracturing, increase the fracture network density as much as possible, and greatly increase the flow-limiting area, which are also the keys to obtain good effects of shale gas development. Jiaoshiba shale gas reservoir, for example, imposes relatively lower requirements for fracturing due to its good porosity and permeability, and has good development effects with the current fracturing technology; in the case of the shale gas reservoir of Longmaxi Formation in Zhaotong area, however, due to its poor physical properties and poor fracturing technology at that time, the development effect is not very ideal, and some gas wells even fail. With the improvement of large-scale volume fracturing technology, it is becoming possible to effectively develop the shale reservoirs with poor permeability and poor permeability. The research shows that the results of physical simulation experiment can be reasonably converted into the production performance curve of full-lifecycle depletion in shale gas well development by using the well testing and similarity theory. It is possible to predict and explain the characteristics of production performance of gas well, optimize fracturing parameters and provide proposals for highly efficient development. 5. Conclusions (1) The physical simulation experimental process of coupling seepage for shale gas is established. By using full-diameter shale core, the full-lifecycle physical simulation experiment of shale gas well is carried out for the first time. The experimental results have good consistency with the development performance of gas well, and can be used to effectively predict the dynamic productivity change, the adsorbed gas production, the free gas production and the final cumulative gas production of shale gas wells, provide a solid base for productivity calculation and production performance prediction for shale gas wells. (2) Based on the data from depletion physical simulation experiment lasting for 1631 days for shale gas well, the analyses show that the critical desorption pressure of shale reservoir is 12 MPa, the free and adsorbed gas production are 3820.8 mL and 2151.2 mL respectively, the total geological reserves is 5972 mL, the ratio of adsorbed gas to free gas is about 1:2, the gas production is 2.8 m3/t, the porosity is 1.03%, and the generalized permeability is about 2 109 mD. By plotting the relationship curves of daily and cumulative gas production of free and adsorbed gas changing with formation pressure and production time, it shows that the adsorbed gas starts to desorb and supply gas in a large amount when the formation pressure is less than 12 MPa, and the lower the formation pressure is, the larger the proportion of adsorbed gas in the daily gas production will be. (3) The physical simulation experimental results demonstrate that the depletion process of shale gas can be divided into three main stages: the early high-speed development stage with rapidly decreasing gas production rate but rapidly increasing cumulative gas production in a short period; the medium-speed development stage with quite high gas production slowing down in a short period; the later long-term steady production stage with low gas production rate and extremely slow reduction.
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(4) According to well testing and similarity theory, the mathematical expression of dimensionless time tD is derived, the conversion of production time between gas reservoir in core physical simulation and that in gas well is implemented. With the application of the numerical inversion, the calculation equation is obtained for the cumulative and daily gas production of gas well in shale gas reservoir. The analysis results of production performance for gas well indicate that both the permeability and the volume fracturing effect (fracture network density) are the keys to the development effect of gas well, and the fundamental factor is the permeability. Acknowledgements The work was supported by the National Science and Technology Major Project (2016ZX05062; 2017ZX05037-001). Symbol annotations x y Gp1 G1 p Z pi Zi Vp1 V Bgi K q psc L A
mg mm, g mt, g p1 p2 t tm tt tD 4 4m 4t Cg Ct, g Cm, g Le ab Gm, p Gt, p Gt Gm qt V
r
Cumulative gas production of core physical simulation, mL; Apparent formation pressure of core physical simulation, MPa Cumulative gas production in the absence of desorption in the early stage, mL; Amount of free gas, mL; Formation pressure, MPa Gas compression factor Original formation pressure, MPa Gas compression factor under the original formation pressure Core pore volume occupied by free gas, mL; Apparent volume of core, mL; Gas volume coefficient under original formation pressure Generalized permeability, mD Flow rate of core holder, mL/min Standard atmospheric pressure, 0.101 MPa Length of core, cm Cross-sectional area of core, cm2 Gas viscosity, mPa$s Gas viscosity of core physical simulation, mPa$s Gas viscosity of gas reservoir in the mine site, mPa$s Outlet pressure of core holder, MPa Inlet pressure of core holder, MPa time, s; Production time of core physical simulation, s; Production time of gas reservoir in the field, s; Dimensionless time; Porosity Porosity of core physical simulation Porosity of gas reservoir in the field Gas compression factor, 1/MPa Gas compression coefficient of gas reservoir in the field Gas compression coefficient of core physical simulation Characteristic length, m; Side length of bedrock after fracturing, m; Cumulative gas yield of core physical simulation, mL; Cumulative gas yield of gas reservoir in the field, mL; Geological reserve of gas reservoir in the field, m3 Geological reserve of core physical simulation, mL; Gas production rate of gas well, m3/s Volume of SRV region of gas reservoir in the field, m3 Bedrock density, kg/m3
190
Ge dx dy dz a b h
sh sH sV
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Gas production of gas reservoir in the field, m3/t X-direction grid spacing, m; Y-direction grid spacing, m; Z-direction grid spacing, m; Length of the elliptic semi major shaft, m; Length of ellipse semi minor shaft, m; Reservoir thickness Minimum principal stress, MPa Maximum principal stress, MPa Vertical directional stress, MPa
