Method of Determining the Threshold Pressure Gradient

Method of Determining the Threshold Pressure Gradient Jing Gao Postgraduate College of Oil and Gas engineering, Southwest Petroleum University, Chengdu 610500, China; e-mail: swpu_gj@sina.com Yingfeng Meng Professor State Key Laboratory of oil and Gas Reservoir Geology and Exploitation; College of Oil and Gas engineering, Southwest Petroleum University, Chengdu 610500, China; e-mail: cwctmyf@vip.sina.com Gao Li Professor State Key Laboratory of oil and Gas Reservoir Geology and Exploitation; College of Oil and Gas engineering, Southwest Petroleum University, Chengdu 610500, China Cong Li Engineer China National Petroleum Corporation(CNPC) of JiDong Oilfield Company, Tangshan, 063200, China; e-mail : licongswpu@163.com Bin Kong Postgraduate College of Oil and Gas engineering, Southwest Petroleum University, Chengdu Minghua Fu Postgraduate College of Oil and Gas engineering, Southwest Petroleum University, Chengdu. Xu Tian Postgraduate College of Oil and Gas engineering, Southwest Petroleum University, Chengdu.. ABSTRACT Low-velocity non-darcy percolation is a common phenomenon when the fluid flowing in the tight sandstone, which is often characterized by the threshold pressure gradient. In order to precisely obtain the value of threshold pressure gradient of oilfield in Western Sichuan, the gas-water two-phase experiments on four cores were conducted. And based on the experiment data, nonlinear percolation feature is shown between gas percolation velocity - 6858 -

Vol. 20 [2015], Bund. 16 6859 and pressure gradient. Then plotting the gas effective permeability versus the inverse of mean pressure and the gas velocity versus the difference of pressure square curves, the threshold pressure gradient are calculated. Meanwhile, the numerical model of four cores was built to simulate the threshold pressure gradient, respectively considering and regardless of the capillary pressure. Research results show that the measured value of threshold pressure gradient is greater than the simulated value, and the value that is considering the capillary pressure is far above that is regardless of it. Eventually, it can be concluded that the capillary pressure is the foremost factor of causing the threshold pressure gradient. KEYWORDS: low-velocity non-darcy percolation; threshold pressure gradient; capillary pressure; core numerical simulation INTRODUCTION How to effectively develop the low and ultra-low permeability gas reservoir has already become the focus of attention, because of the widely distribution and the huge potential that accounts for a quarter of the county's proved gas reservoirs. However, in the process of actual development of low permeability gas reservoir, some problems need to be addressed urgently, such as how to determine the threshold pressure gradient and the driving force. Since the concept of threshold pressure gradient proposed by B. A. Florin [1] who studied the issues about tight mudstone and stiff clay, the international and domestic scholars have never stopped researching the threshold pressure gradient. Bingyu Ji [2] and others have studied the influence of the threshold pressure gradient to the single well pressure propagation rules. Shanpeng Li [3-5] confirmed that threshold pressure gradient has a significant influence on the productivity of gas reservoirs in the actual developing process of low permeability gas reservoirs. Thus, obtaining the accurate threshold pressure gradient is of particular importance to the rational development of low permeability gas reservoirs. The test of threshold pressure gradient is mainly in the laboratory. Ga Yi [6] studied the existence of threshold pressure gradient of gas flow conditions, and provided the relationship between threshold pressure gradient and bound water saturation. Xing Zhang [7] summarized the influence of the value of confining pressure, temperature and mass of gas molecule on the threshold pressure gradient by experiments. The threshold pressure gradient of indoor tests is often conducted under the conditions of low pressure and low speed at present. Nonetheless, since affected by the accuracy of indoor physical experiment instruments and the stable time of pressure transmission, it results in imprecise measurement of micro-gas flow under the condition of low pressure. Hence, it has a certain error

