Water influx Carter-Tracy Model

 This method is an approximate solution to the diffusivity equation. It can be

combined conveniently with a suitable material balance equation to predict the

performance of water-drive reservoirs. The Carter-Tracy aquifer models can be

applied to both finite and infinite-acting aquifers. It can be applied to both radial

and linear aquifers and also applies to edge-water drive reservoirs only. Mathemat￾ically, 

it is calculated as

Steps in Calculating Carter-Tracy’s Aquifer Model

Step 1: Calculate the total pressure drop at each time step

Step 2: Calculate the dimensionless time at each time step

Step 3: Calculate the dimensionless pressure and pressure derivative at each time

step

Step 4: Calculate the water influx at each time step (Table 4.8)

Table 4.8 Carter-Tracy aquifer model calculation

Example 4.5

Repeat Example 4.3 using the Carter Tracy’s aquifer model to calculate the cumu￾lative water influx at each time step.

Water Influx

Introduction

Water influx can also be referred to as water encroachment or aquifer influx. It can be

defined as an underground layer of water-bearing porous rock which flows out into

any available space in the reservoir rock. In this context, an aquifer is referred to as a

large pool of water body underlying a hydrocarbon accumulation in the reservoir

structure that is made up of more than one fluid arranged according to density

differences. Prior to hydrocarbon accumulation, the original system was occupied

or filled with water and during the drainage process; the migrated hydrocarbons from

the source rock displaced some of the water out of the pore space in the reservoir.

This means that majority of hydrocarbon pools discovered globally have an associ￾ated aquifer which could be a key source of energy (primary recovery) for the

hydrocarbon production once a well is drilled.

4.1.1 Classification of Aquifer Influx

Aquifer influx can be classified based on pressure maintenance, outer boundary

conditions, flow regime, flow geometry as shown in Fig. 4.1.

The classification of aquifer system as shown in Fig. 4.1, is key to understanding

and evaluation of hydrocarbon reservoirs performance. As hydrocarbon is produced

from the reservoir, the pressure of the reservoir declines (changes) and the aquifer

responds to offset the pressure decline due to fluids production, which is dependent

on the strength of the aquifer. Besides, if there is a strong support from the aquifer,

there will be a gradual decline in the reservoir pressure leading to a good hydrocar￾bon recovery. Also, there will be fairly steady gas-oil ratio during the life of the

reservoir with excessive water production in shallow wells.

Consequently, in evaluating the performance of hydrocarbon reservoirs, we need

to accurately determine the amount of water encroaching into the reservoir whose

value is dependent on the water viscosity, the permeability of the rock in the aquifer

and the cross-sectional area between the water zone and the region where the

hydrocarbon is accumulated

Aquifer Models

There are several analytical aquifer models presented in the past to estimate the

amount of water encroaching into hydrocarbon reservoirs and some of these models

are briefly presented below. The aquifer analytical models make use of simplified

assumptions that do not consider the heterogeneous nature of the reservoir but a

relatively homogeneous reservoir which has deterred the ideal comparison that is

adopted in the analytical solutions. But when the equations are accurately

discretization, they are relatively easy to program in computer spreadsheets with

the exception of the Van Everdingen & Hurst, whose model does not demand much

computer power.

4.2.1 Pot Aquifer Model

This method is one the simplest model for estimating the amount of water

encroaching into hydrocarbon reservoirs. Mathematically, it is given as

Schilthuis Model

Schilthuis (1936) was the first to develop useful expressions for calculating water

influx in a hydrocarbon reservoir. His steady-state expression is given by:

Hurst Modified Steady-State Model

Analysis of water expansion into a hydrocarbon reservoir indicates that water influx

should often be an unsteady-state process. Hence, the Hurst modified steady-state

eq. (1958) should give better results. The equation is:

Van Everdingen & Hurst Model

Van Everdingen & Hurst method of calculating water influx requires the principle of

superposition which is a tedious exercise, but it provides an exact solution to the

radial diffusivity equation and can be applied at the early stage. To abate the

intricacy of water influx calculations, Carter and Tracy (1960) proposed a direct

water influx calculation technique that does not require superposition. The primary

difference between Carter-Tracy and Van Everdingen & Hurst techniques is that the

former assumes constant water influx rates over each finite time interval. Hence, the

cumulative water influx at any time “tn” can be calculated directly from previous

values obtained at tn-1.

