Summary This paper deals with the competition between effects during miscible displacements through heterogeneous permeability media. Displacements with an even front are dispersive, others are a type of bypassing: fingering, caused by an adverse mobility ratio, or channeling, caused by heterogeneity and autocorrelation. Under most flow circumstances, channeling is the predominant type. Introduction With the advent of computerized imaging and the minipermeameter to infer small-scale inhomogeneities quantitatively, many rocks once thought to be homogeneous, such as Berea sandstone, have been shown to contain significant heterogeneity.1 Even sandpacks and other synthetic media may suffer from packing problems that can create permeability channels, especially along the boundaries of the medium. In nonunit-mobility ratio displacements in heterogeneous media, it is difficult to separate the effects of the mobility ratio (called fingering if the mobility ratio is adverse) and heterogeneity, or channeling. The terms fingering and channeling are often used synonymously because they both result in uneven displacement fronts, poor oil recovery, and premature breakthrough of the displacing fluid. The terms represent separate effects in this paper because they have different causes. We examine channeling through numerical simulation of unit-mobility of unit-mobility-ratio displacements and then show how a mobility change can affect the flow pattern. Heterogeneity. A permeability field is heterogeneous if it is spatially varying. The simplest representation of heterogeneity is a collection of continuous layers, each with a single value for permeability and porosity. One of the goals of reservoir characterization is to emphasize the actual geology of the reservoir. With such a minute fraction of the reservoir actually sampled by a well, however, a complete description of the reservoir is nearly hopeless. Geostatistics addresses this problem by using statistical techniques to create an image of the reservoir from information observed at the wells. Statistical models are not unique; the same set of input parameters will produce different results, or realizations. The choice of the correct realization(s) to use for a reservoir study depends on the fluid-flow behavior through the model compared with the field production history. Statistical models that are based on conditional simulation generate realistic fields, and their flexibility implies that they can be used to represent a wide variety of geologically realistic media. Such flexibility and realism suggests that the results we describe here will apply generally to what is occurring in displacements through naturally occurring permeable media. Generation Technique. We used longitudinal (x-direction) permeability fields, kx(x, z), generated by the turning-bands method (TBM),2 but the results should apply equally well to synthetic permeable media generated by similar statistical techniques. All kx(x, z) fields are log-normally distributed with a spherical variogram model of autocorrelation. Thus, the fields are completely described statistically by a measure of heterogeneity, which we take to be the Dykstra-Parsons3 coefficient, VDP, and the range ?R. The range in kx is oriented longitudinally and is expressed as a fraction of the total medium length, L. Spatial correlation of kx(x, z) in the direction transverse to bulk flow is held constant at 0.2 times the medium thickness, h; the effect of 2D correlation variability is not treated in this work. Different realizations are generated by choosing a different random number seed to enter into the generation program. Porosity was held constant in all runs. The degree of heterogeneity, VDP, measures the variability of permeability values. When VDP=0, all permeabilities are equal, representing a homogeneous medium. As VDP increases, permeability values deviate further from a mean. Typical field values for undifferentiated core data range from 0.6 to 0.8, but values as large as 0.9 have been observed.4 The dimensionless range, ?R, measures how well neighboring permeability values are related to each other. Qualitatively, ?R relates to the depositional environment, ranging from such high-energy environments as valley-fills, which have little correlation, to such low-energy environments as marine bars, which have extensive correlation.5 When ?R=0, there is no correlation between neighbors; as ?R?8, the depositional environment becomes strictly layered (homogeneous in the direction of correlation). Simulation at Vertical Equilibrium (VE) Conditions. Much of this study is based on the VE concept described elsewhere.6-8 Most simulations had very good transverse communication to ensure that VE was a good assumption. Unless noted otherwise, we forced VE by making the effective aspect ratio, RL=(L/h) kz/kx, large. For linear flow (the only kind considered here) RL is a good indicator of the approach to VE.* We performed a few runs at the other extreme of RL=0, but these proved to be unenlightening because good transverse communication is required to propagate fingers.9 We show one such case below; however, RL is generally large for field-scale displacements. A black-oil finite-difference simulator run in a miscible fluids mode8 was used to simulate first-contact-miscible displacements at the viscosity ratio of interest. A simulation grid of 120 x-direction blocks and 20 z-direction blocks was found to be relatively insensitive to further mesh refinement. Method of Study Twelve-Cell Grid. Because the tradeoff between VDP and ?R is expected to be important, we chose a 12-cell grid of cases with three VDP values and four ?R values. We ran each cell in the grid at different mobility ratios, M, to differentiate between mobility stabilization, channeling, and fingering. Table 1 summarizes the input values and resulting properties of the generated fields, as well as the name by which each cell is designated in this paper. For example, a run at VDP=0.86 and ?R=0.17 is called Case 14 or Cell 14. In Table 1, the input values are the geometric mean, µG, and the standard deviation, s, of the log-normally distributed population sampled. The output values are the µG, the