Simulation of Transient Pressure Behavior for a Well With a Finite- Conductivity Vertical Fracture

Paulo Dore Fernandes, Thiago Judson L. de Oliveira, Sylvio Dermeval de Souza, Raphael David and Rodrigo A. C. Dias

Problem Description

• Types of wells

– Vertical Wells

– Horizontal Wells

– Fractured Wells • Productivity Index (PI)

• This work involves near-well reservoir simulations.

• The reservoir simulators fail in the description of fractures. The use of CFD provides a complete description of the region near the well.

Problem Description

• This work involves simulations of oil reservoirs whose pressure is considerably above the bubble pressure.

• The wells considered in the simulations are vertical fractured wells.

• The accounting of the real fracture geometry is a challenge in reservoir simulations because of huge difference between the length scales of reservoir, well and fracture;

• All simulations presented in the study are in transient regime reservoir;

Goals

• The main objective of this work is to analyze the increase in production of a well fractured with a finite conductivity vertical fracture in relation to wells without fractures. The reservoir production is calculated by using computational fluid dynamics (CFD);

• The details of the fracture and well geometries are advantages of the CFD simulation;

• The pressure propagation in fracture is accounted by the simulations. This result is interesting in terms of more accurate values of productivity

Methodology

• Darcy Law + Continuity Reservoir Simulator

pt

pc owt

• Without Fracture

• With Fracture

• The reservoir pressure is at 640 kg / cm ² and the well is at a pressure of 400 kg / cm ²

• The user defined real gas model (UDRGM) enables the implementation the desirable compressibility law.

• Average Theory + UDRGM Fluent

Methodology - Reservoir Without Fracture

• The three-dimensional CFD model was built to reflect the well geometry and its influence radius over the reservoir.

• Length scale : Reservoir and well

• The well details are considered in reservoir simulation using CFD

Symmetry

Symmetry

Wall

Well

Reservoir

Outlet

• Detail level - CFD

Methodology - Reservoir Without Fracture

• The mesh was built using Cut Cell technique

• Mesh with 2.726.364 elements

Results - Reservoir Without Fracture

• The pressure propagates through the reservoir in the transient regime.

• The flow rate falls with time. The reservoir is losing oil and the it is being depleted.

Results - Reservoir Without Fracture

• After five years the flow rate keeps falling and steady reservoir regime has not yet been reached.

• This solution can be found easily from analytical way. The simulation was performed in order to evaluate the increased number of mesh elements on the case with the fracture. The number of layers of permeability can also be easily implemented by CFD.

Methodology - Reservoir With Fracture

• The three-dimensional CFD model was built to reflect the fracture, the well geometry and its influence radius over the reservoir.

• Length scale : Reservoir, well and fracture

Fracture

Well

Reservoir

Detail level - CFD Fracture

Wall (well)

Outlet

• Detail level - CFD • Any type of geometry fracture

Symmetry

Symmetry

Wall

Methodology - Reservoir With Fracture

• The mesh was made using Cut Cell • Reservoir mesh with 9.627.012 elements • Fracture mesh with 3.279.000 elements • The fracture thickness has 4 millimeters. The

radius fracture is 49 meters. Because the difference in scales the mesh has many elements.

• Mesh

Methodology - Reservoir With Fracture

• The mesh was made using Cut Cell • Reservoir mesh with 9.627.012

elements • Fracture mesh with 3.279.000

elements

Results - Reservoir With Fracture - Infinite Conductivity

• The assumption of infinite conductivity is applied in the simulation without considering the fracture mesh.

Results - Reservoir With Fracture - Infinite Conductivity

• The linear regime in the fracture is neglected when the hypothesis of infinite conductivity is applied.

• The flow rate falls with time. The reservoir is losing oil and the it is being depleted.

Results - Reservoir With Fracture - Finite Conductivity

• The linear regime is now considered in the fracture when the hypothesis of finite conductivity is applied.

• Due to the high conductivity of the fracture, the time step had to be decreased.

Results - Reservoir With Fracture - Finite Conductivity

• The propagation of pressure occurs in the first fracture (circular shape).

Results - Reservoir With Fracture - Finite Conductivity

• Half of the length of the fracture is open to the well.

• CFD simulations enable the details of the geometry of the fracture as well as different opening settings.

Results - Reservoir With Fracture - Finite Conductivity

• Initially , the pressure propagation is radial (fracture)

Results - Reservoir With Fracture - Finite Conductivity

• A higher fractured conductivity is considered here. The pressure propagation will be faster inside of fracture.

• In CFD simulations, different geometries of fracture can be considered. In this work only radial fractures are studied.

Results - Reservoir With Fracture - Finite Conductivity

• The pressure in fracture is equal to the well pressure well in almost two years. The higher fracture conductivity leads to a higher pressure propagation.

Results - Comparison

• The presence of fracture increases well productivity for a shorter time.

100

200

300

400

500

600

700

0 5 10 15 20 25 30 35

Ra

te (

m3

/s)

Elapsed Time (month)

Without Fracture

Infinity Conductivity

Finity Conductivity

Finity Conductivity 50%

Next Steps

• Simulation of Horizontal Multi-Fractured Wells

• Simulation of Formation Tests (evaluation of early time Productivity Index and comparison with real well tests).

• Study of near well issues related to pressure behavior of well tests permeability heterogeneity, reservoir geometry, presence of natural fractures, etc...