A Comparison of Travel-Time and Amplitude Matching for Field-Scale Production Data Integration: Sensitivity, Non-Linearity and Practical Implications

2003 ◽  
Author(s):  
Hao Cheng ◽  
Akhil Datta-Gupta ◽  
Zhong He
Keyword(s):  
Data Integration ◽  
Travel Time ◽  
Production Data ◽  
Scale Production ◽  
Field Scale ◽  
Practical Implications

Application of Flow Diagnostics to Rapid Production Data Integration in Complex Grids and Dual-Permeability Models

SPE Journal ◽  
2020 ◽  
Vol 25 (04) ◽  
pp. 2000-2020
Author(s):  
Feyi Olalotiti-Lawal ◽  
Gil Hetz ◽  
Amir Salehi ◽  
David Castineira
Keyword(s):  
High Resolution ◽  
Data Integration ◽  
Travel Time ◽  
Finite Volume ◽  
Time Shift ◽  
Production Data ◽  
Analytical Sensitivity ◽  
Flow Diagnostics ◽  
Naturally Fractured ◽  
Streamline Tracing

Summary Streamline-based methods, as repeatedly demonstrated in multiple applications, offer a robust and elegant framework for reconciling high-resolution geologic models with observed field responses. However, significant challenges persist with the application of streamline-based methods in complex grids and dual-permeability media due to the difficulty with streamline tracing in these systems. In this work, we propose a novel and efficient framework that circumvents these challenges by avoiding explicit tracing of streamlines but exploits the inherent desirable features of streamline-based production data integration in high-resolution geologic models. Our approach features the application of flow diagnostics to inverse problems involving the integration of multiphase production data in reservoir models. Here, time-of-flight as well as numerical tracer concentrations for each well, on the basis of a defined flux field, are computed on the native finite-volume grid. The information embedded in these metrics are used in the dynamic definition of stream-bundles and, eventually, in the computation of analytical water arrival-time sensitivities with respect to model properties. This calculation mimics the streamline-derived analytical sensitivity computation used in the well-established generalized travel-time inversion (GTTI) technique but precludes explicit streamline tracing. The reservoir model property field is updated iteratively by solving the LSQR (sparse least-squares with QR factorization) system composed of the computed analytical sensitivity and the optimal water travel-time shift, augmented with regularization and smoothness constraints. The power and efficacy of our approach are demonstrated using synthetic model and field applications. We first validate our approach by benchmarking with the streamline-based GTTI algorithm involving a single-permeability medium. The flow-diagnostics-derived analytical sensitivities were observed to show good agreement with the streamline-derived sensitivities in terms of correctly capturing relevant spatiotemporal trends. Furthermore, the desirable quasilinear behavior characteristic of the traditional streamline-based GTTI technique was preserved. The flow-diagnostics-based inversion technique is then applied to a field-scale problem involving the integration of multiphase production data into a dual-permeability model of a large naturally fractured reservoir. The results clearly demonstrate the effectiveness of the proposed approach in overcoming the limitations of classical streamline-based methods with dual-permeability systems. By construction, this approach finds direct application in single/multicontinuum models with generic grid designs, both in structured and fully unstructured formats, thereby aiding well-level history matching and high-resolution updates of modern geologic models. This work presents, for the first time, an application of the GTTI to dual-permeability models of naturally fractured reservoirs. This is facilitated by a simplified, yet effective approach to travel-time sensitivity computations directly on finite-volume grids. The proposed approach can be easily applied to subsurface models at levels of complexity identified as challenging for classical streamline-based methods.

Streamline-Based Production Data Integration With Gravity and Changing Field Conditions

SPE Journal ◽  
2002 ◽  
Vol 7 (04) ◽  
pp. 423-436 ◽  
Author(s):  
Zhong He ◽  
Seongsik Yoon ◽  
Akhil Datta-Gupta
Keyword(s):  
Data Integration ◽  
Field Conditions ◽  
Production Data

Compressible Streamlines and Three-Phase History Matching

SPE Journal ◽  
2007 ◽  
Vol 12 (04) ◽  
pp. 475-485 ◽  
Author(s):  
Hao Cheng ◽  
Adedayo Stephen Oyerinde ◽  
Akhil Datta-Gupta ◽  
William J. Milliken
Keyword(s):  
History Matching ◽  
Adjoint Equations ◽  
Production Data ◽  
Time Inversion ◽  
Field Scale ◽  
Flow Equations ◽  
Sensitivity Coefficients ◽  
Adjoint State ◽  
Gradient Based ◽  
Water Cut

