Introduction reservoir engineering 5 ( Unsteady or Transient-State Flow )

 The state of fluid flow is termed unsteady-state flow, if the rate of change of pressure

with respect to time at any position in the reservoir is not zero or constant. It is also

called transient state whose behavior occurs when the boundary effect of the

reservoir has not been felt and at this point, the reservoir is said to be infinite￾acting. It can simply be defined as the flow regime where the distance/radius of

pressure wave propagation from the wellbore has not reached any of the reservoir

boundaries as shown in the figure below. Thus, at a short period of flow, the reservoir

behaves as if it has no boundary, this will continue until the pressure transient gets to

the boundary of the reservoir. Therefore, after the reservoir boundary has been

contacted, the flow will either buildup to steady state or pseudo-steady state flow.

Pseudo-Steady with the Effect of Skin (Tables 1.4, 1.5

and 1.6a, b)

The pressure drop due to skin at the well is

Values of exponential integral,
Ei(
y)

PD vs tD – Infinite

radial system, constant rate at

inner boundary

PD vs tD – Finite radial system with closed exterior, constant rate at inner boundary

reD

¼ 4.5 reD

¼ 5.0 reD

¼ 6.0 reD

¼ 7.0 reD

¼ 8.0 r

Pseudo-Steady or Semi-State Flow

A reservoir attains pseudo-steady state (PSS), if the rate of change of pressure

decline with time is constant. The pressure throughout the reservoir decreases at

the same constant rate, this scenario cannot occur during build-up or falloff tests. In

this state of flow, the boundary has been felt and static pressure at the boundary is

declining uniformly throughout the reservoir. Mathematically, this definition states

that the rate of change of pressure with respect to time at every position in the

reservoir is constant, or a state where the mass rate of production is equal to the rate

of mass depletion. This state can also be referred to as semi-steady state (SSS) or

quasi-steady state.

Introduction reservoir engineering 4 (Types of Fluids in Terms of Flow Regime and Reservoir Geometry)

 The fluid in hydrocarbon reservoirs can be classified in terms of pressure change occurring as fluid flow from various path of the reservoir system to the wellbore. They are further classified in terms of flow regime and reservoir geometry. The reservoir fluid can either by incompressible, slightly compressible or compressible depending on the state of the pressure change in the reservoir. When the volume or density of the fluid does not change with pressure, it is called an incompressible fluid. This implies that as the pressure within the system changes, the volume of the fluid remains the same. This fluid behavior hardly exists but it is an assumption for easy derivation for fluid flow equations. For the case of a slightly Temperature 100% Liquid (Tr Pr) Dry Gas Fluid path in the reservoir Production path Dry gas reservoir (Twf Pwf) 0% Liquid 80% 60% 20% 5% Critical point Well bone Dew point curve Two phase region Bubble point curve Pressure Separator (Tsep, Psep) Fig. 1.14 Dry gas reservoir Table 1.2 Properties of wet and dry gas reservoir fluid Parameter Wet gas Dry gas Effect of pressure reduction There are tracies of liquid at the surface No tracy of liquid at the surface Gas-oil ratio (GOR) 100,000 scf/stb >100,000 scf/stb Color Light straw to water white Water white Viscosity Low Very low API >60 1.5 Types of Fluids in Terms of Flow Regime and Reservoir Geometry 19 compressible fluid, there is a little change in volume or density as pressure changes. Also, for fluid such as gase's are easily compressible and expand to fill the volume of its container; this makes gases to experience large changes in volume as a function of pressure. This is termed a compressible fluid.

1.5.1 Reservoir Geometry Petroleum reservoir is usually trapped with fluids that are looking for ways to flow out; once a well is drilled, cased and perforated, the trapped fluid then flows from all directions in the reservoir to the wellbore where it is produced to the surface facilities. The movement of hydrocarbon fluid towards the wellbore is either characterized as radial or linear depending on the flow direction. 1.5.1.1 Linear Flow Linear flow occurs when the paths at which the fluids flow are parallel to each other such that the movement is in a single direction. In this type of flow, the crosssectional area is assumed to be constant, thereby creating a laminar flow. This is represented in Fig. 1.15. 1.5.1.2 Radial Flow On the other hand, radial flow occurs when fluids move in a multi-direction within the reservoir towards the perforations at the wellbore, thus creating an iso-potential lines. The radial flow system is shown in Fig. 1.16.

