Drill Stem Testing - Procedure Design, Pressure Transient Analysis, and Reservoir Parameter Calculation

A Drill Stem Test (DST) is the most information-dense operation that can be performed on a well before it is completed. In 24-72 hours of testing, a DST provides direct measurement of reservoir pressure, permeability, skin factor, fluid composition, and the presence of reservoir boundaries - data that would otherwise require months of production history or dozens of log interpretations to estimate with less certainty. The difference between a successful DST that drives a production investment decision and one that produces ambiguous data is almost entirely in the design: the test sequence must be long enough to reach radial flow (the regime from which permeability is calculated), the pressure gauges must have adequate resolution to detect the expected pressure changes, and the surface equipment must be designed to handle the anticipated wellstream composition and flow rate. This guide gives you the complete engineering framework.


1. DST Tool String - Components and Functions

1.1 Standard Open-Hole DST Tool String

The DST tool string is assembled as part of the drill string and lowered to the test interval. The sequence from bottom to top:

Component Function Critical Engineering Requirement
Perforated sub / Tail pipe Allows formation fluid to enter the tool string. Provides standoff from the well bottom. Perforation area must be sufficient to prevent restriction at maximum anticipated flow rate
Bottom gauge (memory gauge) Records bottomhole pressure and temperature continuously throughout test. Primary data source for pressure transient analysis. Resolution must be ±0.01 psi or better. Sampling rate 1 measurement per second minimum during buildup.
Bottom packer Isolates the test interval from the wellbore below. Set by rotating or setting down weight on the drill string. Pressure rating must exceed maximum anticipated formation pressure. Confirm packer integrity before opening tester valve.
DST valve (tester valve) Opens and closes to initiate and end flow periods. Controlled from surface by drill string manipulation. Valve must close sharply to initiate pressure buildup - slow valve closure creates a ramp instead of a step in the pressure record, complicating analysis
Safety joint Allows the drill string above to be disconnected if the tool string becomes stuck in the hole Position above the packer - if string sticks, can disengage above the stuck point and fish later
Drill collar / HWDP section Provides weight to set and hold the packer in compression during test Minimum 3,000-5,000 lbs above packer setting force to maintain seal during test pressure differentials
Top gauge (memory or surface readout) Records pressure above the packer. Compares with bottom gauge to confirm packer integrity. If top and bottom gauges show same pressure during buildup: packer has failed and annular fluid is communicating with formation

2. DST Test Sequence Design

2.1 Standard Test Sequence - The IFO-ISIP-FFO-FSIP Pattern

A standard DST uses alternating flow and shut-in periods that provide redundant data and progressively better reservoir characterization:

Standard DST sequence:

1. Initial Flow Period (IFP) - 5-30 minutes
Purpose: Clean up wellbore fluids (drilling mud, kill fluid) ahead of reservoir fluid. Establish initial flow rate.
Decision criterion: Flow must stabilize before shutting in for ISIP

2. Initial Shut-In Period (ISIP) - 30-60 minutes
Purpose: Allow pressure to recover toward initial reservoir pressure (Pi). Provides first estimate of Pi and early indication of permeability.
Decision criterion: Pressure recovery must be >70% before IFP and ISIP are considered successful

3. Final Flow Period (FFP) - 4-24 hours (the critical period)
Purpose: Establish stabilized flow rate for deliverability calculation. Must be long enough to reach radial flow regime (infinite-acting radial flow) for valid permeability calculation.
Decision criterion: FFP must reach radial flow - confirmed by derivative analysis (see Section 3)

4. Final Shut-In Period (FSIP) - 4-24 hours (the analysis period)
Purpose: Pressure buildup for Horner analysis. Provides most accurate Pi, k, and skin calculation.
Decision criterion: FSIP should be at least equal to FFP duration for reliable extrapolation to Pi

2.2 Minimum Flow Period Duration - The Radial Flow Criterion

The most common DST design error is using an insufficiently long flow period that never reaches radial flow. In radial flow, the pressure at the well varies as the logarithm of time - this is the regime from which permeability is calculated. Before radial flow is established (wellbore storage dominated flow or transition), the pressure data cannot be used to calculate k:

Minimum time to end of wellbore storage (hours):
t_ws = 200,000 x C x mu / (k x h)

Where:
C = wellbore storage coefficient (bbl/psi) = Vwb x cf (wellbore volume x fluid compressibility)
mu = fluid viscosity (cp)
k = estimated permeability (md) - from analog wells or log-derived estimate
h = net pay thickness (ft)

