• Energy Research

Fetkovich or Blasingame type rate decline analysis is a common and practical method to obtain reservoir parameters and evaluate well productivity. Pseudo-steady-state constant is an indispensable parameter for establishing these new type rate decline curves and works as a bridge linking conventional productivity and new type productivity. Refracturing is widely used to enhance tight oil wells’ productivity and improve their economic benefits, the pseudo-steady-state constant of refracturing horizontal wells has been presented in our previous research, but an in-depth discussion on the definition, accuracy, sensitivity, and application of this constant has not been conducted. It results in the insufficient understanding of the physical meaning, characteristics, and functions of pseudo-steady-state constant at present. In this study, taking the derived pseudo-steady-state constant for refracturing horizontal wells with fracture reorientation as an example, its accuracy was verified by an equivalent model presented in the literature, and the sensitivity of relevant key parameters on this constant was investigated. For the refracturing horizontal well defined in this study, pseudo-steady-state constant is independent of time, and related to fracture conductivity, fracture face damage, reorientation fracture number and permeability anisotropy. Results show that this constant decreases with the increase of fracture conductivity, but tends to remain unchanged when fracture conductivity increases to a certain extent. Meanwhile, this constant shows a positive correlation with fracture face damage and permeability anisotropy, but an inverse correlation with reorientation fracture number. Blasingame type rate decline curves of refracturing horizontal wells with fracture reorientation were also established, regarding as a practical application of this pseudo-steady-state constant and a concrete manifestation of its bridge-linking function. These type curves are directly conducive to the inversion of reservoir properties and fracturing parameters and the prediction of future productivity for refracturing horizontal wells. More importantly, this study is helpful to understand and strengthen the role and importance of pseudo-steady-state constant, and also beneficial to the establishment of new type rate decline curves of other similar models.

Fracture aperture of a fractured reservoir can be affected by both matrix elasticity and fracture compressibility when the reservoir pressure decreases, namely stress sensitivity. An elasticity parameter coupling Young’s modulus and Poisson’s ratio was introduced to reflect this geomechanical behavior, and a new model incorporating geomechanics was developed to analyze the flow behavior of a horizontal well in a naturally fractured reservoir. Pressure solutions for two cases—uniform-flux and infinite-conductivity—were derived, respectively. For the uniform-flux case, the effect of dimensionless elasticity parameter on the pressure-drop profile becomes stronger with continuing production, and the profile may be like a bow. Nine flow regimes can be observed on the transient response of the infinite-conductivity case. Stress sensitivity mainly affects the late-flow period and a larger dimensionless elasticity parameter causes a greater pressure drop. Due to stress sensitivity, the pressure derivative curve exhibits an upward tendency in the pseudo-radial flow regime, and the slope is greater than “1” in the pseudo-steady flow regime. For KT-I formation in the North Truva field, its elasticity parameter decreases with the increase of Young’s modulus or Poisson’s ratio and ranges from 8 × 10−8 Pa−1 to 1.1 × 10−7 Pa−1. Meanwhile, the transient response of H519 has a slight negative correlation with Young’s modulus and Poisson’s ratio in the pseudo-steady flow regime.

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.