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Ji, W.M., Song, Y., Jiang, Z.X., Chen, L., Wang, P.F., Liu, Q.X., Gao, F.L., Yang, X., 2016. Micro-nano pore structure characteristics and its control factors of shale in Longmaxi Formation, southeastern Sichuan Basin. Acta Pet. Sin. 37 (2), 182e195 (in Chinese). Kong, X.Y., 2010. Advanced Mechanics of Fluids in Porous Media, second ed. University of Science & Technology China Press, Hefei (in Chinese). Li, Z.P., Li, Z.F., 2012. Dynamic characteristics of shale gas flow in nanoscale pores. Nat. Gas. Ind. 32 (4), 50e53 (in Chinese). Meyer, B.R., Bazan, L.W., 2011. A discrete fracture network model for hydraulically induced fractures-theory, parametric and case studies. SPE 7e9, 140514. Sakhaee-pour, A., Bryant, S., 2012. Gas permeability of shale. SPE Reservoir Eval. Eng. 15 (4), 401e409. Schepers, K.C., Gonzalez, R.J., Koperna, G.J., Oudinot, A.Y., 2009. Reservoir modeling in support of shale gas exploration. SPE 8e11, 123057. Su, Y.L., Sheng, G.L., Wang, W.D., Yan, Y., Zhang, X., 2016. A multi-media coupling flow model for shale gas reservoirs. Nat. Gas. Ind. 36 (2), 52e59 (in Chinese). Swami, V., Settari, A., 2012. A pore scale gas flow model for shale gas reservoir. Soc. Petrol. Eng. 10e13. SPE 155756. Swami, V., Settari, A., Javadpour, F., 2013. A numerical model for multi-mechanism flow in shale gas reservoirs with application to laboratory scale testing. Soc. Petrol. Eng. 5e7. SPE 164840. Wang, R., Zhang, N.S., Liu, X.J., Wu, X.M., Yan, J., 2013. The calculation and analysis of diffusion coefficient and apparent permeability of shale gas. J. Northwest Univ.: Nat. Sci. Ed. 43 (1), 75e80 (in Chinese). Wang, Y.P., Zuo, L., Hu, Z.M., Shen, R., Xiong, W., Gao, S.S., Xiao, H.R., 2015. Experiment of supercritical methane adsorption on shale and adsorption modelling. J. Cent. South Univ.: Sci. Technol. 46 (11), 4129e4135 (in Chinese). Wen, Q.Z., Gao, J.J., Li, Y., Zhan, Y.P., Li, M., 2014. Analysis of the factors of influencing stimulated volume of shale reservoir volume fracturing. J. Xi'an Shiyou Univ. Nat. Sci. Ed. 29 (6), 58e64 (in Chinese). Wu, J., Liang, F., Lin, W., Wang, H.Y., Bai, W.H., Ma, C., Sun, S.S., Zhao, Q., Song, X.J., Yu, R.Z., 2017. Reservoirs characteristics and gas-bearing capacity of WufengLongmaxi Formation shale in Well WX-2, northeast Chongqing area. Acta Pet. Sin. 38 (5), 512e524 (in Chinese). Wu, Q., Xu, Y., Wang, T.F., Wang, X.Q., 2011. The revolution of reservoir stimulation: an introduction of volume fracturing. Nat. Gas. Ind. 31 (4), 7e12 (in Chinese). Zhong, G.H., Xie, B., Zhou, X., Peng, X., Tian, C., 2016. A logging evaluation method for gas content of shale gas reservoirs in the Sichuan Basin. Nat. Gas. Ind. 36 (8), 43e51 (in Chinese). Zhu, W.Y., Qi, Q., Ma, Q., Deng, J., Yue, M., Liu, Y.Z., 2016. Unstable Seepage modeling and pressure propagation of shale gas reservoirs. Petrol. Explor. Dev. 43 (2), 261e267 (in Chinese). Zhu, W.Y., Sun, Y.K., Wang, S.H., Ju, Y., Li, Z.K., 2010. Theory and Method for Effective Development of Percolation in Ultra-low Permeability Reservoirs. Petroleum Industry Press, Beijing (in Chinese).
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Full Length Article
Physical simulation experiment and numerical inversion of the full life cycle of shale gas well Shusheng Gao a, b, *, Huaxun Liu a, b, Liyou Ye a, b, Zhiming Hu a, b, Weiguo An b a b
Research Institute of Petroleum Exploration & Development, CNPC, Beijing, 100083, China Department of Porous Flow & Fluid Mechanics, Research Institute of Petroleum Exploration & Development, PetroChina, Hebei, Langfang, 065007, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 November 2018 Received in revised form 26 March 2019 Accepted 3 April 2019 Available online 8 May 2019
The ultra-low porosity and permeability, as well as complex occurrence and transport state of shale reservoir make it possess special L-type production characteristic curve and complicated shale gas flow mechanism. To solve the difficulty of collecting complete production data due to short production time and operation discontinuity, a full-diameter core physical simulation experiment on the full lifecycle production process of shale gas well depletion is conducted with the purpose of obtaining many important production data including complete pressure and daily gas output in the simulated production process of shale gas well. The experimental results show the production characteristic from simulation is consistent with those from gas well. Based on the simulation data, the critical desorption pressure (12 MPa) of core, free gas production (3820.8 mL), adsorbed gas production (2151.2 mL), the proportion of the daily gas production between free and absorbed gas under different time and formation pressure, as well as the production time and final recovery rate corresponding to abandoned pressure, can be determined accurately. Numerical inversion is carried out to calculate the production performance curve of shale gas well and predict the development effect of gas well based on well testing and similarity analysis of the dimensionless time between core experiment and gas well production. Finally, the permeability and the fracturing effect (fracture network density) as the keys to the effective development of shale gas reservoirs are proposed. The permeability is the fundamental factor and the fracturing technology is the major means. © 2019 Chinese Petroleum Society. Publishing Services by Elsevier B.V. on behalf of KeAi. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Shale gas well Full lifecycle Physical simulation experiment Numerical inversion Similarity theory Permeability Fracturing effect
1. Introduction In shale gas reservoir, which is different from the conventional gas reservoir, shale is both the source rock generating natural gas and the reservoir and cap layer for accumulating and storing natural gas. Shale gas is primarily trapped in the fissures, pores and other reservoir spaces of black mud shale as a free phase, adhered to the surface of kerogen, clay particles and pores as an adsorbed phase with the proportion ranging from 20% to 80% (Wu et al., 2011, 2017), or as a dissolved phase with very small amount. The accumulation of shale gas is the typical in-situ accumulation mode near the hydrocarbon source rocks (Dong et al., 2016). In recent years, the exploration and development of shale gas in China has achieved important breakthroughs, many national shale gas demonstration
* Corresponding author. Research Institute of Petroleum Exploration & Development, CNPC, Beijing, 100083, China. E-mail address: [email protected] (S. Gao).