 

Condensate Reservoir Calculation

Condensate Reservoir Calculation

The example applies here for calculating condensate in place was written by Engr.

Ogbarode Napoleon Ogbon in his Lecture note on Natural Gas Engineering II.

3.5.1 Applications of Gas and Condensate Inplace Value

• Determination of economic value of gas and condensate in place to make a

decision on project economic viability

3.5.2 Major Points for Consideration

• As the gas-condensate reservoir fluid pressure drops below the dew point, liquid

hydrocarbon (condensate) will begin to drop.

• It is necessary to recombine the condensate with the gas in a proper ratio to

calculate the original volume of gas-in-place 

in the reservoir 

Data Required to Allow Estimates of the Gas-in-Place

Volume Are

• The geologic data

• The reservoir data

• The production data

• The geologic and reservoir data are used to provide plots of gas

compressibility, etc.

• This method uses standard charts and simple equations to calculate hydrocarbon￾in-place volumes in gas-condensate reservoirs.

3.5.4 Method Basic Requirements

• It is based on correlations established by Rzasa and Katz (2011) and provides a

means to calculate the gas-in-place volume in a gas-condensate reservoir Based

on

– The amount of produced gas

– The amount of produced associated condensate.

• Plots of correlations based on this method are readily available for use.

• However, it requires a clear understanding of the behaviour of oil and gas under

various reservoir and surface operating conditions including:

– Reservoir pressure and temperature, or depth to calculate the required

parameters,

– Compositions of oil and gas or their gravities and molecular weights,

– Gravities and production rates of separator condensate and gas,

– Rock porosity,

– Gas or interstitial water saturation

– Area-thickness, in the absence of which calculations are based on one acre of

reservoir volume.

Deterministic Versus Probabilistic Volumetric estimation reserve

The aspect of uncertainty in hydrocarbon reserves estimation cannot be

overemphasized since the estimation of reserves is done under conditions of uncer￾tainties. There are basically two methods of returning the results of reserves estima￾tion for any of the techniques such as volumetric, material balance, decline curve etc.

employed for reserves estimation. These methods are the deterministic and proba￾bilistic methods. Thus, if a single best estimate of reserves is made based on known

geological, engineering and economic data, the method is called deterministic whose

procedure is to select a single value for each parameter to input into an appropriate

equation (volumetric, material balance, decline curve etc.), to obtain a single answer.

In volumetric method, all input parameters are exactly known and variability is

sometimes ignored.

On the other hand, when the known geological, engineering, and economic data

are used to generate a range of estimates and their associated probabilities; the

method of estimation is called probabilistic. This method is more rigorous and less

commonly used; it utilizes a distribution curve for each input parameter and through

the use of Monte Carlo Simulation. In this method, all input parameters are not

exactly known and variability cannot be ignored.

Since the oil and gas business is associated with some inherent uncertainties, it

implies that a quality control and assurance should be made before making any

decision to develop the hydrocarbon prospect because a wrong evaluation of the

hydrocarbon initial in place leads to a wrong decision which in turn leads to an entire

failure of the field development. However, a comparison of the deterministic and

probabilistic methods can provide quality assurance for estimating hydrocarbon

reserves. This means that when the values of the reserves calculated deterministi￾cally and probabilistically agree with minimal deviation or tolerance of error, then

confidence on the calculated reserves is increased. On the contrary, when there is a

significant difference in value, then the assumptions made need to be reexamined.

A Monte-Carlo technique is employed to evaluate hydrocarbons in place where

each input parameter required for the reserves estimation are represented by statis￾tical distributions. Monte-Carlo methods are mainly used in three distinct problem

classes, such as optimization, numerical integration and generating draws from a

probability distribution. There are basically five types of statistical distribution used

with this method. 

