Applying the Dynamic Two-Step Method to Forecast Remaining Oil Distribution of Lower Series, Xiaermen Oilfield

INTRODUCTION

The distribution of remaining oil is often described qualitatively. The remaining oil distributed in the whole reservoir is calculated according to the characteristics of the space distribution of the saturation of remaining oil. Logging data are required to accomplish this. However, many such projects cannot be completed. This method of studying remaining oil distribution cannot be quantified efficiently and is unable to provide an effective quantitative forecast of the distribution of remaining oil on every flow unit in each well.

Our current proposal explores a dynamic two-step method, based on the Xiaermen Oilfield, which gives timing and position location, and a quantitative way to forecast the distribution of remaining oil.

In order to forecast the flow unit saturation of remaining oil at any time, a variable must be found as a carrier that changes with time. The comprehensive water cut can be treated as a bridge for itself because of the characteristic of the function of time (Chen and Guan, 2003; Ma et al., 1997). With the shifting of time and the growth of accumulative injected water, the comprehensive water cut shows an upward trend in every well. Two steps are needed from the comprehensive water cut to the remaining oil saturation in every flow unit of every oil well.

① The water cut of every flow unit in one well at one time needs to be calculated according to the comprehensive water cut of a single well at one time. This problem can be solved by establishing a plate (Chen and Guan, 2003; Ma et al., 1997).

② The remaining oil saturation of the flow unit of the well at one time needs to be calculated, basedon the water cut of the flow unit at the given time. This can be deduced from the oil reservoir formulation.

The use of the "dynamic two-step method" to forecast the remaining oil of a flow unit can be depicted thus: .

METHOD

The Establishment of F_w-f_wj Plate

The F_w-f_wj plate must be established to solve the water cut (f_wj) in different flow units on the comprehensive water cut of a single well. The Geologic Plan model was designed by Yu (1992). From the model, through the calculation of numerical simulation, there is a big difference of water-out features between the main body with high permeability and the part with low permeability. Figure 1 shows the relationship between F_w and K_max/K_j. K_max represents the highest permeability (the main body permeability). When the main body of the highest permeability reached a certain water cut, the other part water cut with a low permeability is dependent on the rate of K_max to K_j (permeability grading). The higher the rate of the K_max/K_j, the lower the water cut of the oil well. That is, different locations of the oil well have different K_j, the water cut reverses with the K_max/K_j rate. The reason for this regular pattern is the influence of the anisotropic oil layer.

Figure  1.  Water saturation behavior comparison plot for lateral configuration of heterogeneity of oil reservoirs.

DownLoad: Full-Size Img PowerPoint

Once a pattern has been established, more lines can be drawn based on that pattern, each corresponding to the main-body water ratio as it reaches a certain level. We can therefore obtain K_max/K_j if we know the K_j of one well, and then, taking advantage of the line, the water ratio of the well can be checked. In this way, considering the impact of vertical heterogeneity, we established the F_w-f_wj plate (Chen and Guan, 2003; Ma et al., 1997).

Deduction of f_wj-S_o Formula

Suppose the oil reservoir is of horizontal sandstone, the reservoir pressure is higher than the saturation pressure, and the stable permeable condition of the two parts (oil and water) is met (ignoring the capillary pressure and gas dissolution function). According to the two-dimensional Darcy's law radial flow formula, the following can be obtained (Xu et al., 2004; Xie and Zhang, 2003; Wang et al., 2002)

Surface oil yield of oil well

Surface water yield of oil well

where Q_o is oil yield, t/d; Q_w is water yield, t/d; Δp is yield dispersion of oil well, MPa; K_o is oil permeability, μm²; K_w is water permeability, μm²; h is net thickness, m; R_g is supplying radius of oil well, m; r_c is convert radius of oil well, m; ρ_o is oil density, t/m³; ρ_w is water density, t/m³; B_o is oil formation volume factor; B_w is water formation volume factor; μ_o is oil viscosity, mPa s; μ_w is water viscosity, mPa·s.

Formula (2) divided by formula (1)

from formula (3)

Dividing the numerator and denominator in the left part of formula (4) by oil permeability (K), there was

Suppose , which is assumed to be constant, we can rewrite formula (5) into

For , formula (6) can be translated into

In the stable permeable condition of the two parts (oil and water), the relation between the oilwater relative permeability ratio and water saturation can be written (Zhou and Guan, 2004; Wu et al., 2001)

In this formula, m, n are two relative parameters to reservoir structure and liquid characters are constant here.

