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**SPE 56487 Analysis and Interpretation of**

Well Test Performance at Arun Field, Indonesia Authors: T. Marhaendrajana, Texas A&M U. N.J. Kaczorowski, ExxonMobil (Indonesia) T.A. Blasingame, Texas A&M U.

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Summary A comprehensive field case history of the analysis and interpretation of well test data from the Arun Gas Field (Sumatra, Indonesia). 2-zone radial composite reservoir model is effective for diagnosing the effects of conden-sate banking at Arun Field.

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Summary Development and application of a new solution for the analysis and interpretation for wells that exhibit "well interference" effects.

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**Outline Introduction Well Test Analysis Strategy Multiwell Model**

Regional Pressure Decline Analysis Procedure Field Example Conclusions

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**Arun Field N Field Description**

Located in Northern part of Sumatra, Indonesia Retrograde gas reservoir One of the largest gas fields in the world Arun Field has 111 wells: 79 producers 11 injectors 4 observation wells 17 wells have been abandoned N

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**Major Phenomena in Arun**

Liquid accumulation near wellbore (conden-sate banking) Need to know radial extent of condensate banking for the purpose of well stimulation. Well interference effect This well interference effect tends to obscure the radial flow response, and hence, influence our analysis and interpretation efforts.

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**Well Test Analysis Strategy**

Condensate banking phenomenon 2-zone radial composite reservoir model is used, where the inner zone represents the "condensate bank," and the outer zone represents the "dry gas reservoir." (Raghavan, et al, (1995) and then by Yadavalli and Jones (1996) ) Well interference effect Developed a new method for the analysis of well test data from a well in multiwell reservoir where we treat the "well interference" effect as a "Regional Pressure Decline."

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Multiwell Model Bounded Reservoir with Multiple Wells

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**Analytical Solution Matches Numerical Solution**

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**Regional Pressure Decline Model**

Issues: Arun Field has been produced for over 20 years and currently in "blowdown" mode. Drawdown and buildup tests induce local transient effects. Most of the well tests performed at Arun Field are relatively short (< 5 hours producing time), and the pseudosteady-state flow condition is not established in the area of investigation given such short produc-tion times.

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**Regional Pressure Decline Model**

Assumptions: All of the wells in the reservoir are at pseudosteady-state flow conditions at the time the "focus" well is shut-in. Any rate change at the focus well (including a drawdown/buildup sequence) cause transient flow conditions only in the vicinity of the focus well–not in the entire reservoir.

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**Regional Pressure Decline Model**

Pressure at focus well: where:

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**Regional Pressure Decline Model**

Pressure buildup analysis relations: Vs. Straight line on semilog plot

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**Regional Pressure Decline Model**

Pressure buildup analysis relations: Vs. Straight line on Cartesian plot

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**Simulated Case Rate, q Time, t Offset wells are kept**

Focus well is shut-in Offset wells are kept on production. Offset wells are produced at the same flowrate. Focus well is shut-in Rate, q Focus well is put on production Time, t

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**Multiwell Response is Different than Single Well Response**

pbar continues to decline. Pressure builds up to pbar (closed boundary) psD' [pws - pwf(Dt=0)] format DtDA

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**Straight Line on Cartesian Plot**

psDe' = p(aD - 1) DtDA2/ DtDAe psDe' = 0.5 psDe' [pws - pwf(Dt=0)] format DtDA2/ DtDAe

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**Regional Pressure Decline Signature May Not Be Unique**

This portion may be falsely interpreted as regional pressure decline effect. psDe' = p(aD - 1) DtDA2/ DtDAe psDe' = 0.5 psDe' [pws - pwf(Dt=0)] format DtDA2/ DtDAe

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**Analysis Procedures for Multiwell Reservoirs**

To analyze pressure buildup tests taken in multiwell systems, we recommend the following procedures: Step 1: Plot Dte(dpws/dDte) versus Dt2/Dte on a Carte-sian scale. From the straight-line trend we obtain the slope mc and intercept bc. We calculate permeability using the intercept term as:

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**Analysis Procedures for Multiwell Reservoirs**

Step 2: The Horner plot [(pws+mcDt) versus log((tp+Dt)/Dt)] can also be used to estimate formation properties. From the straight-line trend observed on the Horner plot, we obtain the slope msl as well as the intercept term, (pws + mcDt) Dt=1hr. Permeability is estimated using: And the skin factor is calculated using:

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**Analysis Procedures for Multiwell Reservoirs**

Step 3: In order to use standard single-well type curves for type curve matching, we must make the appropriate "corrections". These relations are: Pressure function: Pressure derivative function:

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**[Test Date: 28 September 1992]**

Well C-I-18 (A-096) [Test Date: 28 September 1992] Infinite acting Reservoir Model (Does not include non-Darcy flow) Improvement on pressure derivative. Pseudopressure Functions, psi Condensate banking region. Higher mobility region. Closed boundary at 160 ft? (includes non-Darcy flow). Effective shut-in pseudotime, hrs

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**[Test Date: 28 September 1992]**

Well C-I-18 (A-096) [Test Date: 28 September 1992] Condensate banking region. Higher mobility region. Shut-in Pseudopressure, psia Horner pseudotime, hrs (tp = 1.56 hr)

