PE 212E Rock Properties Mustafa Onur Given Date: March 16, 2007 Due Date: March 23, 2007 Subject: Steady-State Radial Flow Homework No: 6 Problem 1: Compute the production rate (in STB/D) of the following well which was completed in a sandstone reservoir with a permeability of 117 md. The drainage area of the well is 40 acres (Hint: you can approximate this area by a circle to find the drainage radius, r e ). Other pertinent data are Sand thickness: 10 ft, Static reservoir pressure, p e =2000 psia Bottom hole producing pressure, p wf = 1500 psia Reservoir oil viscosity, μ o = 5 cp. Formation volume factor of oil, B o = 1.2 RB/STB Well diameter = 12 inches Skin factor, S = 0. Problem 2: Consider steady-state flow towards a vertical well producing in a reservoir with k = 100 md, B o = 1.2 RB/STB, h = 20 ft, μ o = 2 cp, r w =0.36 feet, and r e = 1000 ft. The static reservoir pressure is 2750 psia and the bottom hole producing pressure is 500 psia, and skin factor is 10 (a) Compute the well’s flow rate in STB/D. (b) If the radius of the skin zone is 1 feet, what is the permeability in the skin zone? (c) What is the maximum possible rate that could be obtained from this well? (d) If we want the flow rate to be equal to 400 STB/D, what should be our producing wellbore pressure? (e) What would the flow rate be flow rate if we reduced the skin factor to zero by acidizing the well? Problem 3: Consider a vertical well in the center of a cylindrical reservoir of radius r e = 2000 feet. Assume that reservoir consists of two layers. The horizontal permeability, thickness and vertical permeability for each layer is given in the table below. In this table, k h denotes the horizontal permeability, h denotes the layer thickness, and k z denotes the layer vertical permeability. (a) Find effective (or average) horizontal permeability. (b) Find the effective vertical permeability for this two-layer system. k h , md k z , md Layer Thickness, ft Layer No. 1 400 40 10 Layer No. 2 150 15 45 Problem 4: Consider steady-state linear flow in the x-direction across a rectangular core of width w, height h and length L. Start with the differential form of Darcy’s Law and derive an expression for the total flow rate in terms of the total pressure drop across the core for the following two cases (a) k(x,z)=k 1 for 0<z<h and 0<x<L/2, and k(x,z)=k 2 for 0<z<h and L/2<x<L: (b) k(x,z)=k 1 for 0<z<h/2 and 0<x<L, and k(x,z) = k 2 for h/2<z<h and 0<x<L. (c) Based on your derivation, what
Given Date: March 16, 2007 Due Date: March 23, 2007 Subject:
Steady-State Radial Flow
Homework No: 6 Problem 1: Compute the production rate (in STB/D)
of the following well which was completed in a sandstone reservoir
with a permeability of 117 md. The drainage area of the well is 40
acres (Hint: you can approximate this area by a circle to find the
drainage radius, re). Other pertinent data are Sand thickness: 10
ft, Static reservoir pressure, pe=2000 psia Bottom hole producing
pressure, pwf = 1500 psia Reservoir oil viscosity, o = 5 cp.
Formation volume factor of oil, Bo = 1.2 RB/STB Well diameter = 12
inches Skin factor, S = 0. Problem 2: Consider steady-state flow
towards a vertical well producing in a reservoir with k = 100 md,
Bo = 1.2 RB/STB, h = 20 ft, o = 2 cp, rw =0.36 feet, and re = 1000
ft. The static reservoir pressure is 2750 psia and the bottom hole
producing pressure is 500 psia, and skin factor is 10 (a) Compute
the wells flow rate in STB/D. (b) If the radius of the skin zone is
1 feet, what is the permeability in the skin zone? (c) What is the
maximum possible rate that could be obtained from this well? (d) If
we want the flow rate to be equal to 400 STB/D, what should be our
producing wellbore pressure? (e) What would the flow rate be flow
rate if we reduced the skin factor to zero by acidizing the well?
Problem 3: Consider a vertical well in the center of a cylindrical
reservoir of radius re = 2000 feet. Assume that reservoir consists
of two layers. The horizontal permeability, thickness and vertical
permeability for each layer is given in the table below. In this
table, kh denotes the horizontal permeability, h denotes the layer
thickness, and kz denotes the layer vertical permeability. (a) Find
effective (or average) horizontal permeability. (b) Find the
effective vertical permeability for this two-layer system.
Problem 4: Consider steady-state linear flow in the x-direction
across a rectangular core of width w, height h and length L. Start
with the differential form of Darcys Law and derive an expression
for the total flow rate in terms of the total pressure drop across
the core for the following two cases (a) k(x,z)=k1 for 0
are the effective permeabilities for each case. (d) Assuming
that we have the same pressure drop across the core for each case,
which configuration of permeability heterogeneity gives the highest
flow rate?
