Chapter 5 Well Testing (III) Weibo Sui Ph.D, Associate Professor College of Petroleum Engineering, CUPB

Type Curve What are type curves? Type curves are graphic plots of theoretical solutions to flow equations under specific initial and boundary conditions of the interpretation model representing a reservoir-well system. Most common type curves are presented in dimensionless pressure (pD) versus dimensionless time (tD) .

Infinite reservoir, line source well (Transient)

Agarwal Type Curve Agarwal et al. (1970)

Type Curve Matching Log-log type curve analysis make use of the dimensionless variables. Since dimensionless pressure and time are linear functions of actual pressure and time, we can calculate kh and φh:

Gringarten Type Curve

Bourdet’s Derivative Plot (1983) The derivative plot provides a simultaneous presentation of log ∆p vs. log ∆t and log dp/d(lnt) vs. log ∆t. Pressure change log-log plot (Gringarten) Pressure change derivative log-log plot

Bourdet’s Derivative Plot (1983)

Wellbore Storage Effect (WBS) During WBS, the pressure change is a linear function of time since the beginning of the transient: Which means the unit slope. For the pressure change derivative:

Infinite Acting Radial Flow (IARF)

Combined Gringarten and Bourdet Plot

The Pressure Derivative

Pressure Derivative

Flow Regimes Wellbore Storage Radial Flow Spherical Linear Bilinear

Radial Flow Regimes for Vertical Wells Top of zone Bottom of zone Partial Radial Flow Pseudoradial Flow to Fracture Hemiradial Flow to Well Near Sealing Boundary Fracture Fracture Boundary Actual Well Image Well Sealing Boundary Complete Radial Flow

Radial Flow Regimes for Horizontal Wells Pseudoradial flow Radial flow Hemiradial flow

Spherical Flow Regimes Spherical Flow to Partially Completed Zone Hemispherical Flow to Partially Completed Zone

Linear Flow Regimes Fracture Linear Flow Linear Flow to Fracture Fracture Boundary Fracture Linear Flow to Fracture Bilinear Flow Linear Flow to Horizontal Well Linear Flow to Well in Elongated Reservoir

Flow Regime Identification Radial Pseudosteady state Well bore storage Linear Bilinear Spherical FRID Tool

Flow Region Identification Wellbore Storage (WBS) - Estimate Cs, wellbore storage coefficient (bbls/psi) Middle time region (MTR) - calculate skin, k & p* Late Time region (LTR) - boundaries, kh variations (pi or p* for depleted reservoir) Radial Pseudosteady state Well bore storage Linear Bilinear Spherical

Time Region Identification

Early and Middle Time Analysis

Drawdown Analysis C, k, s cartesian plot (C) semilog analysis (k, s) log-log derivative (C, k, s)

Drawdown Analysis

Cartesian Drawdown Analysis – C Dp Dt mC Zoom

Semi-log Drawdown Analysis – s

Log-Log Drawdown Analysis – C log Dp (Dt2, Dp2) (Dt1, Dp1)

Log-Log Drawdown Analysis – k, s

PBU Analysis (straight line methods) C, k, s, p* cartesian plot (C) semilog analysis (k, s, p*) - log-log derivative (C, k, s, p*)

PBU Analysis

Cartesian PBU Analysis – C Dp Dt mC Zoom Zoom

Horner PBU Analysis – k, p* Semilog (Horner) Analysis 10 1 2 3 4980. 4985. 4990. 4995. (Tp + dT)/dT P PSI Horner slope, m p*

Horner PBU Analysis – s p* Horner slope, m Semilog (Horner) Analysis 10 1 2 3 4980. 4985. 4990. 4995. (Tp + dT)/dT P PSI Horner slope, m p*

Log-Log PBU Analysis – C, k, s

Log-Log PBU Analysis – C log Dp (Dt2, Dp2) (Dt1, Dp1)

