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# Open Physics

### formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

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Volume 16, Issue 1

# Porous flow characteristics of solution-gas drive in tight oil reservoirs

Xiao Qianhua
/ Wang Zhiyuan
• Corresponding author
• Institute of Porous Flow and Fluid Mechanics, University of Chinese Academy of Sciences, Hebei, China 065007
• Email
• Other articles by this author:
/ Yang Zhengming
• Institute of Porous Flow and Fluid Mechanics, PetroChina Research Institute of Petroleum Exploration & Development, Hebei, China 065007
• Other articles by this author:
/ Liu Xuewei
• Institute of Porous Flow and Fluid Mechanics, PetroChina Research Institute of Petroleum Exploration & Development, Hebei, China 065007
• Other articles by this author:
/ Wei Yunyun
• Institute of Porous Flow and Fluid Mechanics, University of Chinese Academy of Sciences, Hebei, China 065007
• Other articles by this author:
Published Online: 2018-07-19 | DOI: https://doi.org/10.1515/phys-2018-0056

## Abstract

The variation of porous flow resistance of solution-gas drive for tight oil reservoirs has been studied by designing new experimental equipment. The results show that the relation between the porous flow resistance gradient and pressure is the exponential function. The solution-gas driving resistance is determined by a combination of factors, such as the gas-oil ratio, density, viscosity, permeability, porosity and the Jamin effect. Based on the material balance and the flow resistance gradient equation, a new governing equation for solution-gas drive is established. After coupling with the nonlinear equation of elastic drive, the drainage radius of solution-gas drive is found to be very small and decreases rapidly when the bottom-hole pressure approaches the bubble-point value. Pressure distribution of the solution-gas drive is non-linear, and the values decrease sharply as it approaches the well bore. The productivity is rather low despite being strongly influenced by permeability. Therefore, stimulated reservoir volume (SRV) is the essential measure taken for effective development for tight oil reservoirs.

PACS: 47.55; Ca; 47.56.+r

## 1 Introduction

Affected by the successful exploration and development of tight oil in North America, the global development of tight oil has surged, and ten other countries, including China and Russia, have initiated relevant research [1, 2]. Tight oil in China is widely distributed, with a technically recoverable resource of 20 × 108-25 × 108 t[3]. The effective development of tight oil is essential for energy development in China. The current development mode of tight oil is mainly natural depletion, which includes two stages: elastic drive and solution-gas drive. The elastic drive stage is characterized by nonlinear porous flow [4], without interference, and so the key to research should be solution-gas drive. Under the conditions of no outer energy supplement, the process of development continuously depletes the natural energy of the reservoirs. When the formation pressure is lower than the bubble point pressure, the previously dissolved natural gas in the oil will gradually separate and eventually flow in two phases (gas and oil). This development approach of driving crude oil to the bottom-hole via swelling of gas is called solution-gas drive.

Through a visualized experiment, Akin [5] and George [6] studied the whole process of solution-gas drive for heavy oil, involving gas-phase nucleation, gas bubble growth, and eventual coalescence into a continuous gas phase and gas flow, which is significant for the influence of micro- and nanoscale bubbles to flow and to the microscopic mechanism of solution-gas drive for heavy oil. Subsequently, Peng [7], Sheikha [8], Padilla [9], Fattah [10], Ammar [11] carried out research on solution gas, all of which focused on IPR laws of solution-gas drive for heavy oil, the application of numerical simulation or the proposal of a new IPR model, and the design of micro-experiments for explaining the problems encountered during the solution-gas drive.

In recent years, many researchers in China began to study solution-gas drive, including Liu [12], Ren[13], Cheng [14], Liu [15], Zhou [16], Ruan[17], Zhang [18], Cui [19], and Zhang [4]. The aforementioned research is similar to that conducted in other countries and focuses mainly on carrying out the recovery ratio and IPR analysis for solution-gas drive of low permeability reservoirs or heavy oil. However, the study of the inner porous flow mechanism is quite rare. It is noteworthy that Liu [20] of the Chinese Academy of Sciences designed a new experiment to test porous flow resistance and predicted the controlling radius and recovery ratio. However, there are some discrepancies between the calculated results and actual results, thus requiring further and more in-depth research.

