Fikri J. Kuchuk

Estimating permeability distribution from 3D interval pressure transient tests

Abstract In this paper, the basic features of 3D (spatially r and z and time) interval pressure transient testing (IPTT) are described for the estimation of horizontal and vertical permeabilities and delineation of fracture and fault conductivities using the packer module and observation probe tool combination of the multiprobe wireline formation tester. Mathematical models for the pressure behavior of IPTT tests for using the packer module and the observation probes in multilayer (stratified) formations are presented. The maximum likelihood (ML) method is presented for nonlinear parameter estimation to handle uncertainty in error variances (weights) in observed data. The main advantage of the ML method over the traditional weighted least squares (WLS) is that it eliminates the trial-and-error procedure required to determine appropriate weights to be used in the WLS estimation. As shown by the examples presented in the paper, the ML method provides significant improvement in parameter estimation when working with pressure data sets of disparate orders of magnitude and noise, e.g., pressure measurements for the packer–probe and multiprobe interval tests. A field example where eight IPTT tests were conducted in a major carbonate formation is presented for characterization of vertical and horizontal layer permeabilities and vertical communication through the main producing reservoir section. These IPTT tests were conducted with a Formation Tester Dual Straddle Packer and two Probe Modules in a newly drilled well. An IPTT test at each location was interpreted using an appropriate geological model with the packer and probe pressure and flow rate measurements. The interpretation procedure consisted of identification of the different flow regimes followed by history (type curve) matching for the estimation of vertical and horizontal permeabilities for each layer. A detailed interpretation of two of the interval pressure transient tests is presented.

A New Pressure/Rate-Deconvolution Algorithm To Analyze Wireline Formation-Tester and Well-Test Data

Reconstructing constant-rate drawdown-pressure response and its logarithmic time (or Bourdet) derivative by deconvolution from multirate pressure-transient data is very important for wellbore-/ reservoir-system identification and interpretation. In recent years, the use of pressure/rate deconvolution has increased considerably because of significant improvement of the algorithms. In this paper, we present a new deconvolution algorithm based on a weighted Euclidean norm in the Tikhonov (1963) regularized objective function so that one can assign weights to individual pressureand rate-measurement points, and, thus, define different error estimates for different sections of the data. Incorporating such features into the deconvolution algorithm is very useful to mitigate the effects of unreliable pressure and rate measurements and the sections of the data not obviously consistent with the wellbore/reservoir model. We present two applications of the new algorithm using real field pressure/rate transient data sets. In addition to conventional drillstem-test (DST) well-test data, we apply the algorithm to wireline formation-tester (WFT) pressure transients, which are usually also referred to as interval pressure-transient tests (IPTTs). The results show that the new deconvolution algorithm presented in this paper is useful in interpreting pressure/rate transient data from both formation and well tests.

Pressure behavior of the MDT packer module and DST in crossflow-multilayer reservoirs

Abstract General analytical solutions are presented for the pressure behavior of the MDT Packer Module and observation packer-probe in layered (laminated) reservoirs with formation crossflow. These solutions are also applicable to the pressure behavior of partially penetrated wells in layered reservoirs and are particularly useful for the interpretation of DST tests. The reflection and transmission method is used to solve the single-phase fluid flow equation in an infinite anisotropic reservoir, which consists of horizontal layers with crossflow. The solutions are applicable to any possible combination of no-flow, constant-pressure, and infinitely thick layer conditions at the top and bottom boundaries. The advantages of this solution technique are that it always gives solutions with good numerical convergence properties. Indeed, a new computationally efficient analytical solution for a partially penetrated well in a single-layer reservoir is presented. The wellbore storage due to the chamber and flow lines volume and skin effects are included. The pressure variations along the length of the well are taken into account by the use of pressure averaging. It is shown that if the system has only a few layers, it exhibits the transient characteristic features of the system. If the number of layers increases substantially, the systems behavior may not show any characteristic feature if the contrast between the layer permeabilities are high.

Pressure Transient Behavior of Horizontal Wells Intersecting Multiple Hydraulic Fractures in Naturally Fractured Reservoirs

