Characterization and Analysis of Anisotropic Relative Permeability

Summary The relative permeability functions of two-phase reservoirs are extensively used in modern reservoir-engineering theories for calculations and numerical simulations. In recent years, the theory of anisotropic reservoir development has advanced rapidly, and the anisotropic absolute permeability of reservoirs has been characterized and applied accurately. However, if only the anisotropy of absolute permeability is considered while neglecting the anisotropy of relative permeability, the effective permeability used in the calculations will differ significantly from that of an actual reservoir. In this study, an anisotropy experiment on two-phase relative permeability, with oil and water, was conducted using natural sandstone without fractures, which demonstrated the existence of anisotropy in relative permeability and analyzed its mechanism. The properties and calculation methods for anisotropic relative permeability were studied under the symmetry groups of a rhombic system. Numerical simulations of the reservoir considering anisotropic relative permeability were performed. The results demonstrated that the anisotropic relative permeability significantly affected the development of the oil reservoir, which is primarily indicated by the significant difference in the seepage direction of oil and water, and the complicated oil/water distribution. The results of this study differed significantly from the conventional understanding of remaining oil distribution. The deformed well pattern established for the anisotropy of the absolute permeability indicated a decrease in the oil-recoveryratio.

Productivity analysis for a horizontal well with multiple reorientation fractures in an anisotropic reservoir

Reorientation fractures may be formed in soft and shallow formations during fracturing stimulation and then affect well productivity. The principal focus of this study is on the productivity analysis for a horizontal well with multiple reorientation fractures in an anisotropic reservoir. Combining the nodal analysis technique and fracture-wing method, a semi-analytical model for a horizontal well with multiple finite-conductivity reorientation fractures was established to calculate its dimensionless productivity index and derivative for production evaluation. A classic case in the literature was selected to verify the accuracy of our semi-analytical solution and the verification indicates this new solution is reliable. Results show that for a fixed fracture configuration the dimensionless productivity index of the proposed model first goes up and then remains constant with the increase of fracture conductivity, and optimal fracture conductivity can be determined on derivative curves. Strong permeability anisotropy is a negative factor for well production and the productivity index gradually decreases with the increase of anisotropic factor. As principal fracture angle goes up, horizontal well’s productivity index increases correspondingly. However, the effect of reoriented fracture angle on the productivity index is not as strong as that of principal fracture angle. When reoriented fracture angle is smaller than principal fracture angle, reoriented factor should be as low as possible to achieve optimal productivity index. Meanwhile, well productivity index rises up with the increase of fracture number and fracture spacing, but the horizontal well has optimal reorientation fracture number and fracture spacing to get the economical productivity. Furthermore, the influence of the rotation of one central reorientation fracture on productivity index is weaker than that caused by the rotation of one external reorientation fracture. In addition, the asymmetrical distribution of one or more reorientation fractures slightly affects the productivity index when fracture conductivity is high enough.

Pseudo-Steady-State Parameters for a Well Penetrated by a Fracture with an Azimuth Angle in an Anisotropic Reservoir

Many oil wells in closed reservoirs continue to produce in the pseudo-steady-state flow regime for a long time. The principal objective of this work is to investigate the characteristics of two key pseudo-steady-state parameters—pseudo-steady-state constant (bDpss) and pseudo-skin factor (S)—for a well penetrated by a fracture with an azimuth angle (θ) in an anisotropic reservoir. Firstly, a general analytical pressure solution for a finite-conductivity fracture with or without an azimuth angle in an anisotropic rectangular reservoir was developed by using the point-source function and spatial integral method, and two typical cases were employed to verify this solution. Secondly, with the asymptotic analysis method, the expressions of pseudo-steady-state constant and pseudo-skin factor were obtained on the basis of their definitions, and the effects of permeability anisotropy, fracture azimuth angle, fracture conductivity and reservoir shape on them were discussed in detail. Results show that all the bDpss-θ and S-θ curves are symmetric around the vertical line, θ = 90° and form a hump or groove shape. The optimized fracture direction in an anisotropic reservoir is perpendicular to the principal permeability axis. Furthermore, a new formula to calculate pseudo-skin factor was successfully proposed based on these two parameters’ relationship. Finally, as an application of pseudo-steady-state constant, a set of Blasingame format rate decline curves for the proposed model were established.