zones, such as Fuling, ChangningeWeiyuan and Zhaotong, have been established successively with proven gas reserves of 5441.29 108 m3. The industrial production of shale gas in China had been realized with a production capacity of 65 108 m3/a by the end of 2015 and 85 108 m3/a by the end of 2016 (Wu et al., 2017). There are many types of micro- and nano-scale pores in shale gas reservoir, and most of them are nano-scale pores (Ji et al., 2016). Shale gas reservoir is characterized by complex gas occurrence states, extremely low porosity and permeability, basically free of seepage capability, thus the effective diverting capacity of shale gas is mainly dependent on diffusion and fracture (Carlson and Mercer, 1991; Carlson, 1994; Wen et al., 2014; Su et al., 2016). The effective development of shale gas wells fundamental lies in large-scale integrated multi-stage fracturing. The characteristics and development mode of shale reservoir determine the shale gas production has the characteristics of typical L-shaped production curve with high initial output, fast decline, low and stable production for long time in the later stage.
https://doi.org/10.1016/j.ptlrs.2018.04.001 2096-2495/© 2019 Chinese Petroleum Society. Publishing Services by Elsevier B.V. on behalf of KeAi. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
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Some studies suggested that the reservoir characteristics of low porosity and extremely low permeability in shale matrix could be described by double-porosity model (Javadpour et al., 2007; Javadpour, 2009; Ji et al., 2016). The flow of shale gas could be described as a process that free gas generated in the fracture, pressure difference produced between fracture and matrix, adsorbed gas flowed to wellbore along fractures after desorbing from matrix surface, and gas in matrix diffused to surface under concentration difference. The flow of gas in shale matrix followed the molecule diffusion principle, which could be described by Darcy's law when gas flowed from fractures to wellbore and by Langmuir equation during gas desorption. Schepers et al. (2009) and Civan et al. (2011) proposed the triple-porosity and dual-permeability model and believed that flow of gas in both fractures and matrix should follow Darcy's law, shale matrix could play not only the source of gas desorption but also a dominant role in seepage compared with diffusion. Swami and Settari (2012), Swami et al. (2013) put forward the four-porosity gas flow model with considering the free gas in the micro-cracks, the free gas in the nanopores, the adsorbed gas on the pore walls and the kerogen solution gas, established the flow equation of shale nano-pores and solved the numerical solution, considered that Knudsen diffusion, Langmuir gas desorption, gas slippage and diffusion of solution gas should be taken into account during shale production prediction and numerical simulation. Alharthy et al. (2012) proposed the double- and triple-porosity model containing convection, diffusion and slip flow, completed the numerical calculation and believed that the triple-porosity model could better simulate the gas flow in shale gas reservoir and the flow channel of desorption gas would not be affected by the mesoporous. Duan et al. (2011) proposed the mathematical model of macroscopic seepage involving adsorbed gas, free gas and solution gas for dual medium shale gas reservoir fracturing wells and calculated the unstable productivity of shale gas well. Li and Li (2012) considered the nano-pore gas desorption and diffusion and argued that gas desorption could induce shale matrix contraction and increase gas seepage channel and permeability when the formation pressure was lower than the gas critical desorption pressure. If the proportion of gas molecules with free path larger than pore diameter (D) was set to be a and the proportion of molecules with free path smaller than D was set as 1-a, the gas seepage and diffusion equation could be established. Wang et al. (2015) proposed an adsorption model at high-temperature and high-pressure for shale. Guo et al. (2016) established the dual-media gas-water two-phase seepage model with considering the desorption-adsorption, diffusion, slippage and stress sensitivity. Zhu et al. (2016) studied the propagation law of pressure disturbance in the shale matrix reservoir by using the steady state replacement algorithm and analyzed the production decline law of shale gas wells by numerical calculation. According to literature survey, most results of productivity calculation and performance prediction for shale gas well are from the theoretical research, lacking practical basis and having obvious defects. Firstly, all calculation or prediction models are founded on some assumptions that will not happen in most cases; secondly, most of the key parameters used in calculation cannot be accurately obtained; thirdly, it is difficult to accurately determine the amount of free gas and adsorbed gas in production while the analytical gas amount determined according to the Langmuir model has a large error (Wang et al., 2015). In view of the above reasons, through the current productivity calculation and performance prediction, it is difficult to reasonably explain the special production curve for shale gas well, so that it cannot be used to guide the effective development of shale gas wells. Focused on the full lifecycle production performance of shale gas well in this study, full-diameter shale core was used to simulate