To clarify the porous flow mechanism of solution-gas drive during depletion-drive development of tight oil, which needs further study, this paper designed a new porous flow resistance testing system for solution-gas drive of tight oil based on Darcy’s original experiment. During the experiment, samples of the typical tight oil reservoir were selected to test the porous flow resistance of solution-gas drive, and the porous flow resistance model of solution-gas drive was built, from which the new porous flow mathematical model was explored, and the drainage radius of solution gas, pressure distribution, and productivity variations were analysed.

## 2.1 Methods

Based on the porous flow mechanism of two phases, with oil and water for conventional methods, the governing equation has been acquired. The governing equation of oil-phase is as follows:

$∇Kroμo(p)Bo(p)⋅∇p=ϕK∂∂tSoBo(p)$(1)

The governing equation of water-phase is as follows:

$∇C(p)μg(p)Krg∇p+∇Rs(p)ρgaμo(p)Bo(p)Kro∇p=ϕK∂∂t(1−So)C(p)+Rs(p)ρgaBo(p)So$(2)

The equations above were derived through Darcy’s law, while the hypothesis was based on formation with characteristics of horizontal flow, homogeneity and isotropy. The governing equations’ characteristics are as follows:

1. They are significant to the development of theory and enrich and improve porous flow theory, which offers some instruction into the production process.

2. The equations are relatively complicated, and the solution involves too many parameters. The parameters are acquired through PVT experiments with high temperature and high pressure or predicated through the components or relevant properties of crude oil, which is relatively troublesome.

3. The equations are still based on Darcy’s seepage law, which cannot address the generally accepted nonlinear flow of low permeability reservoir or tight reservoir.

4. Although the effects of many parameters have been taken into account, the various microscopic flow effects still cannot be reflected, such as gas-phase nucleation, the growth of gas bubbles, eventual coalescence into a continuous gas phase and the Jamin effect [21], which are the key events of the solution-gas drive.

Many microscopic influencing factors are involved during the porous flow process of solution-gas drive of tight oil introducing tremendous obstacles to solve this problem through theory. An excellent example of solving this problem involves the founder of porous flow theory, Henri Darcy. As to the porous flow problem of complicated engineering, by designing a simple sand-packed model, Darcy devised the famous Darcy’s Law, as follows:

$Q=Av=KμAΔpL$(3)

As to Darcy’s Law, the solid-fluid coupling, and many unknown factors of the flowing process have been incorporated into hydraulic conductivity (K). The complicated engineering problems were solved with the simplest method, although it was a mathematical statistics method. Solution-gas drive of tight oil involves many microscopic effects that could also be integrated into some macro parameters through experimentation. These effects can be fuzzy processed and then introduce the macro parameter into a flow equation to build the porous flow model for a solution-gas drive of tight oil.

As stated above, the Jamin effect and other microscopic effects were incurred during the solution-gas drive, and pressure depletion occurred within the rock sample, which was called porous flow resistance. Through recording of pressure variation data at two ends of the core sample during the solution-gas drive, the author initiated statistics of porous flow resistance variation law and resolved various influencing factors of porous flow resistance to ultimately acquire the porous flow mathematical model.

Based on the ideas mentioned above, we designed a new type of porous flow testing system of solution-gas drive, as shown in Figure 1.

Figure 1

Porous Flow Testing System of Solution-Gas Drive

The experimental system includes the following major parts:

1. Live oil saturated system: pump, intermediate container and activated oil. Constant pressure is supported by the pump for saturated and activated oil.

