(Formation Evaluation and the Analysis of Reservoir Performance) Module for: Analysis of Reservoir Performance Introduction T.A. Blasingame, Texas A&M U. Department of Petroleum Engineering Texas A&M University College Station, TX 77843-3116 (979) 845-2292 t-blasingame@tamu.edu Introduction Analysis of Reservoir Performance Slide 1
Executive Summary Module Summary The overall objective of this module is to familiarize the student with the modern methods for the analysis, interpretation, and modelling (rate/pressure prediction) of hydrocarbon reservoir systems. Module Structure: Module 1: Introductory Concepts History of data analysis, phase behavior, flow concepts. Module 2: Material Balance/Late-Time Flow Behavior Material balance methods and gas flow models. Module 3: Wellbore Phenomena/Near-Well Behavior Module 4: Well Test Analysis Deliverability and well test analysis, well test design. Module 5: Analysis of Production Data Data acquisition, decline curves, EUR, decline type curves. Introduction Analysis of Reservoir Performance Slide 2
Executive Summary Module Objectives Course Objectives: (the student should be able to...) Derive the steady-state and pseudosteady-state flow equations for horizontal linear and radial flow of liquids and gases (including the pseudopressure and pressure-squared formulations). Sketch pressure versus time and pressure versus distance trends for a reservoir system exhibiting transient, pseudosteady-state, and steady-state flow behavior. Derive the "skin factor" variable from the steady-state flow equation and be able to describe the conditions of damage and stimulation using this variable. Define and use dimensionless variables and dimensionless solutions to illustrate the generic performance of a particular reservoir model. Derive the analysis and interpretation methodologies (i.e., "conventional plots" and type curve analysis) for pressure drawdown and pressure buildup tests, for liquid, gas, and multiphase flow systems. This effort should include the use of pseudopressure and pseudotime concepts for the analysis of well test and production data from dry gas and solution-gas drive oil reservoir systems). Apply dimensionless solutions ("type curves") and field variable solutions ("specialized plots") for the following "well test" cases: unfractured and fractured wells in infinite and finite-acting, homogeneous and dual porosity reservoirs. Design and implement a well test sequence, as well as a long-term production/injection surveillance program. Analyze production data (rate-time or pressure-rate-time data) to obtain reservoir volume and estimates of reservoir properties for gas and liquid reservoir systems. Also be able to predict production performance using simplified solutions. Demonstrate the capability to integrate, analyze, and interpret well test and production data to characterize a reservoir in terms of reservoir properties and performance potential (field study project). Introduction Analysis of Reservoir Performance Slide 3
Module 1: Introductory Concepts History of Data Analysis Correlation plots cumulative-ip, rate-time, etc. Rate-time correlations (log-log, semilog, etc.). Arps rate-time relations (exponential/hyperbolic). Phase Behavior Gas z-factor (Standing-Katz correlation plot(s)). Gas compressibility. Gas viscosity. Fundamentals of Fluid Flow in Porous Media General form of the gas diffusivity equation. Pseudopressure-pseudotime form. Pressure-squared form. Pseudotime and pressure-squared criteria plots. Introduction Analysis of Reservoir Performance Slide 4
Module 1: History of Data Analysis Data Plots a. From: Manual for the Oil and Gas Industry Arnold (1919). Production decline analysis: Over 80 years old! Objective was economic, not technical production extrapolations were even referenced to the tax year! Very humble origins "whatever worked" plots seemed to be popular (e.g., Cartesian, log-log, and semilog). b.from: Estimation of Underground Oil Reserves by Oil-Well Production Curves Cutler (1924). Introduction Analysis of Reservoir Performance Slide 5
Module 1: History of Data Analysis Rate Plots a. The "engineer's solution" (i.e., the log-log plot this plot did not stand the test of time). b.the "gee it works" plot "I wonder if there is some theory?"... (yes). From: Estimation of Underground Oil Reserves by Oil-Well Production Curves Cutler (1924). c. The "scratch your head" plot... interesting, but... how does it work? Introduction Analysis of Reservoir Performance Slide 6
