Joe M. Kang

Pressure Behavior of Transport in Fractal Porous Media Using a Fractional Calculus Approach

Many authors have used theories of anomalous diffusion in the field of physics to interpret fractally fractured reservoirs. However, their solutions cannot separate the two fractal dimensions df and dw , and their results are not valid in the early time range. In this study, a new general constant-flow-rate solution, which is applicable to whole spatio-temporal ranges, is derived using the Fox H-function. Sensitivity analyses were carried out for various cases. The solution developed here permits the use of early production data. By combining early and late time data, it is possible to determine the two fractal dimensions separately. From the intrinsic property of the Fox H-function, this model makes it possible to capture the history and nonlocality of transport. Therefore, the model provides a general methodology for characterizing the pressure behavior of fractally fractured reservoirs.Many authors have used theories of anomalous diffusion in the field of physics to interpret fractally fractured reservoirs. However, their solutions cannot separate the two fractal dimensions df and dw , and their results are not valid in the early time range. In this study, a new general constant-flow-rate solution, which is applicable to whole spatio-temporal ranges, is derived using the Fox H-function. Sensitivity analyses were carried out for various cases. The solution developed here permits the use of early production data. By combining early and late time data, it is possible to determine the two fractal dimensions separately. From the intrinsic property of the Fox H-function, this model makes it possible to capture the history and nonlocality of transport. Therefore, the model provides a general methodology for characterizing the pressure behavior of fractally fractured reservoirs.

A new automated scheme of quadrilateral mesh generation for randomly distributed line constraints

This paper presents a new automated method of quadrilateral meshes with random line constraints which have not been fully considered in previous models. The authors developed a new looping scheme and a direct quadrilateral forming algorithm based on advanced front techniques. This generator overcomes the limitations of previous studies such as line constraint, unmeshed hole and mesh refinement. A qualitative test reveals that our algorithm is reliable and suitable at the field needed for very accurate results. The developed direct method to handle line-typed features automatically makes the multiple discretizations without any user interaction and modification.

Modeling of solute transport in a single fracture using streamline simulation and experimental validation

Abstract Streamline simulations have been extensively used in petroleum engineering due to its computational speed and the freedom from numerical dispersion. This study applies streamline simulation to the modeling of solute transport in a single fracture and verifies the streamline method with experimental data. In order to model dispersive transport, a new term, the advection–dispersion ratio is employed, which is defined as the relative extent of advection to dispersion along streamlines. It is observed that the tracer breakthrough curves from the simulation match well with those from the experiments. In addition, the tracer displacement profiles from the simulation also show resemblance to those from the experiments. Simulations with various link transmissivity types result in no serious disparities. The distributions of time of flight and tracer breakthrough curves from the simulations using different link transmissivity types are much alike. Transport simulation is performed by allocating different advection–dispersion ratios along streamlines. Afterwards, the results are compared with the simulation result using single representative advection–dispersion ratio over the flow domain. Although streamlines actually have different advection–dispersion ratios, its effect is found to be not severe. Therefore, a representative advection–dispersion ratio can be used for modeling transport through the whole streamlines in a single fracture.

Development of Pareto-based evolutionary model integrated with dynamic goal programming and successive linear objective reduction

This paper presents a new Pareto-based evolutionary model incorporated with preference-ordering and objective-dimension reduction to improve the multi-directional searches for multi-objective problems.It induces a convergence toward the Pareto-optimal front by adjusting aspiration levels allocated to objectives and by excluding redundant objectives during optimization.Its usefulness was validated for multi-objective test problems comparing to conventional single- and multi-objective optimization models. This study investigates the coupling effects of objective-reduction and preference-ordering schemes on the search efficiency in the evolutionary process of multi-objective optimization. The difficulty in solving a many-objective problem increases with the number of conflicting objectives. Degenerated objective space can enhance the multi-directional search toward the multi-dimensional Pareto-optimal front by eliminating redundant objectives, but it is difficult to capture the true Pareto-relation among objectives in the non-optimal solution domain. Successive linear objective-reduction for the dimensionality-reduction and dynamic goal programming for preference-ordering are developed individually and combined with a multi-objective genetic algorithm in order to reflect the aspiration levels for the essential objectives adaptively during optimization. The performance of the proposed framework is demonstrated in redundant and non-redundant benchmark test problems. The preference-ordering approach induces the non-dominated solutions near the front despite enduring a small loss in diversity of the solutions. The induced solutions facilitate a degeneration of the Pareto-optimal front using successive linear objective-reduction, which updates the set of essential objectives by excluding non-conflicting objectives from the set of total objectives based on a principal component analysis. Salient issues related to real-world problems are discussed based on the results of an oil-field application.

Prediction of nonlinear production performance in waterflooding project using a multi-objective evolutionary algorithm

The paper presents a multi-objective evolutionary algorithm applied to history matching of waterflooding projects, which is to search a feasible set of geological properties showing the reliable future performance. Typical history matching has concentrated on single objective function with linearly weighted terms, even as a realistic field includes many wells and well measurements in time and type. The optimal solution is sensitive to weight factor and competing match criteria of individual term in the objective function often reduce the likelihood of finding an acceptable match. The unacceptable error at a specified well can be observed in a heterogeneous reservoir where shows nonlinear well performances. To overcome the inaccuracy, a new history matching approach is developed that allows the performance characteristics of the whole wells. Individual well performance is optimized separately using genetic algorithm coupled with non-dominated sorting and diversity preservation. The fitness is sorted along to the proximity and then the diversity is added by examining the crowding distance as the approach to arrive at the global optimum. Waterflooding is demonstrated in a heterogeneous oil reservoir with multiple production wells. The predictability of unknown future production performance is compared with that of single objective function, the conventional history matching method. The model represents individualized well-performance more accurately than the conventional history matching. It improves a certainty of the conventional model by showing small error range. The selection of adequate set of reservoir properties is possible among the feasible solutions unlike the conventional model. The developed method can be applied as a useful tool for uncertainty analyses in waterflooding projects.