2. Solution-gas drive system: core holder, confining pressure device and back pressure device. This process simulated solution-gas drive of tight oil reservoir. By setting the back pressure, the pressure variations at the two ends of the core are recorded.

3. Data acquisition system: pressure sensors, pressure collector and computer. The pressure variations at two ends of the tight core sample are collected and transferred to a computer for deep analysis.

The key idea for the experimental system is simulation of depletion-drive development in the thermostat after the sample is saturated with live oil and recording the pressures at two ends of the core with different degrees of back pressure (Figure 2).

Figure 2

Scheme of the Key Idea of Seepage Resistance Testing

The detailed experiment steps for porous flow resistance testing are as follows:

1. Selecting the representative tight core samples and measuring the basic physical parameters;

2. Saturating the cores with simulated formation water and then driving cores with kerosene for establishing the status of bound water;

3. Saturating the cores with live oil, which is one of the key steps. Evacuating the holder with kerosene and then saturating with live oil under the following conditions: constant temperature, constant pressure and a back pressure higher than the bubble point pressure. Driving until the volume is over 10 PV in order for it to be completely saturated;

4. Measuring the porous flow resistance of solution-gas drive. Closing the inlet valve, then driving under condition of a certain back pressure and recording the pressure at two ends of the core when the value is stable. Changing the back pressure and repeating the experiment;

5. Analysing the data and exploring the law of porous flow resistance of solution-gas drive.

## 2.2 Materials

The tight core samples of Sichuan have been selected for porous flow resistance measuring in this study. It is a typical tight oil reservoir with a porosity below 3% and a permeability value below 0.03 mD. In addition, the solution gas/oil ratio of Sichuan tight oil, approximately 140, is larger than that of other tight oil regions so that the solution-gas driving effect is stronger than that at other tight oil regions. The movable fluids in the reservoir are mainly controlled by micro-fractures, and the pore structure is relatively stable. Therefore, there are fewer influencing factors, which makes the process easier to control and analyse. Hence, this study could be much more referential. The basic physical parameters of the cores are shown in Table 1. Because of the low porosity of the cores in Sichuan, cores with a diameter of 3.8 cm have been selected for the experiment, resulting in a relatively larger amount of live oil for cores being saturated to better reveal characteristics of solution-gas drive. A total of three representative samples are selected for exploring the porous flow resistance characteristics of solution-gas drive of tight oil, which is the basis for the establishment of the porous flow model of solution-gas drive.

Table 1

Basic Physical Parameters of Core Samples for Solution-Gas Drive

## 3 Data analysis and discussion

Porous flow resistance (PFR) refers to the pressure depletion of fluid inside the core sample, which shows a certain differential pressure at the ends of the sample after the end of solution-gas drive. Due to length differences of the samples and to strengthen the contrast, the porous flow resistance is converted into porous flow resistance gradient (PFR-G) for comparison analysis.

Through PFR testing, it is found that the PFR-G of all core samples with different permeability varies with back pressure with a good exponential correlation (Figure 3). When the back pressure is relatively high, the amount of gas extracted from oil is relatively small, and so the PFR-G would be relatively small. However, when the back pressure is relatively small, the amount of gas extracted from oil will become large so that the viscosity of oil will become strong, and the Jamin effect will also become strong, resulting in an increase in the PFR-G.

Figure 3

Typical Curve of Porous Flow Resistance Gradient of Solution Gas

The process of solution-gas drive is impacted by multiple parameters, including viscosity variation, permeability variation, GOR variation, porosity variation, and threshold pressure gradient variation. According to the typical variation curve of PFR-G (Figure 3), the law of PFR-G for one dimensional stable porous flow is as follows:

$dP⋆dx=f(μ,Rs,k,ρ,ϕ,Gmin,Gmax,…)=f(p)=m⋆en⋆p$(4)

In this equation, m is porous flow resistance gradient coefficient and n is porous flow resistance gradient index. The solution-gas driving porous flow gradient of the selected tight rock sample in the central Sichuan has a relatively good index correlation. The PFR-G has a relatively good exponent relation for solution-gas driving of cores from Sichuan (Table 2).