Calculating logarithm in formula (8), semilogarithm relation between oil-water relative permeability ratio and water saturation can be obtained

In formula (9), by using the datum of oil-water relative permeability and S_w, which was obtained in a core experiment, we can find the parameters m and n through linear regression.

Substituting formula (8) into (9) and calculating the logarithm, the following result is obtained

Because S_w + S_o = 1, the formula for the relationship between water cut and oil saturation can be written like this

Water saturation and oil saturation in different conditions of water cut can be calculated by substituting parameters m and n and coefficient C into formulae (10) and (11).

This method is used in calculating the quantity of remaining recoverable oil of the flow unit, with the introduction of the distribution coefficient of net thickness (Zhou, 1999)

Thereby, the calculation of the quantity of remaining recoverable oil in the flow unit is

where h_eff is the net thickness, m; λ_j is the distribution coefficient, f; (ΔN_R)_j is the remaining recoverable oil of the jth flow unit, t, and ΔN_R is remaining recoverable oil, t.

Substituting the quantity of remaining recoverable oil at different times, we can calculate the quantity of remaining recoverable oil of a flow unit at the corresponding time.

APPLICATION

Xiaermen Oilfield, the second largest oilfield in Henan Province, is mainly occupied by a fault block oil reservoir. The oil layer of this oilfield is a typical macroscopic-void middle-high permeable reservoir with serious heterogeneity. The oil and gas of Xiaermen Oilfield mainly accumulated in No.2 section and No.3 section of the Hetaoyuan Group, and the latter was divided into nine oil groups, fromⅠ toⅨ, including theⅢ -Ⅳ oil groups in the lower series. Since production testing of the lower series was carried out, from September 1978 to June 2003, Xiaermen Oilfield has developed 30 oil wells and 11 injection wells. The oil-bearing area of the lower series is 3.52 km². The exploitation of geological reserves is 29.99% and the comprehensive water cut is 90.98%. As the distribution of remaining oil in the lower series appears to be extremely complicated, researching the remaining oil seems to be particularly significant.

The Establishment of Plate

First of all, as shown in Fig. 1, the water cut in different wells has no definite relationship. But in this research, a weighted mean relationship exists between F_w and f_wj. If every well of the lower series in Xiaermen Oilfield is divided into 31 flow units, suppose W_j and L_j stand for water yield and liquid yield, respectively, in the jth (j= 1, 2, … …, 31) flow unit, we get W=ΣW_j, L=ΣL_j, namely, the general water and liquid yield. According to the definition of specific yield, W^j = L_j · f_wj.

Therefore

In this formula, F_w is the weighted average of f_wj weighted by every flow unit liquid yield—L_j. Thus, we can use this relationship to design plate Lj. In order to accord with the relationship of weighted mean between F_w and f_wj, K_max is substituted into the weighted average K, which is every flow unit K_j of the same well weighted by available thickness. An analogous supposition is obtained—when the comprehensive water cut F_w of a single well reaches a certain level, the negative line relationship between the water cut f_wj of each flow unit and K/K_j can be reached, that is

For every F_w in formula (15), an equation of linear regression, the corresponding regression line exists. With a series of lines, we can structure the expected plate. Figure 2 is the sketch plan of the designed plate (Ma et al., 1997).

Figure  2.  The sketch plan of designed plate.

DownLoad: Full-Size Img PowerPoint

Specific procedures are as follows.

① In total, six rock cores have been analyzed in lower series of Xiaermen Oilfield, and the common interval of water saturation in these rocks is[0.375, 0.575]. On this condition, the water cut (f_wj) of a given rock can be calculated by an arbitrary value of S_w in the range 0.375 ≤ S_w ≤ 0.575 and the use of K_ro and K_rw (Gao et al., 2004; Zhou and Guan, 2004)

In this way, we can get 6 pairs of data (K_j, f_wj) (j= 1, 2, …, 6). The six K_j work as the permeability value of six flow units in one single well, and the K works as the weight mean. Then, a regression line (f_wj= a + b · K/K_j) can be obtained by calculating the regression line in the group of data.

② Between 0.375 and 0.575, we set S_w at each step distance of 0.025. Then, nine numerical values were obtained. To each (S_w)_i (i= 1, 2, …, 9), there is one regression line: f_wj= a_i + b_i · K/K_j (i= 1, 2, …, 9).

