Reservoir KNW2

Production well assumptions

• the reservoir is considered homogeneous in all rock properties & isotropic w/ respect to permeability

• the well is completed & perforated across the entire formation thickness (quasi 1D)

• the formation is saturated with/ a single fluid

partial différentiel equation factors

• initial cond.

• boundary cond.

const. terminal rate solution scenario

at a point in time at which the res., is at equilibrium pressure p_i, the well starts producing w/ constant. rate q at the wellbore w/ radius r_w

radial flow states

• transient: infinitely acting res.

• semi-steady state (SSS)

• steady state (SS)

=> SSS & SS are stabilised flow cond.

semi steady state

• reservoir has closed/ solid boundaries, meaning there is no influx of fluid from the outside → production is changing p_res

• the pressure decline is proportional to the production rate and invers proportional to the reservoir size

• applied to reservoir that is producing for a sufficient period of time such that the boundary effects are fully developed.

q = const.; ∂p/∂t = const; ∂p/∂r = 0 at r=r_e

Steady state

• influx from boundaries compensates for fluid loss from production

p_e = const; q = const; ∂p/∂t = 0; ∂p/∂r = 0 at r = r_e

Dietz shape factor

considers the irregularities in the drainage area as each well have its own drainage boundary with the symmetry depending on the injection pattern and the geological settings.

• proportional to the well’s production rate under SSS conditions

• NOT the TRUE shape

• cant obtain the orientation

superposition theorem

individual const. rate wells can be placed in any position at any time and each well will drain from within its own no flow boundary quite independently

p_res = ∑piVi/∑Vi = ∑piqi/∑qi

transient flow

the pressure disturbance travels into the field right after starting production & is not affected by the boundaries of the res.

• p = pi at t=0 for all r → p_{before production} = pi

• p = pi at r=∞ for all t → ensures transient cond.: infinite reservoir

• lim r ∂p/r = qµ/2πKh# for t>0 → line-source inner boundary cond.

well testing

the process of measuring the changes of production or injection rate and the downhole pressure under flowing cond. of the testing well, i.e. obtaining input or output signals of the system.

well testing objectives

Provides information about:

• permeability

• formation damage

• productivity index

• res. drive mechanism

• basic res. geometries & other characteristics

well testing methods

• wireline

• drill stem (DST)

• production test

Pressure Measurement Challenges

• Pressure gauge limitations:

  • Gauge type

  • Applicable pressure range

  • Calibration status

• Depth measurement errors:

  • Need for accurate true vertical depth

  • Corrections affected by uncertain fluid density in the well

• Background noise:

  • Pressure variations from nearby producing wells

• Interpretation assumptions

surface rate measurement

accuracy of converting reservoir to surface volumes, effected by conversion factors & exact hydrostatic head

production test process

1. Case off the hole

2. Run a production string

3. Perforate the zone of interest

4. Produce reservoir fluids at controlled rates for a desired period

5. Record reservoir pressure as a function of time

6. Take fluid samples (either downhole or at the surface)

=> basis of field appraisal & development decisions

drill stem test

carried out with a temporary completion using the drill stem as temporary conduit

1. Run DST tool into the wellbore

2. Set packer to isolate test zone

3. Open valve and allow initial flow

4. Close valve for pressure measurement

5. Open valve for main production period

6. Collect fluid samples

7. Close valve for final pressure readings

8. Remove tool from wellbore

=> used for low GOR for safety reasons

pressure transient analysis

creates a controlled disturbance (perturbation) in the reservoir and analyzing its response.

1. Perturbation: Create a change in the reservoir (by producing or shutting in the well)

2. Reservoir Mechanism: The reservoir responds to this change

3. Response: Measure the pressure changes over time (pressure transient)

4. Analysis: Interpret the pressure transient data to derive reservoir properties

transient analysis test types

• drawdown test: log-log plot

  • Input: Constant flow rate (well is opened to produce)

  • Output: Decreasing pressure over time

• build up test: Horner plot (semi-log)

  • Input: Well is shut in (flow rate becomes zero)

  • Output: Increasing pressure over time

transient analysis approaches

• comparison to analytical model: compares observed pressure and flow rate data to theoretical models

• numerical history matching: uses computer simulations to match observed data

transient analysis output parameters

• permeability

• skin factor

• drainage radius

• productivity index

transient flow sensitivties

• reservoir parameters

• Well performance

• well damage

radial flow method

the movement of fluid in a reservoir from the perimeter towards the bottom hole along radial directions in the horizontal plane.

SS & SSS flow sensitivties

• reservoir size

• reservoir boundary conditions

late transient flow sensitivties

• reservoir geometry

• well position

wellbore storage

the effect of fluid expansion or contraction within the wellbore itself, separate from fluid flow from the reservoir

wellbore storage causes

pressure decrease due to:

• expansion of fluids in the well

• changing liquid level in the well annulus

wellbore storage mechanism

1. When production starts or stops, there's a delay before the sandface flow rate matches the surface flow rate

2. During production, fluid in the wellbore expands as pressure decreases

3. During shut-in, fluid in the wellbore compresses

skin factor

damage zone around the production & injection wells caused by invasion of mud filtrate or cement during drilling / completion (a.k.a formation damage)

• S>0: additional pressure drop → formation damage

• S<0: improved wellbore cond. → well simulation

• S=0: no changes in the well cond. → formation permeability

drainage radius

gives an estimate about the size if the reservoir

• at the drainage radius: p(r,t>0) - pi = 0

• max drainage radius: p(r_e, t) - pi = 0

productivity index

measures of the ability of the well to produce

PI = q_total /(p-p_wf) [stb/d.psi]

buildup survey benefits

• less susceptible for noise from fluctuating production rates

• cancel skin effects

buildup survey procedure

the well is producing for a certain time (pressure drawdown) and is then shut-in → the pressure builds up again

Horner plot

a semi-logarithmic analysis in which its time axis is read from right to left

• Right side: Wellbore storage effects

• Middle: Transient flow (straight line)

• Left side: Boundary effects

Horner plot benefits

• Complements drawdown data for verification

• Usually provides cleaner data (less noise)

• Transient flow appears as a straight line

• Permeability calculated from the slope

Sequence of Flow Regimes in horizontal wells

• Wellbore Storage and Skin Effects

  • Occurs immediately after production starts or stops

• Early Radial Flow (in the yz plane)

  • Flow is radial in a vertical plane perpendicular to the wellbore

• Linear Flow (in y direction)

  • Fluid flows linearly towards the wellbore

• Late Pseudoradial Flow (in the xy plane)

  • Occurs when the pressure transient extends beyond the well's ends

elliptical flow

a transitional flow period that occurs between a linear or near-linear flow pattern at early times and a radial or near-radial flow pattern at late times