1.5.2 Flow Regimes 1.5.2.1 Steady-State Fluids Flow This type of flow is referred to the condition at any single or given point in the reservoir where the properties such as pressure, temperature and velocity of the fluid does not change with time. It can be defined as the flow at which the rate of change of pressure (P) with respect to time (t) at any location i in the reservoir is zero as shown in the equation below. At this state of flow, all the boundaries effects have been felt but there is no decline in the static pressure at the boundary (called constant pressure boundary). This implies that in a system of mass flow rate, there is no accumulation of mass within any component in the system. Steady state flow is more applicable to laboratory displacement experiments than to petroleum reservoir conditions which are hardly seen. This scenario can only be seen in reservoirs undergoing pressure maintenance either by water or gas injection or when the reservoir is completely recharging and supported by a strong aquifer. This is to say that; there is a flow of fluid across the boundaries of the reservoir (unbounded reservoir).

Radial Flow Equation for Steady-State (Unbounded Reservoir) Incompressible Fluid By derivation for oil flow

1.5.2.4 Steady State with the Effect of Skin Practically, during drilling and completion operations, the permeability around the wellbore of most wells have been damaged or reduced thereby causes an impairment to flow of fluid and thus create an additional pressure drop near the wellbore. This impairment to flow is known as skin. Incorporating it into the flow equation gives:

1.5.2.5 Radial Flow Equation for Steady-State (Unbounded Reservoir) Slighty Compressible Fluid

Radial Flow Equation for Steady-State (Unbounded Reservoir) Compressible Fluid (Gases) Low pressure approximation

Calculation of Real Gas Potential, m(p) The m(p) can be calculated graphically or read from Tables. The graphical method requires that P, μ, z be given and m(p) calculated from the area under a curve (Table 1.3). This is illustrated below using the trapezoid method to calculate the area under the curve. Trapezoidal rule

Introduction reservoir engineering 3 (Gas Reservoirs)

 Gas Reservoirs

Hydrocarbon reservoir can be called gas reservoir, if the temperature of the reservoir is greater than the cricondentherm of the hydrocarbon fluid. This is only applicable to non-associated gas reservoirs which can either be wet or dry gas depending on the phase present in the reservoir and at the surface separator. 1.4.5.5 Wet-Gas Reservoirs A natural gas system which contains a significant amount of propane, butane and other liquid hydrocarbons is known as wet gas or rich gas. It contains less amount of methane (85%) and more ethane than dry gas. Figure 1.13 shows a wet gas reservoir which exists solely as a gas in the reservoir throughout the reduction in reservoir

pressure. It temperature lies above the cricondentherm of the hydrocarbon mixture similar to a dry gas reservoir. The reservoir fluid will always remain in the vapor phase region as the reservoir is depleted isothermally, along with the production path unlike retrograde condensate; no liquid is formed inside the reservoir. However, separator conditions lie within the phase envelope, causing some liquid to be formed at the surface. This surface liquid is normally called condensate. Wet-gas reservoirs are characterized by gas oil ratios between 60,000 to 100,000 scf/STB, stock-tank oil gravity above 60 API, the liquid is water-white in color and separator conditions lie within the two-phase region. 1.4.5.6 Dry Gas Reservoir The hydrocarbon mixture of a dry gas exists as a gas in the reservoir (even in the two phase region) and in the surface separator characterized with a gas-oil ratio greater than 100,000 scf/STB. It contains mainly methane with some intermediates. The pressure or production path does not enter into the phase envelope (two phase region) as shown in Fig. 1.14, this means that the surface separator conditions fall outside the phase envelope which is in contrast to wet gas reservoir; hence there is no traces of liquid formed at the surface separator. Natural gas which occurs in the absence of condensate or liquid hydrocarbons, or gas that had condensable hydrocarbons removed, is called dry gas. It is primarily methane with some intermediates. The hydrocarbon mixture is solely gas in the reservoir and there is no liquid (condensate surface liquid) formed either in the reservoir or at the surface. The pressure path (line) does not enter into the phase