Development of a robust multi-objective history matching for reliable well-based production forecasts

This article presents a dynamic reservoir characterization using a new multi-objective optimization algorithm to quantify the reservoir uncertainties in history matching. The proposed method formulated Pareto-optimality with preference-ordering to derive multiple trade-off history-matched reservoir models for probabilistic production estimation. The integration of linear programming with multi-objective genetic algorithm enhances the efficiency of a multi-directional search by prioritizing the reservoir models that satisfy the aspiration levels on the discrepancy between the observed and the calculated production data. The preference levels are automatically adjusted in correspondence to the quality of the reservoir models for facilitating the model update process during optimization. An oil-field application result indicates the method outperforms the conventional multi-objective optimization method in terms of the relative average error for the production data despite a small loss of diversity-preservation among the reservoir models.

Numerical Analysis of Diffusion in Discrete Fracture Networks with Fractal Geometry by Using Pressure Transient Data

This article presents numerical analyses on diffusion trend for the fractured media with fractal properties by pressure transient data. The authors develop a discrete fracture model with random fracture pattern and a power-law length distribution, which has not been fully considered in the previous fractal modeling. From the model presented, the fractal dimension and conductivity index is determined, and the pressure behavior is analyzed for the range of length exponent (a) of power-law from 1 and 3. Various fractal geometries are examined depending on the morphology of fractures. A single fractal characteristic is observed in the media dominated by long (a < 2) or small fractures (a > 3), and two distinct fractal dimensions in pertinently mixed system of long and small fractures (2 < a < 3). Also, pressure transient behaviors in the mixed system show their unique characteristics, corresponding to each fractal dimension respectively. It is shown that diffusion effect is relatively small in the early time influenced by a few long fractures, and becomes larger in the late time by long and small fractures.

An Inverse Channel Model for Modeling Contaminant Transport

Recent experimental and theoretical investigations of transport in a fracture indicate that fluid flows preferentially through flow channels in the fracture plane. Several one-dimensional (1D) channel models have been introduced to interpret flow and transport through two-dimensional (2D) fractured media. However, those models are not capable of reproducing a tracer breakthrough curve accurately, and the aperture distributions (i.e., aperture mean and standard deviation) predicted by those models cannot characterize flow channels in the fracture. In this paper, we present a new 1D channel model using an inverse algorithm. At a given breakthrough curve, we divide the time domain into a limited number of intervals based on the principle of superposition and then determine aperture distribution of each channel inversely. The new channel model reproduces the tracer breakthrough curve of a fracture almost exactly at a given pressure drop. In addition, the aperture distributions obtained by the new channel model have good agreement with those of 2D modeling of transport in the fracture. In parameter analyses, we found that flow channeling becomes dominant in fracture flow when the coefficient of variation is > 0.3. Therefore the new channel model can effectively simulate flow and tracer transport in a fracture in that range.

Hydraulic-Unit-Based Fuzzy Model to Predict Permeability from Well Logs and Core Data of a Multi-Layer Sandstone Reservoir in Ulleung Basin, South Korea:

This paper presents a method to predict permeability of an offset well using well logs and core data from a multi-layer sandstone reservoir with various depositional environments. Many studies have been conducted to predict permeability but limited to wells drilled in a formation with a single depositional environment. This study implements fuzzy models to predict the FZI (flow zone indicator) and permeability, and applied HU (hydraulic unit) grouping to classify the rock properties of various depositional environments in terms of the correlation between permeability and porosity. Then, an individual fuzzy model is developed for each HU group. A field application confirms that the method can be applied to permeability prediction using well data from various depositional environments. A comparative study shows that HU grouping plays a key role in grouping cores of similar flow characteristics in the case of core data from multiple layers with various depositional environments.

Reservoir Heterogeneity Affecting Steam Communication between Multiple Well-Pairs for Steam Assisted Gravity Drainage

This paper investigates the effects of reservoir heterogeneity on steam communication and well-interference between multiple steam chambers during SAGD (steam assisted gravity drainage) process. The conventional steam stimulation for developing oil sands uses well pad system composed of several well pairs, so that the heat interference occurs when the steam chambers merge with each other. The numerical simulations using multiple SAGD well pairs were conducted in a heterogeneous formation and compared with those of a homogeneous case in terms of the production performances. Reservoir heterogeneity could make uneven steam communication, unequal chamber growth and leave unrecovered area, thereby giving the negative effect on oil production. Both production profiles of water and oil, and cSOR (cumulative steam to oil ratio) of individual SAGD pair would be good indicators to diagnose steam movement between chambers. The results discussed the negative effect of reservoir heterogeneity making unequal growth of vapor chamber and energy inefficiency due to horizontal movement of injected steam, and the necessity of identifying the indicators to characterize the chamber growth.