Log-Log PBU Analysis – k, s

Finite Conductivity Hydraulic Fracture

Finite Conductivity Hydraulic Fracture Radial Pseudosteady state Well bore storage Linear Bilinear Spherical Bilinear Flow (1/4 slope) Linear Flow (1/2 slope) Finite Conductivity Hydraulic Fracture Time, hrs Dp, Dp’, psi

Late Time Analysis

Late-Time Analysis: Outer Boundary Drawdown Time, hrs Dp, Dp’, psi

Closed Boundary – PSS Flow

Closed Boundary – PSS Flow Drawdown Time, hrs Dp, Dp’, psi

Rectangular Drainage Area

Boundary Models – Single Sealing Fault Characteristic flow regimes: Radial flow Hemi-radial flow

Boundary Models – Single Sealing Fault

Boundary Models – Single Sealing Fault

Semi-log Plot

Boundary Models – Single Sealing Fault

Boundary Models – Single Sealing Fault

Dimensionless Pressure Derivative Plot

Dimensionless Pressure Derivative Plot

Intersecting Fault θ = 60⁰ A 60 deg. angle between the intersecting faults is equivalent to the active well plus 5 image wells for a total of 6 effective wells. The derivative level will rise to 6 times the level of the initial radial flow response.

Intersecting Fault q = 30o

Time Region Analysis Early-time analysis Middle-time analysis wellbore storage skin factor Middle-time analysis reservoir model (IARF, hydraulic fractured, natural fractured reservoir) reservoir properties (permeability etc.) Late-time analysis outer boundary

Well Testing Analysis Procedures Data plots prepare log-log plots of pressure change and pressure change derivative vs. elapsed time during the test. prepare special plots of the data (semi-log plot etc.) Qualitative type-curve analysis identify the appropriate reservoir model identify any characteristic flow regime that can be analyzed with special analysis techniques Semi-log or specialized analysis estimate formation properties Quantitative type-curve analysis confirm or complement specialized analysis results

Cutting-Edge Well Testing Technique Reservoir and well model Various boundaries Constant pressure, closed system, faults, composite reservoir, leaky fault, incomplete boundary Naturally fractured reservoir, multilayer reservoir Hydraulic fractured well, partially penetration well, horizontal well Multiphase flow

Cutting-Edge Well Testing Technique Pressure-Transient-Analysis Software Initialization Test design Loading/editing data Diagnostic tools Modeling capability Model selection, parameter estimation, numerical model Optimization Report generation

Permanent Downhole Gauge

In-Class Exercise PTT Ch2, Problem 16 PTT Ch2, Problem 37 Please use log-log pressure change derivative plot and semi-log plot to solve problem 1 and 2. Beside determining the parameters required in the problem, please determine the early-time, middle-time and late-time flow regime. PTT Ch2, Problem 16 PTT Ch2, Problem 37

In-Class Exercise The following table gives measured data for a buildup test for a finite-acting well. Before shut-in for buildup, the well pressure was declining linearly at 0.431 psi/hr. Use this information to determine the following parameters. (1) Reservoir pore volume, Vp (2) Permeability-thickness product, kh Reservoir Parameters qBo, RB/D 333.3 ct, psi-1 8×10-6 μ, cp 2 m*, psi/hr -0.431

t (hours) p (psia) 1 3138.65 15 3165.94 2 3146.75 16 3166.30 3 3151.31 17 3166.62 4 3154.42 18 3166.89 5 3156.73 19 3167.13 6 3158.54 20 3167.33 7 3160.01 21 3167.50 8 3161.22 22 3167.64 9 3162.24 23 3167.75 10 3163.11 24 3167.85 11 3163.85 25 3167.92 12 3164.49 26 3167.97 13 3165.04 27 3168.00 14 3165.52 28 3168.02

In-Class Exercise A well is opened to flow at 150 STB/day for 24 hours. The flow rate is then increased to 360 STB/day and lasted for another 24 hours. The well flow rate is then reduced to 310 STB/day for 16 hours. Calculate the pressure drop in a shut-in well 700 ft away from the well given: