INSTRUCTOR 2017 John R Fanchi All rights reserved
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INSTRUCTOR © 2017, John R. Fanchi All rights reserved. No part of this manual may be reproduced in any form without the express written permission of the author.
To the Instructor The set of files here are designed to help you prepare lectures for your own course using the text Introduction to Petroleum Engineering, J. R. Fanchi and R. L. Christiansen (Wiley, 2017) File format is kept simple so that you can customize the files with relative ease using your own style. You will need to supplement the files to complete the presentation topics.
TRANSIENT WELL TESTING © 2017, John R. Fanchi All rights reserved. No part of this manual may be reproduced in any form without the express written permission of the author.
Outline Ø Pressure Transient Testing Ø Oil Well PTT Ø Flow Regime Analysis Ø PBU Test and Horner Analysis Ø Interpreting PB Tests Ø Radius of Investigation Ø Wellbore Storage and Skin Ø DST – Drill Stem Test Ø RFT – Repeat Formation Test Homework: IPE Ch. 12
PRESSURE TRANSIENT TESTING
Pressure Transient Testing Procedure Ø Change the flow of a well Ø Record pressure variation with time
Information Obtained from Tests Well Type Production Well Injection Well Ø Ø Ø Change in Flow Rate Decrease Increase Pressure Transient Test Pressure buildup Pressure drawdown Pressure falloff Injectivity Bulk formation permeability Amount of damage or stimulation Average reservoir pressure in the drainage area Estimate reservoir size Estimate location of boundaries
OIL WELL PTT
Common Flow Regimes
Mathematical Model Assumptions Ø Homogeneous and isotropic reservoir, e. g. , constant porosity, thickness, permeability Ø Production well is completed across entire formation thickness, ensuring radial flow Ø Single phase flow in the reservoir Ø Constant fluid viscosity Ø Slightly compressible fluid of constant compressibility Ø Small pressure gradients Ø Negligible gravity forces
Radial Flow Equation where p = pressure r = radial distance t = time c. T = total system compressibility
Applications of Radial Flow Equation Ø PTT uses solutions to radial flow equation Ø Assume constant flow rate. Ø Represent well as line source.
Diffusivity Equation for Single Phase Liquid Dimensionless radius and time where t = time, hr r = radial distance from well, ft k = permeability, md = porosity, fraction ct = total compressibility, 1/psia rw = wellbore radius, ft i = initial conditions
Line Source Solution Constant Terminal Rate Constant terminal rate line source solution for infinite acting reservoir is Exponential integral (Ei):
PRESSURE BUILDUP TEST AND HORNER ANALYSIS
Pressure Buildup Test Procedure Ø Flow the well at a stabilized rate q for a duration t. F. Ø Shut in the well for a duration t. Ø Record pressure vs. time t Ø Stabilized flowing time Ø Consider q as last rate prior to shutting in well Ø Note t. F + Δt is total time for ideal case Ø Real cases use t. F defined by
Pressure Buildup Test Image Well Concept Ø Well shut-in condition equivalent to use of image well Ø Original well flows at rate Q starting at time ∆t = 0 Ø Image well at same location flows at rate −Q starting at time t. F.
Superposition Principle Ø Total pressure change at a point in the reservoir is a linear sum of changes due to each well in the reservoir. Ø Implication Ø A pressure disturbance will propagate through the reservoir even if the source of the disturbance changes or disappears.
Pressure Buildup Analysis Ø Solution of diffusivity equation may be written in terms of dimensionless pressure PD as Ø p. WS is shut in pressure Ø p. D is a function of dimensionless time Ø Define dimensionless time t. D:
Pressure Buildup Analysis - cont. Ø Combining solutions for shut-in pressure of actual well and image well gives shut-in pressure of well
Horner Plot Ø Plot shut-in pressure vs Horner time on a semi-log plot
INTERPRETING PBU TESTS
Common Flow Regimes
Three Flow Periods Ø Assume Ø Pressure decline at well Ø Bounded circular reservoir Ø Constant flow rate Transient Flow Well Pressure Transitional Period (Late Transient) Semi-steady State Flow Time Pressure declines linearly with log(time) Pressure declines linearly with time
Flow Regimes Ø Steady State Ø Pressures do not change with time Ø dp/dt = 0 Ø Pseudosteady State Ø Pressure changes at a constant rate Ø dp/dt = constant Ø Transient State Ø Pressure changes at variable rate Ø dp/dt = f(t)
Steady State Flow Ø Mass flow rate is constant everywhere Ø Pressures do not change with time (dp/dt = 0)
Pseudo-steady State Flow Ø Wellbore and average reservoir pressure Ø change with time Ø change at the same, constant rate Ø Pressure changes at constant rate Ø dp/dt = constant Ø No fluid movement across boundaries Ø system is closed
Transient State Flow Ø Pressure changes with variable rate Ø dp/dt = f(t) Ø Unrestricted fluid movement
Diagnostic Log-Log Plot Ø Plot log ΔP vs. log Δt -- shape of P varies Ø Example log-log plot below Ø Partially Completed Well
“Rules of Thumb” for Interpreting Pressure Transient Tests Effect Wellbore Storage Spherical Flow Radial Flow Linear Flow Bilinear Flow Slope on Log-Log Plot Unit slope (rise 1/run 1) Negative half slope (drop 1/run 2) Zero slope (horizontal) Positive half slope (rise 1/run 2) Positive quarter slope (rise 1/run 4)
“Rules of Thumb” on Log-Log Plot Linear flow Positive half slope log d. P/d(ln ∆t) Radial flow Zero slope Spherical flow Negative half slope Wellbore storage Unit slope log Δt Plot log d. P/d(ln t) vs. log Δt ∆t = shut-in time
Real World Problems Ø Fracturing or wellbore damage or well fill-up affect the early time shapes of pressure buildup graph. Ø The drainage boundary or interference caused by production or injection from adjacent wells affect the long time shape of a pressure buildup graph.