Summary Reconciling high-resolution geologic models to field production history is still by far the most time-consuming aspect of the workflow for both geoscientists and engineers. Recently, streamline-based assisted and automatic history-matching techniques have shown great potential in this regard, and several field applications have demonstrated the feasibility of the approach. However, most of these applications have been limited to two-phase water/oil flow under incompressible or slightly compressible conditions. We propose an approach to history matching three-phase flow using a novel compressible streamline formulation and streamline-derived analytic sensitivities. First, we use a generalized streamline model to account for compressible flow by introducing an "effective density" of total fluids along streamlines. This density term rigorously captures changes in fluid volumes with pressure and is easily traced along streamlines. A density-dependent source term in the saturation equation further accounts for the pressure effects during saturation calculations along streamlines. Our approach preserves the 1D nature of the saturation equation and all the associated advantages of the streamline approach with only minor modifications to existing streamline models. Second, we analytically compute parameter sensitivities that define the relationship between the reservoir properties and the production response, viz. water-cut and gas/oil ratio (GOR). These sensitivities are an integral part of history matching, and streamline models permit efficient computation of these sensitivities through a single flow simulation. Finally, for history matching, we use a generalized travel-time inversion that has been shown to be robust because of its quasilinear properties and converges in only a few iterations. The approach is very fast and avoids much of the subjective judgment and time-consuming trial-and-error inherent in manual history matching. We demonstrate the power and utility of our approach using both synthetic and field-scale examples. The synthetic case is used to validate our method. It entails the joint integration of water cut and gas/oil ratios (GORs) from a nine-spot pattern in reconstructing a reference permeability field. The field-scale example is a modified version of the ninth SPE comparative study and consists of 25 producers, 1 injector, and aquifer influx. Starting with a prior geologic model, we integrate water-cut and GOR history by the generalized travel-time inversion. Our approach is very fast and preserves the geologic continuity. Introduction Integration of production data typically requires the minimization of a predefined data misfit and penalty terms to match the observed and calculated production response (Oliver 1994; Vasco et al. 1999; Datta-Gupta et al. 2001; Reis et al. 2000; Landa et al. 1996; Anterion et al. 1989; Wu et al. 1999; Wang and Kovscek 2000; Sahni and Horne 2005). There are several approaches to such minimization, and these can be broadly classified into three categories: gradient-based methods, sensitivity-based methods, and derivative-free methods (Oliver 1994). The derivative-free approaches such as simulated annealing and genetic algorithm require numerous flow simulations and can be computationally prohibitive for field-scale applications with very large numbers of parameters. Gradient-based methods have been widely used for automatic history matching, although the rate of convergence of these methods is typically slower than that of the sensitivity-based methods, such as the Gauss-Newton or the LSQR method (Vega et al. 2004). An integral part of the sensitivity-based methods is the computation of sensitivity coefficients. There are several approaches to calculating sensitivity coefficients, and these generally fall into one of the three following categories: perturbation method, direct method, and adjoint state methods. The perturbation approach is the simplest and requires the fewest changes to an existing code. This approach requires (N+1) forward simulations, where N is the number of parameters. Obviously, this can be computationally prohibitive for reservoir models with many parameters. In the direct, or sensitivity-equation, method, the flow and transport equations are differentiated to obtain expressions for the sensitivity coefficients (Vasco et al. 1999). Because there is one equation for each parameter, this approach can require the same amount of work. A variation of this method, called the gradient simulator method, utilizes the discretized version of the flow equations and takes advantage of the fact that the coefficient matrix remains unchanged for all parameters and needs to be decomposed only once (Anterion et al. 1989). Thus, sensitivity computation for each parameter now requires a matrix-vector multiplication. This method obviously represents a significant improvement, but still can be computationally demanding for large number of parameters. Finally, the adjoint-state method requires derivation and solution of adjoint equations that can be significantly smaller in number compared to the sensitivity equations. The adjoint equations are obtained by minimizing the production data misfit with flow equations as constraint, and the implementation of the method can be quite complex and cumbersome for multiphase flow applications (Wu et al. 1999). Furthermore, the number of adjoint solutions will generally depend on the amount of production data and thus can be restrictive for field-scale applications.

