Calculating downhole cards in deviated wells

Patent metadata

Field	Value
Publication number	US-9897083-B2
Application number	US-201213663155-A
Country	US
Kind code	B2
Filing date	Oct 29, 2012
Priority date	Oct 28, 2011
Publication date	Feb 20, 2018
Grant date	Feb 20, 2018

Abstract

Diagnosing a pump apparatus having a downhole pump disposed in a deviated wellbore characterizes axial and transverse displacement of a rod string with two coupled non-linear differential equations of fourth order, which include axial and transverse equations of motion. To solve the equations, derivatives are replaced with finite difference analogs. Initial axial displacement of the rod string is calculated by assuming there is no transverse displacement and solving the axial equation. Initial axial force is calculated using the initial axial displacement and assuming there is no transverse displacement. Initial transverse displacement is calculated using the initial axial force and the initial axial displacement. Axial force and friction force are calculated using the initial displacements, and the axial displacement at the downhole pump is calculated by solving the axial equation with the axial force and the friction force. Load at the downhole pump is calculated so a downhole card can be generated.

First claim

What is claimed is:

1. A method of diagnosing a pump apparatus having a downhole pump disposed in a deviated wellbore, having a controller of limited processing capability, and having a motor at a surface of the deviated wellbore, the downhole pump reciprocated in the deviated wellbore by a rod string operatively moved by the motor, the method comprising:
obtaining surface measurements indicative of surface load and surface position of the rod string at the surface;
characterizing axial and transverse displacement of the rod string with two coupled non-linear differential equations of fourth order including an axial equation of motion and a transverse equation of motion by replacing derivatives of the two coupled non-linear differential equations with finite difference analogs;
solving the finite difference analogs of the two coupled non-linear differential equations by performing calculating steps with the controller of limited processing capability comprising:
initially calculating initial axial displacement of the rod string by assuming there is no transverse displacement and by solving the axial equation of motion;
initially calculating initial axial force using the initial axial displacement and assuming there is no transverse displacement;
first calculating initial transverse displacement of the rod string by using the initial axial force as initially calculated and using the initial axial displacement as initially calculated;
second calculating axial force and friction force by using the initial axial displacement as initially calculated and using the initial transverse displacement as first calculated; and
obtaining an axial displacement determination at the downhole pump by third solving the axial equation of motion using the axial force and the friction force as second calculated;

calculating with the controller of limited processing capability load at the downhole pump;
generating with the controller of limited processing capability a downhole card representative of the load relative to the axial displacement determination of the downhole pump obtained by the calculating steps; and
modifying at least one parameter of the pump apparatus based on the generated downhole card by changing operation of the motor.

2. The method of claim 1 , wherein obtaining the surface measurements comprises measuring the surface load and the surface position of the rod string at the surface.

3. The method of claim 1 , wherein obtaining the surface measurements comprises obtaining the surface measurement from a memory storing the surface measurement.

4. The method of claim 1 , wherein the transverse equation of motion is defined by:

EI
⁢

∂
2

∂

s
2

⁡

[

∂
2

⁢
v

∂

s
2

+

1

R
φ

]

+

γ
⁢

⁢
A
⁢

∂
2

⁢
v

∂

t
2

+

n
t

+

n
p

+

D
t

⁢

∂
v

∂
t

+

F
R

-

γ
⁢

⁢
gA
⁢

⁢
sin
⁢

⁢
θ

=
0

,

wherein EI is a bending stiffness of a rod element, E is Young's modulus of elasticity, I is a bending moment, R φ is a radius of curvature of tubing in the deviated wellbore, γ is a density of the rod element, A is a cross-sectional area of the rod element, n t is a transverse normal force from tubing in the deviated wellbore, an n p is a transverse normal force from liquid under pressure p, D t is a viscous damping factor in a transverse direction, F is an axial force on the rod element,

1
R

is an actual radius of curvature given by

1
R

=

1

R
φ

+

∂
2

⁢
v

∂

s
2

,

g i

Assignees

• Pons Victoria M
• Weatherford Tech Holdings Llc

Inventors

• Pons Victoria M

Classifications

• E21B47/009

  Monitoring of walking-beam pump systems · CPC title

• G05B13/042

  in which a parameter or coefficient is automatically adjusted to optimise the performance · CPC title

• F04B2201/1211

  Position of the walking beam · CPC title

• F04B2201/121

  Load on the sucker rod · CPC title

• F04B51/00

  Testing machines, pumps, or pumping installations · CPC title