 

What is a Contour

 Contour is an imaginary line on the ground surface joining points of equal elevation

or a line on which every point is at the same level above or below a chosen reference

surface. In most maps, the reference surface is sea level. This line on the map

represents a contour and is called contour line.

Therefore, a map showing contour lines is known as Contour map. Contour maps

are one of the most effective means of displaying information about the geologic

structure (i.e. the degree of buckling and faulting of the layers) of an area. A contour

map gives an idea of the altitudes of the surface features as well as their relative

positions in the plan. A map showing structure contours for a certain rock layer

throughout an area is called a structure contour map (Fig. 3.1). Such maps are used

to illustrate the size, shape and location of geologic structures.

Contour lines are drawn as fine and smooth freehand curved lines. Sometimes

they are represented by broken lines. They are inked in either in black or brown

colour. A drawing pen gives a better line than a writing pen and French curves

should be used as much as possible. Every fifth contour is made thicker than the rest.

The elevation of contours must be written in a uniform manner, either on the

higher side or in a gap left in the line. When the contour lines are very long, their

elevations are written at two or three places along the contour. In the case of small￾scale maps, it is sufficient to figure every fifth contour. Therefore, the constant

vertical distance between two consecutive contours is called the contour interval.

The contour interval is constant between the consecutive contours

Methods of Contouring

There are basically two main methods of locating contours; these are the Direct

Method and Indirect Method.

Direct Method

This method requires a lot of time to be invested in searching for points of the same

elevation on the ground surface. This implies that it is very slow and tedious but it is

the most accurate method of contouring, thus suitable for small area and where great

accuracy is required. In this method, the contours to be located are directly traced out

in the field by locating and marking a number of points on each contour. These

points are then surveyed and plotted on plan and the contours drawn through them

(Fig. 3.2).

For a radial line, temporary benchmarks are first established at the centre and near

the ends of the radial lines. The contour points are then located and marked on these

lines and their positions are determined by measuring their distances along the radial

lines. They are then plotted on the plan and the contours drawn by joining all the

corresponding points with the help of a plane table instrument (Fig. 3.3).

3.3.1.2 Indirect Method

In this method, the points located and surveyed are not necessarily on the contour

lines but the spot levels are taken along the series of lines laid out over the area. The

spot levels of the several representative points representing hills, depressions, ridge

and valley lines and the changes in the slope all over the area to be contoured are also

observed. Their positions are then plotted on the plan and the contours drawn by

interpolation. This method of contouring is also known as contouring by spot levels.

Conversion from Planimeter Unit to Field Unit

For a map scale of 1:10,000

Volumetric Reserves Estimation

 Overview of Reserve Estimation

The estimation of hydrocarbon reserves for a producing field is a process that

continues throughout the entire life of the field. This process is usually associated

with some level of uncertainties in calculating the reserves. These reserves estima￾tion methods are affected by the reservoir type, sources of reservoir energy (drive

mechanism), quantity and quality of the geologic, engineering and geophysical data,

the assumptions adopted when making the estimation, available technology, the

experience and knowledge of the evaluator(s). The oil and gas reserves estimation

methods can be grouped into the following categories: analogy, volumetric, decline

analysis, material balance calculations for oil and gas reservoirs, and reservoir

simulation.

The selection of appropriate method to estimate reserves and resources, and the

accuracy of the estimation, depend largely on the following factors: The type,

quantity, and quality of geoscience, engineering, and economic data available for

technical and commercial analyses, the complexity of the formation geology, the

recovery mechanism, the stage of development, and the maturity or degree of

depletion. More importantly, reserves and resources assessment rely on the integrity,

skill and judgment of the experienced professional evaluators (PRMS

Guideline 2011)

In the early stages of development, reserves estimations are restricted to the

analogy and volumetric calculations. The analogy method is applied to reserves

estimation by comparing factors for the analogous and current fields or wells. This

implies that in analogy method, the reserves are estimated on the basis of a

relationship of resemblance or equivalence between two fields. This method directly

compares a poorly or newly discovered reservoir to a known reservoir that has

similar geologic and petrophysical properties such as lithology of the formation,

depth, porosity to mention a few. Hence, the accuracy with this method is the least

among other methods of reserve estimation.