Module 1: History of Data Analysis Arps Relations a. From: SPE-Transactions Arps (1944). "Arps" rate decline analysis: Introduction of exponential and hyperbolic families of "decline curves" (Arps, 1944) Introduction of log-log "type curve" for the "Arps" family of "decline curves" (Fetkovich, 1973). Empirical... but seems to work as a general tool. Is this more coincidence or theory? (... theory) b.from: SPE 04629 Fetkovich (1973). Introduction Analysis of Reservoir Performance Slide 7
Module 1: Phase Behavior z-factor (SK-data) a. SK base plot (z vs. p pr ) Poettmann-Carpenter Data (5960 data points). b. SK "revised" plot (z vs. p pr /T pr ) Poettmann- Carpenter Data (5960 data points). c. SK "revised" plot (z vs. ρ pr ) Poettmann- Carpenter Data (5960 data points). z-factor (SK-data): z vs. p pr original Standing-Katz (SK) formulation (data only). z vs. p pr /T pr "modified" Standing- Katz formulation (data only). z vs. ρ pr "modified" Standing-Katz formulation (data only). This serves as the basis for later reduced density correlations (development of an equation of state (EOS)). Introduction Analysis of Reservoir Performance Slide 8
Module 1: Phase Behavior z-factor (DAK-EOS) a. SK base plot (z vs. p pr ) Original Dranchuk- Abou-Kassem data fit (DAK-EOS). b. SK "revised" plot (z vs. p pr /T pr ) Original Dranchuk-Abou-Kassem data fit (DAK-EOS). c. SK "revised" plot (z vs. ρ pr ) Original Dranchuk- Abou-Kassem data fit (DAK-EOS). z-factor (DAK-EOS): z vs. p pr Original Dranchuk-Abou- Kassem data fit (DAK-EOS). z vs. p pr /T pr "modified" Standing- Katz formulation, original Dranchuk- Abou-Kassem data fit (DAK-EOS). z vs. ρ pr "modified" Standing-Katz formulation, original Dranchuk- Abou-Kassem data fit (DAK-EOS). Introduction Analysis of Reservoir Performance Slide 9
Module 1: Phase Behavior Gas Compressibility a. Definition of gas compressibility. b. Definition of reduced gas compressibility. d. "Reduced compressibility" plot (c r vs. p pr, 1.4< T pr <3.0) Mattar, Brar, and Aziz (1975). c. "Reduced compressibility" plot (c r vs. p pr, 1.05< T pr <1.4) Mattar, Brar, and Aziz (1975). Gas Compressibility "Reduced compressibility" concept is used to correlate data. c r function is computed using the Dranchuk-Abou-Kassem EOS convenient analytical form. Introduction Analysis of Reservoir Performance Slide 10
Module 1: Phase Behavior Gas Viscosity a. Jossi, et al plot pure component data. Note the correlation with ρ r. b.jossi, et al plot various data. Note the corelation with ρ r. c. Jossi, et al plot database. Note the temperature (T r ) dependance. Correlations must be created using ρ r and T r. From: The Viscosity of Pure Substances in the Dense Gaseous and Liquid Phases Jossi, Stiel, and Thodos (1962). Introduction Analysis of Reservoir Performance Slide 11
Module 1: Phase Behavior Gas Viscosity a. Jossi, et al revised correlation for gas viscosity. c. New correlation for gas viscosity. New Gas Viscosity Correlation: b. Lee, et al revised correlation for gas viscosity. Introduction Analysis of Reservoir Performance Slide 12
Module 1: Fundamentals of Fluid Flow in Porous Media a. General definition of the gas diffusivity equation. d. Illustration of the pressure-squared criteria. b. Pseudopressure-pseudotime form of the gas diffusivity equation. c. Pressure-squared form of the gas diffusivity equation. e. Illustration of the pseudotime criteria. Introduction Analysis of Reservoir Performance Slide 13
Module 2: Material Balance Gas Material Balance Dry gas reservoir systems. Water drive gas reservoir systems. "Abnormally-pressured" gas reservoir systems. Generalized gas material balance equation. Late-Time Flow Behavior Simplified flow behavior (empirical relations). Exponential decline (liquid flow solution). Simplified (approximate) gas flow relation. Introduction Analysis of Reservoir Performance Slide 14
Module 2: Late-Time Flow Behavior a. Simplified flow behavior (empirical relations (Arps)). b. Exponential decline (liquid flow solution, constant p wf case). d. Log-log "type curve" Arps rate relations. c. Simplified (approximate) gas flow relation (valid for p i <6000 psia, constant p wf case). e. Log-log "type curve" simplified (approximate) gas flow relation. Introduction Analysis of Reservoir Performance Slide 15