the entire production process for the first time in keeping with the gas well. As a result, the production curve obtained from simulation was highly consistent with that from the gas well. The production curve of gas well would be effectively explained as long as that of simulation was reasonably understood. Moreover, the complete production data and key parameters required in the full lifecycle productivity of shale gas well could be obtained through the physical simulation experiment of full-diameter core, so as to solve the current difficulties in shale gas well productivity calculation and performance prediction. 2. Physical simulation experiment of the full lifecycle of gas well 2.1. Experimental scheme and process The full-diameter shale core (with a diameter of 10 cm and a length of 15 cm) is sampled from Longmaxi Formation in Zhaotong area of South Sichuan. In order to maintain the original characteristics of the core, the first time sampling is carried out with the pressure-retained coring device on the drilling site. After simply cleaning the core, we quickly put it into the pressure-retained coring device with saturated natural gas up to 10 MPa, close the valves at both ends of the coring device, and transport it to the lab for standby application. The experimental equipment is a set of physical simulation device for the desorption-diffusion-seepage coupling of shale gas, independently developed by Department of Porous Flow & Fluid Mechanics, PetroChina Research Institute of Petroleum Exploration and Development. The experimental process is shown in Fig. 1. The experimental pressure sensor has the measuring range of 40 MPa and the precision of 0.3%, which meet the measurement requirements of experimental pressure. The specific experimental process is shown as follows: (1) The task includes taking out the full-diameter core holder from the pressure-retained coring device, putting it into a laboratory with constant temperature of 25 C and connecting it with the simulation experiment device, pressurizing the natural gas in the high-pressure vessels with highpressure pumps to maintain the pressure at 28 MPa, opening the regulating valve 1 and 2, charging methane (considering methane accounting for 99% of the natural gas component in the reservoir) from the both ends of the core holder, then carrying out a secondary saturation pressurization until the pressure in the vessels reach the simulated formation pressure of 28 MPa, increasing the confining pressure to 50 MPa synchronously. Since the shale is extremely tight and possesses special adsorption characteristics, it takes a long time to completely restore the shale to the formation state and the saturation pressurization needs to last for 200 days until the pressure of high-pressure vessels at the outlet and inlet of the core holder no longer decreases. Under this condition, the shale gas will be almost completely restored to its original reservoir state. Then we can close the inlet regulating valve 1 and the outlet regulating valve 2, remove the highpressure air source, and get ready for the full lifecycle production simulation experiment.
2.2. Experimental results The full lifecycle depletion simulation experiment of fulldiameter shale core for gas well lasted 1631 days. According to the similarity of dimensionless time, the petrophysical parameters
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Fig. 1. Physical simulation experimental process of the full lifecycle production for gas well. (2) The task includes opening the outlet regulating valve 2 and starting the experiment. In order to control the excessive initial gas flow, the outlet should maintain a reasonable back pressure. When the flow rate dropped to a proper range, the back pressure should be adjusted to atmospheric pressure and then the dynamic simulation of the full lifecycle production of shale gas well could be started. (3) The inlet pressure, outlet pressure and outlet flow rate were measured by the pressure sensor 1 at the inlet, the pressure sensor 2 and the gas flowmeter at the outlet respectively. The whole simulation experimental process was recorded continuously in real time by the computer data acquisition software.
of shale core and the geological parameters of Longmaxi Formation, the production time calculated in shale core simulation was equivalent to 4.5e550 years in shale gas well under different permeability and fracturing conditions, which achieved the purpose of simulating the full lifecycle production of shale gas well. Considering that there was 1 mL dead volume at the outlet of core holder and the early gas production mainly from the dead volume part could not reflect the gas flow in shale core, the early outliers in experimental data should be deleted during the analysis. According to the dead volume, initial pressure, back pressure at outlet and high-pressure physical parameters of gas, the early gas mainly from the dead volume accounted for 260 mL. After eliminating some uncertainty experimental data arising from the defects of experimental process, the daily gas production curve in the simulation experiment was almost identical to that in the shale gas well (Fig. 2a). The simulation results showed that the gas production in the former 40 days dropped rapidly from 135.9 mL/d on the first day to below 9 mL/d, with the cumulative gas production increasing rapidly to 1038.6 mL and the recovery rate of about 17.4%. After that, the decline of daily gas production and the rise of cumulative gas production slowed down simultaneously, the gas
production dropped to 3 mL/d when the production time reached l00 days. Followed by about 1500 days of a low production stage, the gas production slowly dropped from 3 mL/d to about l mL/d, and the cumulative gas production was up to 1909.5 mL when the production time was up to 444 days with the recovery rate of 32%. The gas production increased from 1 mL/d to about 2 mL/d in an obvious recovery process, began to decrease slowly to about l mL/ d after a stable period, and then reached the current cumulative gas production of 3634 mL with the recovery rate of 60.8%. The simulated production curve of shale core is totally different from that of tight sandstone core, which shows that daily gas production and apparent formation pressure are in a continuous decline process with short production time. According to the pressure curve of shale gas production, it is possible to judge that the adsorbed gas in the core begins desorption in large quantities and the desorption increases continuously with the decrease of formation pressure when the apparent formation pressure reaches 14.7 MPa (with the formation pressure of 12 MPa) (Fig. 2b), which can be proved by the curve characteristics that both apparent formation pressure and daily gas production gently decrease after a slight rise.
Fig. 2. Relationships of daily gas production, cumulative gas production and apparent formation pressure of core with time.
