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Restoring Erroneous or Missing Rates in Interfering Wells Using Multiwell Deconvolution


 
 
 Single well deconvolution (von Schroeter et al., 2001) has been added to the well test interpretation toolbox nearly twenty years ago. In recent years, the single well deconvolution algorithm has been extended to multiple interfering wells (Cumming et al., 2013), and further improved with the additions of constraints to account for existing a-priory knowledge on the reservoir (constrained multiwell deconvolution, Cumming et al., 2019).
 The main objective of multiwell deconvolution is to identify the signatures of all wells involved and the interference signals between wells, from which information can be extracted about the reservoir that may not be obtainable otherwise, e.g. heterogeneities, boundaries and compartmentalization. The single well deconvolution algorithm has also been shown to be capable of restoring erroneous or missing rates (Gringarten, 2010).
 As shown in this paper, the same is true with multiwell deconvolution, which is able to restore erroneous or missing rates in all the wells involved.
 
 
 
 Starting with arbitrary initial guesses for the missing rates in the various wells involved, we use multiwell deconvolution to estimate these missing flow rates or correct for erroneous ones.
 Two methods are presented: (1) we use unconstrained multiwell deconvolution as a first step to estimate the missing/erroneous rates, then use constrained multiwell deconvolution with these rates to estimate deconvolved derivatives; and (2) we restore/correct the flow rates and derive deconvolved derivatives simultaneously using constrained multiwell deconvolution. We show that the first approach is more accurate than the second one. In both approaches, we only obtain rates that are proportional to the true flow rates. To obtain the true flow rates, we need to know either one of the actual flow rates in each well, or the corresponding permeabilities.
 
 
 
 We prove the ability of multiwell deconvolution to estimate rates on synthetic oil reservoirs and gas reservoirs with moderate average reservoir pressure depletion, that include non-interfering wells. We then apply to oil and gas field examples and compare restored vs. actually measured rates. In all cases, the agreement is very good.
 
 
 
 Using only measured pressure data, constrained multiwell deconvolution can be used to restore unknown flow rates and/or correct for erroneous rates, in addition to estimating deconvolved derivatives of all wells. This is particularly useful in the case of allocated rates or when rates are missing in some of the interfering wells.
