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**Well Testing — Historical Perspectives**

Petroleum Engineering 613 Natural Gas Engineering Texas A&M University Lecture 08: Well Testing — Historical Perspectives T.A. Blasingame, Texas A&M U. Department of Petroleum Engineering Texas A&M University College Station, TX — PETE 613 (2005A)

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**Well Testing — Historical Perspectives**

Origin of the "Deliverability" (or Backpressure) Relation Empirical. Used to assess "open flow" potential of gas wells. Does not provide a "time-dependent" behavior. Multi-Rate Testing Historically, VERY popular — still used quite often, especially on new wells to estimate deliverability and "non-Darcy" flow effects. Keep it simple — a "4-point" test is appropriate. Isochronal testing is very difficult to implement. Pressure Transient Analysis Expected Results: Pressure Transient Analysis (PTA). Example Data Sets: PTA and Production data. Basic Plots: Lee Text Example 2.2 (Pressure Buildup). PETE 613 (2005A)

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**Origin of the "Deliverability" Relation**

Well Testing — Historical Perspectives Origin of the "Deliverability" (or Backpressure) Relation PETE 613 (2005A)

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**History of the "Deliverability" Equation**

Gas Well Deliverability: The original well deliverability relation was completely empiri-cal (derived from observations), and is given as: This relationship is rigorous (i.e., it can be derived) for low pres-sure gas reservoirs, (n=1 for lami-nar flow). From: Back-Pressure Data on Natural-Gas Wells and Their Application to Production Practices — Rawlins and Schellhardt (USBM Monograph, 1935). PETE 613 (2005A)

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**Well Testing — Historical Perspectives**

Multi-Rate Testing Well Testing — Historical Perspectives Multi-Rate Testing PETE 613 (2005A)

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**Deliverability Testing: Basics**

a. "Standard" 4-point test deliverability test — note that the rates increase (to protect the reservoir). c. Modified "Isochronal" test sequence — note that each "buildup" is not required to achieve pi. b. "Isochronal" test sequence — note that each "buildup" is required to achieve pi. d. Governing equations for "deliverability" test analysis/interpretation. PETE 613 (2005A)

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**Deliverability Testing: Orientation**

a. Basic "pressure-squared" relation that is presumed to describe gas flow — analogous form can be derived from steady-state flow theory (Darcy's law). b.Traditional "deliverability" plot — probably derived from empirical plotting of data. PETE 613 (2005A)

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**Deliverability Testing: Orientation**

a."Rate-squared" (or velocity-squared) formulation — analogous form can be derived from steady-state flow theory (Forchheimer Eq.). b. Modified "deliverability" plot — note that bqsc2 must be known (... need alternative approach). PETE 613 (2005A)

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**Origin of the "Deliverability" Relation**

Well Testing — Historical Perspectives Expected Results: Pressure Transient Analysis (PTA) Production Analysis (PA) PETE 613 (2005A)

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**Expected Results from PTA**

Expected Results of Pressure Transient Analysis (PTA): "Conventional" PTA: Use of semilog and other specialized plots to estimate reservoir properties from a particular "flow regime" (i.e., a flow regime is a characteristic behavior derived from an analytical solution — e.g., the constant pressure derivative function for infinite-acting radial flow (IARF)). Examples of other specialized plots: square-root and fourth-root of time plots for fractured wells. "Model-based" analyses: Using analytical/numerical reservoir models to perform simultaneous analysis/modelling procedures. Provides estimates of dynamic formation properties: (i.e., model parameters) Radial Flow: k, S, CD Fractured Wells: k, xf, FCD, CfD Horizontal Wells: kr, kr/kv, hwell, (effective length) zw (position), ChD Dual porosity reservoir properties: w, l Data Requirements/Assessment/Review: Typically involves very accurate measurements of bottomhole pressures (this is a priority). Rate history is most often the weakest link — must perform "due diligence" and obtain the best possible rate history. Should use downhole shut-in device to minimize wellbore storage. PETE 613 (2005A)

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**Expected Results from PA**

Expected Results of Production Analysis (PA): "Conventional" decline curve analysis: (Arps, etc.) — empirical relations used to provide estimates of recovery and forecasts of future performance. "Model-based" analyses: Using analytical/numerical reservoir models to perform simultaneous analysis/modelling procedures. Provides estimates of dynamic formation properties (k, S, xf, dual porosity properties, etc.) "Model-based" forecasting: A direct extension of model-based analysis — generation of a time-dependent pressure and/or rate forecast. Data Requirements/Assessment/Review: Are production data available? (BOTH rates and PRESSURES!) Is the well completion history available? (review for issues) PVT and static reservoir properties? (must be assessed/included) Is the production "analyzable?" (can major issues be resolved?) PETE 613 (2005A)

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**PTA and PA Data Quality and Data Artifacts**

Well Testing — Historical Perspectives Reservoir Performance Analysis: PTA and PA Data Quality and Data Artifacts PETE 613 (2005A)

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**Production Data: Example 1**

Production Example 1: Sewell Ranch No. 1 (North Texas (US)) Rate and pressure data affected by water loading. Late-time data affected by line pressure (other wells in flow system). PETE 613 (2005A)