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Based on the physical simulation experiment of full-diameter shale core, the depletion process of shale gas development can be divided into three main stages: the high-speed development stage in which the gas production decreases rapidly in the first 40 days; the medium-speed development stage in which gas production slows down from the 40th to 440th day; the long-term low-speed steady production stage in which gas production is stable and decreasing extremely slowly. As shown in Fig. 3, the apparent formation pressure greater than 20 MPa changes little in the first 40 days and the gas production is mainly from free gas; the apparent formation pressure decreases significantly with the increase of cumulative gas production in the following 400 days, showing a linear relationship with the fitting slope value as 0.0068 MPa/mL, and decreases to 14.78 MPa with a small contribution of gas production from desorbed gas; the apparent formation pressure decreases slowly with the increase of the cumulative gas production from the 440th to 1631th day, showing a general linear relationship with the fitting slope value as 0.0038 MPa/mL, and decreases to 9 MPa with an increasing proportion of desorbed gas in gas production. It can be seen that the production performance in the full lifecycle physical simulation experiment of shale core is basically consistent with that in gas well. Therefore, the production performance of shale gas well can be reasonably and effectively explained and predicted by the result of physical simulation experiment. 3. Analysis of experimental data During the 1631 days physical simulation experiment of fulldiameter shale core related to full lifecycle of gas well, all experimental data over time, including confining pressure, inlet pressure and outlet flow, were automatically collected by the computer. By analyzing and processing, it is easy to observe the change of cumulative and daily gas production with the decrease of formation pressure. Combined with the basic theory of gas reservoir engineering, the important parameters such as free gas production, adsorbed gas production, porosity and generalized permeability in the gas production process of the core can be calculated. 3.1. Calculation of the amount of free and adsorbed gas Fig. 3 shows the relationship between apparent formation pressure and cumulative gas production in the full lifecycle gas well production through the full-diameter shale core simulation. For a closed gas reservoir, according to the material balance equation, the apparent formation pressure decreases linearly with the increase of cumulative gas production. Due to the limitation of gas well
development or experimental conditions, however, the initial production data often do not conform to the linear relationship of theoretical calculation. Therefore, to analyze the production performance, the production or experimental data after a period of production are generally used. Unfortunately, that is obviously not applicable to explain the middle and later segments of the development curve from depletion simulation experiment of core in Fig. 3. The linear relationship exists in Fig. 3 when the apparent formation pressure is more than 14.7 MPa (with the formation pressure of 12 MPa), but when the apparent formation pressure is less than 14.7 MPa, the decrease of the apparent formation pressure tends to slow down and the linear relationship starts to deviate. The lower the apparent formation pressure is, the greater the deviation will be. The critical desorption pressure of the adsorbed gas in the shale core at room temperature is 12 MPa, which is consistent with the results obtained in the high-pressure adsorption experimental test (Wang et al., 2015). In case of the formation pressure lower than the critical desorption pressure, a large amount of adsorbed gas will be desorbed, and the cumulative gas production will be higher than the material balance calculation amount. The lower the formation pressure is, the larger the difference in the cumulative gas production will be. In other words, the proportion of desorbed gas production increases with the decrease of formation pressure. At the low-speed steady production stage, the cumulative gas production also has a linear relationship with the apparent formation pressure except that the fitting slope is smaller than that at the medium-speed development stage with more obvious desorption of adsorbed gas, which is the main reason for the long-term steady production of shale gas well at the later low production stage. To sum up, the experimental process of core depletion simulation can be divided into three stages: high-speed development and stable high-pressure stage affected by experimental conditions; the medium-speed development stage with linear decline of apparent formation pressure; the low-speed development stage with linear decline of apparent formation pressure. The last two stages can be used to analyze the production performance of gas well. The red dotted line in Fig. 3 is the material balance curve of free gas in enclosed gas reservoir, calculated on the basis of the known core porosity of 1.03% (parallel sample test result) and the principle of material balance. It represents the production performance of free gas in the shale core, which can be used as benchmark data to distinguish free and adsorbed gas production at different formation pressures: y ¼ 0.0076 x þ 29
(1)
In Eq. (1), the cumulative gas production under different formation pressures is from free gas; the gas production corresponding to the measured point is the sum of free and adsorbed gas; the difference between them is the adsorbed gas production in the gas producing process of core. The curve fitting function of the relationship between cumulative gas production and apparent formation pressure at the medium-speed development stage is: y ¼ 0.0068 x þ 28.46
(2)
The curve fitting function of the relationship between cumulative gas production and apparent formation pressure at the lowspeed steady production stage is shown as follows: Fig. 3. Relationship between apparent formation pressure and cumulative gas production in the full lifecycle of shale core.
y ¼ - 0.0038 x þ 22.43
(3)
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In order to correct the deviation of test data caused by the experimental errors, the linear fitting functions at the mediumspeed development stage [Eq. (2)] and the low-speed steady production stage [Eq. (3)] are used to calculate the cumulative gas production under the corresponding apparent formation pressure. Then subtracting the free gas production under the same apparent formation pressure, which is calculated with the material balance equation [Eq. (1)] for closed gas reservoir, the cumulative adsorbed gas production can be obtained (Fig. 4a). The daily gas production (Fig. 4b) can be obtained by differentiating the cumulative adsorbed and free gas production with respect to time. The calculated results are almost completely consistent with the measured results. The elimination of measured outliers caused by the experiment error and the smoothing of curve have no influence on the final experimental results, so that the accurate separation of adsorbed and free gas in the gas production of full-diameter shale cores can be achieved. The initial free gas production of the core calculated with the porosity of the full-diameter shale core is 3820.8 mL and the adsorbed gas production calculated with the fitting curve at lowspeed steady production stage is 2151.2 mL. Therefore, the total gas production of shale core in the initial state is about 5972 mL. The adsorbed gas production accounts for about 36% of the total gas production, with the ratio of adsorbed gas to free gas being about 1:2, equivalent to 2.8 m3/t gas production of shale reservoir rocks, which is basically consistent with the gas production test in the studied area and relatively low in the total gas production (Zhong et al., 2016).