VDP, the standard deviation of the permeability data after a log-transformation back to a normal distribution, slnk, and the heterogeneity index, Ih, to be discussed later. Heterogeneity. A permeability field is heterogeneous if it is spatially varying. The simplest representation of heterogeneity is a collection of continuous layers, each with a single value for permeability and porosity. One of the goals of reservoir characterization is to emphasize the actual geology of the reservoir. With such a minute fraction of the reservoir actually sampled by a well, however, a complete description of the reservoir is nearly hopeless. Geostatistics addresses this problem by using statistical techniques to create an image of the reservoir from information observed at the wells. Statistical models are not unique; the same set of input parameters will produce different results, or realizations. The choice of the correct realization(s) to use for a reservoir study depends on the fluid-flow behavior through the model compared with the field production history. Statistical models that are based on conditional simulation generate realistic fields, and their flexibility implies that they can be used to represent a wide variety of geologically realistic media. Such flexibility and realism suggests that the results we describe here will apply generally to what is occurring in displacements through naturally occurring permeable media. Generation Technique. We used longitudinal (x-direction) permeability fields, kx(x, z), generated by the turning-bands method (TBM),2 but the results should apply equally well to synthetic permeable media generated by similar statistical techniques. All kx(x, z) fields are log-normally distributed with a spherical variogram model of autocorrelation. Thus, the fields are completely described statistically by a measure of heterogeneity, which we take to be the Dykstra-Parsons3 coefficient, VDP, and the range ?R. The range in kx is oriented longitudinally and is expressed as a fraction of the total medium length, L. Spatial correlation of kx(x, z) in the direction transverse to bulk flow is held constant at 0.2 times the medium thickness, h; the effect of 2D correlation variability is not treated in this work. Different realizations are generated by choosing a different random number seed to enter into the generation program. Porosity was held constant in all runs. The degree of heterogeneity, VDP, measures the variability of permeability values. When VDP=0, all permeabilities are equal, representing a homogeneous medium. As VDP increases, permeability values deviate further from a mean. Typical field values for undifferentiated core data range from 0.6 to 0.8, but values as large as 0.9 have been observed.4 The dimensionless range, ?R, measures how well neighboring permeability values are related to each other. Qualitatively, ?R relates to the depositional environment, ranging from such high-energy environments as valley-fills, which have little correlation, to such low-energy environments as marine bars, which have extensive correlation.5 When ?R=0, there is no correlation between neighbors; as ?R?8, the depositional environment becomes strictly layered (homogeneous in the direction of correlation). Simulation at Vertical Equilibrium (VE) Conditions. Much of this study is based on the VE concept described elsewhere.6-8 Most simulations had very good transverse communication to ensure that VE was a good assumption. Unless noted otherwise, we forced VE by making the effective aspect ratio, RL=(L/h) kz/kx, large. For linear flow (the only kind considered here) RL is a good indicator of the approach to VE.* We performed a few runs at the other extreme of RL=0, but these proved to be unenlightening because good transverse communication is required to propagate fingers.9 We show one such case below; however, RL is generally large for field-scale displacements. A black-oil finite-difference simulator run in a miscible fluids mode8 was used to simulate first-contact-miscible displacements at the viscosity ratio of interest. A simulation grid of 120 x-direction blocks and 20 z-direction blocks was found to be relatively insensitive to further mesh refinement. Twelve-Cell Grid. Because the tradeoff between VDP and ?R is expected to be important, we chose a 12-cell grid of cases with three VDP values and four ?R values. We ran each cell in the grid at different mobility ratios, M, to differentiate between mobility stabilization, channeling, and fingering. Table 1 summarizes the input values and resulting properties of the generated fields, as well as the name by which each cell is designated in this paper. For example, a run at VDP=0.86 and ?R=0.17 is called Case 14 or Cell 14. In Table 1, the input values are the geometric mean, µG, and the standard deviation, s, of the log-normally distributed population sampled. The output values are the µG, the VDP, the standard deviation of the permeability data after a log-transformation back to a normal distribution, slnk, and the heterogeneity index, Ih, to be discussed later.
Time-lapse 3D – or 4D – seismic data have been tried in several fields to date, with some good case studies published to demonstrate the utility of the 4D seismic information. While another 4D case study would be useful, this paper describes two novel aspects of a recent application in the Gulf of Mexico. First, the target reservoir contains a gas condensate fluid under primary depletion, so pressure, rather than saturation, changes create the observed 4D acoustic response. Further, the primary impact of the pressure change is to the fluid composition as the initially dense gas phase lightens as condensate drops out below the dew point. The result was a 2.8% change in acoustic impedance predicted in the feasibility study. Second, the 4D seismic result was used to constrain an optimized history-matching procedure, along with the production data. After describing the method used, the paper will discuss the changes to the reservoir model that resulted. While the results should not be considered unique, they do give some insight intothe structure of the reservoir that should be considered for optimal reservoir management.