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**Production Data: Example 2**

Production Example 2: UPR22 Gas Well (Mid-Continent (US)) Rate and pressure data affected by fluid loading. Seasonal cycles in demand/production. PETE 613 (2005A)

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**Pressure Transient Data: Example 1**

a. No Rate History: (Dt format) Pressure drop and pressure drop derivative versus shut-in time (Bourdet (SPE 12777)). b. Rate History: (Dte format) Pressure drop and pressure drop derivative versus Agarwal superposition time (Bourdet (SPE 12777)). Pressure Transient Example 1: Bourdet (SPE 12777) Production history effects are obvious. Interpretation should consider "no rate" and "rate" history cases. PETE 613 (2005A)

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**Pressure Transient Data: Example 2**

Pressure Transient Example 2: DaPrat (SPE 13054) Dual porosity/naturally fractured reservoir (PSS interporosity flow). Illustrates the sensitivity of the pressure derivative function. PETE 613 (2005A)

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**Data Artifacts: Example 1**

Data Artifacts Example 1: Womack Hill Field (Alabama (US)) Note the various events (value of annotated production records). No pressure data (typical). PETE 613 (2005A)

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**Data Artifacts: Example 2**

Data Artifacts Example 2: Told Well 3 (Colombia) pwf NOT synchronous with qo (pwf from fluid levels). Note that effect of pump change is captured by pwf and qo. PETE 613 (2005A)

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**Data Artifacts: Example 3**

Data Artifacts Example 3: Canada Gas Well pwf NOT synchronous with qg at early/intermediate times. Dispersion in pwf at middle times not reflected in the qg function. PETE 613 (2005A)

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**Data Artifacts: Example 4**

Data Artifacts Example 4: Southeast TX Gas Well (US) Multiple completion changes. Issues related to pressure profile — measure bottomhole pressure? PETE 613 (2005A)

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**Data Artifacts: Example 5**

a. Semilog Plot: (Dt format) Pressure versus shut-in time (South Texas Gas Well (US)) — Packer leak (most likely cause). b. Log-log Plot: (Dt format) Pressure drop and pressure drop derivative versus shut-in time time (South Texas Gas Well (US)) — Packer leak (most likely cause). Data Artifacts Example 5: South Texas Gas Well (US) Gas well with anomalous pressure "jump" — packer leak? No "reservoir" mechanism (other than injection) could produce feature. PETE 613 (2005A)

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**Data Artifacts: Example 6**

Data Artifacts Example 6: Mid-Continent Gas Well (US) Changing wellbore storage and condensate banking (very high skin). Interpretation depends on understanding of reservoir and fluids. PETE 613 (2005A)

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**Well Test Analysis — Basic Plots**

Well Testing — Historical Perspectives Well Test Analysis — Basic Plots PETE 613 (2005A)

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**Well Test Analysis: Basic Plots (Lee Text Example)**

a. Log-log "preliminary analysis" plot — wellbore storage and radial flow (Cs, k). b. Cartesian "early-time" plot — used to analyze wellbore storage (p0, Cs). c. Cartesian "Arps" plot — used to estimate average reservoir pressure. d. Semilog "middle-time" plot — used to analyze radial flow behavior (k, s). e. Horner "middle-time" plot — used to analyze radial flow behavior (k, s, p*). f. Log-log "summary" plot — summary of all analysis (Cs, k, s, A, etc). PETE 613 (2005A)

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**Basic Plots: "Preliminary" Log-log Plot**

Pressure drop function does not give much resolution. Pressure drop derivative function shows wellbore storage/radial flow. PETE 613 (2005A)

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**Basic Plots: Early Cartesian Plot**

Used to estimate wellbore storage coefficient (slope of trend). Pressure at start of the test estimated from extrapolation. PETE 613 (2005A)

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**Basic Plots: Late Cartesian Plot (PBU)**

Basic Plots: Late Cartesian Plot (Pressure Buildup) NOT a universally valid plot (ONLY valid for very late times). Average reservoir pressure estimated from extrapolation. PETE 613 (2005A)

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**Basic Plots: Semilog Plot (MDH)**

Basic Plots: Semilog Plot (Miller-Dyes-Hutchinson) NOT corrected for rate history. Can be difficult to interpret (semilog straight line needs orientation). PETE 613 (2005A)

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**Basic Plots: Horner Semilog Plot**

CORRECTED for rate history. Used to estimate permeability, skin factor, average reservoir pressure. PETE 613 (2005A)

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**Basic Plots: "Summary" Log-log Plot**

Used to show simulated reservoir response (based on analysis). Multiple data functions used to orient analysis/interpretation. PETE 613 (2005A)

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**Module 4: Well Test Analysis — Work Relations**

Given data — Lee text (1st edition), Example 2.2. Working relations — Lee text (1st edition), Example 2.2). PETE 613 (2005A)

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**Well Testing — Historical Perspectives**

Petroleum Engineering 613 Natural Gas Engineering Texas A&M University Lecture 08: Well Testing — Historical Perspectives (End of Lecture) T.A. Blasingame, Texas A&M U. Department of Petroleum Engineering Texas A&M University College Station, TX — PETE 613 (2005A)

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