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3.2. Porosity In the developing shale gas well, if reservoir porosity and permeability parameters are absent, it is feasible to use the gas well production data to calculate the reservoir porosity. In terms of the desorption characteristics of shale gas (Wang et al., 2015), the produced gas in shale under high pressure is mainly free gas. According to the material balance equation for closed gas reservoir, the cumulative gas production has linear relationship with the apparent formation pressure:
Zp Gp1 ¼ G1 1 i Zpi
(4)
Eq. (4) shows that the cumulative gas production of shale in the early stage has linear relationship with the apparent formation pressure, with a slope of G1zi/pi and an intercept of the total free gas production G1. The total production of free gas G1 and the pore volume Vp1 and porosity 4 occupied by free gas can be determined on the basis of the curve slope of the early-stage cumulative gas production and the apparent formation pressure: Vp1 ¼ G1Bgi
(5)
4 ¼ Vp1/V
(6)
The linear segment of the relationship between the cumulative gas production and the apparent formation pressure at the medium-speed development stage is selected for analysis (Fig. 3).
Fig. 4. Dynamic characteristic of cumulative and daily gas production for free and adsorbed gas in the depletion process of shale core simulation.
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The linear slope is given as 144.9 mL/MPa. The calculated free gas production is 4191.7 mL, slightly greater than that calculated according to the core porosity. By introducing high-pressure physical properties (Wang et al., 2015) and shape parameters of rock sample, using Eq. (5) and Eq. (6), the calculated pore volume is 13.18 mL and the porosity is about 1.13%, which is slightly larger than the porosity of parallel rock samples in that some of the produced gas came from the adsorbed gas and a small amount of adsorbed gas desorbed at the medium-speed development stage. Although the shale porosity determined according to the cumulative gas production curve at the medium-speed development stage is slightly large, the detection method is feasible due to the relatively small desorbed gas production and deviation at that stage.
3.3. Generalized permeability Shale pore throats are fine, mostly at the nanometer level and contain multiple forms of complex flows, such as continuous flow, slippage flow, transition flow or molecular free flow. Due to the lack of effective technical means to characterize the shale gas flow at present, the equivalent generalized permeability K is usually used to characterize the strength and weakness of flow capacity (Sakhaee-pour and Bryant, 2012; Wang et al., 2013), with the same calculation equation as that of conventional gas.
K¼
200qmg Zpsc L A p22 p21
(7)
The generalized permeability of core under different formation pressure is calculated according to the inlet pressure, outlet pressure and flow rate of core holder in physical simulation (Fig. 5). It can be observed that the generalized permeability of the experimental shale core is very low, about 109 mD in order of magnitude. When excluding a few abnormal points at the high-pressure stage, the generalized permeability of shale core under different formation pressures is basically the same, which implies that the gas flow capacity is basically the same in the whole process of core depletion development experiment. Although the mechanism of gas production in different stages may be different, the daily gas production at the macro level is the same. Therefore, it is feasible to introduce equivalent generalized permeability of shale and calculate the gas well productivity through Darcy's flow model.
Fig. 5. Generalized permeability changes of shale cores under different formation pressures.
4. Similarity analysis and numerical inversion 4.1. Numerical inversion method for physical simulation experiment According to the discrete fracture network (DFN) model proposed by Meyer and Bazan (2011) on the basis of self-similarity principle and dual medium model, the body of volume fracturing stimulation is an ellipsoid structure, containing one primary fracture and several secondary fractures. The main fracture is perpendicular to the direction of minimum principal stress; secondary fractures and primary fracture cut shale matrix into regular cube units (Fig. 6). The fracture network conductivity of shale gas reservoir after volume fracturing stimulation is at the level of 100 mD$m (Cheng et al., 2013), so that the fracture network can be considered to be composed of the infinite conductivity fractures. In other words, the productivity of shale gas well is determined by the gas supply capacity of bedrock to fractures. According to the dimensionless theory in well testing (Kong, 2010), the production time of gas reservoir in core physical simulation can be converted into that of gas well in real gas reservoir through dimensionless time tD, where the calculation of tD is:
tD ¼
Kt
mg fCg L2e
(8)
Since there is gas leakage on all six sides of bedrock block in shale gas reservoir, according to literature (Zhu et al., 2010), the relationship between characteristic length Le and side length a of bedrock block can be described as follows:
Le ¼
pffiffiffi 3 a 6 b
(9)
By converting the production time of gas reservoir in core physical simulation, the production time of gas well in the real gas reservoir can be obtained as:
tt ¼
mt;g ft Ct;g a2b Km tm 12mm;g fm Cm;g L2e Kt
(10)
Fig. 7 shows the relation curves of similarity between the production time in gas well calculated according to Eq. (10) and the gas production time from core physical simulation; the five curves indicate the corresponding similarity relationship under different volume fracturing effects (i.e., fracture network densities, represented by the side lengths of equivalent cube matrix rock with the value ranges from 0.55 m to 30 m). When the side length of bedrock is 0.55 m, the gas production time in core physical simulation is equal to that in gas well. That means, for the shale gas reservoir with extremely low porosity and permeability, good development effects can also be achieved if the fracturing scale is large enough. As the side lengths of bedrock increases, the production time of gas well starts to be greater than that of the core, and the larger the side length of bedrock is, the greater the difference will be. When the side length reaches 10 m, the production time of gas well is about 300 times higher than that of the core simulation. When the side length reaches 30 m, the production time of gas well is about 3000 times higher than that of the core simulation. Therefore, for the shale gas reservoir with extremely low seepage capacity, the volume fracturing directly determines the development effect of the gas reservoir. Fig. 7a shows the similarity relationship of corresponding production time between gas well and core physical simulation under different permeability conditions (permeability distribution from
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Fig. 6. Three-dimension and plane top view of DFN geometric model.
