Paolo Macini

Non-Darcy Flow: Laboratory Measurements in Unconsolidated Porous Media

In recent years, the petroleum industry has shown a renovated interest in Non-Darcy flow, in order to better understand reservoir performances. Non-Darcy flow is typically observed in gas wells when the fluids converging to the wellbore attains the velocity peculiar of turbulent flow. As a consequence, pressure drop around the wellbore cannot be estimated from the classic Darcy equation, where the pressure gradient is a linear function of the flow velocity. In that case, in fact, the use of Darcy equation would lead to inaccurate production performances evaluation. In order to describe correctly this phenomenon, the well-known Forchheimer equation is normally used, where the inertial coefficient β is defined. In gas wells this coefficient is usually determined by the analysis of multi-rate pressure tests performed on site. Unfortunately, such data are not easily available (or not economical) in many cases. So, it is a common practice to use particular theoretical and empirical correlations that can be derived by exploiting experimental values of the inertial coefficient. This paper reports a laboratory study in which the inertial coefficient β can be correlated to the structure of the porous media, and, in particular, of its grain size distribution. Gas flow laboratory experiments have been performed on laboratory models of glass beads and natural sands of different sizes. Moreover, porosity and permeability, together with the Klinkenberg constant, have been determined on natural sand cores with both flat and peaked grain size distribution, and a correlation with the Forchheimer equation has been checked. Forchheimer’s number has been calculated and correlated to the superficial velocity as well. In the light of the above, specific laboratory equipment has been devised in order to rely on a wide range of flow rate under appropriate pressure gradients. Introduction When a fluid is flowing through a porous medium there are different flow regimes that may exist, depending on local fluid velocity through the porous space. These are generally known as Darcy flow, Weak Inertia flow (Pre-Darcy flow, according to Basak), Non-Darcy flow or turbulent flow. As a consequence, pressure losses in the different flow regimes may be described by different equations that are reasonably valid also for describing the flow in fractured porous media. As far as fluid flow in reservoir conditions is concerned, in regions sufficiently far from the wellbore fluid velocity is low and Darcy’s law remains valid. It is possible to reproduce such flow rates in the lab and to study the fluid behavior. On the contrary, in the region near the wellbore the high pressure gradient induces both large condensate saturation and high gas velocity which may lead to significant deviations from Darcy’s law, in both single-phase and two-phase flow. Thus, the near wellbore region plays a key role in the productivity decline of the well. At the present time physically relevant models exist which take into account these Non-Darcy (or inertial) two-phase flow effects. A better description of flowing properties may lead to improved predictions of well performances and its productivity decline. Inertial effects appear to be stronger for a gas phase flowing at high flow rates in a porous medium in the presence of a mobile liquid rather than a non-mobile one, even though this has never been supported by any conclusive experiment and reliable correlation haven’t been yet fully formulated. In recent years, the petroleum industry has shown a significant interest in Non-Darcy flow studies, especially applied to the field of fractured rocks. Hydraulic fracturing treatment is in fact necessary to put on stream low permeability hydrocarbon reservoirs at commercial flow rates. Hydraulic fracturing is the process of injecting high pressure fluid into a well to create tensile stresses in the formation exposed to the fluid pressure. If the stresses become large enough they will break down the formation and fractures are initiated. The fracturing fluid must contain a proppant so that the fractures will remain open beyond the period of pumping and crack propagation. Actually, in this case the productive well capability and the overall reserves recovery estimation can be lowered by the effect of reduction of a propped half-length to a considerably shorter

Darcy's Law from Water to the Petroleum Industry: When and Who?

Henry Darcy, in an appendix of his work Les Fontaines Publiques de la Ville de Dijon , described the law governing the flow of water through a saturated sand filter. In this law, flow velocity is correlated to hydraulic gradient by means of a linear proportionality constant K, defined as permeability ( permeabilite ). In using this terminology, Darcy apparently followed the practice of hydraulic engineers of his time. Indeed, the permeability concept formulated by Darcy is known today as hydraulic conductivity, a flow parameter describing both the physical properties of the porous medium and the characteristics of the fluid. Only in the 1950s did M. K. Hubbert provide a complete theoretical foundation to Darcys empirical expression, deriving it from the general Navier-Stokes equations. It is important to remember that Darcys law was already utilized in many technical fields, and especially in the petroleum industry. In the petroleum industry Darcys law is formulated in terms of pressure gradient and generalized for oil and gas flow, which led to the concept of multiphase flow. This was accomplished by separating the properties of the rock from that of the fluid by manipulating the proportionality constant K, thereby obtaining a generalized law. By doing so, permeability becomes a property of the porous media, dictated by pore geometry alone. The origin of the generalization of Darcys law can be traced back to the work of American geoscientists at the end of the 1920s. The present paper proposes to establish when and by whom Darcys law was first generalized and made suitable for petroleum reservoir engineering. In particular, the paper retraces some historical developments of the permeability concept by reviewing the earliest studies that contributed to the popularization of the generalized form of Darcys law for fluid flow other than water.

Preliminary Investigations on Glycol-enhanced Water-based Drilling Fluids

Abstract This paper investigates the inhibitive effects of some water-based muds prepared with polymers, glycol and inorganic electrolytes formulated to reduce the instability of shaly formations encountered in the drilling of hydrocarbon wells. Experimental have been carried out by means of hot rolling test and capillary suction time techniques. Results show that the addition of small amounts of glycol to inhibitive systems, such as KCl + PHPA water based drilling fluids, allow the acquisition of inhibition values typical of oil-based muds, a class of fluids which is subject to stricter and stricter environmental regulations. Glycol enhanced water-based drilling fluids are environmentally acceptable and potentially non-toxic.