Seismic data provide essential information for guiding reservoir development. Improvements in data quality hold the promise of improving performance even further, provided that the value of these data exceeds their cost. Previous work has demonstrated value-of-information (VOI) methods to quantify the value of seismic data. In these examples, seismic accuracy was obtained by means of expert assessment instead of being based on geophysical quantities. In addition, the modeled seismic information was not representative of any quantity that would be observed in a seismic image.Here we apply a more general VOI model that includes multiple targets, budgetary constraints, and quantitative models relating poststack seismic amplitudes and amplitude-variation-withoffset (AVO) parameters to the quantities of interest for reservoir characterization, such as porosity and reservoir thickness. Also, by including estimated changes in data accuracy based on signal-tonoise ratio, the decision model can provide objective estimates of the reliability of measurements derived from the seismic data. We demonstrate this methodology within the context of a west Texas 3D land survey. This example demonstrates that seismic information can improve reservoir economics and that improvements in seismic technology can create additional value. Value of Seismic (VOS) Information.Consider an exploration and production (E&P) company that is designing a land-based infill-drilling program. The company has identified m infill targets but faces a budget constraint such that it can drill only b wells. Such a constraint could be the result of a limited capital budget or of rig availability. Let d=(d 1 , . . . , d m ) be an m-vector of drilling decisions, or a drilling program where d i 1ס if target i is to be drilled and 0 otherwise. Each drilled well will produce a value for the company, which is a function of the underlying reservoir properties (e.g., porosity, thickness, water saturation). Let v i represent the expected net present value (ENPV) (Brealey and Myers 1991) of Well i. We represent the reservoir properties at location i with the n-vector i , where n is the number of properties. Then ⍀(ס 1 , . . . , m ) is a matrix that describes the reservoir properties at each of the m locations. If we consider only porosity, thickness, and water saturation, then each reservoir-property vector contains three elements. At the time of the drilling decision, these properties are unknown and, hence, i is a random vector with prior probability distribution f i ( i ). The joint distribution over the reservoir properties at all locations is f(⍀).* This name is based on an analogy to a hiker that wants to fill his/her knapsack with the most-valuable items but is restricted as to how much can be carried. In our setting, we want to the most-valuable wells but can select only b of them.
Integration of time-lapse seismic and production data provides an effective tool for reservoir management. However, extensive work is required to build a "common" earth model1,2 honoring both types of data. This typically leads to longer turnaround times for time-lapse seismic projects. This paper demonstrates a method to shorten this time by reconciling production data with time-lapse seismic data in the data domain rather than in the earth model domain. The results from this method demonstrate that this quick evaluation can reveal whether or not the observed seismic differences represent reservoir changes associated with production, and can provide a basis for a more extensive model based evaluation. This method was applied to a gas reservoir in the Gulf of Mexico where preliminary rock physics modeling showed that water replacement would lead to more than 10% impedance change for approximately 30% of gas saturation change. The saturation-amplitude relation used to threshold the seismic difference volume was calibrated at the well or predefined locations. The threshold was optimized through solving the material balance relation obtained from production data with the time-lapse seismic data, thus making it more likely that the seismic differences are representative of saturation changes in the reservoir. This work:provides a new procedure for gas reservoir time-lapse analysis under certain geological and production conditions; anddemonstrates a new first order method to reconcile time-lapse seismic data and production data without employing time consuming reservoir characterization and flow simulations. This approach greatly reduces the turnaround time involved in the use of time-lapse seismic information for reservoir management. Further, the result could lead to better subsequent model based analyses1,2. Introduction A pilot study was initiated to evaluate the feasibility of using legacy 3D seismic time-lapse data as a potential reservoir monitoring tool to assist in planning future development efforts in a shallow oil and gas field in the Gulf of Mexico. The reservoir selected for initial evaluation was the shallowest of a series of stacked oil and gas pays. This choice was based both on seismic data quality and the desire to eliminate any possible effects of production in overlaying reservoirs. The target reservoir produces gas from a faulted anticlinal trap at a depth of about 3000 feet, and is normally pressured by a strong water drive. The reservoir has been producing from three wells, two of which are no longer producing due to high water production. Two 3D seismic surveys have been acquired since the time of initial production; one in 1987 and another one in 1995. During this interim period approximately 26.6 BCFG has been produced. Maps based on the 3D data show good structural conformance of seismic amplitude with known hydrocarbon/water contacts, and indicate potential drilling locations in undrilled fault blocks up-dip from the depleted wells. The technique developed in this study involves use of the two existing (legacy) 3D seismic datasets, in conjunction with well logs and production engineering data, to provide spatial constraints on estimates of produced and remaining reserves. Methodology Material balance is a popular and effective tool for reservoir engineering. The use of material balance can help to estimate reserve in the reservoir at a specified time, and analyze the production mechanism. However, it is difficult to provide spatial information for the reserve calculated from production data alone. On the other hand, time-lapse seismic does contain information of the spatial change of fluid, but unfortunately suffers from ambiguity with respect to fluid saturation. Integration of the two types of information will help to resolve much of this ambiguity, providing spatial information for the change in reserve with time. This in turn provides a way to monitor the reserve spatially in an efficient way.
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