WoPhO 2012, Теория — Задача 2. Vertical Well

Theoretical 2: Physics of the Oil and Gas Production

Условие

Often the reservoir can be modeled as a cylinder (see Figure 7). For this problem all properties were averaged out as in the previous part, so the reservoir is assumed homogeneous with uniform permeability $k$. Oil can be viewed as an incompressible fluid with viscosity $\mu$. Because the rocks above and below the reservoir are impermeable and the height of the cylinder is much less than its radius ($h \ll R$), one can conclude that the fluid flows only in the radial direction.

(a) Find the velocity of the oil $v_w$ inside the well with radius $r_w = 0.1$ m, if the flow rate is 30 $\frac{m^3}{day}$. Estimate the fluid velocity in the reservoir near the well $v_r$. [0,4 т.]

(b) The calculated fluid velocity in the reservoir is rather small therefore the reservoir pressure can be treated as a constant for several months or even years, especially if the reservoir is connected with an underground source of water. Let $P_b$ be the pressure at the outer boundary of the reservoir and $P_w$ be the pressure at the bottom of the well. In this part assume that both $P_b$ and $P_w$ are constants (time-independent values), as well as the radial pressure distribution.

Calculate pressure drop $P_b - P_w$ , which is required to produce oil with flow rate $q$. [1 т.]

(c) Make a sketch of pressure distribution in the reservoir $P(r)$ as a function of the distance from the well. [0,4 т.]

Отговори

Решение

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Оригинал в Архива: WoPhO_2012_Q12.pdf · официални решения: WoPhO_2012_S12.pdf