Pressure-Transient Behavior of Horizontal Wells With and Without Gas Cap or Aquifer

1991 ◽  
Vol 6 (01) ◽  
pp. 86-94 ◽  
Author(s):  
F.J. Kuchuk ◽  
P.A. Goode ◽  
D.J. Wilkinson ◽  
R.K.M. Thambynayagam
Keyword(s):  
Horizontal Wells ◽  
Transient Behavior ◽  
Pressure Transient

Pressure-Transient Behavior of Multisegment Horizontal Wells With Nonuniform Production: Theory and Case Study

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Youwei He ◽  
Shiqing Cheng ◽  
Jiazheng Qin ◽  
Yang Wang ◽  
Zhiming Chen ◽  
...  
Keyword(s):  
Horizontal Wells ◽  
Transient Behavior ◽  
Field Application ◽  
Pressure Derivative ◽  
Pressure Transient ◽  
Type Curves ◽  
Horizontal Wellbore ◽  
Estimate Rate ◽  
Calculated Average

Field data indicate production profile along horizontal wells is nonuniform. This paper develops an analytical model of multisegment horizontal wells (MSHWs) to estimate rate distribution along horizontal wellbore, interpret the effective producing length (EPL), and identify underperforming horizontal sections using bottom-hole pressure (BHP) data. Pressure solutions enable to model an MSHW with nonuniform distribution of length, spacing, rate, and skin factor. The solution is verified with the analytical solution in commercial software. Type curves are generated to analyze the pressure-transient behavior. The second radial-flow (SRF) occurs for the MSHWs, and the duration of SRF depends on interference between segments. The pressure-derivative curve during SRF equals to 0.5/Np (Np denotes the number of mainly producing segments (PS)) under weak interference between segments. The calculated average permeability may be Np times lower than accurate value when the SRF is misinterpreted as pseudoradial-flow regime. The point (0, 0, h/2) are selected as the reference point, and symmetrical cases will generate different results, enabling us to distinguish them. Finally, field application indicates the potential practical application to identify the underperforming horizontal segments.

Determination of Pressure-Transient and Productivity Data for Deviated Wells in Layered Reservoirs

1999 ◽  
Vol 2 (01) ◽  
pp. 95-103 ◽  
Author(s):  
Leif Larsen
Keyword(s):  
Analytical Methods ◽  
Horizontal Wells ◽  
Transient Behavior ◽  
Laplace Transforms ◽  
Analytical Models ◽  
Single Plane ◽  
Pressure Transient ◽  
Productivity Data ◽  
Half Length ◽  
Deviated Wells

