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Both the Rawlins and Schellhardt and Houpeurt analysis techniques are presented in terms of pseudopressures. Flow-after-flow tests, sometimes called gas backpressure or four-point tests, are conducted by producing the well at a series of different stabilized flow rates and measuring the stabilized BHFP at the sandface. Each different flow rate is established in succession either with or without a very short intermediate shut-in period. Conventional flow-after-flow tests often are conducted with a sequence of increasing flow rates; however, if stabilized flow rates are attained, the rate sequence does not affect the test. Fig 1 illustrates a flow-after-flow test.
The Merriam-Webster Dictionary defines simulate as assuming the appearance of without the reality. Simulation of petroleum reservoir performance refers to the construction and operation of a model whose behavior assumes the appearance of actual reservoir behavior. A model itself is either physical (for example, a laboratory sandpack) or mathematical. A mathematical model is a set of equations that, subject to certain assumptions, describes the physical processes active in the reservoir. Although the model itself obviously lacks the reality of the reservoir, the behavior of a valid model simulates--assumes the appearance of--the actual reservoir. The purpose of simulation is estimation of field performance (e.g., oil recovery) under one or more producing schemes. Whereas the field can be produced only once, at considerable expense, a model can be produced or run many times at low expense over a short period of time. Observation of model results that represent different producing conditions aids selection of an optimal set of producing conditions for the reservoir.
Abstract The construction of unified compositional model is important for modeling of production surface network. The produced streams are described by different multicomponent PVT models, while total production calculation requires a single consistent PVT system. The method for constructing a compositional model which is optimal in terms of components number is proposed. As a first step, all components from all initial mixtures are split by molecular weight into two groups: light and heavy, which are considered separately from that point on. The basis component set for the light group is constructed from the pure hydrocarbons and inorganic substances. Then the components from the light group are expanded over it using the method of numerical minimization. The objective function used is the sum of the moduli of the relative differences of corresponding parameters of initial components and their decompositions. The parameters considered are critical properties (pressure, temperature, volume) and the acentric factor. The condition of equality of molecular weights is enforced, to ensure the conservation of material balance during decomposition of the initial components. Two methods are proposed for the characterization of heavy components: either proceed the same way as it is done for the light group, with the construction of a corresponding basis, or use fractionation by the number of carbon atoms. All properties of the components of the final set are fully known after the above algorithm has been applied. Each component in the initial mixtures is decomposed using the resulting set of components with uniquely defined coefficients. The proposed method is successfully used to construct a unified compositional model for production surface networks. The sources (pipelines or wells) with different PVT models are connected in the single production network computed by resulting compositional PVT properties.
Figure 1.1--Production System and associated pressure losses. Mathematical models describing the flow of fluids through porous and permeable media can be developed by combining physical relationships for the conservation of mass with an equation of motion and an equation of state. This leads to the diffusivity equations, which are used in the petroleum industry to describe the flow of fluids through porous media. The diffusivity equation can be written for any geometry, but radial flow geometry is the one of most interest to the petroleum engineer dealing with single well issues. The radial diffusivity equation for a slightly compressible liquid with a constant viscosity (an undersaturated oil or water) is ....................(1.1) The solution for a real gas is often presented in two forms: traditional pressure-squared form and general pseudopressure form. The pressure-squared form is ....................(1.2) and the pseudopressure form is ....................(1.3) The pseudopressure relationship is suitable for all pressure ranges, but the pressure-squared relationship has a limited range of applicability because of the compressible nature of the fluid.
This article discusses the implementation and analysis of the modified isochroncal testing for gas well deliverability tests. Both the Rawlins and Schellhardt and Houpeurt analysis techniques are presented in terms of pseudopressures. The time to build up to the average reservoir pressure before flowing for a certain period of time still may be impractical, even after short flow periods. Consequently, a modification of the isochronal test was developed to shorten test times further. The objective of the modified isochronal test is to obtain the same data as in an isochronal test without using the sometimes lengthy shut-in periods required to reach the average reservoir pressure in the drainage area of the well.
Summary Much work has been performed on the optimal well placement/control problem, including some investigations on optimizing well types (injector or producer) and/or drilling order. However, to the best of our knowledge, there are only a handful of papers dealing with the following problem that is sometimes given to reservoir‐engineering groups: given a potential set of reasonable drilling paths and a drilling budget that is sufficient to drill only a few wells, find the optimal well paths, determine whether a well should be an injector or a producer, and determine the drilling order that maximizes the net present value (NPV) of production over the life of the reservoir. In this work, the optimal choices of drilling paths, types, and drilling order are found using the genetic algorithm (GA) with mixed encodings. A binary encoding for the optimization variables pertaining to well‐location indices and well types is proposed to effectively handle a large amount of categorical variables, while the drilling sequence is parameterized with ordinal numbers. These two sets of variables are optimized both simultaneously and sequentially. Finally, control optimization using a stochastic simplex approximate gradient (StoSAG) is performed to further improve the NPV of life‐cycle production. The proposed workflow is tested on two examples: a 3D channelized reservoir where the potential well paths are either vertical or horizontal, and the Brugge model where only vertical wells are drilled. Both numerical examples indicate that GA combined with StoSAG is a viable solution to the problem considered.
