Adaptive identification and interpretation of pressure transient tests of horizontal wells: challenges and perspectives

The paper deals with a topical issue of defining oil reservoir properties during transient tests of horizontal wells equipped with information-measuring systems and reducing well downtime. The aim is to consider challenges and perspectives of developing models and algorithms for adaptive identification and interpretation of transient tests in horizontal wells with pressure buildup curve analysis. The models and algorithms should allow analyzing flow behavior, defining oil reservoir properties and determining well test completion time, as well as reducing well downtime. The present paper is based on the previous theoretical and practical findings in the spheres of transient well testing, systems analysis, system identification, function optimization and linear algebra. Field data and results of transient well tests with pressure buildup curve analysis have also been considered. The suggested models and algorithms for adaptive interpretation of transient tests conducted in horizontal wells with resulting pressure buildup curve make it possible to analyze flow behavior, as well as define the reservoir properties and determine well test completion time. The algorithms for adaptive interpretation are based on the integrated system of radial flow PBC models with time- dependent variables, account of additional a priori information and estimates of radial flow permeability. Optimization problems are solved with the case study of PBC interpretation for five horizontal wells of the Verkhnechonsk field.


Introduction
Today, oil and gas companies intensively drill and exploit horizontal wells, which is attributed to implementation of resource efficient technologies. These wells are equipped with informationmeasuring systems to conduct transient well tests. Since petroleum reservoirs are structurally complex and the monitoring technologies of field exploration and development need to be improved, transient testing enhancement is a critical issue, which implies development of methods and algorithms to process research data and reduce well downtime.
It is noteworthy that the main source of information on the reservoir properties is transient well testing based on pressure buildup curve (PBC). The obtained data are necessary to manage oil recovery, work out field exploration and development projects, develop geological and technical models of petroleum recovery processes.
Currently, there are three basic approaches to develop methods and algorithms for adaptive identification and interpretation of PBC data: 1. Conventional approach to transient test data interpretation based on PBC analytical models [1][2][3]. 2. Interpretation of transient test data based on hydrodynamic simulation of the reservoir using differential equations containing partial derivatives [4][5]. 3. Adaptive identification and interpretation of transient tests in wells equipped with information-measuring systems [6,7]. Conventional approach to transient test data interpretation using PBC analytical models implies flow behavior analysis and solving an inverse problem of identifying filtration properties essential for the reservoir and well using a reservoir simulator corresponding to the definite flow.
One of the methods widely applied in transient test interpretation by both Russian and foreign specialists is the analysis of bottom hole pressure derivative (grapho-analytical method). For example, for the radial flow the slope of the tangent line to the bottomhole pressure derivative '  is equal to zero, while for the linear flow it is 0.5 [1][2][3]. However, with intensive implementation of telemetric systems, which allows monitoring hydrodynamic properties and real-time well operations, the application of conventional methods becomes challengeable.
This makes adaptive identification of transient tests in horizontal wells a promising method of realtime flow behavior analysis [6,7].
The challenge of transient test data interpretation based on hydrodynamic simulation of the reservoir using equations for flow filtration and their finite difference analogues is solving an inverse problem of identification during well test time. Currently, solving problems of real-time identification is a critical issue, since this is one of the limitations for hydrodynamic simulation to be applied in в real-time processing of data obtained via transient tests conducted in horizontal wells [8].
Another limitation essential for conventional methods of transient test data identification and interpretation based on PBC analytical models is their being quite expensive. This is due to the fact that the data are interpreted after well test completion, which results in well downtime and decrease in the amount of hydrocarbon recovery.
Today, obtaining real-time data necessitates implementation of new technologies, which ensure identifying filtration properties and to classify the reserves during well test time, without setting a time limit for test completion in advance. This approach was suggested and is currently developed by the Department of Geology and Oil Field Development, Tomsk Polytechnic University. It based on adaptive identification and interpretation of transient test conducted in the wells equipped with information-measuring systems [6,7,9,10].
The present paper continues the research on adaptive identification and interpretation of transient tests conducted in horizontal wells. It describes new data obtained in the course of the research on real-time flow behavior analysis and identification of reservoir properties during transient well test based on PBC models with time-varying parameters and additional a priori obtained data on the radial flow permeability of the reservoir.

Models and Algorithms of Real-Time Flow Behavior Analysis and PBC Interpretation
The method of flow behavior analysis during transient tests in horizontal wells is based on the estimate of radial flow permeability * , rt k , obtained at the current moment t : (1) and (2) The criterion to define the start of the radial flow regime is such a value of * Therefore, formula (6), as well as (5), can be used to define time instants of the radial flow.

Results of PBC interpretation with flow behavior analysis
The results of a case study of PBC interpretation with flow behavior analysis for five horizontal wells of the Verkhnechonsk field are given in figures 1-4 and tables 1, 2. For example, figure 1 shows the data on bottomhole pressure in wells 1 and 2. Figures 2-4 shows estimates of radial flow permeability (1), (3), estimates of radial flow permeability derivative (6) and PBC derivative      Table 1. Initial and additional a priori data on wells 1 and 2 It is worth noting that the horizontal flow observed between radial flows can be easily identified by the maximum point of the estimate derivative for the radial flow permeability (4), which is proved by the results of data interpretation for other horizontal wells (see table 2). Table 2 shows that the method of adaptive interpretation with radial flow behavior analysis allows reducing well downtime compared to that caused by the planned tests via Saphir software. For the five wells presented in table 2 there is a fivefold reduction in the test time, from 1053.55 to 213.03 hours. The cost of five wells downtime is $ 1 500 000 if the price is $ 50 per barrel.

Conclusion
The present research has described the challenges concerning identification and interpretation of transient tests conducted in horizontal wells equipped with information-measuring systems by analyzing PBC. The perspectives of adaptive identification and interpretation have been explored.
The algorithms have been developed to carry out adaptive identification and interpretation of the data on flow behavior analysis during the time of transient well test with resulting PBC, as well as to define the reservoir properties and determine well test completion time.
The case study of PBC interpretation with flow behavior analysis for five horizontal wells of the Verkhnechonsk field has indicated that the suggested models and optimal algorithms of adaptive identification and interpretation make it possible to significantly reduce well downtime, which results in cost advantage.