In the process of oil and gas field development, the waterflooding volumetric sweep efficiency serves as a crucial basis for evaluating the effectiveness of oilfield development and formulating adjustment strategies [1]-[3]. Some scholars [4]-[6] derived methods for predicting the waterflooding sweep efficiency based on Type A and Type C waterflooding curves, respectively. However, both methods can only describe one type of fw-R* curve and have a narrow range of applicability. Reference [7] used Zhang Jinqing’s waterflooding curve to derive a method for predicting the volumetric sweep efficiency of waterflooding oil fields. None of these references have obtained a relationship between the volumetric sweep efficiency of waterflooding and the development duration. In view of this, based on previous research, the author utilizes two cumulative growth prediction models, the HCZ model and the Hubbert model, and through dimensionless mathematical transformation, derives dimensionless correlation equations for the volumetric sweep efficiency of waterflooding for the two models. A standardized prediction chart is established, and combined with Zhang Jinqing’s waterflooding curve, a quantitative relationship between the volumetric sweep efficiency of waterflooding and the production duration of the oilfield is established, thereby predicting the variation pattern of the volumetric sweep efficiency of waterflooding. After determining the ultimate water content, the final volumetric sweep efficiency of waterflooding can be obtained using the relationship proposed in this paper. This method reflects the waterflooding performance in different production stages of the oilfield and is practical for predicting and evaluating development indicators in the later stages of oilfield production.

Both the HCZ model established by Hu Jianguo and the Hubbert model established by Hubbert belong to cumulative growth prediction models. In this paper, we perform non-dimensionalization on the HCZ model and Hubbert model, propose non-dimensional relational expressions for the prediction models, and establish typical curve charts for the prediction models.

Taking C Oilfield as an example, the sand body was put into production in 2007, the Oilfield is buried at a depth of 1200 m, geological reserves is 2340.20 × 10⁴ m³, porosity is 0.28, permeability is 8650 mD, original formation pressure is 12.0000 MPa, and formation crude oil viscosity is 220 mPa∙s. The actual development and production data are shown in Table 1.

Table 1. Actual production data of C oilfield.

First, utilized the actual production performance data in Table 1, finded Q_max and t_peak, t_peak = 9, Q_max = 35.8, utilized Q_D = Q_o/Q_max and t_D = t/t_peak, Q_D and t_D are obtained for the different values of Q_oand t, used the corresponding data of Q_D and t_D , fitted with HCZ model and Hubbert model charts, as shown in Figure 3 and Figure 4, finally, fitted the best value of a/bor A.

Figure 3. Curve fitting diagram of actual data and HCZ model.

Figure 4. Curve fitting diagram of actual data and Hubbert model.

As shown in Table 2, compared to actual value N_pD and HCZ and Hubbert model N_pD, the HCZ model relative error is 0% - 7.2%, the Hubbert model relative error is −10.1% - 8.6%, the Hubbert model has a larger relative error, the HCZ model is more suitable for C oilfield, if the Hubbert model is used to predict the production of C oil field, predicted recoverable reserves N_R = N_peak/2 = 434.52 × 10⁴ m³, it has lower than the current cumulative oil production, it is evidently unreasonable to utilize the Hubbert model. Analyze the reasons, the Hubbert model is effectively applicable to oil and gas fields that have reached the decline stage after extracting 50% of their recoverable reserves. However, the production situation of Oilfield C does not meet this scope of application.

Figure 5 depicted the fitting diagram between actual data and predicted values, with both results generally located near the 45˚ diagonal line. This indicates that the HCZ model has a high credibility in prediction. Therefore, this paper utilizes

Table 2. Comparison between actual value and model chart of C oilfield.

Figure 5. Fitting graph of actual data and predicted data.

the HCZ model to predict the waterflooding sweep efficiency coefficient under different production years.

Determine the best fitting value based on the HCZ chart a/b = 4, t_max = 9, obtain b = 0.154, a = 0.616, substitute it into formula (2), obtain the annual oil production forecasts for different production years, substitute it into formula (1), obtain the corresponding cumulative oil production N_p。

As shown in Figure 6, Based on actual development data of the oilfield of cumulative oil production N_p, cumulative water production W_p, calculated W P / N P and W P / N P 2 separately, used the production curve after 10 years, the water content is greater than 80%, the water drive curve gradually enters a straight line segment, the production tends to stabilize, the regression is better, perform linear regression according to formula (6), obtain C=4.71, D=963.

Figure 6. Zhang Jinqing’s water drive curve fitting diagram.

Substitute the values of C and D, N_p calculated from formula (1), into formula (14), the relationship between different development years and f_w is obtained. Substitute the values of water content f_w and C calculated from formula (14) into formula (14), combine formulas (14) and (24), the waterflooding sweep volume coefficient E_v under different development years can be obtained.

As can be seen from Figure 7, when development years less than 15a, when the water content is less than 90%, E_v exhibits an upward-curving increase; when development years is greater than 15a and the water content is greater than 90%, E_v shows a gradual increase. In the later stage of oilfield development, the number of water-producing wells gradually increases. When the oil wells fully produce water and enter the high water-cut stage, the increase in E_v becomes relatively slow. As the oilfield enters the later stage of extremely high water content, the next step involves restructuring the well network of the layer series and making precise adjustments to waterflooding to reconstruct the underground flow field. This approach resolves the development contradictions of uneven utilization among layers and inefficient cycles, fine-tunes the remaining oil between wells, improves the development effect.

Figure 7. Waterflooding sweep volume coefficient and development years curve.

(1) Two cumulative growth forecast models HCZ and Hubbert were processed with dimensionless treatment to obtain dimensionless typical curve templates, combined with Zhang Jinqing’s waterflooding curve, a relational expression between the waterflooding volume sweep efficiency, water content f_w, and development years was derived.

(2) Based on the verification of production data from C Oilfield, the adaptability of HCZ is significantly better than the Hubbert model, making it more suitable for quantitative prediction of the waterflooding volumetric sweep efficiency in this type of reservoir.

(3) The case of C oilfield demonstrates when development years less than 15a, when the water content is less than 90%, E_v exhibits an upward-curving increase; when development years is greater than 15a and the water content is greater than 90%, E_v shows a gradual increase. This method can be utilized for predicting the waterflooding effect in oil fields and guiding the later-stage development and production of oil fields.

Sun, E.H Wrote the manuscript; Peng, Q revised the manuscript.