ABSTRACT Path-integral migration is a method for creating a migrated image without previous knowledge of the true velocity model by summing the migrated images from a representative set of velocity models. This concept can be expanded to automatically extract a velocity model, a technic called Migration Velocity Analysis by Double Path-Integral Migration (MVA by DPIM). In MVA by DPIM, a second, weighted image is created, with the weight containing the velocities used in the individual migrations. Division of the two images provides the velocity model. Here we discuss several practical aspects of implementing MVA by DPIM, ranging from the parametrization of the weight function to the stabilization of the division and the selection of only meaningful velocities. By means of tests on a wide range of velocity models, we find a robust implementation of the method. Presentation Date: Wednesday, September 18, 2019 Session Start Time: 1:50 PM Presentation Start Time: 2:40 PM Location: Poster Station 11 Presentation Type: Poster
Hui, Mun-Hong (Robin) (Chevron Energy Technology Company) | Karimi-Fard, Mohammad (Stanford University) | Mallison, Bradley (Chevron Energy Technology Company) | Durlofsky, Louis J. (Stanford University)
Summary A comprehensive methodology for gridding, discretizing, coarsening, and simulating discrete-fracture-matrix models of naturally fractured reservoirs is described and applied. The model representation considered here can be used to define the grid and transmissibilities, either at the original fine scale or at coarser scales, for any connectivity-list-based finite-volume flow simulator. For our fine-scale mesh, we use a polyhedral-gridding technique to construct a conforming matrix grid with adaptive refinement near fractures, which are represented as faces of grid cells. The algorithm uses a single input parameter to obtain a suitable compromise between fine-grid cell quality and the fidelity of the fracture representation. Discretization using a two-point flux approximation is accomplished with an existing procedure that treats fractures as lower-dimensional entities (i.e., resolution in the transverse direction is not required). The upscaling method is an aggregation-based technique in which coarse control volumes are aggregates of fine-scale cells, and coarse transmissibilities are computed with a general flow-based procedure. Numerical results are presented for waterflood, sour-gas injection, and gas-condensate primary production for fracture models with matrix and fracture heterogeneities. Coarse-model accuracy is shown to generally decrease with increasing levels of coarsening, as would be expected. We demonstrate, however, that with our methodology, two orders of magnitude of speedup can typically be achieved with models that introduce less than approximately 10% error (with error appropriately defined). This suggests that the overall framework may be very useful for the simulation of realistic discrete-fracture-matrix models.
Abstract This study demonstrates a successful application of Wavelet Analysis to fracturing pressure data across various conventional and unconventional formations to evaluate post treatment data and enhance future stimulation practices. This methodology was compared to the proven Moving Reference Point (MRP) technique developed by Pirayesh et al (2013), to improve the understanding of wavelet analysis. As a fracturing diagnostic tool, the wavelet analysis technique can also be used as companion diagnostic tool alongside previously published methods (such as MRP etc.) Wavelet analysis of a signal is the mathematical decomposition of that signal into orthogonal wavelet components. The level of decomposition is chosen to discern high and low-resolution parts of the signal. The process represents the signal as a sum of translations and scalings of the chosen wavelet to obtain coefficients of each wavelet. Fracturing treatment pressure signals occur at various frequencies with finite durations that makes it possible to divide the pressure signals into many components and analyze them individually by wavelet transformation. Discrete Wavelet Transformation by Daubechie wavelets was implemented on fracture propagation pressure to various resolution levels to reveal necessary information within the data. The detail coefficients were analyzed by examining the anomalies at various resolution levels. Wavelet analysis was performed on various shale and conventional fracturing data. Some interesting patterns are readily discernable from the wavelet detail coefficients. For instance, during the injection of proppants, there is an amplitude change in the detail coefficients at the exact moment when the proppant contacts the formation surface. This is expected because wavelet analysis is sensitive to any discontinuity in the system. Furthermore, such amplitude changes are also observed in the analyzed pressure data corresponding to tip screen-out and near wellbore sand-out events. Comparing such events along-side the MRP method paves the way for early detection of screen-out events. A comparison with the MRP technique is also provided in this study. This method reduces the uncertainty in analysis of Nolte-Smith and MRP method by providing an independent estimate of fracture propagation characteristics. There have been publications discussing wavelet transformations of various formation and reservoir parameters (permeability, reservoir pressure, etc.), and discussing the application of wavelets for noise reduction and data smoothing. However, this is the first study mainly about wavelet analysis of fracture injection pressure data to understand and detect anomalies during various completion treatments. Ultimately, this technique helps to improve treatment designs and efficiency by analyzing fracture and formation behavior of the treatment and enhance decision making during execution, by providing early screen-out detections.