Module 2: Gas Material Balance Concepts a. Material balance concept for a dry gas reservoir with water influx and pore/water compressibility. c. Illustration of the "pore collapse concept for p/z data (Fetkovich, et al (SPE 22921)). b. Illustration of the "pore collapse concept (Fetkovich, et al (SPE 22921)). d. Field analysis using generalized material balance relation (Fetkovich, et al (SPE 22921)). Introduction Analysis of Reservoir Performance Slide 16
Module 2: Gas Material Balance Relations a. Material balance relation for a dry gas reservoir. b. Generalized material balance relation (Dake). c. Generalized material balance relation (Fetkovich, et al (SPE 22921)). (Warning) Do not use statistical methods (e.g., regression analysis) as the sole mechanism to solve material balance problems physically inconsistent parameter estimates are likely. Introduction Analysis of Reservoir Performance Slide 17
Module 3: Wellbore Phenomena/Near-Well Behavior Calculation of Bottomhole Pressures General relation (energy balance) Static (non-flowing) bottomhole pressure (dry gas). Flowing bottomhole pressure (dry gas). Near-Well Reservoir Flow Behavior Steady-state "skin factor" concept used to represent damage or stimulation in the near-well region. "Variable" skin effects: non-darcy flow, well cleanup, and gas condensate banking. Introduction Analysis of Reservoir Performance Slide 18
Module 3: Calculation of Bottomhole Pressure a. Basic energy balance for flow in inclined pipes. b. Solution assuming average T and z-values. d. Schematic illustration of wellbore configuration. c. Cullender-Smith solution of the energy balance. e. Wellbore diagram surface pressure measurement. Introduction Analysis of Reservoir Performance Slide 19
Module 3: Near-Well Behavior Skin Concept a. Simple skin concept steady-state flow of a liquid in the "altered" zone. b. Governing relations for steady-state flow of a liquid in the "altered" zone (k s =permeability in the "altered" zone). c. Schematic pressure behavior in a "steady-state" skin zone. Introduction Analysis of Reservoir Performance Slide 20
Module 3: Extensions of the Skin Concept a. Concepts of "infinitesimal" skin as well as use of the effective wellbore radius these schematics seek to represent the concept of "skin" as a physical phenomena, as well as a (simple) mathematical model. b. 2-zone, radial "composite" model (condensate bank). Skin Concept Generally speaking, use of the skin concept (or skin "factor") tends to "isolate" pressure behavior that cannot be directly attributed to the reservoir. This is an oversimplification, but it is convenient, and is widely used. Introduction Analysis of Reservoir Performance Slide 21
Module 4: Well Test Analysis Orientation This module will focus specifically on the analysis and interpretation of deliverability test data and pressure transient test data. The issues must be clear: test design, data acquisition/data quality control, and test execution are critical activities. Deliverability Testing: Keep it simple a "4-point" test is appropriate. Isochronal testing is very difficult to implement. Pressure Transient Test Analysis/Interpretation: Conventional analysis is consistent/appropriate. Model identification (log-log (or type curve) analysis). Test design keep it simple. Introduction Analysis of Reservoir Performance Slide 22
Module 4: 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 p i. b. "Isochronal" test sequence note that each "buildup" is required to achieve p i. d. Governing equations for "deliverability" test analysis/interpretation. Introduction Analysis of Reservoir Performance Slide 23
Module 4: 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). c.traditional "deliverability" plot probably derived from empirical plotting of data. b."rate-squared" (or velocity-squared) formulation analogous form can be derived from steady-state flow theory (Forchheimer Eq.). d. Modified "deliverability" plot note that bq sc 2 must be known (... need alternative approach). Introduction Analysis of Reservoir Performance Slide 24