In this study, we present a mesh-free semi-analytical technique for modeling pressure transient behavior of continuously and discretely hydraulically and naturally fractured reservoirs for a single-phase fluid. In our model, we consider a 3D reservoir, where each fracture is explicitly modeled without any upscaling or homogenization as required for dual-porosity media. Fractures can have finite or infinite conductivities, and the formation (matrix) is assumed to have a finite permeability. Our approach is based on the boundary element method. The method has advantages such as the absence of grids and reduced dimensionality. It provides continuous rather than discrete solutions. The uniform-pressure boundary condition over the wellbore is used in our mathematical model. This is the true physical boundary condition for any type of well, whether fractured or not, provided that the friction pressure drop in the wellbore is small and the fluid is Newtonian. The method is sufficiently general to be applied to many different well geometries and reservoir geological settings, where the spatial domain may include arbitrary fracture and/or fault distribution, a number of horizontal wells with and without hydraulic fractures, and different types of outer boundaries. The model also applies to multistage hydraulically fractured horizontal wells in homogenous reservoirs. More specifically, it is applied to investigate the pressure transient behavior of horizontal wells in continuously and discretely naturally fractured reservoirs, including multistage hydraulically fractured horizontal wells. A number of solutions have been published in the literature for horizontal wells in naturally fractured reservoirs using the conventional dual-porosity models that are not applicable to many of these reservoirs that contain horizontal wells with multiple fractures. Most published solutions for fractured horizontal wells in homogenous and naturally fractured reservoirs ignore the presence of the wellbore and the contribution to flow from the formation directly into the unfractured horizontal sections of the wellbore. Therefore, some of the flow regimes from these solutions are incorrect or do not exist, such as fracture-radial flow regime. In our solutions, all or some of multistage hydraulic fractures may intersect the natural fractures, which is very important for shale gas and oil reservoir production. The number and type of fractures (hydraulic or natural) intersecting the wellbore and with each other are not limited in both homogeneous and naturally fractured reservoirs. Our solutions are compared with a number of existing solutions published in the literature. Example diagnostic derivative plots are presented for a variety of horizontal wells with multiple fractures in homogenous and naturally fractured reservoirs.

Permanent Gauge Pressure and Rate Measurements for Reservoir Description and Well Monitoring: Field Cases

This paper presents a procedure for interpreting data acquired with permanent downhole pressure sensors in association with surface or downhole rate measurements. The usefulness of this data source in reservoir description and well performance monitoring is illustrated. Unlike previously published examples, the interpretation is based on the analysis on a stream of data acquired over large periods of time, thus utilizing the continuous nature of the measurements. Three field cases are presented using the pressure and rate data in decline-curve analysis for wells with a variable downhole flowing pressure, and through more sophisticated models that are similar to the ones used in well test analysis. Because such interpretation is conducted while continuing production, it is particularly well suited for a well or group of wells under extended testing, which are equipped with downhole gauges and are flowing through surface separation and metering systems. Wells completed with both permanent downhole rate and pressure measurements are also ideal candidates for this type of analysis. Finally, the influence of the pressure sensor long term drift and the rate measurement error on the interpretation results and future forecasts are investigated.

Integrated Interpretation for Pressure Transient Tests in Discretely Fractured Reservoirs

In 2005, Petrobras discovered a fractured Albian carbonate reservoir in Campos Basin. During the evaluation of an appraisal well, a full sequence of well tests (DSTs) and a 4-month extended well test (EWT) were performed to monitor reservoir behavior and to define the most probable geological reservoir model before the final development decision was made. While the results of the well test sequence were sufficiently favorable for development, the well test analysis raised concerns about the quantitative use of these tests for reservoir characterization. The seismic sections of the field indicated faulting, and open fractures were interpreted from image logs in the appraisal wells. However, the response of the DSTs and EWT did not indicate classical dual porosity type behavior that is consistent with an extensive connected fracture network system. The fractures in this reservoir are considered to be predominantly open in one direction only. Few methods exist for the interpretation of the pressure transient response of discretely fractured reservoirs where fractures provide conduits for fluid flow and displacement, but where the fracture network is poorly connected compared to dual porosity models. In this paper, we first outline the gaps in the existing pressure transient well test interpretation methodology for these reservoirs, then we introduce two new techniques developed to address these gaps: 1) A reservoir model-based inversion technique for parameter estimation from pressure transient data, and 2) A boundary element method for determining the pressure transient behavior of the reservoir with arbitrarily distributed finite and/or infinite conductivity vertical fractures. We define a new integrated interpretation methodology for reservoirs with discrete natural fractures making use of these techniques and incorporating openhole log data, seismic and the preliminary geological reservoir model. Finally, we illustrate the use of the methodology using the tested well.

Nonlinear Regression Analysis of Well-Test Pressure Data with Uncertain Variance

The main objective of this study is to explore the use of parameter estimation techniques that handle cases where error variances (weights) in observed well-test data are uncertain. There are two main sources of uncertainty: 1) The gauge resolution and 2) measurement environment. Many gauges are used in well testing are not well characterized in terms of accuracy and resolution. The measurement environment in the wellbore is very noisy because of high frequency events in the wellbore (any producing interval), eg phase segregation. Because of these uncertainties, in this study, we investigated the use of parameter estimation methods based on the maximum likelihood and presented a new efficient method based on this method. The maximum likelihood method enables one to estimate error variances in pressure data along with the unklnown formation parameters. It is shown that the new method is efficient and powerful in estimating formation parameters from well-test data with uncertain variance. A simulated interval test from the multiprobe wireline formation tester in a single layer system as well as a field interval test in a three layer cross-flow system are used to demonstrate the applicability of the proposed methods.

