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We present semianalytical solutions for cocurrent displacements with some degree of countercurrent flow. The solution assumes a one-dimensional horizontal displacement of two immiscible incompressible fluids with arbitrary viscosities and saturation-dependent relative permeability and capillary pressures. We address the impact of the system length on the degree of countercurrent flow when there is no pressure drop in the nonwetting phase across the system, assuming negligible capillary back pressure at the inlet boundary of the system. It is shown that in such displacements, the fractional flow can be used to determine a critical water saturation, from which regions of both cocurrent and countercurrent flow are identified. This critical saturation changes with time as the saturation front moves into the porous medium. Furthermore, the saturation profile in the approach presented here is not necessarily a function of distance divided by the square root of time. We also present approximate solutions using a perturbative approach, which is valid for a wide range of flow conditions. This approach requires less computational power and is much easier to implement than the implicit integral solutions used in previous work. Finally, a comprehensive comparison between analytical and numerical solutions is presented. Numerical computations are performed using traditional finite-difference formulations and convergence analysis shows a generally slow convergence rate for water imbibition rates and saturation profiles. This suggests that most coarsely gridded simulations give a poor estimate of imbibition rates, while demonstrating the value of these analytical solutions as benchmarks for numerical studies, complementing Buckley-Leverett analysis.

We investigate the impact of capillary backpressure on spontaneous counter-current imbibition. For such displacements in strongly water-wet systems, the non-wetting phase is forced out through the inlet boundary as the wetting phase imbibes into the rock, creating a finite capillary backpressure. Under the assumption that capillary backpressure depends on the water saturation applied at the inlet boundary of the porous medium, its impact is determined using the continuum modelling approach by varying the imposed inlet saturation in the analytical solution. We present analytical solutions for the one-dimensional incompressible horizontal displacement of a non-wetting phase by a wetting phase in a porous medium. There exists an inlet saturation value above which any change in capillary backpressure has a negligible impact on the solutions. Above this threshold value, imbibition rates and front positions are largely invariant. A method for identifying this inlet saturation is proposed using an analytical procedure and we explore how varying multiphase flow properties affects the analytical solutions and this threshold saturation. We show the value of this analytical approach through the analysis of previously published experimental data

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Since the early stage of the oil industry, many authors have recognized the importance of capillary pressure measurements using the mercury injection method (MICP) method in estimating permeability values. For that reason, numerous permeability models have been developed and proposed in literature. MICP is a very popular technique to determine pore size distributions and pore-throat properties. The capillary pressure profiles determined using this method are influenced generally by certain parameters that are controlled by permeability, including: degree of sorting, pore size distributions and pore throat properties. Since MICP offers direct relation to permeability-related information, a good estimation of permeability should be obtained. Most of the available correlations produce high errors when compared to actual permeability measurements. To address this issue, a feedforward neural network (ANN) model was developed to predict permeability from the MICP measurements. The neural network consists of two hidden layers with 15 neurons each and one output layer. A dataset of 206 core samples were used to train the ANN model. The dataset was divided into three sets: 70% for training, 15% for internal validation, and 15% for blind testing. A variety of parameters — porosity, displacement pressure, Swanson parameter, Winland parameter, Dastidar parameter, Pittman parameter, and Purcell integration — were extracted from the MICP data and inputted to the ANN model. In the analysis to evaluate the developed model against conventional models, graphical and statistical comparisons were used to determine the best technique for use. Comparison between permeability models available in literature and the developed ANN model indicated significant improvement with the proposed model. Error measures — including: maximum absolute percent error (MAE), average relative percent error (ARE), average absolute relative percent error (AARE), correlation coefficient (R2), standard deviation (SD) and root mean squares (RMSE) — were used as the basis for interpreting the results and evaluating the comparative performance of the models. The developed ANN model demonstrated a reduction of about 50% in AARE and RMSE. Correlation coefficient also improved from 0.91 for the best conventional model to 0.98.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractHydraulic Flow Unit (HU) has been used extensively as a technique in permeability modeling and rock typing. Amaefule et al. (1993) introduced for the first time the concept of Reservoir Quality Index (RQI) and Flow Zone Indicator (FZI) by using the Kozeny-Carmen (K-C) model to characterize HU and predict permeability in uncored wells and intervals.This technique has helped in enhancing the capability to capture the various reservoir flow behavior based on its respective characters. Yet, there are challenges in using the original correlation due to its inherent limitations and over simplified assumptions that prevent accurate HU definitions. This study highlights some of those shortcomings and proposes a modified K-C correlation that enhances the HU characterization.It is found that the conventional K-C model ignores the inherent nonlinear behavior between the tortuosity and porosity. Hence, handling the tortuosity term in a more representative manner demonstrates a more rigorous correlation that extends the applicability of this powerful technique into more heterogeneous rocks -such as those found in carbonate reservoirs. This paper presents a reservoir simulation case study that is conducted to validate the applicability of the proposed model as a rock typing technique in a heterogeneous carbonate reservoir in the Middle East region. Relative permeability curves, Leverett J-Function curves and initial water saturation distribution show good agreement within each HU generated using the proposed model.It is recognized that modified Kozeny-Carmen technique give better matching of initial water saturation model than the conventional technique when compared to open-hole logs which, in turn; adds confidence to initial hydrocarbon-in-place calculations and reservoir behavior predictions. This result will ultimately enhance the prediction of reservoir performance under various scenarios in reservoir simulation.

We apply steady-state capillary-controlled upscaling in heterogeneous environments. A phase may fail to form a connected path across a given domain at capillary equilibrium. Moreover, even if a continuous saturation path exists, some regions of the domain may produce disconnected clusters that do not contribute to the overall connectivity of the system. In such cases, conventional upscaling processes might not be accurate since identification and removal of these isolated clusters are extremely important to the global connectivity of the system and the stability of the numerical solvers. In this study, we address the impact of percolation during capillary-controlled displacements in heterogeneous porous media and present a comprehensive investigation using random absolute permeability fields, for water-wet, oil-wet and mixed-wet systems, where J-function scaling is used to relate capillary pressure, porosity and absolute permeabilities in each grid cell. Important information is revealed about the average connectivity of the phases and trapping at the Darcy scale due to capillary forces. We show that in oil-wet and mixed-wet media, large-scale trapping of oil controlled by variations in local capillary pressure may be more significant than the local trapping, controlled by pore-scale displacement.