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Dynamic analysis of bottom hole pressure of a horizontal well in fracture-cavity reservoirs

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Abstract

This paper presents a new method to obtain a semi-analytical solution for bottom hole pressure (BHP) of a horizontal well in fracture-cavity reservoirs. The basic building block of the method is to build a new source function suitable for the seepage of carbonate rock for the first time and obtain BHP step by step. This paper uses Laplace transform and Perturbation method to solve the diffusivity equation, which is different from the traditional method of using Green’s function presented by Gringarten and Ramey. We validated it with the available published analytical solution and numerical simulation. The sensitivity analysis of pressure and pressure derivative is carried out, and the influence of fracture number, fracture angle, fracture half-length, skin factor, horizontal well segment length, and horizontal well segment spacing on pressure and pressure derivative is analyzed in detail. The findings of the research have led to the conclusion that the number of fractures and fracture direction mainly affect the radial flow stage. In contrast, the length of horizontal subsection and skin factor mainly affect the karst cave fluid flows to the fracture stage. The matrix fluid flows to the fracture stage that is more obvious when the fracture half-length and the horizontal sublevel interval of the horizontal well are small. The advantage of this method is to incorporate well geometry (skin factor) and hydraulic fracturing design (fracture parameters), which are helpful to improve the accuracy of well test interpretation. In addition, this new method has the characteristics of easy calculation. The findings of this study can help for better understanding of transient pressure behavior of horizontal well in fracture-cavity reservoirs.

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modified from Deng et al. 2019)

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Abbreviations

k x, k y and k z :

The permeability in x, y and z directions, mD

μ :

The viscosity of crude oil, mPa s

∆p:

Pressure difference, MPa

\(\phi\) :

The porosity, decimal

C :

T he compressibility coefficient, Pa−1

\(\alpha ,\beta ,\chi\) :

The angle between the fracture and the x, y, z axes, °

δ :

The Dirac Delta function.

k xi :

The initial permeability of the natural fracture system in the x direction, 10−3 μm2

p i :

The initial formation pressure, MPa

α :

The permeability modulus, MPa−1

a, b :

The length and width of the reservoir, m

h :

Effective thickness, m

L :

Horizontal section length of horizontal well, m

(x 0, y 0, z 0):

Fracture center coordinates

w x, w y, w z :

The projection width of the fracture in the x, y, z direction, m

m :

Matrix system

f :

Fracture system

v :

Karst cave system

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Authors and Affiliations

  1. China University of Geosciences (Beijing), Haidian District, Beijing, 100083, China

    Liu Hailong

  2. Sinopec Petroleum Exploration and Development Research Institute, Haidian District, Beijing, 100083, China

    Liu Hailong

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  1. Liu Hailong
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Hailong, L. Dynamic analysis of bottom hole pressure of a horizontal well in fracture-cavity reservoirs. Environ Earth Sci 81, 295 (2022). https://doi.org/10.1007/s12665-022-10396-8

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