③ Calculating the intersection point of each regression line and the line K/K_j= 1 (1, (F_w)_i) (i= 1, 2, …, 9) is the calculation of each (F_w)_i by the use of (F_w)_i = a_i + b_i (i= 1, 2, …, 9).

So, each regression line corresponds to one numerical value of S_w. We can also make a series of regression lines through interpolation. In this way, if the comprehensive value of a water cut at one time of the oil well had been known, we can use the corresponding regression line of F_w to calculate f_wj of the corresponding K/K_j.

The Establishment of f_wj-S_o Formula

By using oil-water relative permeability ratio and water saturation, the following formula can be reached

Then, the computation expression of oil saturation is

Hence, if the comprehensive water cut of one oil well at one time and the permeability value of every flow unit of the same well were known, we could use the plate to calculate the water cut of every flow unit at one time in the oil well; the remaining oil saturation of every flow unit in the oil well at one time could be calculated through formula (18), then, by using formulae (12) and (13), we could work out the quantity of remaining recoverable oil of every flow unit in the oil well at one time.

In fact, the remaining oil that cannot move has no use for the oil yield. On the contrary, the more the remaining active oil, the greater significance to the oilfield. Hence, the saturation of remaining oil should not be the only evaluation index in the study of the remaining oil. The remaining active oil was also analyzed using core test data from the core well of the lower series in Xiaermen Oilfield, and the regression plate of residual oil saturation was reached

where S_or is residual oil saturation, f; S_om is remaining active oil saturation, f.

By the use of formulae (18), (19) and (20), we can work out the saturation of the remaining active oil of every flow unit in the oil well at one time.

The Distribution of Remaining Oil

Using the "dynamic two-step method", the remaining oil saturation and remaining active oil saturation of 31 flow units of every oil well were calculated in three time spots (June 2001, June 2002, June 2003). By utilizing the result of the above calculations to draw out the isogram, the distribution of remaining oil is provided.

For example, here we just make a brief analysis of the remaining oil distribution in No. 17 flow unit, which shows the isogram of the remaining active oil saturation at the end of June in 2003.

The west and the southeast areas of the 17th flow unit have developed very quickly in recent years. Compared to this, other areas have been relatively slow, so the exploitation of the 17th flow unit was unbalanced. The remaining active oil saturation changed gradually, the high remaining oil saturation district reduced gradually, and injection water cut the underground oil into a banding and potato form (mostly potato form). All of these factors caused greater difficulties in development.

Because the permeability is relatively bad in the northwestern part, these areas can not be developed greatly until the well net is adjusted. We have developed two oil wells in small well space, where the well net was in perfect conditions. In addition to the influence of J4-707 injection water, the remaining active oil saturation reduced quickly in this area. The remaining active oil saturation reduced even more from > 0.2 to about 0.1. Therefore, there is little remaining oil in this area now.

Close to the location of well 5-53 and well 4-72, the remaining active oil saturation is rich and reducing slowly. In these areas the net thickness is great, the permeability and connectivity are good. So, the remaining oil is concentrated, and the remaining oil saturation changes slowly. It will be the main area to develop in the near future.

Since the 4-802 well lies under the fault, and the T4-907 well lies in the vicinity of the positive ministructure part, the reservoir attribution in these areas is relatively difficult. The remaining oil in these areas is concentrated, and the remaining oil saturation changes gently. All of this makes these areas as key areas to adjust afterwards.

Table 1 gives the summary of the regulation about remaining active oil saturation of each flow unit. From Table 1 and Fig. 3, we can see the distribution of remaining oil in the lower series of Xiaermen Oilfield presented banding and potato form, remaining oil was relatively concentrated in faultage neighborhood and imperfect well netting position, and the net thickness of the place was great.

Table  1.  Summary of remaining oil changing law about each flow unit in lower series of Xiaermen Oilfield

 | Show Table

DownLoad: CSV

Figure  3.  Isogram of the 17th flow unit remaining active oil saturation.

DownLoad: Full-Size Img PowerPoint

CONCLUSIONS

(1) The "dynamic two-step method" can give timing and position location, and a quantitative way to forecast the distribution of remaining oil.

(2) The "dynamic two-step method" has the characteristics of simplicity and convenience. It is especially suitable for the study of remaining oil distribution at high water-cut stage.

(3) Using the "dynamic two-step method", the remaining oil distribution of lower series of Xiaermen Oilfield was studied. Our conclusions were that the distribution of remaining oil presented banding and potato forms, remaining oil was relatively concentrated in faultage neighborhood and imperfect well netting position, and the net thickness of the place was great.