Well test analysis for a well adjacent to a no-flow boundary or a fault presents a significant interpretation challenge. The interpretation difficulty stems from the fact that early-time skin- and storage-dominated period and the subsequent boundary-dominated period obscure the middle-time data. Consequently, conventional semilog or type-curve analyses are difficult to perform. Because of dominating influence of inner and outer boundary conditions, an appropriate interpretation model is necessary for the estimation of reservoir parameters. This work presents analytical models to analyze data for a well located at various distances from a fault, having wellbore storage and skin effects. The models are cast in the familiar graphical format with dimensionless variables - known as type curves. These type curves exhibit a different character than those of Gringarten et al (or an infinite-acting reservoir. Both constant wellbore storage and exponential decline storage cases are considered in this work. The new type curves offer the potential for reservoir parameter estimation of permeability, skin and wellbore storage coefficient. Additionally, the distance to a fault could be estimated. Application of the new type curves, using an automated matching technique, is demonstrated through field examples. Data from several wells located in highly faulted off-shore gas and oil reservoirs in south-east Asia are used for the purpose. Difficulty of analyzing the data using conventional semilog analysis is also shown in this work. This study further shows that only the very early-time data (less than 10 minutes) that are affected by the wellbore storage effect are amenable to pressure- rate-time or convolution analysis, obeying the radial-cylindrical flow model.
Petroleum reservoirs often contain linear barriers in the form of sealing faults, discontinuities and the like. Presence of these impermeable barriers have a profound effect on transient pressure behavior of a nearby well. Since 1951, many authors have studied wellbore pressure behavior in presence of a single fault, faults intersecting at an angle and in presence of parallel faults. A comprehensive review of these works published until 1977 appear in Reference 2. Appropriate models for locating a pinchout boundary have also been developed recently. Horner first reported doubling of slope on a pressure buildup semilog graph because of presence pressure buildup semilog graph because of presence of a no-flow boundary. On the other hand, Russell and Pinson have shown the existence of similar characteristic features during two-rate flow testing. A number of other authors show the detection of no-flow boundaries from pressure buildup interpretation. The time of intersection of the two semilog straight lines yields information on distance to the fault. In particular, Gray and Earlougher and Kazemi give criteria for producing time necessary for development of doubling of slope on the Horner graph. However, methods, are also suggested to estimate the distance to a fault even when the second semilog line does not develop on the Horner graph because of inadequate producing time. Reservoir anisotropy plays an important role on fault detection as indicated by Overpeck and Holden. They show that the distance to the fault could be in error by as much as 20 percent if anisotropy is not accounted for. None of the published work consider the effects of wellbore storage and skin, however. The many cases the early-time data, distorted by wellbore storage and skin effects, are the only data available for analysis because of close proximity of the well to a fault. The other words, storage-dominated early-time period and boundary-dominated late-time period may period and boundary-dominated late-time period may cause either the middle-time period to disappear or cause too severe a distortion to allow conventional semilog analysis. The such a situation, conventional models are not suitable for transient analysis. The purpose of this work is to investigate the effects of a single linear barrier on pressure behavior of a well with wellbore storage and skin. Analytical models are presented that account for both constant and variable wellbore storage coefficients for a well located in a faulted reservoir. Automated type curve matching is used to interpret field data. This work further shows that only by convolving the simultaneously measured bottomhole pressure (BHP) and bottomhole flow rate (BHF) could pressure (BHP) and bottomhole flow rate (BHF) could we interpret the early-time data, using the radial- cylindrical flow model. For the field examples considered here, radial-cylindrical flow model could be applied only up to a flow time of 10 minutes, beyond which boundary effects start to distort the transient response.
Constant Rate Case: Without Skin and Storage Effects
A fully-penetrating well, in a horizontal, homogeneous reservoir having a constant viscosity, slightly compressible fluid is considered here. The fault cuts the infinite reservoir, containing the well, at a distance x = d as shown on Figure 1. The dimensionless pressure for a well described above produced at a constant rate without the effects of wellbore storage and skin is given by Horner as : d 2 1 D p (r,t) = - E (- - Ei (-) ,.......(1) p (r ,t) = - E (- - Ei (-) ,.......(1) D D D i 4t 4t D D
where, kh (t) pD = [pi - pwf] pD = [pi - pwf] 41.2qB o
0.000264 kt tD = C r 2 t w
rD = r/r w dD = 2d/r w r = radial distance from the wellbore axis
d = distance from wellbore axis to the linear barrier
For a constant producing rate and in the absence of wellbore storage effect, interpretation of transient data using Equation 1 is straightforward as shown in References 1 and 22. However, the wellbore storage may mask the partial or entire pressure response of a well given by Equation 1. Conceivably, the characteristic behavior of a reservoir with a linear barrier could be distorted if the distance, d, is short and/or the wellbore storage duration is long. The effect of wellbore storage could be easily eliminated or reduced if the downhole flowrate is measured and analyzed along with the bottomhole pressure. Practicality may however limit downhole pressure. Practicality may however limit downhole flowrate measurement in every well.