Vol. 20 [2015], Bund. 16 6860 when calculating the threshold pressure gradient. In this paper, the value of threshold pressure gradient is even more accurate through the numerical techniques on the basis of experiments, and it has a certain guiding significance to the development of low permeability gas field. THRESHOLD PRESSURE GRADIENT EXPERIMENT OF THE CORE This experiment is adopting steady-state method to calculate the threshold pressure gradient. The way is to establish a certain displacement pressure on both ends of the core that can measure the differential pressure and flow of the system under the condition of stability. According to experimental data, it can be obtained the gas effective permeability versus the inverse of mean pressure and the gas velocity versus the difference of pressure square curves that to calculate the threshold pressure gradient. Experimental condition In order to keep gas in a single-phase flow state in the cores, it is of great importance to strictly control the change of water saturation is not more than 3% in the experiments so that it can make sure the water in the cores remaining. Displacement pressure could not be more than 1Mpa, for the reason that the research of seepage velocity makes no sense under the large pressure gradient. The experimental temperature is 20, the medium is nitrogen, the formation water salinity is 20000ppm. The experiment has chosen four cores which come from the western Sichuan, and the physical parameters are shown in table 1. Table 1: The basic physical parameters of cores Water saturation Core Length Diameter Porosity Permeability before displacement number /cm /cm /% /md /% 1 4.412 2.501 16.060 0.360 44.090 2 4.494 2.516 13.470 0.167 31.410 3 4.496 2.500 14.170 1.120 25.770 4 4.510 2.510 14.040 0.040 40.300

Vol. 20 [2015], Bund. 16 6861 Experimental results The relationship of the four cores between gas effective permeability and inverse of mean pressure is obtained by the experiments, and it is shown in Figure 1. a. Sample number 1 b. Sample number 2 c. Sample number 3 d. Sample number 4 Figure 1: Klinefelter regression curve Calculating the threshold pressure gradient Based on Darcy's law, the relationship [8] between seepage velocity and differential pressure can be obtained: v f 2 2 ( 1 p0) q 10k p = = (1) A 2 p µ L 0 In the formula: v f is the gas velocity through the core, cm/s; q is the gas flow through the core, cm 3 /s; A is the cross-sectional area, cm 2 ; k is permeability of the core, μm 2 ; p 1 is the fluid pressure

Vol. 20 [2015], Bund. 16 6862 on the core, MPa; p 0 is the atmospheric pressure under the conditions of experiment, MPa; μ is the air viscosity, mpa s; L is the length of the core, cm. Fan Wu [8] believe that the seepage velocity v f versus the difference of the square pressure (p 2 1 - p 2 0 ) is shown in linear function that disjointed to the origin, when the gas seepage in the core exists low-speed nonlinear flow: f 2 2 ( 1 0) v = a p p b (2) In the formula: a and b is respectively the coefficient and constant term of the line. Assuming v f =0, the threshold pressure of the core is: p λ 1 2 2 0 b = + p a (3) According to formula (3), the threshold pressure gradient of the core is: 1 b 2 2 + p0 p0 λ p 0 a p λ = = L L (4) Taking an example of number one core, the concrete computing process of threshold pressure gradient is being introduced: from the ascent stage experimental data of Figure 1a,the corresponding seepage velocity under the difference of the square pressure is obtained, as is shown in table 2. Table 2: Value of v f under different p 2 2 1 -p 2 (p 2 1 -p 2 0 )/MPa 2 v f /(cm/s) 0.000317 0.000040 0.000353 0.000053 0.001233 0.000222 Tracing point mapping to the experimental data, and obtained the gas velocity versus the difference of pressure square which is shown in Figure 2: v f =0.1948(p 2 1 -p 2 0 )-2E-05. Comparing with formula (1), a=0.194,b=2e-05, and then the threshold pressure gradient of the core can be calculated, is 1.2043 10-2 MPa/m. Similarly, the threshold pressure gradient of the other three cores can be calculated.