Module 4: Multirate Testing Example Case a. Multirate (4-point) rate sequence (note pressure match (solid trend through the data). b. Log-log "summary plot" note good agreement in comparison of data and model. c. Results summary note that non-darcy flow, changing wellbore storage, and an infiniteacting reservoir system were considered in this analysis. Introduction Analysis of Reservoir Performance Slide 25
Module 4: "Well Interference" Example Case a. "Well Interference" plot note the linear trend through the data functions (confirms interference). b. Log-log "summary plot" note the corrected and uncorrected data (well interference). c. Horner semilog plot note the two semilog trends confirm the radial composite model. Discussion: "Well interference" is much more common than previously thought and we must recognize the characteristic behavior on each plot: Log-log plot (b) Semilog plot (c) Specialized plot (a) Introduction Analysis of Reservoir Performance Slide 26
Module 4: Pressure Transient Testing Basics a. Log-log "preliminary analysis" plot wellbore storage and radial flow (C s, k). c. Semilog "middle-time" plot used to analyze radial flow behavior (k, s). e. Cartesian "Arps" plot used to estimate average reservoir pressure. b. Cartesian "early-time" plot used to analyze wellbore storage (p 0, C s ). d. Horner "middle-time" plot used to analyze radial flow behavior (k, s, p*). f. Log-log "summary" plot summary of all analysis (C s, k, s, A, etc). Introduction Analysis of Reservoir Performance Slide 27
Module 5: Analysis of Production Data Production data "low frequency" (taken at large (or even random) intervals) and "low resolution" (data quality (i.e., accuracy) is minimal). Simple Analysis: Rate-time decline curve analysis. EUR analysis (usually rate-cumulative or variation). New stuff advanced analysis based on a simple, yet robust model (e.g., Knowles q g -G p analysis) Decline type curve analysis: Systematic, model-based analysis approach. Model identification transient data analysis. Volume estimates pseudosteady-state behavior is dictated by material balance (very consistent). Introduction Analysis of Reservoir Performance Slide 28
Module 5: Production Analysis Example Case Rate and pressure profile for a mid-continent (U.S.) gas well, note the daily and seasonal fluctuations in the data. Introduction Analysis of Reservoir Performance Slide 29
Module 5: Production Analysis EUR Analysis Estimated ultimate recovery (EUR) profile for a mid-continent (U.S.) gas well there is considerable variation in the data. Introduction Analysis of Reservoir Performance Slide 30
Module 5: Production Analysis WPA Approach Note that the WPA approach provides a unique analysis/ interpretation of the well performance history. Introduction Analysis of Reservoir Performance Slide 31
Module 5: Production Analysis New Stuff (Gas) New analysis and interpretation methodologies based on the "Knowles" rate-time solution for pseudosteady-state gas flow. The result of interest for this work is the quadratic "rate-cumulative" production relation given as: "Knowles" rate-time relations for gas flow: Approximation valid for p i <6000 psia. Assumes p wf = constant. Quadratic "rate-cumulative" is basis for this work. Introduction Analysis of Reservoir Performance Slide 32
Module 5: Production Analysis New Stuff (Gas) a. q g vs. t: Simulated Gas Case b. q Dd and q Ddi vs. G pd (Quadratic Relation): Simulated Gas Case c. q Dd and q Ddi vs. G pd (Hyperbolic Relation): Simulated Gas Case Example Behavior: Note that the gas rate-time data are matched extraordinarily well by the Knowles equation. Quadratic q Dd and q Ddi vs. G pd type curve reflects gas flow behavior. Quadratic q Dd and q Ddi vs. G pd type curve presented for comparison/completeness. Introduction Analysis of Reservoir Performance Slide 33
Module 5: Production Analysis New Stuff (Gas) a. q g vs. G p : Simulated Gas Case b. q gi,t vs. G p : Simulated Gas Case q g vs. G p : Used "spreadsheet" approach, with multiple data functions (on different plots) being matched simultaneously. Data match is shown with "high" and "low" trends (+/- 10 percent) as well as the correct trend (overlain in this figure). q gi,t vs. G p : Similar to the q q vs. G p plot (and used simultaneously with this plot). Smoother than q q data. q gi,t definition: q gi 1 t, t = t 0 q g dt Introduction Analysis of Reservoir Performance Slide 34
