The Imperial College Lectures in Petroleum Engineering

The following sections are included:

• Preface
• About the Author
• Contents

The main aim of this work is to understand how oil, water and gas flow deep underground with application to hydrocarbon recovery.

As mentioned previously, material balance is one of the fundamental principles of reservoir engineering: keeping track of mass, and being able to convert readily from reservoir to surface conditions. In this section, we will encounter this concept several times. This is an essential, standard and powerful tool for using production data to predict recovery and to determine the principal reservoir drive mechanisms. It is used mainly to analyse primary production, but can — and should — be used as a check for any producing field…

Decline curve analysis is an empirical way to forecast production decline from measurements of production rate; it acts as a simple complement to material balance analysis, where rate dependence is not included…

We now divert our attention away from oil fields and petroleum recovery to the details of the science of how fluids are arranged in the pore space of rocks at the micron scale. This is necessary to have a good understanding of how multiple fluids — oil, water and gas — are configured in the pore space of the rock and how they flow…

We now properly introduce multiple phases in a porous medium. Before proceeding with the description of macroscopic, averaged properties, we will first use some illustrative examples in an attempt to provide some insight into displacement and fluid configurations at the pore scale. The emphasis in this section will be on understanding and appreciating the complexity of the pore space at the micron (pore) scale.

Now consider a porous medium that is initially fully saturated with water, and is water-wet. Then a non-wetting phase (oil) enters the porous medium. Imagine that this is done sufficiently slowly that the pressure drop across the oil (from Darcy’s law, described later) is small in comparison with the capillary pressure. This process is called primary drainage and is the process by which oil migrates from source rock to fill a reservoir. It is also the process by which injected carbon dioxide displaces brine in a storage aquifer…

Imbibition is the opposite process to drainage, where wetting fluid invades a porous medium containing non-wetting fluid. We normally only consider secondary imbibition, which is the invasion of wetting fluid into non-wetting fluid after primary drainage; i.e. there is some wetting fluid initially present in the porous medium. This is the process that occurs when water is injected to displace oil in a reservoir, when the aquifer encroaches into a gas field during production, or when brine displaces stored carbon dioxide, as the carbon dioxide rises in the storage aquifer…

The Leverett J-function is a way of expressing the capillary pressure in dimensionless form, which takes account for different average pore size and interfacial tensions. This is a very useful scaling for dealing with laboratory measurements that may be performed with fluid pairs and at conditions — in terms of average porosity and permeability — different from in the field…

As we discussed before, most reservoir rocks contain both oil-wet and water-wet regions. This means that during water invasion a negative capillary pressure (a water pressure higher than the oil pressure) needs to be applied to force oil out of the oil-wet regions…

We now introduce flow into our analysis — in particular Darcy’s law for flow in a porous medium — and provide a pore-scale basis for the relationship between flow rate and pressure gradient. We start with a consideration of single-phase flow (one fluid — by default water — saturates the pore space completely, and we consider the water movement and that of solutes dissolved in the water) before extending the analysis to multiphase flow (where oil, water and gas may all be present).

Darcy’s law describes the flow of a single species in a porous medium — typically water or oil. Later we will return to study flow with multiple phases; however, before broaching this difficult subject, we will first discuss transport of species dissolved in a single phase…

Now we will derive an equation for the conservation of mass of a component α in a porous medium. This component is considered to be dissolved in water where C^α is the density of species α per unit pore volume. The porosity is ϕ. Then ϕC^α is the mass of α per unit volume of the soil or rock. We start by considering flow in one direction (the x-direction) through a small volume of length Δx along x with cross-sectional area A…

Now we will return to multiphase flow in porous media and the concept of capillary pressure. In these notes, I presume that the fluid configurations are controlled by the Young–Laplace equation and contact angles. Fluid flow is slow and — as we show later — we presume that each phase flows independently…

We will now extend Darcy’s law to cases when multiple fluid phases are flowing. We assume that each phase flows in its own sub-network of the pore space without affecting the flow of the other phases. This is applicable for flow at low capillary and Bond numbers, where capillary forces dominate at the pore scale…

Oil, water and gas may all flow together in reservoirs. Examples include gas injection, including carbon dioxide injection, solution gas drive (when the reservoir pressure is dropped below the bubble point), gas cap expansion and steam injection. In environmental settings, when a non-aqueous phase pollutant migrates downwards towards the water table in a moist soil, there are three mobile fluid phases: the pollutant, water and air…

The approach so far in this volume has been physically motivated, with a minimum of equations. However, to provide some rigour and background to our comments on recovery, we will now derive flow equations for multiple phases in a porous medium.

We will now begin to construct an analytical solution for multiphase flow in one dimension. The derivation can be somewhat cumbersome and is helped if we first develop the concept of the fractional flow: the fraction of the total flow of oil and water that is taken by water alone…

The following sections are included:

• Counter-current Imbibition
• Extensions to Analytic Theory and Reservoir Simulation

Here are the references of the papers mentioned in the notes as well as other papers that are useful for reference and further reading…

These problems are useful to understand much of the material in these notes…

The following sections are included:

• Reservoir Engineering Examinations
• Flow In Porous Media Questions

The following section is included:

• Index