A Semi-Analytic Model for Productivity Testing of Multiple Wells  (SPE94153)

Fokker, Petrus Adrianus; Brouwer, Geert; Verga, Francesca; Ferrero, D.

doi:10.3997/2214-4609-pdb.1.c027

Cited by 3 publications

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Steady-State Productivity Equations for a Multiple-Wells System in Sector Fault Reservoirs and Channel Reservoirs

Zhu

Tiab

2009

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Currently in the oil industry, pseudo-steady state productivity equations for a multiple wells system are used in all reservoir systems, regardless of the outer boundary conditions. However, if the reservoir is under edge water drive or with infinite lateral extension, pseudo-steady state is no longer applicable. When producing time is sufficiently long, productivity equations based on the steady state are required. This paper presents steady-state productivity equations for a multiple-wells system in homogeneous, anisotropic sector fault reservoirs and channel reservoirs. Taking fully penetrating vertical wells as uniform line sinks, and solving a square matrix of dimension n, where n is the number of wells, simple, reasonably accurate multiple-wells system productivity equations are obtained. The proposed equations which relate the production rate vector to the pressure drawdown vector provide a fast analytical tool to evaluate the performance of multiple wells, which are located arbitrarily in a sector fault reservoir or a channel reservoir. This paper also gives an equation for calculating skin factors of each well. It is concluded that, for a given number of wells, well pattern, anisotropic permeabilities, skin factor, pressure difference between reservoir outer boundary and flowing bottomhole pressure, have significant effects on single well productivity and total productivity of the multiple-wells system. In a sector fault reservoir, the production rates are increasing functions of the sector angle; in a channel reservoir, the production rates are increasing functions of the reservoir width. Introduction Well productivity is one of primary concerns in field development and provides the basis for field development strategy. To determine the economical feasibility of drilling a well, petroleum engineers need reliable methods to estimate its expected productivity. We often relate the productivity evaluation to the long time performance behavior of a well, that is, the behavior during pseudo-steady state or steady-state flow.

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Steady-State Productivity Equations for a Multiple-Wells System in Sector Fault Reservoirs and Channel Reservoirs

Zhu

Tiab

2009

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Pseudo-Steady State Productivity Equations for a Multiple-Wells System in a Sector Fault Reservoir

Ghedan

2010

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Wells producing from their own individual drainage area is only true for reservoirs at their early development. However, in matured oil reservoirs it would be acceptable to imagine several wells producing from the same drainage domain. Each well, then, will have an effect on the pressure of other wells. The flowing bottomhole pressure of a well producing at a constant rate is a function of its own production as well as the production from surrounding wells. Currently, in the oil industry, productivity equations for single wells are erroneously used, as they do not consider the interference effects on flow rates of different wells in the same drainage domain.This paper presents a pseudo-steady state productivity equation for a multiple-wells system in a homogeneous, anisotropic sector fault reservoir with impermeable boundaries. Assume sector angle Φ is equal to π/n, n is an integer bigger than 1, take fully penetrating vertical wells as uniform line sinks, and use symmetry principle, a simple, reasonably accurate productivity equation for a multiple-wells system is obtained by solving a square matrix of dimension 2nm, where m is the number of wells. The proposed equation relates the production rate vector to the pressure drawdown vector, is applicable to a multiple-wells system arbitrarily located in a closed sector fault reservoir. Convenient algorithms to calculate shape factors for sector fault reservoirs, equilateral triangle reservoirs and isosceles right triangular reservoirs are provided. The value of the shape factor from the proposed equation is very close to its corresponding value published in the literature.The benefit of the analytical model can be emphasized when the reservoir data deviate from their idealistic representation. It is concluded that, the proposed equations provide a fast analytical tool to evaluate the performance of a multiple-wells system in a closed sector fault reservoir.

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A Semianalytic Model for the Productivity Testing of Multiple Wells

Fokker¹,

Verga

2008

SPE Reservoir Evaluation &Amp; Engineering

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Summary We present a semianalytic method for modeling the productivity testing of vertical, horizontal, slanted, or multilateral wells. The method is applicable to both oil and gas reservoirs and automatically accounts for well interference. The use of analytic expressions ensures that short-time transient behavior and long-time semisteady-state behavior are handled appropriately, whether close to the well or further into the reservoir. Calculation times are still very limited—on the order of a few minutes to a few seconds when all wells are vertical. This makes the tool suitable for evaluating well testing and determining well productivity. We based the approach on an earlier derived productivity prediction tool, in which the steady-state equations were solved. It has now been extended to solve the time-dependent diffusion equation. In our current method, the equations have first been transformed using the Laplace transformation. The expressions for the producing wells are combined with auxiliary sources outside the reservoir. The crux of the semianalytic method involves an adjustment of the positions and strengths of these sources in order to approximate the boundary conditions at the reservoir boundaries. The solution obtained is transformed back into the time domain by use of a Stehfest algorithm. The new approach has been validated with numeric tools, including both reservoir simulators and well-test interpretation software. Validations were performed with artificial cases and with field production data, using both single-well and multiple-well production tests. The results of these tests were excellent.

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A Semi-Analytic Model for Productivity Testing of Multiple Wells (SPE94153)

Cited by 3 publications

References 0 publications

Steady-State Productivity Equations for a Multiple-Wells System in Sector Fault Reservoirs and Channel Reservoirs

Steady-State Productivity Equations for a Multiple-Wells System in Sector Fault Reservoirs and Channel Reservoirs

Pseudo-Steady State Productivity Equations for a Multiple-Wells System in a Sector Fault Reservoir

A Semianalytic Model for the Productivity Testing of Multiple Wells

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