Minimum time to establish radial flow (hours):
t_radial = 3,790 x phi x mu x ct x rw^2 / k

Example: phi = 0.18, mu = 1.2 cp, ct = 15 x 10^-6 psi^-1, rw = 0.35 ft, k = 50 md:
t_radial = 3,790 x 0.18 x 1.2 x 15e-6 x 0.35^2 / 50
= 3,790 x 0.18 x 1.2 x 15e-6 x 0.1225 / 50
= 3,790 x 3.969e-7 / 50 = 1.504e-3 / 50 = 3.0 x 10^-5 hours = 0.1 seconds

Radial flow onset is nearly instantaneous for this permeability. The minimum flow period is determined by wellbore storage, not by the radial flow onset. Use t_ws as the minimum FFP duration and ensure FSIP > FFP.

3. Pressure Transient Analysis - Extracting Reservoir Parameters

3.1 Horner Analysis - The Classic Buildup Method

The Horner plot is the standard method for analyzing pressure buildup data from a DST to calculate permeability (k), skin factor (S), and initial reservoir pressure (Pi):

Horner time ratio = (tp + dt) / dt

Where:
tp = producing time (hours) = duration of FFP
dt = shut-in time (hours) = time elapsed since well was shut in

Plot: Bottomhole shut-in pressure (Pws) on Y-axis vs log((tp + dt)/dt) on X-axis (time increases to the left on this plot)

On the straight-line portion of the Horner plot:
Slope m (psi/log cycle) = -162.6 x q x mu x Bo / (k x h)

Solving for permeability:
k (md) = -162.6 x q x mu x Bo / (m x h)

Where q = flow rate (STB/day), mu = viscosity (cp), Bo = FVF (RB/STB), h = net pay (ft)

Skin factor:
S = 1.1513 x [(P1hr - Pwf) / m - log(k / (phi x mu x ct x rw^2)) + 3.2275]

Where P1hr = pressure on the straight line extrapolated to dt = 1 hour, Pwf = flowing bottomhole pressure just before shut-in

Initial reservoir pressure Pi:
Pi = pressure at Horner time ratio = 1 (i.e., dt → infinity): Extrapolate the straight line to the Y-axis intercept at (tp + dt)/dt = 1

3.2 Worked Horner Analysis Example

DST data: q = 450 STB/day, tp = 8 hours, mu_oil = 1.8 cp, Bo = 1.25 RB/STB, h = 35 ft, phi = 0.18, ct = 12 x 10^-6 psi^-1, rw = 0.35 ft. Pwf at shut-in = 2,840 psi.

Horner plot data (selected points):

dt (hours) (tp+dt)/dt Pws (psi)
0.5 17.0 3,245
1.0 9.0 3,410
2.0 5.0 3,520
4.0 3.0 3,605
8.0 2.0 3,670

Slope from straight-line portion (dt = 1 to 4 hours):

Pressure change from (tp+dt)/dt = 9 to 3 (one log cycle): m = 3,605 - 3,410 = 195 psi/log cycle

Permeability:

k = -162.6 x 450 x 1.8 x 1.25 / (-195 x 35) = -162.6 x 1012.5 / (-6,825) = -164,531 / (-6,825) = 24.1 md

P1hr from straight line = 3,410 psi (at dt = 1 hr)

Skin factor:

S = 1.1513 x [(3,410 - 2,840) / 195 - log(24.1 / (0.18 x 1.8 x 12e-6 x 0.35^2)) + 3.2275]

= 1.1513 x [570/195 - log(24.1/2.721e-7) + 3.2275]

= 1.1513 x [2.923 - log(88,571,000) + 3.2275]

= 1.1513 x [2.923 - 7.947 + 3.2275] = 1.1513 x (-1.796) = S = -2.07

Interpretation: Negative skin (S = -2.07) indicates natural fractures or stimulation effect - the well is performing better than the Darcy skin model predicts. Pi extrapolated ≈ 3,720 psi.

