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Radial Flow and Radius of Investigation 2 Upon completion of this section, the student should be able to: 1. Given formation and fluid properties, be able to calculate the radius of investigation achieved at a given time or the time necessary to reach a given radius of investigation. 2. Describe, without looking at the equation, how each of the following parameters affects the time required to reach a given radius of investigation: permeability, compressibility, viscosity, porosity, net pay thickness, flow rate.
Radial Flow and Radius of Investigation 3 Assumptions Single-phase liquid with constant μ , c, B Formation with constant φ , h Well completed over entire sand thickness Infinite reservoir containing only one well Uniform pressure in reservoir prior to production Constant production rate q beginning at time t=0 Homogeneous reservoir

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Radial Flow and Radius of Investigation 4 The Ei-function solution to the diffusivity equation assumes line source well (finite size of wellbore can be neglected). This solution is valid only for r > r w . It predicts the pressure response in the reservoir as a function of both time t and distance from the center of the wellbore r.
Radial Flow and Radius of Investigation 5 The argument of the Ei-function, x, is given by: Short times or large distances large x Long times or short distances small x For short times, A, pressure response predicted by the Ei- function is negligible. For long times, B, pressure response may be calculated using the logarithmic approximation to the Ei-function. For intermediate times, C, the full Ei-function must be used to calculate the pressure response. kt r c 948 x 2 t μ φ =

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Radial Flow and Radius of Investigation 6 At any given point in the reservoir, at sufficiently early times, the pressure response is essentially negligible. This approximation applies whenever . 10 kt r c 948 2 t μ φ
Radial Flow and Radius of Investigation 7 At any given point in the reservoir, at sufficiently late times, the pressure response is approximately logarithmic in time.

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