Questions to Ask Ø Where is the correct straight line, if there is one in the available data? Ø Which type of pressure buildup graph should be used? Ø Can short-time pressure buildup data be used, if it is obtained before the semi-log straight line appears? Ø How do you design a proper well test so that useful information is obtained?
RADIUS OF INVESTIGATION
Applications of Solutions Ø Transient solution used to analyze Ø Ø Drawdown Buildup Injectivity Falloff tests Ø Pseudo-steady state solution used to analyze reservoir limit tests.
Radius of Investigation Ø Radius of investigation Ø Distance travelled by pressure transient away from wellbore in specified time. Ø Estimate radius of investigation assuming Ø Ø radial flow steady-state conditions infinite reservoir single-phase flow
Radius of Investigation - cont. where ri = radius of investigation, ft ∆t = shut in time, hr k = permeability, md = porosity, fraction μ = viscosity, cp ct = total compressibility, psia-1
WELLBORE STORAGE
Wellbore Storage Ø Definition Ø Synonyms Ø Wellbore pressure drops when well is first open to flow. Ø afterflow Ø First fluid production includes expansion of wellbore fluid due to wellbore pressure decline. Ø afterinjection Ø afterproduction Ø wellbore unloading Ø wellbore loading
Types of Wellbore Storage Ø Compressive Storage Ø Wellbore completely full of single-phase fluid Ø Changing liquid level Ø Occurs in production wells on pump or gas-lift Ø Occurs in injection wells taking fluid on vacuum Ø Observation Ø Wellbore storage from changing liquid level usually much larger than compressive storage.
Wellbore Storage Ø Early-time pressure data that is dominated by wellbore storage is given by P = (κ/C)t Ø Proportionality constant κ and wellbore storage coefficient C are independent of time. ØDiagnostic Analysis ØCalculate time derivative -- find d. P/dt = κ /c. ØPlot log P vs. log t -- find line with unit slope. ØExample ØP = κ(C)t implies log P = log t + log (κ /C)
SKIN
Skin Effect Ø Actual flowing wellbore pressures less than pressures predicted by radial flow when the wellbore is damaged. Ø Additional pressure drop is proportional to rate Ø Can be thought of as a “zone” of reduced permeability around the well bore. Ø This “zone” of reduced permeability has negligible thickness and is called “skin. ” Ø The resulting effect is called the “skin effect. ”
Skin Factor Ø Skin factor is a dimensionless constant, S, which relates the pressure drop in the skin to the flow rate: Ø Normally, -5 <S < 50; hence: Pactual = Pline source + Pskin Ø Note Ø If S > 0 implies damage Ø If S = 0 implies no damage Ø If S < 0 implies stimulation
Well PI with Skin for Radial, Single-Phase Liquid Flow From Darcy’s law for steady-state, radial, horizontal, single -phase liquid flow in a porous medium: PI μℓ Bℓ re rw S ke krℓ kabs hnet = = = = = productivity index (STB/D/psi) viscosity of phase ℓ (cp) FVF of phase ℓ (RB/STB) drainage radius (ft) wellbore radius (ft) dimensionless skin effective permeability (md) = krℓ kabs relative permeability of phase ℓ absolute permeability (md) net thickness (ft)
Skin and Flow Efficiency Ø Flow Efficiency with skin where P = average reservoir pressure in the drainage area.
DST – DRILL STEM TEST
Drill Stem Testing A DST is an economical well evaluation method. Ø Primary Purpose Ø determine well productivity Ø recover formation fluid samples Ø estimate reservoir pressure Ø measure formation permeability Ø Secondary Purpose Ø estimate transmissibility Ø detect barriers, e. g. , faults, pinchouts Ø assess wellbore damage
Drill Stem Testing - cont. Initial Flow and relatively short duration Shut-in Period remove mud filtrate near wellbore Second Flow and relatively long duration Shut-in Period easier to analyze than initial flow and shut-in data A DST is a pressure buildup test.
Drill Stem Testing Horner Analysis Ø Assume Ø Ø radial flow steady-state conditions infinite reservoir single-phase flow radial flow
Drill Stem Testing Horner Equation Solve where pf = formation pressure during buildup, psig p 0 = shut-in reservoir pressure, psig q = rate of flow, STB/D μ = fluid viscosity, cp B = formation volume factor, RB/STB k = permeability, md h = net productive zone, ft t. P = flowing time, min ∆t = shut-in time, min
Drill Stem Testing Horner Analysis - Some Observations Ø Flowing time t. P to use in Horner time (tp + ∆t) / ∆t should be the sum of initial and final flow periods. Ø Production rate should be the average rate measured during the final flow period.
Drill Stem Testing Horner Interpretation Ø The Horner equation is a straight line on semilog paper
Drill Stem Testing Horner Analysis - More Observations Ø Wellbore storage effects should be minimal because of bottom hole shut-in. Ø Extrapolation of semilog straight line to P* gives a usually reliable estimate of initial reservoir pressure Ø unless the reservoir is small relative to the amount of fluid withdrawn during the DST.
RFT – REPEAT FORMATION TEST
Repeat Formation Test Ø Primary Purpose Ø measure vertical pressure distribution Ø Secondary Purpose Ø recover formation fluid samples Ø measure formation permeability Ø Standard RFT obtained using open hole wireline tool. Ø Spherical pressure buildup followed by cylindrical buildup.
QUESTIONS?
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