Reference no: EM131268524
PETE Project: Flow in a 1-D reservoir
Part A -
Consider slight compressible but constant fluid property flow in under saturated reservoir (i.e. pressure remains above bubble point) with no dip and wells represented as mass source/sink. Following governing equation describes such flow in porous media:
φρct(∂p/∂t) = ∂/∂t((ρ/μ)kxx(∂p/∂x)) + q
Where the fluid density and rock porosity is described as: ρ = 0.85 SG and φ = 0.15
Define the total compressibility as ct = 1.2 microsips (cf = 1 microsips and cR = 0.2 microsips) and assume that fluid viscosity is constant (= 3 cp) for your problem. All boundaries are no flow (i.e. set transmissibility coefficient to zero). Each grid block has the dimension of 100 ft X 100 ft (assume no variation in the third direction). Initial reservoir pressure MUST be hydrostatic with the first grid block pressure set as the datum value of 3000 psia. Reference fluid density and rock porosity evaluated at 3000 psia are 0.85 SG and 0.15.
? Producer Well -- Apply the average grid block pressure of 1500 psia in the grid block# 8 to model the producer well. In other words, q can be set to zero in rest of the grid blocks.
HINT: Convert into consistent units before you discretize the terms in governing equation. All unit conversions and definitions are available in any introductory textbook for petroleum engineering.
|
P1 10 mD 0.15
|
P2 10 mD 0.15
|
P3 10 mD 0.15
|
P4 10 mD 0.15
|
P5 10 mD 0.15
|
P6 10 mD 0.15
|
P7 10 mD 0.15
|
P8 10 mD 0.15 •
|
P9 10 mD 0.15
|
P10 10 mD 0.15
|
Task 1: Write a linear algebraic solver for N X N system for the gridblock pressures as unknowns.
Task 2: Determine the transmissibility coefficients for your system and solve it. Present the results (i.e. pressure distribution in the reservoir) at three different time instances of 10, 30, and 90 days by solving the system of equations using time steps of 1, 2, and 3 days respectively.
Part B -
Consider slight compressible flow in under saturated reservoir (i.e. pressure remains above bubble point) with a dip of 3° and wells represented as mass source/sink. Following governing equation describes such flow in porous media:
φρct(∂p/∂t) = ∂/∂x ((ρ/)kxx((∂p/∂x) - ρgtanθ)) + q
Where the fluid density and rock porosity is described as: ρ = ρ0ec_f(p-p0) and φ = φ0ec_R(p - p0).
Define the total compressibility as ct = cf + (φ0/φ)cR (cf = 1 microsips and cR = 0.2 microsips) and assume that fluid viscosity is constant (= 3 cp) for your problem. All boundaries are no flow (i.e. set transmissibility coefficient to zero). Each grid block has the dimension of 100 ft X 100 ft (assume no variation in the third direction). Initial reservoir pressure MUST be hydrostatic with the first gridblock pressure set as the datum value of 3000 psia. Reference fluid density and rock porosity evaluated at 3000 psia are 0.85 SG and 0.15.
X: Injector Well,
Producer Well -- Apply the specified flow rate (at reservoir condition - to avoid using FVF) for injector well as 2000 res. Bbl/day and use the average drawdown of 100 psia for the producer well.
HINT: Convert into consistent units before you discretize the terms in governing equation.
|
P1 10 mD 0.15
|
P2 10 mD 0.15
|
P3 10 mD 0.15 x
|
P4 10 mD 0.15
|
P5 10 mD 0.15
|
P6 10 mD 0.15
|
P7 10 mD 0.15
|
P8 10 mD 0.15 •
|
P9 10 mD 0.15
|
P10 10 mD 0.15
|
Task 1: Write a linear algebraic solver for N X N system for the gridblock pressures as unknowns.
Task 2: Determine the transmissibility coefficients for your system and solve it. Present the results (i.e. pressure distribution in the reservoir) at three different time instances of 10, 30, and 90 days by solving the system of equations using time steps of 1, 2, and 3 days respectively.
Attachment:- Project Hint.rar
|
Options cost great lakes automotive same amount of money
: Great Lakes Automotive (GLA) is considering producing, in-house, a gear assembly that it currently purchases from Delta Supply for $6 per unit. GLA estimates if it chooses to manufacture the gear assembly, it will cost $23,000 to set up the process a..
|
|
Plus-minus grading system at a university
: Test at α =.05 and 0.10 the hypothesis that a majority (more than 50%) of students favor the plus/minus grading system at a university if in a random sample of 500 students, 265 favor the system?
|
|
Use differentials to estimate volume of the fiberglass shell
: A cube with 10-inch sides is covered with a coat of fiberglass 0.2 inch thick. Use differentials to estimate the volume of the fiberglass shell.
|
|
Confidence interval for the population mean weight
: A sample of 25 items yields = 50.0 grams and s = 2.5 grams. Assuming a normal distribution, construct a 99 percent confidence interval for the population mean weight.
|
|
Determine the transmissibility coefficients for your system
: PETE 2060 Fall 2016 Project: Flow in a 1-D reservoir. Determine the transmissibility coefficients for your system and solve it. Present the results (i.e. pressure distribution in the reservoir) at three different time instances of 10, 30, and 90 da..
|
|
What is the error rate performance of a simple dfe
: What is the error rate performance of a simple (one-tap) DFE that estimates α and removes the ISI? Sketch the detector structure that employs a DFE.
|
|
Average variable cost of production
: A firm produces 1,000 units of output at an average variable cost of production of 50 cents. The firms total fixed costs equal $700. The total cost of producing 1,000 units of output equals:
|
|
Explain the use of time lines in business finance
: Discussion Question- 100 words to explain computing interest rates (finance). 100 Words to explain using present value and future value. 100 words to explain the use of time lines in business finance.
|
|
Context of international tourism
: In the context of international tourism, discuss with examples, the reasons why the East Asia/Pacific region is the fastest growing international tourist generating region.
|