Module 5: Production Analysis New Stuff (Gas) a. (q g -q i )/G p vs. G p : Simulated Gas Case b. (q gi,gp -q i )/G p vs. G p : Simulated Gas Case q gi,gp vs. G p : A specialized extrapolation function that is tailored to the quadratic rate-cumulative behavior. q gi,gp definition: q c. (q gi,gp -q)/g p vs. G p : Simulated Gas Case 1 gi, Gp = Gp G 0 p q g d Gp Introduction Analysis of Reservoir Performance Slide 35
Module 5: Production Analysis the hard way... "Van Everdingen-Meyer Method: "Analysis by simulation" (use analytical solution to define x- axis plotting function). Considers all of the data, needs a complete model to generate an appropriate analysis/interpretation. Theoretically simple, practical. Pro: Theoretically simple and practical (can use field data). Con: Limited by solution model as well as data quality. From: SPE 15482 Whitson and Sognesand (1988). Introduction Analysis of Reservoir Performance Slide 36
Module 5: Production Analysis History Lessons From: SPE 04629 Fetkovich (1973). Composite Transient Type Curve: Collapses the transient flow trends into "stems" related to reservoir size and skin factor (Fetkovich, 1973). Composite Total Type Curve: Addition of the "Arps" empirical trends for "boundary-dominated flow behavior (Fetkovich, 1973)." Assumptions: Constant bottomhole pressure. "Liquid" flow (not gas). From: SPE 04629 Fetkovich (1973). Introduction Analysis of Reservoir Performance Slide 37
Module 5: Production Analysis History Lessons From: SPE 28688 Doublet, et al (1994). Fetkovich Derivative Type Curve: Good concept, but just try to take the derivative of production data... Fetkovich-McCray Type Curve: Concept is to generate "integral" functions for data analysis, much better performance than simply using rate. Still Need: Variable pressure/rate methods. Other models fractured wells, horizontal wells, etc... From: SPE 25909 Palacio, et al (1993). Introduction Analysis of Reservoir Performance Slide 38
Module 5: Production Analysis History Lessons From: SPE 25909 Palacio, et al (1993). UNFRACTURED Well Case Variable Rate/Pressure Approach: Use "material balance time" (xaxis) and "pressure drop normalized rate" (y-axis) functions. Good news: New concept provides unique behavior during boundarydominated flow regime. Not-So-Good-News: Wellbore pressure data are critical. From: SPE 28688 Doublet, et al (1994). Introduction Analysis of Reservoir Performance Slide 39
Module 5: Production Analysis History Lessons MULTIWELL Analysis Multiwell case can be "recast" into single well case using cumulative production for entire field. Homogeneous reservoir example shows that all cases (9 wells) align same behavior observed for heterogeneous reservoir cases. From: SPE 71517 Marhaendrajana (2001). From: SPE 71517 Marhaendrajana (2001). From: SPE 71517 Marhaendrajana (2001). Introduction Analysis of Reservoir Performance Slide 40
Module 5: Production Analysis Scaling Production data analyses and pressure transient analyses "see" the reservoir as a volumeaveraged set of properties. New solutions/models will also have this view of the reservoir, but quantifying heterogeneity may be possible by the analysis of data at the "local" level. Scaling will remain a major issue regardless of the mechanism used to analyze reservoir performance. From: Simulator Parameter Assignment and the Problem of Scaling in Reservoir Engineering Halderson (1986). Introduction Analysis of Reservoir Performance Slide 41
Module 5: Production Analysis Future Future of Production Data Analysis: Evolutionary changes: Better data acquisition (major issue). Multiwell analysis (major issue). Better software (major issue). More reservoir/well solutions (minor issue). Revolutionary changes: Direct dataflow into integrated packages for analysis/simulation (5-10 years). Real-time rate-pressure optimization, simultaneous monitoring and control (5-10 years). Introduction Analysis of Reservoir Performance Slide 42
(Formation Evaluation and the Analysis of Reservoir Performance) Module for: Analysis of Reservoir Performance Introduction End of Presentation T.A. Blasingame, Texas A&M U. Department of Petroleum Engineering Texas A&M University College Station, TX 77843-3116 (979) 845-2292 t-blasingame@tamu.edu Introduction Analysis of Reservoir Performance Slide 43