Numerical Simulation Study on Fracture Parameter Optimization in Developing Low-Permeability Anisotropic Reservoirs

The diamond-shape inverted nine-spot well pattern is widely used in developing low-permeability reservoirs with fractures. However, production wells with equal fracture lengths will lead to nonuniform displacement, especially in anisotropic reservoir. Previous researches mainly focused on equal-length fractures, while studies on the unequal-length fractures which can dramatically improve the development efficiency were little. In this paper, a corresponding numerical model with unequal length of fracture designed in the edge and the corner wells was built in a low-permeability anisotropic reservoir. The main objective was to examine and evaluate the effects of anisotropic permeability and fracture parameter on the waterflooding in the diamond-shape inverted nine-spot well pattern. The results indicate that different fractures penetration ratio and anisotropic permeability both result in different development efficiency. Fracture of the edge well are more easily to be water breakthrough, while the increase of penetration ratio of injection well effectively enhance oil recovery. Moreover, the most optimal penetration ratios of production well fractures under different kx : ky are determined. With the increase of kx : ky, the optimized penetration ratio of corner wells fracture decrease, while that of the edge wells increase. Setting unequal length fractures in low-permeability anisotropic reservoirs can effectively improve the oil displacement efficiency in the waterflooding process.

Diagnosis of Water-Influx Locations of Horizontal Well Subject to Bottom-Water Drive through Well-Testing Analysis

Horizontal well (HW) has been widely applied to enhance well productivity and prevent water coning in the anisotropic reservoir subject to bottom-water drive. However, the water-cut increases quickly after only one or two years’ production in China while oil recovery still keeps at a very low level. It becomes a major challenge to effectively estimate production distribution and diagnose water-influx locations. Ignoring the effect of nonuniform production distribution along wellbore on pressure response may cause erroneous results especially for water-influx location determination. This paper developed an analytical method to determine nonuniform production distribution and estimate water-influx sections through well-testing analysis. Each HW is divided into multiple producing segments (PS) with variable parameters (e.g., location, production, length, and skin factor) in this model. By using Green’s functions and the Newman-product method, the novel transient pressure solutions of an HW can be obtained in the anisotropic reservoir with bottom-water drive. Secondly, the influences of nonuniform production-distribution on type curves are investigated by comparing the multisegment model (MSM) with the whole-segment model (WSM). Results indicate that the method proposed in this paper enables petroleum operators to interpret parameters of reservoir and HW more accurately by using well-testing interpretation on the basis of bottom-hole pressure data and further estimate water-influx sections and nonproducing segments. Additionally, relevant measures can be conducted to enhance oil production, such as water controlling for water-breakthrough segments and stimulation treatments for nonproducing locations.

Well-flow behavior of reorientation fracture considering permeability anisotropy

Purpose In petroleum industry, hydraulic fracturing is essential to enhance oil productivity. The hydraulic fractures are usually generated in the process of hydraulic fracturing. Although some mathematical models were proposed to analyze the well-flow behavior of conventional fracture, there are few models to depict unconventional fracture like reorientation fracture. To figure out the effect of reorientation fracture on production enhancement and guide the further on-site operating, this paper aims to investigate the well-flow behavior of vertical reorientation fracture in horizontal permeability anisotropic reservoir. Design/methodology/approach Based on the governing equation considering horizontal permeability anisotropy, the mathematical models for reorientation fractures in infinite reservoir are developed by using the principle of superposition. Furthermore, a rectangular closed drainage area is also considered to investigate the well-flow behavior of reorientation fracture, and the mathematical models are developed by using Green’s and source functions. Findings Computational results indicate that the flux distribution of infinite conductivity fracture is uniform at very early times. After a period, it will stabilize eventually. High permeability anisotropy and small inclination angle of reorientation will cause significant end point effect in the infinite conductivity fracture. The reorientation fractures with small inclination angle in high anisotropic reservoir are capable of improving 1-1.5 times more oil productivity in total. Originality/value This paper develops the mathematical methods to study the well-flow behavior for unconventional fracture, especially for reorientation fracture. The results validate the production enhancement effect of reorientation fracture and identify the sensitive parameters of productivity.