scholarly journals Groundwater Flux, Travel Time, and Radionuclide Transport

1994 ◽  
Vol 353 ◽  
Author(s):  
Dwayne A. Chesnut
Keyword(s):  
Rock Mass ◽  
Travel Time ◽  
Fractured Rock ◽  
Site Characterization ◽  
Total System ◽  
Radionuclide Transport ◽  
Field Scale ◽  
Groundwater Flux ◽  
Permeability Distribution ◽  
Log Normal

AbstractInflow measurements at Stripa and in other underground openings in Sweden, as well as observations elsewhere in mines and tunnels, reveal that there is generally an extremely broad distribution of groundwater flux in fractured rock. Non-sorbing and sorbing tracer tests typically show similar variability in groundwater travel time (GWTT) and tracer transport.In the U.S. Nuclear Waste Program, Nuclear Regulatory Commission regulations require the GWTT from the disturbed zone to the accessible environment to exceed 1000 years. The regulations seem to envision a rather uniform and narrow distribution of travel time, with perhaps a few identifiable “fast pathways” contained within the rock mass surrounding a potential repository. The premise is that most of these features could be mapped during site characterization, and that regions of the potential repository host rock containing such features could be avoided during waste emplacement.However, both field experience and theoretical studies in recent years provide strong evidence that groundwater flux, GWTT, and aqueous transport of dissolved substances exhibit extremely heterogeneous behavior, even in intact porous media and in fractured rock regions between major features. These phenomena are all dominated by the spatial distribution of permeability within the rock mass of interest. The permeability distribution is often approximately log-normal, with a natural log standard deviation, σ. For unfractured porous rock, σ typically ranges from about 0.6 to about 1.2 for field-scale investigations, and for fractured permeable media, it frequently exceeds 2. Values of σ smaller than 0.6 may be observed in small field-scale projects when the macroscopic flow regime is essentially linear within very uniform sediments and in laboratory displacement experitments.With some additional assumptions, a log-normal permeability distribution implies that groundwater flux, GWTT, and the transport of radionuclides from a potential repository are also log-normal. To first order, the appropriate value of σ describing these distributions is the same as the value for the permeability distribution. This allows σ to be estimated from a large number of hydraulic or pneumatic packer tests within the fractured rock mass of interest.We define a groundwater transport function (GWTF) for the rate of radioactivity release to the accessible environment (AE) at time t resulting from the release of a pulse of unit activity at time 0. The GWTF depends on the mean groundwater travel time, tw, and σ, as well as the retardation factor and decay constant. As σ increases from 0 (a hypothetical completely homogeneous system), the radioactivity breakthrough at early time increases from 0 to 100%. This behavior is consistent with our intuitive notions of “fast transport pathways” in heterogeneous systems, and σ is thus seen to be a parameter for quantifying the effects of heterogeneity.Convolution of the GWTF with a time-dependent release function for the Engineered Barrier System (EBS) is easily performed numerically, resulting in the rate of release to the AE as a function of time, which can then be integrated numerically to calculate the cumulative release as a function of time. The convolution approach clearly separates the effects of uncertainty and heterogeneity on repository performance and is extremely useful for sensitivity analyses. An example calculation shows the combinations of σ and tw required for compliance with total system release standards.Since the effect of heterogeneity is captured by a single parameter in a deterministic calculation, uncertainty can be investigated separately by Monte Carlo sampling from distributions of such parameters as σ, tw and source term strength, allowing (in the future) specific and scientifically meaningful goals to be defined for both site characterization and design.Finally, we emphasize that this approach, in its present form, does not include thermal effects. These effects may dominate both the EBS failure rate and hydrogeochemical behavior, including radionuclide transport, for most of the compliance period and beyond. It cannot be used directly to support any particular thermal loading strategy.

Field Scale Production Decline Characteristics During Gravity Drainage

2012 ◽  
Author(s):  
Akshay Sahni ◽  
Dale Beeson ◽  
David A. DiCarlo
Keyword(s):  
Gravity Drainage ◽  
Scale Production ◽  
Field Scale
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