Vol. 20 [2015], Bund. 16 6863 Figure 2: Relation curve between v f and p 1 2 -p 2 2 NUMERICAL SIMULATION OF THE CORE Setting the model parameter In this paper, the commercial software Eclipse is being used to numerical simulation on the basis of experiment. The simulation is by using the homogeneous one-dimensional model that is equivalent to the core samples. And the parameters of the size of the model, porosity, permeability and water saturation are the same as the core samples. Taking an example of number 1 core, according to the determination method of two-phase fluid relative permeability and the capillary pressure curve the corresponding curve can be obtained, as is shown in Figure 3. The grid number of the model is 40 1 1, setting a gas injection and production well respectively on both sides. The bottom-hole pressure of the gas injection well is set to the entrance pressure of the core under each test point in the experiment, and the bottom-hole pressure of the production well is set to the atmospheric pressure, as is shown in Figure 4.

Vol. 20 [2015], Bund. 16 6864 Figure 3: The curve bwtween relative permeability and capillary pressure Figure 4: The model of one-dimensional numerical simulation THE PROCESS AND RESULT OF SIMULATION The process of dynamic simulation is the staged injection pressure fitting the seepage velocity so that it can obtain the relationship between the seepage velocity and pressure gradient of the core samples. The benefits of this approach are that multiple groups of displacement differential pressure can be set at the beginning of the simulation, and the precision limit of experimental equipment can also be overcome. After the simulation, converting the production (namely the rate of flow) into gas seepage velocity, and plotting the curve of pressure gradient versus seepage velocity under the conditions of

Vol. 20 [2015], Bund. 16 6865 simulation. With the increase of time step, the displacement pressure is also increased gradually and the errors of seepage velocity that measured in experiment decreases. In that case, the seepage velocity that is obtained from simulation and experiment can be fitted. Because there is a certain error between phase permeability curve and actual measured curve, it is of great importance to complete history matching through adjusting the phase permeability curve within a certain range, the fitting results are shown in Figure 5. Due to the setting of displacement differential pressure is small at the beginning of simulation, so carrying on linear regression to the initial simulation of seepage velocity under the corresponding time step, and the intersection of seepage velocity and pressure gradient is namely the fitting of threshold pressure gradient value. In order to explore the influence of capillary pressure to the low speed percolation and threshold pressure gradient, the simulation of the characteristic of low speed percolation without capillary pressure is also proceed. By the regression analysis of simulation results of number 1 core, the threshold pressure gradient under the conditions of considering and regardless the capillary pressure is respectively 1.052MPa/100m and 0.026MPa/100m. Figure 5: Relation curve between the percolation velocity and the pressure gradient The experimental and numerical simulation methods were used respectively to measure the value of the four cores' threshold pressure gradient, as is shown in table3.

Vol. 20 [2015], Bund. 16 6866 Table 3: Comparison between the experiment and simulation value Simulation value Core number Experimental value (MPa/100m) Considering capillary pressure Regardless of capillary pressure (MPa/100m) (MPa/100m) 1 1.2043 1.052 0.026 2 6.3486 2.547 0.047 3 3.4569 2.038 0.052 4 12.7778 2.202 0.103 RESULT ANALYSIS It can be seen from table 3, the value of threshold pressure gradient is less than the experimental calculation value when the displacement differential pressure is very small by using the technology of numerical simulation. Due to the experimental test is being limited by the precision of equipment; the displacement differential pressure can't be infinite decreased. Besides, in the process of experiment, people have mistaken the weak seepage velocity for zero, thus causing the value of threshold pressure gradient higher by the experimental testing calculation [9-10]. The simulation value of threshold pressure gradient that is considering the capillary pressure is far above that is regardless of it, so it is can be assumed that the capillary pressure is the foremost reason that is causing the threshold pressure gradient. For the hydrophilic rock, capillary pressure has blocked the non-wetting phase [11]. The core has been proceeded vacuum formation water saturation before the experiment, and can be determined that the core is hydrophilic. With nitrogen driving the water in core, the water saturation was gradually reduced until reaching the residual water saturation. As wetting phase, the residual water adsorbed on the pore surface under the effect of interfacial tension that formed a continuous water film which could reduce the pores and channels further. Although the residual water could not flow, but because of the existence of capillary pressure, it caused a continuous additional drag that reflected though the threshold pressure. CONCLUSION (1) Proposing a new method that can determine the threshold pressure gradient through the technology of numerical simulation. And this method is closer to real value.

