Taking the Daqing oilfield as the evaluation target, based on the reservoir geological data and production monitoring results, the related thief zone evaluation index is selected, and the MLWPCA method is used to evaluate the thief zone, and the evaluation results are verified by tracer tests.
3.1. Overview of Research Blocks
The Daqing oilfield is heterogeneous sandstone reservoirs with positive rhythmic deposition. The burial depth of reservoir is 780~1300 m. The average effective thickness is 43.5 m. The average porosity is 18%. The original oil saturation is 52~61%. The original formation pressure of the reservoir is 11.07 Mpa. The difference of ground saturation pressure is 8.23 MPa. The temperature of the oil layer is 42.7~51 °C. The density of underground crude oil is 0.89 g/cm3. There are 11 water injection wells and 36 production wells.
Since 1978, the Daqing oilfield has been developed and experienced three stages. The depletion development mode was used in the early stage. At this stage, the formation pressure dropped rapidly with no stable period. The second stage started with water injection. As the water injected increased, the liquid production in the oil field increased and the decline rate slowed down. The third stage is the full water injection stage. The oil production and water content are all increased greatly at this stage. At present, the Daqing oilfield has entered the high water cut stage. The water cut rose sharply (the comprehensive water cut in 2016 was 71%) and the recovery rate was low (the geological reserves recovery rate in 2016 was 7.23%). The maximum daily water injection for a single well is about 1000 m3/d. Average oil pressure of the injection well is 9.8 MPa. The comprehensive water content is 89.8%.
From the geological point of view, the oil reservoir has large thickness and is obviously affected by the gravitational differentiation of oil and water. The reservoir is highly heterogeneous. These characters provide a geological basis for the development of thief zones. According to the production process, the oil field has high water content with a cumulative annual growth rate of water production up to 15%. After the water injection capacity is enhanced, the daily oil production does not increase significantly. The analysis shows a large scale thief zone has appeared in the reservoir. The reservoir heterogeneity is aggravated. The injected water ineffective circulated. The water drive sweep volume is greatly reduced, which will seriously reduce the final recovery. Therefore, it is of great significance to analyze and identify the thief zone to improve the development effect of the oil field. The development status of Daqing oilfield in 2016 is shown in
Table 1.
3.2. Evaluation Index Selection
In sandstone reservoirs, due to their larger porosity, permeability, and effective thickness, reservoir heterogeneity is prominent. Gravity differentiation between oil and water has great effects on the reservoir which will form thief zones relatively easily. After the thief zone is formed, the resistance of fluid flow through the reservoir decreases and the underground conductivity is enhanced, which may cause a decrease of the pressure difference between injection and production wells, rapid increase of water cut, and a significant increase of the liquid productivity index. If the gray correlation degree is used to characterize the interwell connectivity, the connectivity between injection and production wells will be significantly enhanced after the formation of the thief zone. Based on the basic theory of reservoir engineering combining the characteristics of thief zone, nine evaluation indexes are selected according to systematic, scientific and representative principles, as shown in
Table 2.
The connectivity between injection and production well can be calculated by Formulas (8)~(11).
The time series of water injection for injection wells is:
X0 is the time series of daily water injection of the injection well, m3/d; x0 is the volume of daily water injection under different times, m3/d; t is water injection time, d; n is the total number of water injection days, d.
The oil production time series of a production well connected around is:
Xi is the time series of daily oil production of production well, m3/d; xi is the volume of daily oil production under different water injection times, m3/d; t is water injection time, d; n is the total number of water injection days, d.
The correlation coefficient of sequence
Xi and
X0 is:
represents the minimum of absolute difference, m
3/d;
represents the maximum of absolute difference, m
3/d;
is absolute difference, m
3/d;
is resolution coefficient, usually the value is 0.1~0.5.
The correlation degree is defined as:
ri is the correlation degree between subsequence i and sequence 0, and n is the sequence length. The data required to calculate connectivity of water injection and oil production are obtained by actual measurements onsite.
The coefficient of permeability variation is calculated by Equation (12):
VK is the coefficient of permeability variation, %; Ki is the permeability of sample i, μm2, is the average permeability of all samples, μm2; n is the number of samples. The permeability data are obtained by well logging.
The apparent injectivity index and the liquid productivity index are calculated by Equations (13) and (14), respectively:
AK is apparent injectivity index, m3/d·MPa; AO is liquid productivity index, m3/d·MPa; Qw is the volume of daily water injection from injection well, m3/d; QL is the volume of daily oil production from production well, m3/d; Pw is wellhead pressure of injection well, MPa; PO is wellhead pressure of production well, MPa. The volume of daily water injection and daily oil production, and the wellhead pressure data involved in the calculation are obtained from actual on-site measurements.
3.3. Principal-Component-Analysis-Method
The standardized original data of evaluation index for the Daqing oilfield is shown in
Figure 1. The principal-component-analysis is performed after that. According to the principle that the cumulative contribution rate of eigenvalues is greater than 85%, three principal components are selected (Eigenvalue > 1). The eigenvalues of the three principal components were 5.499, 1.433 and 1.058 respectively (the Scree plot is shown in
Figure 2). The contribution rates of eigenvalue were 61.104%, 15.919% and 11.754% respectively. The cumulative contribution rate of eigenvalue was 88.777%. The principal-component-analysis analyzes the correlation coefficient matrix shown in
Table 3.
