Behavior of compacting reservoirs with restricted entry wells

We investigate the simultaneous effect of changes in thickness, permeability and porosity. These depend on changes in fluid pressure. Fluid withdrawal in stress-sensitive reservoirs may have serious environmental, technical and economic ramifications. Appraisal wells are often vertically drilled to delineate fluid contacts, reservoir extension, etc. Some of these may be of restricted entry type when tested. In addition, restricted entry production wells may be designed to mitigate fluid coning. The objective of this study is to predict the change in formation thickness and/or permeability in compacting reservoirs. The proposed method depends on the assumption of exponential pressure dependency of thickness, permeability and porosity, Pedrosa (1986). We consider vertical wells in confined reservoirs. The method depends on an initial value property, which may be explained as follows: the ratio between two pressure-dependent variables of the same type will remain constant and equal to its initial value. For example, the well penetration ratio will remain constant during fluid withdrawal. The initial value property is valid for any arbitrary dimensionless pressure function. Our restricted entry model is a generalization of a classical one. The methodology depends on the use of the finite cosine transform in the vertical direction and the Laplace transform in the radial (Hantush in J Hydraul Div 87(HY 4):83–98, 1961). His method depends on “primed values”. Any vertical distance normalized to the thickness is a primed variable. Hence, the primed variable is characterized by the initial value property. Then, his methodology may be extended to shrinking reservoirs. A reduction in fluid pressure may lead to altered permeability and reduced thickness. This may lead to reduced well performance and well integrity. In some cases, even subsidence at the surface and earthquakes may occur. Such dramatic consequences are rare. They are costly to amend, if possible at all. In the majority of reservoirs, the effect of stress sensitivity is mild. Severe cases, however, have occurred in many places around the world. Due to the environmental costs, possible problems should be identified and preventive actions are taken as soon as possible. We find that pressure transient analysis offers a promising and cost-effective technique to predict future consequences of compaction. A well test has the advantage that it may be conducted once a producing formation has been penetrated. Fluid injection with, or without, extraction may mitigate further damage. We find that fluid withdrawal at a reduced rate may have a palliative effect on reservoir compaction. Likewise, increasing the productive interval and/or the radial permeability has the same effect. Furthermore, a decreased viscosity will also alleviate the problem. Despite possible adverse consequences, reservoir shrinking has received little attention in pressure transient analysis

Deliverability of Wells in Shallow Confined Aquifers of Non-Integer Spatial Dimensions

We propose a generalized methodology to predictthe deliverability of wells in fractional drainage areas. Afractional model is characterized by a single term power-lawvariation of the rock properties. Such a model may provide amore realistic alternative than the traditional homogeneousreservoir model. For example, the traditional models may not be applicable for sparse fracture networks. We assume the validity of the fractional model and find that the homogeneous solution is included in the generalized model as a special case. Simultaneous solution of the reservoir- and vertical lift equation leads to an algebraic equation of second degree. Hence, the prediction of the flow rate delivered into a pipe-line at any pressure is easily available. We investigate the sensitivity of the flow rate to variations in wellbore head, reservoir and flow string properties

Analytical modeling of sub-surface porous reservoir compaction

Fluid extraction has led to compaction, land subsidence, flooding and even earthquakes many places around the world. Although rare, the environmental costs could be overwhelming. Once compaction has been identified, possible future consequences should be investigated. If deemed adverse, preventive actions should be started as soon as possible to mitigate future damage. The purpose of this study is to enable simultaneous prediction of possible changes in thickness and permeability by a simplified analytical model. These changes may occur simultaneously or separately. Although best, studies by numerical simulation are time consuming and expensive. A fluid extraction period may also be necessary to match the model to observed behavior. A pressure transient test, on the other hand, may be conducted once a formation has been penetrated. Due to simplicity and ease of application, we believe our methodology will be useful, at least as screening tool. Our model, which is a generalization of a classical one, Raghavan et al. (SPEJ 253:267–386, 1972) and Pedrosa (1986), has been extended to account for boundary dominated flow and for the effect of wellbore storage and skin. During the last decades, many studies have expanded and improved the Pedrosa theory. We rediscover the Pedrosa (1986) equations, but with a composite (sum) modulus replacing the permeability modulus and an additional modulus to thickness in the storability coefficient. Our model will simplify to the Pedrosa model and many others by simple changes in the input data. The traditional well test model, without stress-sensitivity, is included as limiting behavior. Most commercial well test simulators already include the majority of coding to take advantage of the proposed technique. We find that the value of the sum modulus may either enhance or mask the existence of stress-sensitivity. The latter may be an important problem in case of a negative permeability modulus. This could reduce the value of the sum modulus due to appearance of additional fractures. Then, results obtained with the present model are likely to be misleading. The present methodology should be used with caution under this condition. Important in situ fracture generation may be detected by strong micro seismic activity. Core analysis may also give a forewarning of brittle formations. The use of the proposed well test model leads to many different possible interpretations (non-uniqueness). Hence, selecting a plausible reservoir model depends on the existence of information that is independent of well testing. The proposed model may be of interest in ground water hydrology, for wastewater disposal, geothermal- and petroleum reservoirs. We derive equations for the dynamic behavior of the thickness and permeability