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Objectives/Scope This paper uses pseudo-time to extend the application of constrained multiwell deconvolution algorithm to gas reservoirs with significant pressure depletion. Multiwell deconvolution is the extension of single well deconvolution to multiple interfering wells. Constraints are added to account for a-priori knowledge on the expected deconvolved derivative behaviors and to eliminate non-physical solutions. Methods, Procedures, Process Multiwell deconvolution converts pressure and rate histories from interfering wells into constant-rate pressure responses for each well as if it were producing alone in the reservoir. It also extracts the interference responses observed at each of the other wells due to this single well production. The deconvolved responses have the same duration as the pressure history. This allows to identify reservoir features not visible during individual build ups. Deconvolution techniques can only be applied to pressure and rate data when flow can be represented by linear equations. In strongly depleted gas reservoirs, fluid properties, and gas compressibility in particular, are pressure dependent, which makes the flow problem non-linear. The paper uses pseudo-pressure and pseudo-time transforms to linearize the problem in such conditions. Results, Observations, Conclusions The pseudo-time method developed by Levitan and Wilson (2010) is extended to constrained multiwell deconvolution in highly depleted gas reservoirs. It is an iterative process, which yields the correct initial gas in place, whereas the use of real time does not. The algorithm is validated with a two gas well synthetic example, and successfully applied to a field case with four gas producers. Novel/Additive Information The paper extends the application of constrained multiwell deconvolution to strongly depleted gas reservoirs. Constrained multiwell deconvolution is an efficient way to exploit data recorded by permanent downhole pressure gauges and provides information not otherwise available. It can help to identify field heterogeneities and compartmentalization early in field life, making it possible to modify the field development plan and to improve locations of future wells. It can accelerate history-matching with the reservoir model by doing it on the constant rate pressure responses rather than on the actual, usually complex, production history. An added advantage is that comparison between the pressure derivatives of the model and the actual deconvolved derivatives allows identification of mismatch causes.
Objectives/Scope This paper uses pseudo-time to extend the application of constrained multiwell deconvolution algorithm to gas reservoirs with significant pressure depletion. Multiwell deconvolution is the extension of single well deconvolution to multiple interfering wells. Constraints are added to account for a-priori knowledge on the expected deconvolved derivative behaviors and to eliminate non-physical solutions. Methods, Procedures, Process Multiwell deconvolution converts pressure and rate histories from interfering wells into constant-rate pressure responses for each well as if it were producing alone in the reservoir. It also extracts the interference responses observed at each of the other wells due to this single well production. The deconvolved responses have the same duration as the pressure history. This allows to identify reservoir features not visible during individual build ups. Deconvolution techniques can only be applied to pressure and rate data when flow can be represented by linear equations. In strongly depleted gas reservoirs, fluid properties, and gas compressibility in particular, are pressure dependent, which makes the flow problem non-linear. The paper uses pseudo-pressure and pseudo-time transforms to linearize the problem in such conditions. Results, Observations, Conclusions The pseudo-time method developed by Levitan and Wilson (2010) is extended to constrained multiwell deconvolution in highly depleted gas reservoirs. It is an iterative process, which yields the correct initial gas in place, whereas the use of real time does not. The algorithm is validated with a two gas well synthetic example, and successfully applied to a field case with four gas producers. Novel/Additive Information The paper extends the application of constrained multiwell deconvolution to strongly depleted gas reservoirs. Constrained multiwell deconvolution is an efficient way to exploit data recorded by permanent downhole pressure gauges and provides information not otherwise available. It can help to identify field heterogeneities and compartmentalization early in field life, making it possible to modify the field development plan and to improve locations of future wells. It can accelerate history-matching with the reservoir model by doing it on the constant rate pressure responses rather than on the actual, usually complex, production history. An added advantage is that comparison between the pressure derivatives of the model and the actual deconvolved derivatives allows identification of mismatch causes.
Summary This paper proposes the application of the eigenmode decomposition to the problem of pressure-rate deconvolution. The method enabled us to write the solution of the pressure-rate deconvolution as an infinite series of eigenmodes (eigenfunctions). Each eigenmode is associated with a hydraulic diffusion time scale (eigenvalue) that depends on the intrinsic reservoir properties. The set of eigenmodes forms a basis of the solution space and the analytical solution shows some desirable properties: It is smooth, physically constrained for a closed system, and some parameters have a physical interpretation. As a result, in both single and multiwell problems, the late-time unit slope appears naturally and the curvature penalty does not have to be imposed, thus addressing current knowledge gaps. As an additional contribution, we also propose a mathematically well-defined expression in terms of eigenfunctions to the concept of investigated volume during a well test and a procedure for untangling the single-well deconvolved response from interference effects of neighboring wells under certain conditions. Applications to the analysis of drillstem tests (DST) and reservoir characterization are presented.
Objectives/Scope 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. Methods, Procedures, Process 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. Results, Observations, Conclusions 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. Novel/Additive Information 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.
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