Prediction of Production-Inflow Profile of a Well Producing Single-Phase Flow of Slightly Compressible Fluid from Multilayer Systems by Temperature and/or Pressure Transient Data

This study focuses on the prediction of the production-inflow profile of a well producing a single-phase flow of slightly compressible fluid (water or oil flow) in a multilayered system using the layer permeability and skin values estimated by history matching spatial and temporal temperature and/or pressure data sets along the completion interval. Such data may be acquired by wireline formation testing, production-logging-tool (PLT), or distributed temperature sensing (DTS) fiber-optic cables. We use an in-house thermal, transient coupled reservoir/wellbore simulator developed during this study. It solves transient mass, momentum, and energy conservation equations simultaneously for both reservoir and wellbore. The effects of the Joule-Thomson (J-T), adiabatic expansion, conduction, and convection are all included for predicting the flow profiles across the wellbore. The results from our in-house simulator are verified with the results from a commercial simulator for the single-phase fluid flow of a vertical well producing geothermal brine and oil in a two-zone multilayer system. We also compare the results from our rigorous transient coupled wellbore/reservoir model with the results from a model assuming steady-state thermal wellbore model used in the previous studies. We find that the steady-state thermal wellbore model used in the previous studies that ignore accumulation terms in mass, momentum, and thermal energy balances is a reasonably accurate model for predicting wellbore pressures and temperatures when it is coupled with a nonisothermal reservoir model for slightly compressible fluid because the transient effect in the wellbore is less important with the slightly compressible fluid. We investigate the nonlinear parameter estimation problem based on the use of single or multiple observed temperature and/or pressure (if available) profiles recorded spatially inside the wellbore and at the sandface. The purpose is to identify if the wellbore or sandface data profiles are more useful to accurately estimate the permeability and skin information and predict a production-inflow profile of the well depending on the representation of an actual multilayer system by a reduced-layered or fine-layered model. We show that using an upscaled-layered model (e.g., representing each heterogeneous layer with a lumped single layer with uniform permeability and skin) provides estimates that are more toward the thickness-average permeability and skin factors of the layers and may not provide a good prediction of the well’s production-inflow profile. We show that including the sandface temperature data in regression worsens, while the use of wellbore temperature data sets improves the quality of parameter estimation if an upscaled multilayered model is used. We also show that regressing on multiple temperature profiles, preferably at the sandface, alone could be used to predict the production-inflow profile accurately if a “fine” multilayered heterogeneous model is used. We also investigate if including or excluding the temperature and/or pressure measurements at the nonperforated sections along the completion interval could help enhance the parameter estimation problem. The results show that when multiple profiles of temperatures including the data at nonperforated zones at different production rates are regressed, reliable estimates of the individual layer properties that predict the production-inflow profile accurately can be obtained, though layer permeability and skin factors may often exhibit wide 95% confidence intervals and high correlations among them. Adding sandface or wellbore pressure data, if available, into observed data sets in history matching always improves the quality of parameter estimation.