Furthermore, a close-to-abandonment analogous field is taken as an approxima￾tion to the current field. This method is the most useful technique when running the

economics on the current field; which is supposed to be an exploratory field

(Petrobjects 2003).

3.2 Volumetric Method

The volumetric method is probably the easiest method used by engineers to estimate

reserves. It requires a limited amount of data for the estimation, this implies that

immediately after discovery of the hydrocarbon accumulations, during initial delin￾eation and development of a field, the volumetric method is the key to hydrocarbon

volume estimation. Reserves estimation is often high with this method, because it

does not consider the heterogeneity of the reservoir and it includes the undrained

compartments that do not account to flow and are included in making up the bulk

rock volume of the reservoir or accumulation. At this stage, the level of inherent

error can be reduced if the reservoir is accurately described or characterized.

3.2.1 Errors in Volumetric Method

Volumetric method is subject to considerable error because it is often used to

evaluate reserves when little data are available; it requires the estimation of the

reservoir rock and fluid properties and the reservoir volume from spot measurements

of the properties that are then applied to the entire reservoir. The porosity and

saturation are measured either from core samples or logs that are measured from a

small portion of the reservoir and under best circumstances, it only approximates the

condition in the reservoir. The areal extent of the reservoir is rarely known until

many wells are drilled while the volume is estimated using zone thickness measured

at one or more points in the reservoir. The volumetric method is only seen as a gross

estimate of oil or gas in place.

Application of Volumetric Method

• The volumetric result is useful in reserves estimation of the initial oil and gas in

place.

• The volumetric result is useful in reserves estimation of oil and gas in place at any

time of depletion.

• Volumetric estimation is useful during the development period before reservoirs

limit have been defined.

• Later in the life of the reservoir, when reservoir volume is defined and perfor￾mance data are available, volumetric estimation provide valuable checks on oil

and gas in place estimates obtained from material balance and reservoir simula￾tion methods.

The volumetric method is a straightforward approach which requires determination

of the areal extent of the reservoir or bulk volume (calculated as area times pay

thickness), the rock pore volume, and the fluid content within the pore volume to

calculate the amount of hydrocarbons-in-place. The ultimate recovery can thus be

estimated by applying an appropriate recovery factor. Each of the variables used in

the volumetric reserves calculation above has inherent uncertainties, and when

combined; cause significant uncertainties in the reserves estimate (Petrobjects

2003). Therefore, the following steps consist the volumetric method of reserves

estimation:

Step 1: Determination of hydrocarbon rock bulk volume (hydrocarbon saturated

portion) from area and thickness (isopach map). Explanation of this method is

presented in the next page.

Step 2: Determination of average porosity either from core analysis or well logs.

From core analysis

Calculation of Reservoir Bulk Volume (Table 3.1)

The volumetric method of reserves estimation largely depends on the bulk volume,

calculated as follows:

(a) Prepare a structure map with contours from top to bottom of the reservoir, in

subsea depths

(b) Mark out a small square on the map e.g. (10 cm 10 cm). Use the scale on the

map to determine the area of the square in acres. Planimeter the square and

determine the area in planimeter units. Then determine the planimeter constant in

acres/planimeter unit by dividing the actual area in acres by the area into

planimeter units. Use the planimeter constant to covert the areas of the map

from planimeter units to acres.

Trapezoidal Rule 

Pyramidal Rule

To calculate the bulk volume of the reservoir from Isopach or contour map, there

is need to understand the concept of contouring which can be defined as the process

of tracing contour lines on the surface of the earth. This is not only applicable to

petroleum engineers but contour survey is also carried out at the beginning of any

engineering project such as a road, a railway, a canal, a dam, a building etc.

