Transient deliverability evaluation for a slanted well in a slab gas reservoir

ABSTRACT

The present work provides an algorithm to calculate transient deliverability of a slanted well in a slab gas reservoir. Firstly, transient pressure response of a slanted well has been analyzed and the solutions in Laplace space under three boundary conditions have been derived by point source function and Green function. The solutions in real space can be obtained through the Stehfest inversion by using the superposition principle. Based on the transient pressure analysis, a transient productivity analysis method has been presented in this paper. The influence factors of productivity such as the deviation angle of a slanted well, perforation length, permeability anisotropy ratio, and horizontal permeability to the IPR curve and open-potential rate have been discussed.

KEYWORDS:

• Point source solution
• slanted well
• slab reservoir
• transient pressure behavior
• transient productivity

Acknowledgments

The authors would also like to appreciate the reviewers and editors whose critical comments were very helpful in preparing this article.

Nomenclature

$\mathit{P}$	=	Pressure, MPa
$P_i$	=	Initial pressure, Mpa
$\mathit{r}$	=	Radial distance, m
$r_w$	=	Well radius, m
$\mathit{x},\mathit{y},\mathit{z}$	=	Space coordinates of field point in Cartesian coordinates, m
$\mathit{K}$	=	Permeability, md
$K_{\mathrm{h}}$	=	Horizontal permeability, md
$K_{\mathrm{v}}$	=	Vertical permeability, md
$p_{\mathrm{D}}$	=	Dimensionless pressure
$C_t$	=	Total compressibility, $\mathrm{MP}{\mathrm{a}}^{-1}$
${\psi }_{\mathrm{i}}$	=	Initial pseudo pressure, MPa2/mpa.s
${\psi }_{\mathrm{wf}}$	=	Well bottom hole pseudo pressure, MPa2/mpa.s
$\mathit{\varphi }$	=	Porosity, %
$\mathit{\mu }$	=	Viscosity, mpa.s
${\theta }_{\mathrm{W}}$	=	Inclination angle of well measured from the vertical axis
$z_D$	=	Dimensionless reservoir thickness
$\mathit{s}$	=	Laplace variable
$x_{\mathit{WD}},y_{\mathit{WD}},z_{\mathit{WD}}$	=	Dimensionless space coordinates of field point in Cartesian coordinates
$\mathit{t}$	=	Time, h
$t_D$	=	Dimensionless time
$L_w$	=	Length of slanted well, m
$Z_{\mathrm{W}}$	=	Distance between the slanted well to the reservoir bottom, m
$\mathit{\eta }$	=	Diffusivity, cm2/s
$\mathit{\xi }$	=	Variable in Poisson equation
$K_0$	=	Modified Bessel function of second kind of order zero
$r_{\mathit{wD}}$	=	Dimensionless well radius
$q_{\mathit{sc}}$	=	Rate of active well, m3/d
$\mathit{c}$	=	Wellbore storage constant
$C_D$	=	Dimensionless wellbore storage constant
${\theta }_{\mathrm{wD}}$	=	Dimensionless inclination angle of well measured from the vertical axis
$L_{\mathit{wD}}$	=	Dimensionless length of slanted well

Additional information

Funding

This work was financially supported by the National Science and Technology Major Project (2017ZX05013-005).

Notes on contributors

Guoqing Feng

Guoqing Feng, Doctor of Petroleum Engineering, Associate Professor (. Graduated from Southwest Petroleum Institute in 2001). Worked in school of oil & Natural Gas Engineering, Southwest Petroleum University. His research interests include Reservoir Engineering, EOR, reservoir modelling and simulation.

Zhidong Yang

Zhidong Yang, Master of Petroleum Engineering, a PhD candidate in school of oil & Natural Gas Engineering, Southwest Petroleum University. His research interests include Reservoir Engineering, EOR, reservoir modelling and simulation.

Liehui Zhang

Liehui Zhang, Doctor of Petroleum Engineering, Professor (. Graduated from Southwest Petroleum Institute in 1995). Worked in school of oil & Natural Gas Engineering, Southwest Petroleum University. His research interests include Reservoir Engineering, EOR, reservoir modelling and simulation.

Yaru Feng

Yaru Feng, postgraduate in school of oil & Natural Gas Engineering, Southwest Petroleum University. Her research interests include Reservoir Engineering, EOR, reservoir modelling and simulation.