The correlation coefficient matrix (
Table 4) shows that the injection-production-pressure has negative correlation with the other eight evaluation indexes. This is because with the thief zone, the flow resistance of the fluid through the formation decreases resulting in decreased injection-production-pressure. At the same time, an evident negative correlation between injection-production-pressure and interwell connectivity indicates that pressure plays a significant role in driving fluid flow to a local area. A clearly positive correlation between permeability and permeability coefficient is observed for the remaining eight evaluation indexes. This is because the permeability coefficient is obtained by the ratio of the permeability standard deviation and the average permeability, but the physical meaning of these two evaluation indexes is different. Permeability is mainly used to evaluate the development of the thief zone near the well, while the permeability coefficient is used to evaluate the heterogeneity of the entire formation.
Calculating the communalities of the three principal components shows they retain at least 85% of the information from the original data except for the index of liquid productivity and water content information. It shows that the principal-component-analysis (PCA) has good effects on dimension reduction and simplifying the original complex multi-dimensional evaluation system. The results of the calculation of the communalities are shown in
Table 4.
The load values of the three principal components are calculated (the load diagram is shown in
Figure 3). The functional expression of each principal component is obtained according to the load values as follows.
According to the scores of principal components, the comprehensive evaluation scores
Y1 (shown in
Table 4) of the thief zone between injection and production wells in Daqing oilfield are obtained, ranging from −2.600 to 4.704. The thief zone developed with the increase of comprehensive score. When the comprehensive score is negative, the seepage channel between injection and production wells is in good condition and the water drive power is sufficient. When the comprehensive score is greater than 0.0 but less than 1.0, the thief zone is moderately developed. At this time, close observation and appropriate measurements are needed to avoid further development into a big pore throat. When the comprehensive score is greater than 1.0, the thief zone is well developed and water channeling has occurred. A large amount of injected water is circulating inefficiently between injection and production wells. According to
Figure 4, the Daqing oilfield has 10 well developed thief zones, accounting for 19.61% of the total number of thief zones; and eight moderately developed thief zone, accounting for 15.69% of the total number of thief zones. Improvements, such as profile control and water plugging, are needed for the injection-production wells with thief zones to avoid further development which may influence the final recovery ratio of the oilfield.
3.4. Multi-Layer Weighted Principal-Component-Analysis-Method
The PCA method cannot accurately extract and analyze the development of the thief zone in the same class. In order to improve the accuracy of the evaluation results using PCA, the MLWPCA method was constructed. Firstly, nine indexes are classified according to the result of factor analysis. According to the principle of cumulative contribution rate, greater than 75%, two factors are selected. The contribution rate is 61.104% and 15.919% respectively. The rotated load matrix is shown in
Table 5. The score coefficient matrix obtained by the maximum orthogonal rotation method shows that the load values of
x1,
x3,
x4,
x7 and
x9 evaluation indexes are higher in factor 1. These indexes are grouped into index subsystem 1. In factor 2,
x2,
x5,
x6,
x8, the index load is higher. These indicators are divided into index subsystem 2. Using Equation (8) for weight calculation the weights of subsystem 1 and 2 are 0.777 and 0.223, respectively.
PCA was carried out for the evaluation index of the above two thief zone subsystems. The contribution rates of subsystem 1 and subsystem 2 were 90.302% and 86.157%, respectively. The synthesis scores
Y21 and
Y22 (
Y22’ and
Y22’’) are expressed in the following equations. Based on these scores
Y21 and
Y22, the synthesis score
Y2 of thief zone is calculated shown in
Figure 5. The thief zones of the Daqing oilfield are evaluated by the comprehensive score
Y2.
Through the comprehensive score Y2, it can be seen that there are 10 well developed thief zones in Daqing oilfield, eight moderate developed thief zones, and the remaining 34 thief zones are not formed. By comparing and analyzing the original basic data, we found that the effective thickness and the coefficient of permeability variation are the main indexes affecting the development of thief zone in subsystem 1. Such a thief zone has a large effective thickness. The formation of thief zones is clearly affected by the oil-water gravity differentiation. The reservoir is highly heterogeneous, which provides the geological basis for developing thief zones. Subsystem 2 developed a more advanced thief zone than subsystem 1. Interwell connectivity is the main indicator affecting the development of dominant channels in subsystem. 2. Such a thief zone has large throat radius, strong fluid diversion between wells, and very fast rate of further deterioration. Therefore, the corresponding measurements should be taken as soon as possible to control it. It can be concluded from the above analysis that the MLWPCA method is more targeted and differentiated than the traditional PCA method. It is an effective evaluation method for thief zone determination worthy of popularization.
By comparing with the thief zone identification results using the PCA method in
Section 3.3, we found that the two methods give consistent identification results for the thief zone. The thief zones, J1, J3, J5, J7, J9, J11, J13, J15, J23 and J31, are seriously developed; while the thief zones, J8, J12, J16, J17, J19, J21, J25, and J27, are moderately developed. Comparing the composite scores of the thief zones between the two methods (as shown in
Table 6), we found more obvious differences in the comprehensive score for the thief zones obtained using the MLWPCA method than from PCA method. This can highlight the differences in grade among different thief zones. This can also make the evaluation results more specific and differentiated.
In the process of thief zone evaluation, an interwell tracer test was used to verify the accuracy of the MLWPCA method. As shown from the test results (
Table 6), tracer was detected at 10 well developed thief zones by the MLWPCA method, and the average tracer breakthrough time was 6.4 months. Tracer was detected in seven of the total of eight moderately developed thief zones with an average breakthrough time of 10.6 months. Tracer was not detected for J8 interwell which may be due to the relatively small amount of injected tracer not reaching the oil well. According to the tracer test, the accuracy rate of evaluating the thief zones using the MLWPCA method is 94.44%. This method is proved to be effective in identifying thief zones.