Analytic Wellbore Temperature Model for Transient Gas-Well Testing
- A. Rashid Hasan (U. of Minnesota) | C. Shah Kabir (Chevron Corp.) | Dongqing Lin (U. of Minnesota-Duluth)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- June 2005
- Document Type
- Journal Paper
- 240 - 247
- 2005. Society of Petroleum Engineers
- 5.5 Reservoir Simulation, 1.14 Casing and Cementing, 5.3.2 Multiphase Flow, 5.6.3 Pressure Transient Testing, 4.6 Natural Gas, 5.8.9 HP/HT reservoirs, 5.6.4 Drillstem/Well Testing, 2.2.2 Perforating, 4.2 Pipelines, Flowlines and Risers, 4.3.1 Hydrates, 5.9.2 Geothermal Resources, 5.1.5 Geologic Modeling
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Questions arise whether bottomhole pressures (BHPs), derived from theirwellhead counterpart (WHP), lend themselves to transient analysis. That isbecause considerable heat exchange may affect the wellbore-density profile,thereby making the WHP translation a nontrivial exercise. In other words, gasdensity is dependent on both spatial locations in the wellbore and time duringtransient testing. Fully coupled wellbore/reservoir simulators are available totackle this situation. However, they are not readily adaptable for theirnumeric formulations.
This paper presents analytic expressions, derived from first principles, forcomputing time-dependent fluid temperature at any point in the wellbore duringboth drawdown and buildup testing. The simplicity of the analytic expressionsfor Tf (z, t) is profound in that one can compute flowing or shut-in BHPs on aspreadsheet.
Two tests were considered to verify the new analytic formulae. In one case,measurements were available at both sandface and surface, and partial wellheadinformation was available in the other case. We explored a parametric study toassess whether a given wellbore/reservoir system will lend itself to wellheadmeasurements for valid transient analysis. Reservoir flow capacity (kh) turnedout to be the most influential variable.
Gas-well testing is sometimes conducted by measuring pressures at thewellhead. Both cost and circumstance (high pressure/high temperature, or HP/HT)often necessitate WHP monitoring or running the risk of having no tests at all.Methods for computing BHP from wellhead pressures for steady flow in gas wellsare well established in the literature. For dry-gas wells, the widely usedmethod of Cullender and Smith is most accurate, as confirmed by subsequentstudies. For wet gas, either a two-phase model, such as the one offered byGovier and Fogarasi, or the modified Cullender-Smith approach appearssatisfactory.
However, these methods apply to steady-state gas flow and implicitlypresuppose that the wellbore is in thermal equilibrium with the formation.These assumptions may be tested during a transient test. That is becauseunsteady-state wellbore heat transfer occurs even after the cessation of thewellbore-fluid-storage period. Steady-state fluid flow ordinarily implies theabsence of wellbore effects from the viewpoint of transient testing.
Consequently, one needs to develop working equations by conserving mass,momentum, and energy in the wellbore to capture physical phenomena. Earlier, wepresented a forward model and showed its capability to reproduce BHP, WHP, andwellhead temperature (WHT) given reservoir and wellbore parameters. However,translation of WHP to BHP was not demonstrated clearly.
The intent of this work is to present a framework for rigorous computationof BHP from WHP. To achieve this objective, we developed analytic expressionsfor depth- and time-dependent fluid temperature during both flow and shut-intests. These temperature relations, in turn, allow computation of gas densityand, therefore, pressure at any point in the wellbore.
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