Using Deconvolution to Estimate Unknown Well Production from Scarce Wellhead Pressure Data
Authors: Aluko Lekan , Cumming Jonathan , Gringarten Alain 
Published: October 2020

Abstract
Well test analysis requires the knowledge of bottomhole pressure and rates from the well of interest, and from any other well involved in the case of interferences. Sometimes, bottomhole pressures are not available and must be estimated from wellhead pressures, which usually are of lower quality, due to multiphase flow and possible tubing leaks. Converting flowing wellhead pressures to bottomhole pressures can be performed with a number of models, all of which assumes knowledge of the well production rate, which is usually determined with flowmeters or separators at the surface. In some cases, for instance when there is a blow out, production rate information is not available. The question is then how to determine well production rate in the absence of rate measurements when only wellhead pressures are available.
In this paper, we use an iterative process based on well test deconvolution (von Schroeter et al. 2001-2004) to estimate unknown well production from wellhead pressure data. The procedure is as follows: (1) we assume a constant unit production rate and apply deconvolution to wellhead pressures: this yields a deconvolved wellhead pressure derivative and corrects the rates to make them compatible with the wellhead pressures; (2) we calibrate the rates with permeability from a trusted source e.g. core measurements or sampling wireline formation test analysis; (3) we use the calibrated deconvolved rates to convert wellhead pressures into bottomhole pressures; (4) we again assume a constant unit production rate and apply deconvolution to calculated bottomhole pressures: this yields a deconvolved bottomhole pressure derivative and corrects the rates to make them compatible with the calculated bottomhole pressures; and (5) we calibrate the calculated rates with trusted permeability information.
We have applied the procedure described above to DST data from an oil well for which a complete data set is available, including permeabilities from cores, wellhead pressures, production rates, bottomhole pressures and well test analysis results. For the purpose of this study, we assume that we only know wellhead pressures, and we compare calculated results with measurements, i.e. calculated vs. measured bottomhole pressures, calculated vs. measured rates, and calculated vs. measured cumulative production.
We assess the uncertainty in the results by applying a Bayesian approach to deconvolution (Cumming et al. 2020) which accounts for uncertainties in all input parameters, including permeability from different sources, and also uncertainty in deconvolution. In all cases, good to excellent agreement is reached between calculated results and measured data, thus validating the approach and providing confidence in the validity of the results.
The procedure described in this paper provides a very good estimate of production rates from only wellhead measurements and permeability estimates: rather than using a welltest to determine reservoir properties knowing the rates and pressures, we do the inverse i.e. we use known reservoir properties and pressures to determine the rates. This approach can be used with confidence when measured rates are not available.