Fig. 7. The similarity relationship of corresponding production time between shale core physical simulation and gas well.
1 103 mD to 1 107 mD) based on the side length of 30 m of equivalent bedrock and porosity of 2.5% controlled by fractured network. When the core permeability reaches 1 103 mD, the production time in gas well is about 0.006 times of that in core simulation, far less than the latter. Although the side length of bedrock is up to 30 m, the gas reservoir has a good development effect due to the high permeability and large drainage area. The production time in gas well begins to increase as the permeability decreases. When the permeability drops to 1 105 mD, the production time in gas well is about 0.6 times of that in core simulation. When the permeability drops to 1 107 mD, the production time in gas well is about 60 times of that in core simulation. It is observed that permeability and volume fracturing effect (fracture network density) are the two most important parameters determining the development effect of shale gas reservoir. If the permeability is greater than 1 105 mD, the fracturing effect on the gas reservoir development is not very obvious; if the permeability is less than 1 107 mD, the gas reservoir development depends on the fracture network density. A good combination of both is the premise for the effective development of shale gas reservoir. When the gas reservoir in core physical simulation is consistent with the shale gas reservoir in the field in terms of the initial pressure and temperature (a consistent initial state), as well as the boundary conditions (closed boundaries in both), according to the
theories of seepage mechanics and similarity, the recovery rate of gas well in gas reservoir shall be consistent with that in core physical simulation at the same dimensionless time tD. In other words, the gas reservoir state both in the physical simulation and in the field shall be constantly consistent:
Gt;p Gm;p ¼ Gt Gm
(11)
Where
Gt ¼ V rGc =Z
(12)
The cumulative gas production of real gas reservoir can be obtained by converting Eq. (11) as below:
Gt;p ¼
Gm;p Gt Gm
(13)
Therefore, when the physical property parameters of real gas reservoir are known, the relation or relation curve between cumulative gas production and time can be obtained according to Eq. (10). Eq. (13) and the physical simulation experiment, and the corresponding daily gas production of gas well is as follows:
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vGt;p qt ¼ vtt
(14)
4.2. Numerical inversion and analysis of the production performance curve of gas well Taking the core from gas reservoir of Longmaxi Formation in Zhaotong area of South Sichuan as an example, the production performance of gas well is analyzed. The original formation pressure of reservoir is 28 MPa; the permeability is 2 109 mD; the porosity is 1.03%; and the gas production is 2.8 m3/t. The production performance analysis is carried out on the assumption that the pore volume of SRV region is 10 106 m3, the geological reserve is 0.44 108 m3, and the equivalent side lengths of the bedrock are 0.55 m and 10 m respectively for two different fracturing scales. Fig. 8a shows the production performance curves of gas well under the condition that the reservoir permeability is 2 109 mD and the side length of bedrock is 0.55 m. As shown in Fig. 7, the production time ratio of gas well to core physical simulation under that condition is 1:1, and at the same recovery rate, the development time of both is completely identical. The production performance curve in Fig. 8a shows that the reservoir permeability is extremely low, if the fracturing scale (fracture network density) is sufficiently large and possessing sufficiently good efficiency, better development effect can be achieved. It is indicated that the initial gas production capacity is up to 100 104 m3/d, and then rapidly decreases to 3 104 m3/d, lasting for a period of 100 days, and the cumulative gas production reaches 10 106 m3, mainly the free gas, followed by a small amount of desorbed gas of about 26 104 m3. At the medium-speed development stage lasting for about 1 year,
the gas production is about 2 104 m3/d, and the cumulative gas production is about 13 106 m3, while the desorbed gas is only about 85 104 m3. Finally, at the long-term low-speed steady production stage lasting for more than 3 years, the gas production is about 1 104 m3/d, the cumulative gas production reaches 26.46 106 m3, and the desorbed gas production is up to about 700 104 m3, accounting for about 25% of the cumulative gas production. That proves the desorption of adsorbed gas is the main gas supply source for the long-term low-speed steady production in the later development period of shale gas reservoir. The final recovery rate is consistent with the physical simulation, up to 60%. Obviously, despite of extremely low seepage capacity, the reservoir can be developed efficiently as long as the development fracturing technology meets the requirement, the volume fracturing effect is good and the fracture network density is large enough. Fig. 8b shows the production performance curves of gas well under the condition that reservoir permeability is 2 109 mD and side length of bedrock is 10 m. The production time ratio of gas well to core physical simulation is 300:1, the development time difference between the two is huge under the same recovery rate, completely different from the production performance above mentioned. It can be found that under that production condition, the gas well needs to produce nearly 550 years before satisfying the current recovery rate in the physical simulation experiment. In the initial stage, the maximum gas production is only 0.3 104 m3/d so that it requires about 114 years for the cumulative gas production of 10 106 m3. The gas production at the later long-term steady stage is only about 0.002 104 m3/d, which obviously has no industrial production value. The permeability and the volume fracturing effect (fracture network density) of shale gas reservoir are the keys to determine whether the gas reservoir can be effectively developed. As the
Fig. 8. Numerical inversion of daily and cumulative gas production at different fracture scale.