Table 2

Testing Results of PFR-G

Hence, the correlation coefficients are very high for PFR-G matched in equation (4) for cores with different permeability. The lower the permeability, the lower the PFR-G coefficient m, but a change in the PFR-G index n is not apparent. The core is very short so that back pressure could be regarded as the pressure of a certain point and would generate a PFR-G at this station.

Based on the analysis above, PFR-G is influenced by many factors. However, these factors could be unified to f(p), which could be acquired through experiments. As for tight oil reservoirs, the PFR-G variation law with pressure of different reservoirs with different permeability can be obtained through experiments. Therefore, the PFR-G distribution can be obtained on the basis of pressure distribution of reservoirs. Then, the work of a well patterned, optimized arrangement and production prediction can be carried out through numerical simulation.

In addition to being able to be applied to numerical calculations, the new governing equation of solution-gas driving can be deviated on the basis of porous flow mechanics. The equation still meets the law of mass conservation, and the continuous and state equations are the same as those of elastic drives. However, the pattern of motion equation is changed compared with conventional nonlinear flow. As to some point in the reservoir, there is an additional PFR-G under the current pressure status during solution-gas driving process. Therefore, the PFR-G should be deducted from the current pressure gradient in the motion equation. The modified motion equation is shown below:

$v=Kμdpdx−f(p)$(5)

The solution-gas drive is an unsteady process, and viscosity, permeability and many other parameters change during this process. In fact, all these variations have been included into the PFR-G equation, f(p). As a result, with the application of the original viscosity and permeability during the equation deviation, a one-dimensional and one-way solution-gas drive governing equation is derived, as follows:

$ddxdpdx−f(p)=0$(6)

The elastic drive initially occurs during the flowing of tight oil to wellbore, and solution-gas drive occurs near the wellbore, as shown in Figure 4.

Figure 4

Porous Flow Status Variations of Tight Oil

Therefore, the boundary conditions are:

$PL=L1=PbPL=0=Pw$(7)

Obviously, the governing equation of solution-gas drive still followed nonlinear flow and strong nonlinear flow. The drainage radius, reservoir pressure distribution and production variation laws could be acquired through the coupling calculation of the solution-gas drive governing equation and nonlinear elastic drive.

This paper used a two-parameter model proposed by Yang (2007) [22] as the nonlinear elastic drive governing equation.

$ddx[dpdx(1−1a+b|dp/dx|)]=0$(8)

The average values of nonlinear parameters a and b could be acquired through non-linear experiments of Sichuan tight reservoir. The characteristic parameters of Sichuan tight reservoir are as follows: The viscosity of crude oil is 1.4 mPa · s, the density of crude oil is 0.85 g/cm3, and the bubble point pressure of crude oil is 28 MPa. The oil drainage radius of solution-gas drive and the corresponding production can be calculated through the methods mentioned in this paper, and the calculation results are shown in Table 3.

Table 3

Characteristics, Parameters and Calculations of Solution-Gas Drive

In Table 3, Pw is the bottom pressure, P0 is the original reservoir pressure, Pb is the bubble point pressure, L1 is oil drainage radius of solution-gas drive, ρ is the density of crude oil and Q is production.

The oil drainage radius values of solution-gas drive are very small, and the values of the samples with permeability 0.0022 mD and 0.0074 mD are within 10 m, and less than 40 m for the sample with 0.027 mD. Reservoir permeability value is an important factor influencing the oil drainage radius value of the solution-gas drive. The larger the permeability value is, the larger the oil drainage radius value will be. When the permeability value decreased, the oil drainage radius value decreased dramatically.

