Open Access
Radespiel, Eduardo
Graduate Program:
Energy and Mineral Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
July 29, 2010
Committee Members:
  • Turgay Ertekin / Luis Ayala, Dissertation Advisor
  • Turgay Ertekin, Committee Chair
  • Luis Ayala, Committee Member
  • Zuleima T Karpyn, Committee Member
  • Savas Yavuzkurt, Committee Member
  • Ronaldo Vicente, Committee Member
  • wellbore temperature
  • flux vector splitting
  • wellbore-reservoir coupling
  • black-oil
  • reservoir simulation
  • non-isothermal
  • horizontal well
Traditionally, isothermal condition is assumed in reservoir simulation. Although this assumption works effectively in reservoir characterization and prediction of pressure and total flowrates during producing life of the well, the assessment of wellbore temperature behavior may yield valuable new information for the personnel involved in production management. Recently, some successful field implementations concerning the application of fiber-optic-distributed temperature monitoring system have been reported in the literature. In this work, we developed a numerical model (coded in Compaq Visual Fortran Standard Edition 6.6.a) that investigates the potential use of temperature measurement aiming at enhanced reservoir management practices. The non-isothermal, three-phase, black-oil numerical model couples reservoir to the wellbore through the Peaceman’s well model. The one-dimensional wellbore is placed into the three-dimensional reservoir sub-domain, which can handle heterogeneities regarding permeability and porosity accordingly. A homogeneous fluid model is used to derive the wellbore governing equations. Both reservoir and wellbore governing equations are treated according to Newton-Raphson protocols and the resulting Jacobian matrices are solved by different in-house made algorithms. The reservoir system of equations is solved using an iterative sparse preconditioned restarted Generalized Minimum Residual (m-GMRES) routine in which the Incomplete LU decomposition without fill-ins (ILU0) preconditioner is used. Wellbore solution is obtained through the banded QR decomposition solver. Both reservoir and wellbore equations are discretized using finite-difference schemes. The discretization of the hyperbolic wellbore system of equations is assessed through the Flux Vector Splitting method (FVS) which allows us to write positive and negative parts of the fluxes at interfaces based upon the eigenvalues and eigenvectors of the system. In the developed code, all hydrocarbon fluid properties are calculated using the Peng-Robinson Equation of State (EOS) whereas water properties are evaluated via data table. Hydrocarbon fluid calculations (oil and gas) are performed according to a synthetic Composite Differential Liberation (CDL) in which a Differential Liberation synthetic experiment is combined with the flash of all liberated gas throughout the separation facility. Therefore, in spite of oil and gas being treated as black-oil fluids throughout this work and the formulation of the governing equations, the available data are close to what one could expect from a real experiment with real fluids. Developed model results showed that influx of different fluids into the wellbore can be noted by changes in temperature behavior within the wellbore and depends upon fluid type and flowrates. Therefore, the model indicated that a distributed-temperature measurement system can help spotting the exact zones where different fluids breakthrough into the wellbore. Simulated case studies showed that for an injection rate of around 6,000 STB/D of water in a 4,000 ft long wellbore led to a total temperature drop of about 0.25oF. On the other hand, a production rate of 11,000 STB of oil per day caused a 1oF temperature drop across the wellbore, whereas 5,000 gas MSCF/D lead to a 3oF total drop. Additionally, one of the simulated case studies indicated that a uniform produced water profile of 650 STB/D in a 4,000 ft long wellbore, whose oil production is around 11,000 STB/D, caused a 0.5oF decrease in total temperature drop when compared to a no-water-influx case. Additionally, a simplified theoretical model was developed in order to answer a recurrent fundamental question in industry: what drives temperature behavior inside the wellbore? The derived non-isothermal, one-dimensional, single-phase theoretical wellbore model treats the fluid as a pure substance, and, through the use of appropriate thermodynamical relationships, we obtained a set of governing equations in which the dependent variables are pressure, velocity and temperature, making the analysis more evident. One of the conclusions we could come into with the simplified theoretical model was that temperature always drop in the flow direction, in spite of what is believed by many in the literature regarding Joule-Thomson effect. Another point is that temperature profile depends on fluid type and flowrate which agrees with our findings in analyzing the simulated case studies when using the numerical model. A new coefficient arises (units of temperature over pressure) as a major player in temperature behavior and could be identified in the simplified model. It depends on fluid sound speed, isothermal compressibility and the inverse of heat capacity. Although it can be also expressed as a function of Joule-Thomson coefficient, it is always positive, and because it is strongly dependent on compressibility, it determines that the expected total temperature drop in water shall be smaller than in oil which, in turn, shall be smaller than in gas. That finding also corroborates to what is observed in the simulated case studies using the numerical model.