The high pressure static adsorption curves of shale samples from Silurian Changning-Weiyuan Longmaxi Formation were tested by using high pressure isothermal adsorption equipment. The physical modeling of depletion production was tested on single cores and multi-core series by using self-developed shale gas fluid-solid coupling experiment system. The adsorption and desorption laws were summarized and a high pressure isothermal adsorption model was established. The calculation formula of gas content was corrected, and the producing law of adsorption gas was determined.
DUAN Xianggang1, HU Zhiming1, GAO Shusheng1, SHEN Rui1, LIU Huaxun1, CHANG Jin1, WANG Lin1, 2
1.PetroChina Research Institute of Petroleum Exploration and Development, Langfang 065007, China; 2.Institute of Porous Flow & Fluid Mechanics, University of Chinese Academy of Sciences, Langfang 065007, China
Received date: 07 May 2017; Revised date: 23 Dec. 2017.
The study results show that the isothermal adsorption law of the shale reservoir under high pressure was different from the conventional low pressure. The high pressure isothermal adsorption curve had the maximum value in excess adsorption with pressure change, and the corresponding pressure was the critical desorption pressure. The high pressure isothermal curve can be used to evaluate the amount of adsorbed gas and the producing degree of adsorption gas. The high pressure isothermal adsorption model can fit and characterize the high pressure isothermal adsorption law of shale.
The modified gas content calculation method can evaluate the gas content and the proportion of adsorbed gas more objectively, and is the theoretical basis of reserve assessment and production decline analysis. The producing degree of adsorption gas is closely related to the pressure, only when the reservoir pressure is lower than the critical desorption pressure, the adsorption gas can be produced effectively. In the process of gas well production, the pressure drop in the near-well area is large, the production of adsorption gas is high; away from the wellbore, the adsorption gas is low in production, or no production.
With abundant micro- and nano-scale pores, organic-rich shale reservoir can form self-generating and self-preserving unconventional gas pool. A large amount of shale gas (generally more than 40%) exists in adsorption state in shale pores. Therefore, it is of great significance to study the shale adsorption rule for gas content calculation, reserves estimation and production prediction[1-2]. Current studies on isothermal adsorption rule of shale are mostly based on the CBM adsorption theory by in-door isothermal adsorption test[3-4].
This type of test is often conducted at the pressure of 6 to 15 MPa, which is much lower than the pressure of the shale reservoirs put into development in China[5-8] (reservoirs in Changning- Weiyuan regions of Sichuan Basin range 70 ºC to 120 ºC in temperature and 30 to 60 MPa in pressure). It’s still uncertain whether the test methods and theories under low-temperature & low-pressure can reflect the real gas adsorption/desorption rules of actual shale reservoir. Studies by foreign researchers[9-12] suggested that different from the conventional adsorption rule, the isothermal adsorption curve of shale under high-pressure tends to rise first and then drop, which indicates that calculating the gas content under the reservoir condition with low-pressure test curve and the Langmuir model has some limitation[13-15].
Adsorbed gas accounts for a large proportion of the total gas content, and is the major gas source for gas well during the low-production and stable production periods. Determining the adsorption/desorption rules of shale gas under reservoir conditions is the basis for preparing shale gas development program and studying production decline rule. No consensus has reached on the mechanism of isothermal adsorption of shale under high pressure, and the adsorption/desorption rules remain unclear, which will lead to inaccurate calculation of gas content and large error in development program.
Therefore, with shale samples recovered from the Silurian Longmaxi Formation in the Changning-Weiyuan regions, Sichuan Basin, several tests are carried out under reservoir pressure by using the high-pressure isothermal adsorption instrument (at the maximum testing pressure of 69 MPa), such as the isothermal adsorption test, and tests on producing characteristics and rule of adsorbed gas. On the basis of these tests, an isothermal adsorption model is built and a revised shale gas content calculation method is proposed, to explore the fundamental theory of high-efficiency development of shale gas.
Samples for test were recovered from the Long11 sub-member of the Longmaxi Formation in the Changning-Weiyuan region, Sichuan Basin. Some fundamental parameters are listed in Table 1. Samples were split into two groups: one group was dried and then crushed into 0.15-0.25 mm (100 to 60 meshes) shale grains for isothermal adsorption test; the other group includes columnar samples for developing characteristics test.
The isothermal adsorption test was carried out by using the classic volumetric method, with a high-pressure gas isothermal adsorption instrument which has a maximum operating pressure of 69 MPa, the precision of the pressure sensor of 0.05% of the maximum measuring range, the maximum con stant temperature of oil bath of 177 ºC, and the control precision of 0.1 ºC. The developing characteristics test was conducted on a self-developed instrument for physically modeling the depletion development of shale gas, which can model shale gas flow with different scales, gases and cores.
Table 1. Fundamental parameters of samples.
Test for high-pressure isothermal adsorption
The experimental instrument is shown in Fig. 1, and the procedure is as follows: (1) place 100 g samples into the sample cylinder, check the gas tightness, and measure the free space volume in the test system using a benchmark cylinder (including space volume of reference cylinder and associated line, residual free space of sample cylinder and associated line space volume, shale intergranular pore) repetitively until the error was below 3%; (2) vacuumize and close the sample cylinder, fill the reference cylinder with methane gas with a certain pressure, open the sample cylinder valve after the pressure stabilized to connect the gas in the two cylinders, and record the equalized pressure after the pressure stabilized; the adsorption amount is given by:
(3) Close the sample cylinder, fill the reference cylinder with gas, and repeat the above-mentioned equalizing process until the completion of the whole test.
Fig. 1. Instrument for isothermal adsorption test using the volumetric method.
Test for modeling the shale gas development
The test was carried out by the instrument shown in Fig. 2, with the procedure as follows: (1) columned shale samples recovered from the same formation were dried and placed into a displacement system, after saturated with methane gas to the initial formation pressure state, the outlet was opened for modeling the depletion development process under the reser voir condition; (2) comparison test was carried out using inert gas, He with negligible adsorption effect, to analyze the influence of adsorption on gas production rule; (3) modeling test with multiple pressure measuring points using five shale samples in series was carried out to find out the relationship between the pressure propagation distance and the adsorbed gas producing pressure, and, based on variation in pressure at these measuring points, the gas production rule and the production proportion of adsorbed gas were investigated by combining the physical property parameters of shale with the material balance equation.
Fig. 2. Instrument for modeling the shale gas development characteristics.
High-pressure isothermal adsorption characteristics
Definition of adsorption quantity
Adsorption refers to the phenomenon that bulk phase composition accumulates at the interface of phases under the effect of residual force field. Adsorption quantity is the difference of quantity of solutes between the interface layer and the bulk phase, which is also known as excess quantity.
Fig. 3. Sketch diagram showing the methane molecule adsorbed to shale.
For example, when methane is adsorbed to shale (Fig. 3), an adsorption force field appears at pore wall surface, and within the adsorption layer the methane molecular density is much higher than the methane density in free space far from the wall surface. Adsorption quantity is given by:
In the case where pressure is relatively low, the free phase density ρg tends to be low, much lower than the adsorbed phase density ρa. Therefore, the impact of ρgVa on the amount of adsorption is small, it is generally believed that ρaVa is adsorption quantity of shale. In fact, all methane gas molecules in adsorption space should be named as absolute adsorption quantity (which is ρaVa), according to the definition proposed by Gibbs. Whereas the actual amount of shale adsorption capacity is excess adsorption. In high-temperature & high-pressure shale reservoirs, free gas exists in super-critical state, free phase density is relatively high, and there will be a great difference between the testing result and the shale adsorption quantity if ρgVa is neglected. Thus, the adsorption characteristics under high pressure and low pressure must be differentiated to better characterize high-pressure isothermal adsorption curve of shale.
There is no method currently available to obtain the adsorption phase density and volume directly. Both the volumetric and gravimetric methods provide an indirect measurement of the excess adsorption quantity. Equation (1) reveals that, the measured adsorption quantity is actually the reduced quantity of free gas. The initially calibrated free volume of the sample cylinder includes the volumes of adsorption space and the free space. As adsorption progresses, adsorbed molecules gradually occupy a proportion of free volume and the occupied volume changes with pressure. Thus, it is required to correct the calculated adsorption quantity with free volume to deduct the adsorbed phase volume. The measured absolute adsorption quantity should be given by:
Accurate measurement of adsorbed phase volume is difficult. None of the methods currently available correct the volume. The measured adsorption quantity is actually excess adsorption quantity rather than the absolute adsorption quantity. Similarly, the gravimetric method also yields excessive adsorbed quantity. Therefore, all current tests give the excessive adsorption quantity rather than the absolute adsorption quantity. The relationship between the excessive adsorption quantity and the absolute adsorption quantity is:
It is noteworthy that there is yet no high-precision technology for measuring the absolute adsorption quantity, and the absolute adsorption quantity is usually calculated with assumed density or volume of adsorbed phase[19, 20].
High-pressure isothermal adsorption characteristics of shale
By comparing high-pressure isothermal adsorption curves of different shale samples (Fig. 4), it can be seen that samples recovered from different regions and different wells from the Longmaxi Formation, exhibited different maximum isothermal adsorption quantity. Samples recovered from the Weiyuan region have the maximum excess adsorption quantity of 1.11 to 2.16 m3/t, and those from two wells in the Changning region have the maximum excess adsorption quantity of 1.45 to 1.68 m3/t. In the low-pressure (less than 10 MPa) stage, adsorption quantity rises rapidly as pressure increases. However, after exceeding a certain pressure (10-20 Mpa), adsorption quantity drops as pressure increases.
Fig. 4. Isothermal adsorption curves of shales in different regions.