A new method for determination of reservoir pressure

Frequently, well tests in low-permeability (tight) or low-pressure reservoirs are difficult to interpret because they do not flow to the surface or sustain the now rate long enough for conventional interpretation methods to be used. An impulse-test technique has been developed to determine reservoir pressure from pressure-buildup tests. ○ The technique is based on the wellbore-pressure solutions to an instantaneous source, including wellbore-storage (afterflow) effects. ○ It is applicable to different flow regimes, such as cylindrically and spherically radial. ○ It is general enough that it may be applied to a wide variety of well/test configurations, such as drillstem tests (DSTs) and wireline formation tests in vertical and horizontal wells. ○ It can be applied to wells in unconsolidated formations where produced sand plugs the wellbore during flow periods.

A Novel Analysis Procedure for Estimating Thickness-Independent Horizontal and Vertical Permeabilities from Pressure Data at an Observation Probe Acquired by Packer-Probe Wireline Formation Testers

This paper presents a new spherical-flow cubic-analysis procedure for estimating horizontal and vertical permeabilities solely from pressure transient data acquired at an observation probe of the dual-packer-probe wireline formation testers (WFTs) for all inclination angles of the wellbore.

Grid-Based Inversion Methods for Spatial Feature Identification and Parameter Estimation from Pressure Transient Tests

We present and compare three different grid-based inversion methods for estimation of formation parameters and spatial geological feature identification based on pressure transient test (PTT) data from multiple-well locations. The first and second methods employ efficient adjoint schemes to determine the gradient of the objective functions resulting in the most likely set of reservoir parameters and an ensemble of updated realizations of the parameters, respectively. The second method is based on the Langevin equation. The third method uses ensemble Kalman filtering (EnKF) for data assimilation, in which the outcome is an ensemble of updated parameter realizations. These three methods use a grid-independent prior model (in view of the limited prior knowledge of the system expected to be available), described by as few parameters as possible, and consider a non-uniform grid with the highest resolution near the wells. With these methods, the existence of and location of many subseismic features such as strong spatial permeability variations, faults, fractures and pinch outs may be determined using exploration and production data. Such features may not be known a priori, particularly in the exploration of heterogeneous carbonate reservoirs. We examine each method considering the degree of prior information required, the computational overhead and the applicability to the reservoir characterization workflow. Our results indicate that the first method provides a good history match to the observed PTT data and is suited for the early exploration phase of the reservoir. However, the parameters must be convolved with the smaller scale data to produce multiple realizations away from the implausibly smooth most-likely solution. The observed PTT data lies within the ensemble of predicted pressures in the EnKF and Langevin-based methods which are both applicable to probabilistic workflows where uncertainty is treated rigorously. However, EnKF seems to be computationally more efficient than the Langevin approach. Introduction Pressure transient testing (PTT) is a long established procedure for determining the productivity of a well and the properties of the formation (reservoir) from downhole and/or surface pressure and flow rate measurements. The main steps for interpretation are:1. Model identification: a possible set of reservoir models are found that may fit the data, 2. Model parameter estimation: the model parameters are adjusted until the model behavior matches the observed data, 3. Model verification: the consistency of the final model is verified by measuring the mismatch between the real system and the model or by comparison with other data. Using conventional interpretation methods (semilog methods such as Horner or MDH, and/or type-curve matching of measured pressure and/or derivative), reservoir pressure, an effective ‘average’ permeability of the formation, skin factor, wellbore storage, etc. can be estimated from the PTT data. In such interpretation, some sort of prior modeling is always necessary to constrain the non-linear parameter estimation because a model with many non-physical reservoir parameters may match the observed PTT data. This prior knowledge may be available at small scale from logs and cores and, at a larger scale, from seismic and outcrop analogies. Recently, non-linear least-squares optimization has been applied to pressure transient data using numerical models with a similarly limited number of parameters; often models that are divided into a small number of regions, within which the reservoir parameters are assumed to be constant. As the need for more spatial resolution of the parameters increases, we turn to “pixel” methods where the physical properties of the reservoir are discretized on a pixel-like grid over the reservoir domain. Pixel or grid based methods have been applied for classical history matching on a field scale with multi-well data (Oliver 1996; Oliver et al. 2001). Based on