Chapter 5 Pressure Transient Testing (I) Weibo Sui Associate Professor College of Petroleum Engineering, CUPB
Scope of the Chapter What reservoir/well testing is What can be learned from a reservoir test How to analyze test data
Reservoir/Well Testing Dynamic reservoir description based on measurement of: - flow rate (sandface/wellbore) - pressure (sandface/wellbore) - (temperature, density)
Schematic Diagram of a Well Test packer water separator choke oil gas pressure, temperature gauge wireline perforations formation
Typical Job Sequence Flow well at single or multiple rates for time, tp Shut well in for pressure buildup for time, Dt Measure surface flow rates of all flowing phases, and bottomhole p, T
Test Types Drawdown Test Buildup Test DST (Drill Stem Test) difficult to maintain constant rate analysis unreliable no lost production Buildup Test rate known, q = 0 analysis more reliable production lost DST (Drill Stem Test)
Drawdown Test (5500 psi) (2000 STB/D, 24 hrs)
Pressure Buildup Test (5800 psi) (1000 STB/D, 24 hrs) (shut in for 24 hrs)
Multi-rate Test (2000 STB/D) (1500 STB/D) (2500 STB/D) (1000 STB/D)
Drill Stem Test – Flow to Surface p q 3 9 15 hr Run in hole Short flow, cleanup Short buildup Long flow Final buildup Pull out of hole pmud pR Time, hr
Well Test – Field Case
Well Test – Field Case
Objectives for Transient Testing Production Engineers Average reservoir pressure Productivity index Skin Rate dependent skin Skin components Post treatment skin after perforating, gravel packing, acid injection, or hydraulic fracturing
Objectives for Transient Testing Reservoir Engineers Reservoir characterization Test radius of investigation Formation permeability (vertical, horizontal) Barriers to flow (sealing or leaky) Shale bed boundaries Structural limits (fault, salt dome, pinch out) Stratigraphic limits (flow units, unconformities)
Objectives for Transient Testing Exploration well : confirm the exploration hypothesis; establish a first production forecast: nature and rate of produced fluids, initial pressure etc. Appraisal well : well and reservoir description can be refined (well productivity, reservoir permeability, reservoir boundaries etc.) Development well : (periodic tests) adjust the reservoir description evaluate skin factor and the need of a well treatment, such as workover, perforation strategy etc. evaluate communication between wells (interference testing) monitor the average reservoir pressure
Well Testing Analysis Techniques Mathematical models Conventional straight line analysis Type curve analysis pressure change type curve (semi-log plot) pressure derivative type curve (log-log plot) Commercial software
Mechanisms Governing Transient Testing Diffusivity Equation (P, q, r, t) Assumption circular, homogeneous reservoir with uniform thickness well located in the center of reservoir, and fully penetrated producing intervals guarantee radial flow slightly compressible fluid
Diagram of the Reservoir and Well
Diffusivity Equation Derivation of the diffusivity equation Solutions for the diffusivity equation Limiting forms for solutions of the diffusivity equation
Derivation of the Diffusivity Equation Continuity equation – mass conservation Darcy’s Law – flow through porous media Equation of state
Continuity Equation – Mass Conservation
Continuity Equation – Mass Conservation
Continuity Equation – Mass Conservation
Continuity Equation – Mass Conservation
Continuity Equation – Mass Conservation
Continuity Equation – Mass Conservation
Continuity Equation – Mass Conservation Assumptions: velocity in vertical and angular directions are zero
Darcy’s Law – Flow Through Porous Media
Darcy’s Law – Flow Through Porous Media
Equation of State - Liquid
Equation of State - Liquid
Diffusivity Equation - Liquid
Diffusivity Equation Derivation of the diffusivity equation Solutions for the diffusivity equation Limiting forms for solutions of the diffusivity equation
Reservoir Fluid Flow Regime Transient flow Pseudo-steady-state flow Steady-state flow
Transient Flow Pressure wave has not reached the reservoir boundary, reservoir acts like infinite. dp/dt varies with r, t.
Pseudo-Steday-State Flow (PSS) Pressure wave has reached the reservoir outer boundary, there is no flow across the outer boundary. dp/dt = const.
Steady-State Flow (SS) Pressure wave has reached the reservoir outer boundary, the outer boundary pressure is constant, and the rate of fluid flow into the reservoir at the outer boundary is equal to the well production rate. dp/dt = 0.
Solution for the Diffusivity Equation Constant terminal rate solution (inner boundary) (Well testing analysis) Outer boundary Infinite reservoir (Transient flow) Bounded cylindrical reservoir no-flow outer boundary (PSS) constant-pressure outer boundary (SS) Well treatment Line source well (rw → 0) Cylindrical source well (rw ≠ 0) Constant terminal pressure solution (inner boundary) (Aquifer influx model)
Bounded cylindrical reservoir, constant-pressure outer boundary (SS)
Bounded cylindrical reservoir, constant-pressure outer boundary (SS) (SI Unit)
Bounded cylindrical reservoir, no-flow outer boundary (PSS)
Bounded cylindrical reservoir, no-flow outer boundary (PSS)
Bounded cylindrical reservoir, no-flow outer boundary (PSS) (SI Unit)
Infinite reservoir, line source well (Transient)
Infinite reservoir, line source well (Transient)
Infinite reservoir, line source well (Transient)
Solution Derivation Using the Boltzman Transform
Solution Derivation Using the Boltzman Transform
Solution Derivation Using the Boltzman Transform
Solution Derivation Using the Boltzman Transform
Infinite reservoir, line source well (Transient)
Applicability of line source solution
Diffusivity Equation Derivation of the diffusivity equation Solutions for the diffusivity equation Limiting forms for solutions of the diffusivity equation
Limiting Forms
Flow States – Transient SI Units: Field Units: Write equation in alternative form Limited form: In ‘log10’ :
Flow States – Pseudo-Steady State (PSS) SI Units: Field Units: (Field Unit)
Flow States – Steady State SI Units: Field Units: (Field Unit)
Exercise Sketch the pressure profile as a function of ln r for Steady state Pseudo-steady state Transient state