As Fig. 5 shows, the isothermal desorption curve of No.2 sample from Well N03 shows distinctly different change rule from the curve measured under low-pressure condition. Under high-pressure, rather than a monotonically increased curve, isothermal adsorption curve of shale has a maximum excess adsorption quantity, which is physically the maximum adsorption capacity of shale and provides a basis for estimating the adsorbed gas quantity of different regions. The pressure corresponding to maximum excess adsorption quantity is the critical desorption pressure, which means physically that desorption of adsorbed gas commences only when the pressure in the system is below the critical desorption pressure.
The decline of the isothermal adsorption curve is an inevitable trend of shale gas under high-pressure reservoir condition and accords with the ultra-critical adsorption characteristics of shale gas. This is because the test yields the curve of excess adsorption quantity, which is a relative quantity rather than the traditional absolute adsorption quantity, according to its definition and Equation (2). The adsorbed molecules are affected by the dispersion force of solid molecules in rock (e.g., organic matter and clay minerals) to methane molecules.
As high-pressure adsorption stage commences (at about the pressure of over 15 MPa), the adsorption force field of pore wall surface to methane molecules remains basically unchanged when pressure increases, as more and more molecules are adsorbed and reach saturation state, and the density of the adsorbed phase tends to stabilize under high-pressure on the density log (Fig. 6). Free molecules, however, are affected only by intermolecular force of gas, as pressure increases, the acting force between free molecules increases continually, resulting in an increase in free phase density. When reaching a certain level of pressure, there must be an extreme value of the difference between their densities. Therefore, there must be a maximum value of excess adsorption quantity at the corresponding pressure.
It is noteworthy that, the decrease of excess adsorption quantity with pressure when exceeding the critical pressure does not mean that the adsorption capability of shale decreases. In fact, the absolute adsorption quantity in the ad- sorption space always increases with pressure, in a way similar to the adsorption quantity variation curve fit by the conventional Langmuir absolute adsorption quantity model shown in Fig. 5. As for the high-pressure adsorption of shale, the proportion of free gas in adsorption space increases, since the acting force of free molecules increases continually. This process is manifested by decrease of excess methane molecules. Therefore, the measured excess adsorption quantity decreases.
Fig. 5. Maximum excess adsorption quantity and critical desorption pressure.
High-pressure isothermal adsorption model
Excess adsorption quantity tends to rise and then declines when the pressure increases. It is difficult to characterize the high-pressure isothermal adsorption rule of shale gas with the Langmuir model and other subcritical model that can be used to characterize absolute adsorption quantity. Thus, it is necessary to build a new model. According to Equations (2) and (4), the relationship between the excess adsorption quantity and the absolute adsorption quantity is:
The density of adsorbed phase shall be assumed when using this equation. Based on studies of some researchers, the liquid phase density is assumed to be 423 kg/m3 and the Van der Waals density is 373 kg/m3, and the critical density is taken as the adsorbed phase density to fit the excess adsorption quantity curve[18, 21]. Although it is possible to characterize the decline of excess adsorption quantity by using a variety of adsorbed phase densities to some extent, the density of adsorbed phase varies and approaches a constant value only when a saturated adsorption state reaches, since the same adsorbed phase density is adopted at different pressure stages, while the volume of methane adsorbed varies as pressure rises. Therefore, the method needs to be modified.
Molecules in adsorption state occupy a certain volume. This volume will increase continually with the increase of excess adsorption quantity until the saturated adsorption is reached. Thus, if we assume that the volume of adsorbed phase approximates the total volume occupied by the adsorbed phase molecules and this total volume can be given by multiplying the number of molecules corresponding to the adsorption quantity with the volume occupied by every adsorbed molecule, it is possible to obtain the relationship between the excess adsorption quantity and the absolute adsorption quantity by modifying the volume of the adsorbed phase:
The Langmuir monolayer adsorption model is used to characterize the absolute adsorption quantity of shale under the ultra-critical condition. The fitting result matches well with the adsorption characteristics under the ultra-critical condition, demonstrating the practicability. However, one major assumption in the Langmuir model is the homogeneity of the solid surface, which is out of accordance with the heterogeneity of the shale pore wall surface. It is therefore decided to adopt the Freundlich isothermal adsorption equation to modify this heterogeneity. The resulted L-F equation is used to characterize the absolute adsorption quantity, which further yields the model of the excess adsorption quantity:
Assuming that each adsorbed phase molecule occupies a spherical volume, the characteristic volume is given by:
It can be seen that the key to the modified equation is the calculation of the characteristic diameter occupied by adsorbed phase molecule. The characteristic diameter of adsorbed molecule is considered to be equivalent to the thickness of the adsorption layer, since the acting force of wall surface to molecule is much greater than the force between gas molecules and the adsorption of shale to methane occurs in the monolayer. References [16, 22] suggest that the adsorption thickness of monolayer molecule was equivalent to the moving diameter of gas molecule, adsorption was saturated when the critical desorption pressure was reached, and the thickness of the monolayer adsorption layer was ca. 0.5 nm.
Fig. 7. Fitting results with the excess adsorption quantity model.