Identification of Uncertainty in Reserves Estimation

Numerous uncertainties exist in estimating reserves and remaining recoverable

resources of conventional oil held by countries. These uncertainties include: geo￾logic, production performance, product market and uncertainties in oil price forecast,

the use of ambiguous definitions and inclusion of different subcategories of conven￾tional oil by reporting sources, the inclusion of politics in reserves estimation, the

inconsistent and unclear effects of aggregation of reserve data to country and

regional estimation, the anticipated volume of undiscovered oil, and the nature and

extent of reserve growth and its allocation to individual countries.

2.5.1 Uncertainty in Geologic data

Uncertainties arising from geological data include errors in getting the exact loca￾tions of the geologic structure, the field size, pay thickness, porosity and permeabil￾ity variation, reservoir and aquifer sizes, reservoir continuity, fault position,

petrofacies determination, and insufficient knowledge of the depositional environ￾ment. A number of techniques are available for the quantification of geologic

uncertainties. One of the widely used techniques is to quantify the uncertainty in

the geological model with a geostatistical tool. Geostatistics involves synthesizing

geological data using statistical properties such as a variogram (Bennett and Graf

2002). This process enables the geologists to generate multiple realizations of the

geological models (Stochastic) which allows quantification and minimization of

uncertainties associated with the geological information.

Uncertainty in Seismic Predictions

• The quality of the seismic data (bandwidth, frequency content, signal-to-noise

ratio, acquisition and processing parameters, overburden effects, etc.)

• The uncertainty in the rock and fluid properties and the quality of the reservoir

model used to tie subsurface control to the 3D seismic volume

2.5.3 Uncertainty in Volumetric Estimate

The uncertainties in reservoir volume estimate will arise from several properties and

characteristics of the reservoir.

2.5.3.1 Gross Rock Volume (GRV) of a Trap

• The incorrect positioning of structural elements during the processing of the

seismic and lack of definition of reservoir limits from seismic data

• Incorrect interpretation

• Errors in the time to depth conversion

• Dips of the top of the formation

• Existence and position of faults

• Whether the faults are sealing to prevent further lateral migration of the

hydrocarbon

2.5.3.2 Rock Properties: Net-to-Gross and Porosity

The uncertainty associated with the properties of the reservoir rock originates from

the variability in the rock. It is determined through petrophysical evaluation, core

measurements, seismic response, and their interpretation. Most times, the core

samples are not properly handled carefully in the process of transporting it from

the field to the laboratory for analysis. Also in the laboratory, artificial properties are

induced during the core preparation and analysis. While petrophysical logs and

measurements in the laboratory may not be quite accurate, the samples collected

may be representative only for limited portions of the formations under analysis.

Thus, there are some risks associated with the petrophysical parameters estimation

such as depth matching, operational risks, log interpretation and reservoir

heterogeneities.

Fluid Properties

For fluid properties, a few well-chosen samples may provide a representative

selection of the fluids. The processes of convection and diffusion over geologic

times have generally ensured a measure of chemical equilibrium and homogeneity

within the reservoir, although sometimes gradients in the fluid composition are

observed. Sampling and analysis may be a significant source of uncertainty. PVT

or fluid properties vary with pressure, temperature, and chemical composition from

one region to another. As a result of this regional trend, correlations developed from

regional samples that are predominantly paraffinic in nature may not provide

acceptable results when applied to other regional crude oil systems that are dominant

in naphthenic or aromatic compounds.

The effective use of PVT correlations depends on the knowledge of their devel￾opments and limitations. In addition, samplings of these properties are not always

readily available due to cost and time. Thus, the engineers in view of achieving their

goals resort to the use of empirically derived correlations in estimating these

properties. However, a significant error is usually associated with the estimation of

these fluid properties which in turn propagates additional errors in all petroleum

engineering calculations.

2.5.3.4 Fluid Contacts

One of the parameters required for the estimation of hydrocarbon reserve is the gross

rock volume (bulk volume of the rock) whose accuracy is dependent on the fluid

contacts (gas-oil and/or water-oil contact). Therefore, if the contacts are not ade￾quately determined, it will lead to either over or under estimation of the bulk volume.

Thus, affecting the overall value of the estimated reserve.