Vol. 20 [2015], Bund. 16 6867 (2) Respectively used the methods of experiment and numerical simulation to determine the value of threshold pressure gradient. It turns out that the value of threshold pressure gradient which is obtained by experiments is greater than which is obtained by simulation. (3) The value of threshold pressure gradient that is considering the capillary pressure is far above that is regardless of it, so it is can be assumed that the capillary pressure is the foremost reason that is causing the threshold pressure gradient. REFERENCES [1] Gorbunov A.T. Abnormal oilfield development[m]. Shubao Zhang, translate. Beijing: Petroleum industry press, 1987. [2] Bingyu Ji, Yingfu He. Formation pressure distribution of a single well based on low-velocity non-darcy flow[j]. Acta Petrolei Sinica, 2011, 3(32): 466-469. [3] Shanpeng Li, Kai Wu, Yanbing Fang. Study on the starting pressure phenomenon in ultra-low permeability reservoir: An example from Houshi area[j]. Lithologic reservoirs, 2009, 1(21): 125-127. [4] V.Kadet, D.Polonsky, State Gubkin Oil &Gas Academy, Fluid Dynamics Department, Percolation Modeling and Non-Newtonian Flows in Oil Reservoirs, Society of Petroleum Engineers, SPE39028. [5] PASCAL F. Consolidation with threshold gradient[j]. Inter. J. for Numerical and Analytical Methods in Geomechanics, 1980(5): 247-261. [6] Ga Yi, Hai Tang, Dongliang lv, et al. The study and analysis of starting pressure gradient in low permeability gas reservoirs[j]. Offshore Oil, 2006, 26(3): 51-54. [7] Xing Zhang, Shenglai Yang, Jie Zhang, et al. Experimental study on threshold pressure gradient of tight and low permeability gas reservoirs[j]. Special Oil and Gas Reservoirs, 2011, 18(5): 103-104. [8] Gengsheng He. Reservoir physics[m]. Beijing: Petroleum industry press, 1995. [7] Fan Wu, Lijuan Sun, Guoan Qiao, et al. A research on gas flow property and starting pressure phenomenon[j]. Natural Gas Industry, 2001, 21(1): 82-84. [9] Chuanliang Li, Yongquan Yang. There is not a Starting Pressure Gradient in Low-Permeability Reservoirs at all[j]. Journal of Southwest Petroleum University (science & Technology Edition), 2008, 30(3): 167-169. [10] Wang S J, Huang Y Z, Civan F. Experimental and theoretical investigation of the Zaoyuan field heavy oil flow through porous media[j]. Journal of Petroleum Science and Engineering, 2006, 50(2): 83-101. [11] Zhixin Wang. Is capillary power a driving force for the primary migration of oil and gas?[j]. Experimental petroleum geology, 2000, 22(3): 195-196. 2015 ejge

The Electronic Journal of Geotechnical Engineering Jing Gao Author of Method of Determining the Threshold Pressure Gradient Co-authored by Yingfeng Meng and Cong Li State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Southwest Petroleum University Jing Gao is a postgraduate student of the oil and natural gas engineering at southwest petroleum university where she specializes in oil-gas field development engineering using the numerical simulation. She is presently active in the application of the commercial software of Eclipse and practiced on multiple oilfields. Mailing Address: Southwest Petroleum University State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Room B-507 tel. 18215665272 e-mail: swpu_gj@sina.com