4. Flow Rate and Deliverability Analysis

4.1 Productivity Index from DST Data

Productivity Index (PI, STB/day/psi) = q / (Pi - Pwf)

From the worked example:
PI = 450 / (3,720 - 2,840) = 450 / 880 = 0.511 STB/day/psi

Absolute Open Flow Potential (AOFP) = PI x Pi
AOFP = 0.511 x 3,720 = 1,901 STB/day maximum theoretical rate if Pwf = 0

More practically, maximum sustainable rate (at Pwf = bubble point or minimum BHP for artificial lift):
If bubble point = 1,200 psi and artificial lift limit = 1,500 psi:
q_max = 0.511 x (3,720 - 1,500) = 0.511 x 2,220 = 1,134 STB/day sustainable production rate

4.2 Deliverability Plot for Gas Wells

For gas wells, deliverability is expressed using the back-pressure equation (Rawlins-Schellhardt) because gas flow is not linear with pressure differential at high rates. The DST must include multiple flow rates at different choke sizes to define the deliverability curve:

Back-pressure equation (gas):
q = C x (Pi^2 - Pwf^2)^n

Where C = deliverability coefficient (Mscf/day/psi^2)^n, n = flow behavior index (0.5 to 1.0)
n = 1.0: Darcy (laminar) flow only
n = 0.5: Fully turbulent (non-Darcy) flow dominates

Determine C and n from log-log plot of q vs (Pi^2 - Pwf^2) using multi-rate DST data.
Slope of the straight line = n. Intercept at (Pi^2 - Pwf^2) = 1 gives C.

AOFP (gas) = C x Pi^(2n) (at Pwf = 0)

5. Flow Regime Identification - The Derivative Plot

5.1 Log-Log Diagnostic Plot

The log-log plot of pressure change (dP) and its logarithmic derivative (dP' = dP/d(ln(dt))) versus shut-in time is the most powerful diagnostic tool in modern pressure transient analysis. Each flow regime produces a characteristic slope on the derivative curve:

Flow Regime Derivative Slope Interpretation Reservoir Implication
Wellbore storage Unit slope (+1) dP and dP' parallel with slope = 1 Early time - compressibility of wellbore fluid dominates. No reservoir information yet.
Radial flow (infinite-acting) Zero slope (flat) dP' is horizontal - constant value The flat portion provides k x h from the level of the flat derivative: k x h = 70.6 x q x mu x Bo / dP'_level
Linear flow (fracture or channel) Half slope (+0.5) dP and dP' parallel with slope = 0.5 Flow channeled through a fracture or linear channel - natural fracture or hydraulic fracture present
Boundary (no-flow) Unit slope (+1) late time Derivative turns up after radial flow Closed boundary detected. Reservoir volume calculable from time of boundary effect.
Constant pressure boundary Negative slope, approaching -1 Derivative turns down after radial flow Aquifer support or gas cap - indicates reservoir pressure maintenance

6. Surface Testing Equipment - Handling the Wellstream

During the flow periods of a DST, formation fluid flows to surface and must be separated, measured, and disposed of safely. The surface test equipment must be designed for the anticipated maximum flow rate and fluid composition before the test begins:

Equipment Function Design Requirement
Choke manifold Controls flow rate by restricting flow through calibrated orifices Rated for maximum anticipated wellhead pressure. Multiple choke sizes to achieve target flow rates.
Test separator Separates gas, oil, and water for individual measurement and metering Sized for maximum anticipated GOR and flow rate. Rated pressure must exceed wellhead shut-in pressure.
Flare/burner boom Burns gas produced during the test - required when no sales pipeline connection is available Rated for maximum gas rate. Positioned downwind from rig. H2S gas requires special burner design.
Downhole shut-in tool Closes the DST valve at the bottom of the drill string to initiate the buildup period Must provide a sharp, instantaneous shut-in for clean pressure buildup signal. Surface shut-in creates afterflow that distorts early buildup data.

Conclusion

The Horner analysis in this article transforms three numbers - slope m = 195 psi/log cycle, flow rate q = 450 STB/day, pay thickness h = 35 ft - into permeability k = 24.1 md, skin S = -2.07, and initial pressure Pi = 3,720 psi. These three parameters fully characterize the reservoir's near-wellbore condition and answer the fundamental production engineering question: how much can this well produce, and is there near-wellbore damage restricting that production below its natural potential? The negative skin of -2.07 answers that question definitively - the well is not damaged, it is naturally fractured and performing above the Darcy model prediction. The decision to complete and produce this well rather than abandoning it is supported by quantitative evidence, not by interpretation of a flow test where "we saw oil at surface."

The derivative plot diagnoses what the Horner analysis cannot: whether the radial flow regime was reached (flat derivative), whether a fracture is present (half-slope), and whether a boundary was detected (upturn). A DST where the derivative never reaches a flat portion has not tested the reservoir - it has tested the wellbore storage. Designing DST flow periods long enough to reach and confirm radial flow is the single most important design decision for a test that will produce actionable data.

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