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**[Test Date: 28 September 1992]**

Well C-I-18 (A-096) [Test Date: 28 September 1992] pp,bar = psia Data deviate from the "Muskat line" --indicating an interference effect from surrounding wells. Onset of boundary dominated flow. Shut-in pseudopressure, psia "Transient flow" dppws/dDta, psi/hr

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**[Test Date: 28 September 1992]**

Well C-I-18 (A-096) [Test Date: 28 September 1992] (Dpp')Dtae, psi Dta2/ Dtae

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**Example 3: Log-log Summary Plot**

Well C-IV-11 (A-084) [Test Date: 5 January 1992] Raw data Corrected Improvement on pressure derivative. Pseudopressure Functions, psi Closed boundary at 150 ft? (includes non-Darcy flow). Infinite-acting Reservoir Model (Does not include non-Darcy flow) Effective shut-in pseudotime, hrs

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**Example 3: Horner (Semilog) Plot**

Well C-IV-11 (A-084) [Test Date: 5 January 1992] Shut-in Pseudopressure, psia Raw data Corrected Horner pseudotime, hrs (tp = 1.62 hr)

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**Example 3: Muskat Plot (single well pavg plot)**

Well C-IV-11 (A-084) [Test Date: 5 January 1992] pp,bar = 1920 psia Onset of boundary dominated flow. Shut-in pseudopressure, psia "Transient flow" dppws/dDta, psi/hr

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**Example 3: "Well Interference" Plot (radial flow only)**

Well C-IV-11 (A-084) [Test Date: 5 January 1992] Intercept is used to calculate permeability. Slope is used in the pressure correction. (Dpp')Dtae, psi Presence of multiwell interference effects is unclear Dta2/ Dtae

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**Example 4: Log-log Summary Plot**

Well C-IV-11 (A-084) [Test Date: 4 May 1992] Raw data Corrected Improvement on pressure derivative. Pseudopressure Functions, psi Condensate banking region. Infinite-acting Reservoir Model (Does not include non-Darcy flow) Closed boundary at 197 ft? (includes non-Darcy flow). Higher mobility region. Effective shut-in pseudotime, hrs

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**Example 4: Horner (Semilog) Plot**

Well C-IV-11 (A-084) [Test Date: 4 May 1992] Condensate banking region. Shut-in Pseudopressure, psia Higher mobility region. Raw data Corrected Horner pseudotime, hrs (tp = 1.63 hr)

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**Example 4: Muskat Plot (single well pavg plot)**

Well C-IV-11 (A-084) [Test Date: 4 May 1992] pp,bar = psia Onset of boundary dominated flow. Shut-in pseudopressure, psia "Transient flow" dppws/dDta, psi/hr

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**Example 4: "Well Interference" Plot (radial flow only)**

Well C-IV-11 (A-084) [Test Date: 4 May 1992] Intercept is used to calculate permeability. Slope is used in the pressure correction. (Dpp')Dtae, psi (Dpp')Dtae >0, no clear indication of multiwell interference effects. Dta2/ Dtae

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**kh Map kh distribution ap-pears reasonable.**

3 major "bubbles" of kh noted, pro-bably erroneous. kh shown is for the "outer" zone (when the radial compo-site model is used). kh Map

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**D (Non-Darcy) Map This map indicates a uniform distribution.**

"high" and "low" regions appear to be focused near a single well. Relatively small data set (30 points). D (Non-Darcy) Map

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Condensate Radius Map Good distribution of values—"high" spots probably indicate need for individual well stimulations. Relatively small data set (32 points).

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**D (Non-Darcy)—kh Crossplot**

D-kh crossplot indi-cates an "order of magnitude" correla-tion. Verifies that non-Darcy flow effects are systematic. Slope = 2

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Conclusions The new "multiwell" solution has been successfully derived and applied for the analysis of well test data taken from a multiwell reservoir system. The appearance of "boundary" effects in pressure buildup test data taken in multiwell reservoirs can be corrected using our new approach. Care must be taken so as not to correct a true "closed boundary" effect.

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Conclusions The 2-zone radial composite reservoir model has been shown to be representative for the analysis and interpretation of well test data from Arun Field (most of the wells exhibit radial composite reservoir behavior).

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Conclusions The effect of non-Darcy flow on pressure buildup test analysis seems to be minor for the wells in Arun Field. Although not a focus of the present study, our analysis of the pressure drawdown (flow test) data appear to be much more affected by non-Darcy flow effects.

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**SPE 56487 Analysis and Interpretation of**

Well Test Performance at Arun Field, Indonesia Authors: T. Marhaendrajana, Texas A&M U. N.J. Kaczorowski, ExxonMobil (Indonesia) T.A. Blasingame, Texas A&M U.

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**The "Regional Pressure Decline" Improves The Derivative**

tpDA=10-5 tpDA=10-4 tpDA=10-3 Shut-in time tpDA=10-2 Dim. Pressure Derivative Functions Agarwal eff. shut-in time DtDA or DtDAe

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**psD or psDc [pws - pwf(Dt=0)] format**

tpDA=10-5 tpDA=10-3 tpDA=10-2 tpDA=10-4 psD or psDc [pws - pwf(Dt=0)] format MDH Agarwal effective time DtDA or DtDAe

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