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fundament, the higher the permeability, the lower the requirement on volume fracturing will be, namely the density of fracture network can be appropriately small. The cognition is basically consistent with that in literature (Gao et al., 2017), further demonstrating the reliability of conversion result of physical simulation experiment in this study. However, if the permeability is very low, the premise for effective development is only to improve the effects of volume fracturing, increase the fracture network density as much as possible, and greatly increase the flow-limiting area, which are also the keys to obtain good effects of shale gas development. Jiaoshiba shale gas reservoir, for example, imposes relatively lower requirements for fracturing due to its good porosity and permeability, and has good development effects with the current fracturing technology; in the case of the shale gas reservoir of Longmaxi Formation in Zhaotong area, however, due to its poor physical properties and poor fracturing technology at that time, the development effect is not very ideal, and some gas wells even fail. With the improvement of large-scale volume fracturing technology, it is becoming possible to effectively develop the shale reservoirs with poor permeability and poor permeability. The research shows that the results of physical simulation experiment can be reasonably converted into the production performance curve of full-lifecycle depletion in shale gas well development by using the well testing and similarity theory. It is possible to predict and explain the characteristics of production performance of gas well, optimize fracturing parameters and provide proposals for highly efficient development. 5. Conclusions (1) The physical simulation experimental process of coupling seepage for shale gas is established. By using full-diameter shale core, the full-lifecycle physical simulation experiment of shale gas well is carried out for the first time. The experimental results have good consistency with the development performance of gas well, and can be used to effectively predict the dynamic productivity change, the adsorbed gas production, the free gas production and the final cumulative gas production of shale gas wells, provide a solid base for productivity calculation and production performance prediction for shale gas wells. (2) Based on the data from depletion physical simulation experiment lasting for 1631 days for shale gas well, the analyses show that the critical desorption pressure of shale reservoir is 12 MPa, the free and adsorbed gas production are 3820.8 mL and 2151.2 mL respectively, the total geological reserves is 5972 mL, the ratio of adsorbed gas to free gas is about 1:2, the gas production is 2.8 m3/t, the porosity is 1.03%, and the generalized permeability is about 2 109 mD. By plotting the relationship curves of daily and cumulative gas production of free and adsorbed gas changing with formation pressure and production time, it shows that the adsorbed gas starts to desorb and supply gas in a large amount when the formation pressure is less than 12 MPa, and the lower the formation pressure is, the larger the proportion of adsorbed gas in the daily gas production will be. (3) The physical simulation experimental results demonstrate that the depletion process of shale gas can be divided into three main stages: the early high-speed development stage with rapidly decreasing gas production rate but rapidly increasing cumulative gas production in a short period; the medium-speed development stage with quite high gas production slowing down in a short period; the later long-term steady production stage with low gas production rate and extremely slow reduction.
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(4) According to well testing and similarity theory, the mathematical expression of dimensionless time tD is derived, the conversion of production time between gas reservoir in core physical simulation and that in gas well is implemented. With the application of the numerical inversion, the calculation equation is obtained for the cumulative and daily gas production of gas well in shale gas reservoir. The analysis results of production performance for gas well indicate that both the permeability and the volume fracturing effect (fracture network density) are the keys to the development effect of gas well, and the fundamental factor is the permeability. Acknowledgements The work was supported by the National Science and Technology Major Project (2016ZX05062; 2017ZX05037-001). Symbol annotations x y Gp1 G1 p Z pi Zi Vp1 V Bgi K q psc L A
mg mm, g mt, g p1 p2 t tm tt tD 4 4m 4t Cg Ct, g Cm, g Le ab Gm, p Gt, p Gt Gm qt V
r
Cumulative gas production of core physical simulation, mL; Apparent formation pressure of core physical simulation, MPa Cumulative gas production in the absence of desorption in the early stage, mL; Amount of free gas, mL; Formation pressure, MPa Gas compression factor Original formation pressure, MPa Gas compression factor under the original formation pressure Core pore volume occupied by free gas, mL; Apparent volume of core, mL; Gas volume coefficient under original formation pressure Generalized permeability, mD Flow rate of core holder, mL/min Standard atmospheric pressure, 0.101 MPa Length of core, cm Cross-sectional area of core, cm2 Gas viscosity, mPa$s Gas viscosity of core physical simulation, mPa$s Gas viscosity of gas reservoir in the mine site, mPa$s Outlet pressure of core holder, MPa Inlet pressure of core holder, MPa time, s; Production time of core physical simulation, s; Production time of gas reservoir in the field, s; Dimensionless time; Porosity Porosity of core physical simulation Porosity of gas reservoir in the field Gas compression factor, 1/MPa Gas compression coefficient of gas reservoir in the field Gas compression coefficient of core physical simulation Characteristic length, m; Side length of bedrock after fracturing, m; Cumulative gas yield of core physical simulation, mL; Cumulative gas yield of gas reservoir in the field, mL; Geological reserve of gas reservoir in the field, m3 Geological reserve of core physical simulation, mL; Gas production rate of gas well, m3/s Volume of SRV region of gas reservoir in the field, m3 Bedrock density, kg/m3
190
Ge dx dy dz a b h
sh sH sV
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Gas production of gas reservoir in the field, m3/t X-direction grid spacing, m; Y-direction grid spacing, m; Z-direction grid spacing, m; Length of the elliptic semi major shaft, m; Length of ellipse semi minor shaft, m; Reservoir thickness Minimum principal stress, MPa Maximum principal stress, MPa Vertical directional stress, MPa
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