Summary Analytical methods are presented to determine pressure-transient and productivity data for deviated wells in layered reservoirs. The computational methods, which are based on Laplace transforms, can be used to generate types curves for use in direct analyses of pressure-transient data and to determine the effective skin of such wells for use in productivity computations. Introduction Deviated wells with full or limited flow entry are very common, especially in offshore developments. The pressure-transient behavior of fully penetrating deviated wells were investigated by Cinco et al.1 for homogeneous reservoirs. Reference 1 also contains a correlation for the pseudoradial skin factor for wells with deviation up to 75°, with modification indicated for anisotropic reservoirs. To investigate the behavior of deviated wells in layered reservoirs, the model from Ref. 1 can be used as a first approximation, modified to limited flow entry if necessary, but it has been difficult to use more exact models. It is possible, though, to generalize the methods used by Larsen2,3 for vertical wells to also cover deviated wells in layered reservoirs with and without crossflow. For reservoirs without crossflow away from the wellbore, i.e., commingled reservoirs, it is well known how Laplace transforms can be used to handle any model with known solution for individual layers. Deviated wells fall into this category. It is therefore enough to consider systems with crossflow. By including deviated wells with limited flow entry, horizontal wells will also be covered as a special subcategory. Analytical models of this type for horizontal wells have been considered by several authors, e.g., by Suzuki and Nanba4 and by Kuchuk and Habashy.5 Reference 4 is based on both numerical methods and analytical methods based on double transforms (Fourier and Laplace). Reference 5 is based on Green's function techniques. Mathematical Approach To accurately describe flow near deviated wells, and also to capture crossflow in layered reservoirs, three-dimensional flow equations are needed within each layer. If the horizontal permeability is independent of direction within each layer, flow within layer j can be described by the equation k j ( ∂ 2 ∂ x 2 + ∂ 2 ∂ y 2 ) p j + k j ′ ∂ 2 p j ∂ z 2 = μ ϕ j c t j ∂ p j ∂ t ( 1 ) under normal assumptions, where kj and kj′ denote horizontal and vertical permeability, and the other indexed variables have the standard meaning for each layer. Since an approach similar to that used in Refs. 2 and 3 will be followed, the vertical variation of pressure within each layer must be removed, at least temporarily. One way to accomplish this is to introduce the vertical average P j ( x , y , t ) = 1 h j ∫ z j − 1 z j p j ( x , y , z , t ) d z ( 2 ) of the pressure within layer j, where zj−1 and zj=zj−1+hj are the z coordinates of the lower and upper layer boundaries. There is one apparent problem with the approach above, it cannot handle the boundary condition at the wellbore directly. For each perforated layer, the well segment will therefore be replaced by a uniform flux fracture in the primary solution scheme, as illustrated in Fig. 1 for a fully perforated deviated well and in Fig. 2 for a partially perforated well with variable angle, with a transient skin effect used to correct from a fractured well solution to a deviated well solution. With well angle θj (as deviation from the vertical) and completed well length Lwj in layer j, the associated fracture half-length will be given by the identity x f j = 1 2 L w j s i n θ j ( 3 ) for each j. The completed well length Lwj is assumed to be a single fully perforated interval. The fracture half-length in layers with vertical well segments will be set equal to the wellbore radius rw. To capture deviated wells with more than one interval within a layer, the model can be subdivided by introducing additional layers. Although the well deviation is allowed to vary through the reservoir, the well azimuth will be assumed constant. The projection of the well in the horizontal plane can therefore be assumed to follow the x axis, and hence assume that y=0 along the well. Keeping the well path in a single plane is actually not necessary, but it simplifies the mathematical development and the computational complexity. If Eq. (1) is integrated from zj−1 to as shown in Eq. (2), then the flow equation k j h j ( ∂ 2 ∂ x 2 + ∂ 2 ∂ y 2 ) P j + k j ′ ∂ p j ∂ z | z j − k j ′ ∂ p j ∂ z | z j − 1 = μ ϕ j c t j h j ∂ P j ∂ t ( 4 ) is obtained, with the gradient terms representing flux through the upper and lower boundaries of layer j. In the standard multiple-permeability modeling of layered reservoirs, the gradient terms are replaced by difference terms in the form k j ′ ∂ p j ∂ z | z j = k j + 1 ′ ∂ p j + 1 ∂ z | z j = λ j ′ ( P j + 1 − P j ) ( 5 ) for each j, where λj′ is a constant determined from reservoir parameters or adjusted to fit the well response. For details on how to choose crossflow parameters, see Refs. 2 and 3 and additional references cited in those papers. Additional fracture to well drawdown is assumed not to affect this approach.

scholarly journals Pressure Transient Analysis for Horizontal Wells in Coal Bed Methane Reservoirs with Pressure-Sensitive Permeabilities

2021 ◽  
Author(s):  
Juan Camilo Sepúlveda ◽  
Sebastián Díaz ◽  
Edwin Alexander López
Keyword(s):  
Flow Behavior ◽  
Horizontal Wells ◽  
Transient Behavior ◽  
Production Performance ◽  
Coal Bed ◽  
Coal Bed Methane ◽  
Coal Seams ◽  
Pressure Transient ◽  
Type Curves ◽  
Flow Mechanisms

Abstract: Coal bed methane (CBM) reservoirs are complex systems whose properties differ from those of conventional reservoirs. Coal seams are dual-porosity systems that comprise the porosities of the matrix and cleat system. Gas in the coal seams can be stored as free gas in the cleat system and as adsorbed gas in the porous medium. The flow mechanisms of the natural gas through the formation include desorption, diffusion, and Darcy’s flow regimes. The permeability of CBM reservoirs is more sensitive to pressure variations than conventional gas reservoirs. To study the flow behavior of CBM reservoirs it is mandatory to use a model that considers their unique characteristics. The objective of this study was to propose a physical and mathematical model of production performance for horizontal wells in CBM reservoirs whose permeability is dependent on pressure. A solution for the model was obtained by applying Pedrosa´s transformation, perturbation theory, Laplace transformation, the point source method, and Sthefest´s algorithm. The solution to this problem was validated with previous work thoroughly. The type curves of the model were built and the pressure transient behavior of the model was analyzed and discussed. The effects of several parameters on pressure behavior were also discussed.

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