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:

$$\begin{array}{}{\displaystyle \frac{d{P}^{\star}}{dx}=f(\mu ,{R}_{s},k,\rho ,\varphi ,{G}_{min},{G}_{max},\dots )}\\ {\displaystyle \phantom{\rule{2em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=f(p)={m}^{\star}{e}^{n\star p}}\end{array}$$(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 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:

$$\begin{array}{}{\displaystyle v=\frac{K}{\mu}\left[\frac{dp}{dx}-f(p)\right]}\end{array}$$(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:

$$\begin{array}{}{\displaystyle \frac{d}{dx}\left[\frac{dp}{dx}-f(p)\right]=0}\end{array}$$(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:

$$\begin{array}{}{\displaystyle \mathit{P}\left(L={L}_{1}\right)={P}_{\mathrm{b}}}\\ {\displaystyle \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}P\left(L=0\right)={P}_{\mathrm{w}}}\end{array}$$(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.

$$\begin{array}{}{\displaystyle \frac{d}{dx}[\frac{dp}{dx}(1-\frac{1}{a+b|dp/dx|})]=0}\end{array}$$(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/cm^{3}, 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 Characteristics, Parameters and Calculations of Solution-Gas Drive

In , *P*_{w} is the bottom pressure, *P*_{0} is the original reservoir pressure, *P*_{b} is the bubble point pressure, *L*_{1} 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.

## Comments (0)

General note:By using the comment function on degruyter.com you agree to our Privacy Statement. A respectful treatment of one another is important to us. Therefore we would like to draw your attention to our House Rules.