The water–oil relative permeability curve is mainly obtained from linear displacement experiments. Few radial displacement experiments have been carried out. In the process of linear displacement experiments, the flow properties of the water–oil two phase are linear. Nevertheless, it is radial near the bottom holes of an actual reservoir. With regard to both kinds of displacement experiments, the flow characteristics are various, which may result in great deviation to apply the linear calculation theory of the relative permeability curve to an actual reservoir. As a result of the above-mentioned problems, on the basis of radial displacement experiments, using the Levenberg–Marquardt algorithm for automatic history matching, this paper performs optimization of production performance and relative permeability representation models. Finally, a novel numerical inversion method for the radial water–oil relative permeability curve is established. A test based on the basic data of a radial laboratory displacement experiment is performed to verify the effect of the proposed method. The results show that oil relative permeability is more sensitive to the cumulative production data, while water relative permeability is more sensitive to the bottomhole pressure data of the producers. It also indicates that the cubic B-spline model (CBM) is far more general and flexible and has the advantage of local fitting compared to the power law model (PM). In addition, the numerical inversion method proposed for the radial water–oil relative permeability curve is reliable and can meet the engineering requirement, which provides a basic calculation theory for the estimation of the water–oil relative permeability curve.

The capillary pressure is the key parameter to affect the inversion accuracy of the water–oil relative permeability curve. The existing analytical inversion methods have neglected the influence of capillary pressure, which may cause low precision for the estimated relative permeability curve in some cases. On the basis of the numerical inversion method for the water–oil relative permeability curve established in part 1 (10.1021/ef300018w), taking the one-dimensional radial numerical experiment for example, the rules of relative permeability variation and influence of different displacement conditions on relative permeability deviation when neglecting the capillary pressure are investigated. With regard to water-wet cases whose oil–water viscosity ratio is greater than 1.5, it indicates that the estimated water-phase relative permeability curve is higher and the estimated oil-phase relative permeability curve is lower compared to the true relative permeability curve when the capillary pressure is neglected. The main displacement conditions influencing the inversion accuracy of the relative permeability curve include the injection rate, average permeability, and shape factor of the core sample. As the injection rate increases, the degree of relative permeability deviation caused by neglecting the capillary pressure becomes smaller. Moreover, the deviation trends of the water–oil relative permeability curve are the same as those of the increasing injection rate when average permeability decreases or the shape factor of the core sample increases. Finally, the orthogonal experimental design technique is used to establish the experimental conditions considering the combined effect of multiple factors, and then the water–oil relative permeability curve under every experimental condition is estimated implicitly. On this basis, the multivariate analysis is performed to obtain the threshold value charts of radial displacement experimental parameters, such as the injection rate, average permeability, and shape factor of the core sample, and their corresponding rational value domains are also achieved, which can be used to reduce the influence of neglecting capillary pressure data as much as possible and provide a calculation theory for estimation of the water–oil relative permeability curve accurately.

The waterÀoil relative permeability curve has a great effect on the rules of water cut increase and production variation. It is one of the most important data in reservoir development. With regard to a reservoir with a high degree of heterogeneity, the flow properties are various in different positions of the reservoir. Therefore, neither a single average relative permeability curve for the whole reservoir nor different curves for different sedimentary facies can precisely describe the reservoir flow characteristics, which will cause great difficulties for the remaining oil prediction and potential tapping. Therefore, it is of great importance to build a prediction model for the waterÀoil relative permeability curve, which can provide a calculation theory of the relative permeability curve for reservoir simulation using different relative permeability curves in different grid cells. The existing prediction models for the relative permeability curve have established the correlations between petrophysical properties and endpoint values of the relative permeability curve and between end-point values of the relative permeability curve and the relative permeability curve independently. However, the relationship between petrophysical properties and the relative permeability curve has not been developed. For this reason, it is impossible to achieve the spatial distribution of the relative permeability curve according to petrophysical properties. Furthermore, the end-point values of the relative permeability curve are usually calculated directly by petrophysical properties, which may result in all predicted relative permeability curves shifting to the left or right unrealistically compared to the reservoir average relative permeability curve. As a result of the above-mentioned problems, taking into consideration the correction effect of the average relative permeability curve on predicting relative permeability curves in different positions of the reservoir, this paper obtains a correlation between petrophysical properties and the relative permeability curve on the basis of the statistical analysis technique and normalization method of the reservoir average relative permeability curve. Finally, a prediction model for the waterÀoil relative permeability curve is established. A test based on the basic data of the relative permeability curve is performed to verify the effect of this model. The test result shows that the prediction procedure of this model is quick, easy, and reliable. It also indicates that the spatial distribution of the relative permeability curve satisfying the migration rule can be generated from petrophysical properties, which provides a basic calculation theory of the waterÀoil relative permeability curve for reservoir simulation using different relative permeability curves in different grid cells.

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A network model is established through the techniques of image reconstruction, a thinning algorithm, and pore-throat information extraction with the aid of an industrial microfocus CT scanning system. In order to characterize actual rock pore-throat structure, the established model is modified according to the matching of experimental factors such as porosity, permeability, and the relative permeability curve. On this basis, the impacts of wetting angle, pore radius, shape factor, pore-throat ratio, and coordination number as applied to microscopic remaining oil distribution after water flooding are discussed. For a partially wetting condition, the displacement result of a water-wet pore is somewhat better than that of an oil-wet pore as a whole, and the possibility of any remaining oil is relatively low. Taking the comprehensive effects of various factors into account, a prediction method of remaining oil distribution is presented through the use of fuzzy comprehensive evaluation. It is seen that this method can predict whether there is remaining oil or not in the pore space with satisfactory accuracy, which is above 75%. This method thus provides guidance for a better understanding of the microscopic causes of the remaining oil.