Design of Objective Function for Interference Well Testing
Authors: Booth Richard , Bertolini Andre Carlos , Morton Kirsty Lorna , Fitzpatrick A. J. 
Published: June 2014

Abstract
Multi-well interference tests are performed among neighboring wells for reservoir characterization, to assess heterogeneity, and to estimate formation mobility and storativity in the area of these wells. Interference tests are particularly useful where there is some uncertainty in the geology between two wells, such as the conductivity of a fault, fracture corridors in naturally fractured media, or other sources of significant heterogeneity. However, the analysis of such interference tests can be challenging. During an interference test, a volume of influence develops around and between the wells, and the dynamic pressure response from the two wells may be used for interpretation. Reservoir transmissibility and borehole storage are the main elements affecting the attenuation of the pressure response. Accurate, high resolution, pressure measurements become more important for smaller pressure responses, to enable the data to be used for reservoir description. The relative size of the pressure differences observed at each well and the small absolute pressure change at the observation well(s) may become a challenge to the interpretation of the data.
In this paper we review the methods available to quantitatively interpret interference test data from multiple wells simultaneously. Concentrating on grid-based parameter estimation methods, we propose an objective function that is designed to effectively combine data from source and observation wells. Combining data from different wells requires weighting and scaling of the measurement errors in the objective function to ensure the relative impact of each data set is correctly accounted for. Different weighting strategies are tested to explore the impact on pressure match.
Our objective function permitted us to simultaneously incorporate the data from both the observation and source wells. This allowed us to more effectively apply methods grid-based parameter estimation for the inversion of reservoir properties from pressure transient test data for interference tests. By determining what values of measurement error used in the objective function lead to the best interpretation, we are able to suggest an acceptable level of noise in test design.

Introduction
In single-well testing, the primary objective is to focus on the near-well region. Significant information is collected during the well test that can improve the reservoir characterization in this region. To investigate the area between wells, more than one well must be directly involved in the test. Multi-well interference tests are performed among neighboring wells for reservoir characterization, to assess heterogeneity, and to estimate formation mobility (k/µ) and storativity (f, c), where k = permeability, µ = viscosity, f = porosity, and c = compressibility in the area of these wells. The most common interference test is done between two wells: one is the active (producing) well and the other one is the observation well. In the active production (or injection) well, single or multiple drawdown tests and a subsequent buildup test are performed while the observation well is shut-in for the duration of the test. Interference well tests are particularly useful to delineate fault conductivities (or non-conductivities), natural fracture conductivities and distribution within the reservoir, and heterogeneity in general. Combined with conventional single-well testing, interference well test can also improve the understanding of reservoir layering, fracture orientation and the location of barriers to the flow. In most applications of interference testing, flow rates are measured at the surface, wellbore pressures are measured downhole, and wellbore storage significantly affects pressure measurements at both wells.