The productivity of natural depletion is rather low, which is apparently affected by permeability. As a result, carrying out large-scale SRV and establishing artificial oil reservoirs are essential for effectively increasing production. The distribution characteristics of pressure (Figure 5) show that the closer the wellbore is, the stronger the solution-gas driving effect will be, and the faster the pressure will drop, which presents a non-linear distribution. However, the pressure variations are relatively slow during the elastic drive.

Figure 5

Reservoir Pressure Distribution

The solution-gas drive is strongly influenced by the pressure. When the pressure is high, the degasification of the crude oil is slow; when the pressure is low, the degasification is fast. Therefore, the physical properties of fluids are strongly influenced by pressure. With the increase of bottom pressure, the oil drainage radius of solution-gas decreases (Figure 6), and when the pressure nears the bubble point pressure, the oil drainage radius can decrease over 30%. As to the reservoirs with extremely low permeability, such as the sample with 0.0074 mD, the oil drainage radius value of solution-gas is less than 0.2 m when the bottom pressure is 25 MPa, which means extremely poor liquidity. In addition to SRV, fluid modification could also be adopted to improve the liquidity of fluids.

Figure 6

Variation Correlation Between the Oil Drainage Radius and Bottom Pressure

The pressure variation is related to the changing of bottom pressure during solution-gas driving (Figure 7). The pressure near the wellbore decreased rapidly when bottom pressure was relatively small. The pressure variation of the whole solution-gas driving region becomes slow when the bottom pressure is close to bubble point pressure. The reason is as follows: when bottom pressure is relatively high, the oil drainage radius value of solution-gas drive is already very small, which exerts a small effect on the whole pressure distribution, and reservoir production mainly depends on elastic drive. When the bottom pressure is relatively low, the oil drainage radius of solution-gas drive is relatively large, solution-gas driving is dominated by the whole pressure distribution and oil recovery ratio.

Figure 7

Pressure Distribution under Conditions of Different Bottom Pressure k=0.027mD

The oil drainage radius, reservoir pressure distribution and productivity are evaluated through the coupling of the new governing equation of solution-gas drive and nonlinear elastic drive. In fact, the PFR-G distribution graphs can be drawn on the basis of PFR-G data acquired through a PFR testing system. Then, the changing process of pressure can be acquired through numerical simulation. In addition, the variation process of oil drainage, productivity and other parameters can also be acquired, which would offer essential guidance for the monitoring and adjustment of production parameters and the optimization of well networks.

## 4 Conclusions

A PFR testing system of solution-gas drive for tight oil reservoirs was designed that was found to be a successful solution for a typical, yet complicated, engineering problem, based on a simple idea. The experimental system included a live oil saturating system, solution-gas driving system and data collecting system.

The PFR f(p) met exponential correlation with pressure, involving characteristic parameters such as viscosity, permeability, porosity, GOR, and density, which solved the problem of incomplete consideration of various micro-factors theoretically.

Based on the mass conservation equation and PFR-G relation, a new solution-gas driving governing equation was acquired. The calculation proved that the oil drainage radius of solution-gas drive was very small, apparently impacted by permeability. The pressure decreased faster near the wellbore, presenting a non-linear distribution. In addition, the production of natural depletion was very low, and it needs SRV. Only new driving modes and fluid modification techniques may improve recovery fundamentally.

## Acknowledgement

This paper is financially supported by the National Science and Technology Project of China (Grant no. 2017ZX05013-001), the National Natural Science Foundation of China (Grant no. 51604053), the Chongqing Research Program of Basic Research and Frontier Technology (Grant no. cstc2016jcyjA0126) and the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant no. KJ1601313).

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Accepted: 2018-04-17

Published Online: 2018-07-19

Conflict of InterestConflict of Interests: The authors declare that there is no conflict of interests regarding the publication of this paper.

Citation Information: Open Physics, Volume 16, Issue 1, Pages 412–418, ISSN (Online) 2391-5471,

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