Summary
Unlike liquid formation tests, in a gas formation test, both compressibility and viscosity vary with pressure, and non-Darcy flow is more likely. In this study, the gas formation rate analysis technique is developed to analyze gas pressure tests. We calculated gas pseudopotentials, utilized the geometric factor concept, and replaced Darcy's equation with Forchheimer's equation to study non-Darcy flow effects. The technique is applied to a field test, and the results are verified by history matching it with a three-dimensional near wellbore simulator.
Introduction
Wireline formation tests (WFT) can provide valuable, cost-effective information on undisturbed reservoir pressure (p*) vertical pressure gradients, formation fluid samples, formation fluid contacts, and an estimate of near-wellbore permeability. Various log responses (nuclear magnetic resonance, resistivity, acoustic) are calibrated with formation test permeabilities to obtain detailed permeability profiles.1,2 Permeability profiles are vital in identifying perforation and hydraulic fracturing intervals. Well-to-well correlation of permeability profiles can result in a lateral connectivity map, which can be used to calculate improved recovery efficiencies.
A formation test is initiated when a probe from the tool is set against the formation. A measured volume of fluid is then withdrawn from the formation through the probe. The test continues with a buildup until the pressure stabilizes. Pressure in the tool is continuously monitored throughout the test.
Historically, the cylindrical and the spherical flow analysis techniques are used to analyze wireline formation test data.3–5 An alternative to the conventional interpretation techniques has recently been developed by Kasap.6 In a recent publication, Kasap et al.7 compared conventional techniques with the formation rate analysis (FRA) technique and concluded that it was difficult to determine the spherical and the cylindrical flow periods for the conventional techniques that are applied to the buildup data only. The formation rate analysis technique combines the drawdown and the buildup data. Furthermore, early termination of the test would not hinder its analysis.
Kasap et al.'s study was restricted to slightly compressible fluids, which is valid for testing liquid-saturated formations. For gases, however, both the compressibility and viscosity are strong functions of temperature and pressure and, thereby, variable during the test. Large gas compressibility and much smaller gas viscosity complicate the analysis. Gas flow because of low viscosity is more prone to non-Darcy flow effects. In this study, a new gas formation rate analysis (GFRA) technique is developed for gas formation testing. The technique calculates gas pseudopotentials and analyzes variation of pseudopotential versus formation rate during a formation test by utilizing the geometric factor concept. The technique is verified by history matching a field test with a three-dimensional (3D) near-wellbore simulation result.
Analysis Technique
The analysis technique is developed from the material balance considered for the volume of probe and flow lines. The mass rate of accumulation is equal to the difference between mass flow in from the formation and mass flow taken out by the pump. The mass flow rate in from the formation, pqf is defined;
m f = ρ q f = M R T k G 0 r i L ∫ p ( t ) z μ d p , ( 1 )
where the density is substituted with an equation of state.8ri is the inner radius of the tool probe. G0 is the dimensionless geometric factor that accounts for flow geometry and is independent of flow rate, formation permeability, fluid viscosity, fluid type, and pressure drop in the system. A weak dependency to the wellbore radius can be ignored when the probe radius is about four times smaller than the wellbore radius. G0 also varies slightly with the probe radius. This variation, however, is not considered a drawback because the probe size of a formation test tool hardly changes. A one-time calculation of G0 is sufficient for a specific type of tool design. G0 is calculated from a numerical simulation of a specified formation test conducted with a specified tool. For the tests we analyzed, the probe size radius was 0.5 in., and the corresponding G0 was 4.27.
We continue with the development of the analysis equations. The mass rate out from the tool is
m d d = ρ q d d = p ( t ) M z R T q d d , ( 2 )
where ?qac is the pump drawdown rate. The mass rate of change or the accumulation rate, qdd in the tool is defined as
m a c = ρ q a c = V s y s c t p ( t ) M z R T ∂ p ( t ) ∂ t , ( 3 )
where Vsys is the volume in the tool and ct is the compressibility of the fluid in the tool.
The Lagrangian kinematics of three-dimensional Darcy flow