Interpretation of interwell connectivity tests in a waterflood system

This study is an extension of a novel technique to determine interwell connectivity in a reservoir based on fluctuations of bottom hole pressure of both injectors and producers in a waterflood system. The technique uses a constrained multivariate linear regression analysis to obtain information about permeability trends, channels, and barriers. Some of the advantages of this new technique are simplified one-step calculation of interwell connectivity coefficients, small number of data points and flexible testing plan. However, the previous study did not provide either in-depth understanding or any relationship between the interwell connectivity coefficients and other reservoir parameters. This paper presents a mathematical model for bottom hole pressure responses of injectors and producers in a waterflood system. The model is based on available solutions for fully penetrating vertical wells in a closed rectangular reservoir. It is then used to calculate interwell relative permeability, average reservoir pressure change and total reservoir pore volume using data from the interwell connectivity test described in the previous study. Reservoir compartmentalisation can be inferred from the results. Cases where producers as signal wells, injectors as response wells and shut-in wells as response wells are also presented. Summary of results for these cases are provided. Reservoir behaviours and effects of skin factors are also discussed in this study. Some of the conclusions drawn from this study are: (1) The mathematical model works well with interwell connectivity coefficients to quantify reservoir parameters; (2) The procedure provides in-depth understanding of the multi-well system with water injection in the presence of heterogeneity; (3) Injectors and producers have the same effect in terms of calculating interwell connectivity and thus, their roles can be interchanged. This study provides flexibility and understanding to the method of inferring interwell connectivity from bottom-hole pressure fluctuations. Interwell connectivity tests allow us to quantify accurately various reservoir properties in order to optimise reservoir performance. Different synthetic reservoir models were analysed including homogeneous, anisotropic reservoirs, reservoirs with high permeability channel, partially sealing fault and sealing fault. The results are presented in details in the paper. A step-by-step procedure, charts, tables, and derivations are included in the paper.

Sparse Neural Networks for Inference of Interwell Connectivity and Production Prediction

Summary A new neural network-based proxy model is presented for prediction of well production performance and interpretation of interwell connectivity in large oil fields. The workflow consists of two stages. The first stage uses feature learning to describe the general input-output relations that exist among the wells and to characterize the interwell connectivity. In the second stage, the identified interwell connectivity patterns are used as network topology to develop a multilayer neural network proxy model, with nonlinear activation functions, to predict the production performance of each producer. The estimation of connectivity patterns in the first stage serves as an interpretable feature-learning step to improve the effectiveness of the proxy model in the second stage. Identification of interwell connectivity is based on the selection property of the ℓ1-norm minimization by promoting sparsity in the estimated connectivity weights. The sparsity of the network is motivated by the domain knowledge that each production well is mainly supported by a few nearby injection wells. That is, a proxy model that allows each producer to communicate with all the other wells in the field is inherently redundant and must have an unknown sparse representation. The sparse structure of the connection weights in the resulting network is detected by promoting sparsity during the training process. Two synthetic numerical examples, with known solutions, are first used to demonstrate the functionality and effectiveness of ℓ1-norm regularization for interwell connectivity identification. The workflow is then applied to a real field waterflooding example in Long Beach to predict oil production and to infer interwell connectivity information. Overall, the workflow provides a proxy model that effectively combines the implicit physical information from simulated data with reservoir engineering insight to identify interwell connectivity and to predict well production trends.

Inferring interwell connectivity in a reservoir from bottomhole pressure fluctuations of hydraulically fractured vertical wells, horizontal wells, and mixed wellbore conditions

A technique using interwell connectivity is proposed to characterise complex reservoir systems and provide highly detailed information about permeability trends, channels, and barriers in a reservoir. The technique, which uses constrained multivariate linear regression analysis and pseudosteady state solutions of pressure distribution in a closed system, requires a system of signal (or active) wells and response (or observation) wells. Signal wells and response wells can be either producers or injectors. The response well can also be either flowing or shut in. In this study, for consistency, waterflood systems are used where the signal wells are injectors, and the response wells are producers. Different borehole conditions, such as hydraulically fractured vertical wells, horizontal wells, and mixed borehole conditions, are considered in this paper. Multivariate linear regression analysis was used to determine interwell connectivity coefficients from bottomhole pressure data. Pseudosteady state solutions for a vertical well, a well with fully penetrating vertical fractures, and a horizontal well in a closed rectangular reservoir were used to calculate the relative interwell permeability. The results were then used to obtain information on reservoir anisotropy, high-permeability channels, and transmissibility barriers. The cases of hydraulically fractured wells with different fracture half-lengths, horizontal wells with different lateral section lengths, and different lateral directions are also considered. Different synthetic reservoir simulation models are analysed, including homogeneous reservoirs, anisotropic reservoirs, high-permeability-channel reservoirs, partially sealing barriers, and sealing barriers.The main conclusions drawn from this study include: (a) The interwell connectivity determination technique using bottomhole pressure fluctuations can be applied to waterflooded reservoirs that are being depleted by a combination of wells (e.g. hydraulically fractured vertical wells and horizontal wells); (b) Wellbore conditions at the observations wells do not affect interwell connectivity results; and (c) The complex pressure distribution caused by a horizontal well or a hydraulically fractured vertical well can be diagnosed using the pseudosteady state solution and, thus, its connectivity with other wells can be interpreted.

Potential for Evaluation of Interwell Connectivity under the Effect of Intraformational Bed in Reservoirs Utilizing Machine Learning Methods

Machine learning method has gradually become an important and effective method to analyze reservoir parameters in reservoir numerical simulation. This paper provides a machine learning method to evaluate the connectivity between injection and production wells controlled by interlayer in reservoir. In this paper, Back Propagation (BP) and Convolutional Neural Networks (CNNs) are used to train the dynamic data with the influence of interlayer control connectivity in the reservoir layer as the training model. The dataset is trained with dynamic production data under different permeability, interlayer dip angle, and injection pressure. The connectivity is calculated by using the deep learning model, and the connectivity factor K is defined. The results show that compared with BP, CNN has better performance in connectivity, average absolute relative deviation (AARD) below 10.01% higher. Moreover, CNN prediction results are close to the traditional methods. This paper provides new insights and methods to evaluate the interwell connectivity in conventional or unconventional reservoirs.

Improved capacitance model considering bottom-hole flowing pressure and interference between oil wells

With the continuous production of oil wells, the reservoir properties, such as permeability and porosity, are changing accordingly, and the reservoir heterogeneity is also enhanced. This development is vulnerable to the problem of the one-way advance of injected water and low efficiency of water flooding. The interwell connectivity between injection and production wells controls the flow capacity of the subsurface fluid. Therefore, the analysis of interwell connectivity helps to identify the flow direction of injected water, which is of great significance for guiding the profile control and water plugging in the later stage of the oilfield. In this study, based on the principle of mass conservation, a capacitance model considering the bottom-hole flowing pressure was established and solved by using the production dynamic data of injection–production wells. Then, the validity of the capacitance model was verified by numerical simulation, and the influences of well spacing, compression coefficient, frequent switching wells, injection speed, and bottom-hole flowing pressure on interwell connectivity were eliminated. Finally, a practical mine technique for inversion of connectivity between wells using dynamic data was developed. The advantage of this model is that the production dynamic data used in the modeling process are easy to obtain. It overcomes the shortcomings of previous models and has a wider range of applications. It can provide a theoretical basis for the formulation of profile control and water-plugging schemes in the high-water-cut period.