2.5.3.5 Recovery Factor (RF)

Recovery is based on the execution of a project and it is affected by the shape and the

internal geology of the reservoir, its properties and fluid contents, and the develop￾ment strategy. If a reservoir is poorly defined, material balance calculations or analog

methods may be used to arrive at an estimate of the range of RFs. Uncertainty ranges

in the RF can often be based on a sensitivity analysis. Besides, the reservoir drive

mechanism and the problem of reservoir monitoring or management of some level of

uncertainties

Economic Significant of Reservoir Uncertainty

Quantification

During the life of a reservoir, the pre-reservoir and post-reservoir performance

evaluations are generally not equal. This is due to inadequate quantification of

uncertainties associated with the reservoir model input parameters and the resulting

composite uncertainty associated with the pre-reservoir performance prediction. The

decision to develop a reservoir is based on the prediction of production performance

following history-matching process. Likewise, in some instances, the decision to

obtain additional reservoir measurement data is taken when the uncertainty of the

forecast is great.

Hence, acquisition of further data is the reason for accurate quantification of

uncertainty associated with reservoir performance forecast so that projected recovery

will be accurately estimated for economic decisions. These vital reasons underline

the economic importance of increasing interest to properly quantify the uncertainties

associated with reservoir performance simulation.

2.6 Reservoir Characterization

An accurate description of reservoir rock, fluid contents, rock-fluid systems, fluid

description and flow performance are required to provide a sound basis for reservoir

engineering studies. Hence, proper reservoir characterization is important to analyze

the effects of heterogeneity on reserve estimation and reservoir performance due to

primary, secondary, and/or enhanced oil recovery operations. Porosity and perme￾ability are important flow properties; an accurate reservoir characterization requires

accurate porosity and permeability description as a function of space.

Reservoir characterization is a process carried out to reduce geological uncer￾tainties by quantitatively predicting the properties of a reservoir and define reservoir

structural changeability or variability. It is a process ranging from the discovery

phase to the management phase of a reservoir. Prior to performing a reservoir

simulation, accurate characterization is the first key step to undertake which helps

to identify uncertainty range inherent in reservoirs. Here we try to assess the range of

reservoir performance from an understanding of the subsurface uncertainties. This

concept is a limitation and it is not considered in the material balance method

presented in Chap. 5 of this book.

At this point, we need not border ourselves with a thorough review of literature in

reservoir rock characterization which would not be practically possible because of

the wide nature of this discipline and it is not incorporated in this present book.

However, the process combines the technical disciplines of geology, geophysics,

reservoir engineering, production engineering, petrophysics, economics, and data

management with key objectives on modeling each reservoir unit, understanding and

predicting well behavior, understanding past reservoir performance, and forecasting

future reservoir performance. Hence, it is used to assert a strong impact on plans for

the development and performance of a field.

 

Resources and Reserves 1

 Introduction

The development of oil and gas fields today depend solely on the amount of the

recoverable hydrocarbon fluid (reserves) discovered in the subsurface formation

(reservoir) and its economic viability. The estimation of these reserves are usually

associated with some level of uncertainties and when these uncertainties are not

factored into the prospect evaluation, the result is a wrong estimation of the reserves.

This means that the value of reserves estimation is a key driver for exploration and

production companies to decide whether to develop or abandon the prospect based

on their set criteria. Therefore, in estimating oil and gas reserves, we rely on the

integrity, skill and the judgment of the evaluator based on the amount of data

available, the complexity of the formation geology and the degree of depletion of

the reservoir (SPE, 1997)

Parties that Use Oil and Gas Reserves

• Companies operating oil and gas field or own an interest in petroleum operations

for in-house valuation

• Banks and other financial institutions involved in financing

• Stock markets around the world

• Regulatory bodies to protect the general public, to manage natural resources, and

to promote uniformity

• Taxation agencies with authority over petroleum products

• Investors in petroleum companies

• Mineral rights owners

• Arbitration (negotiation, settlement, etc) parties. i.e. to work out a deal

• Government for energy policies and strategic planning

2.3 Reasons for Estimating Reserves

• To obtain approvals from relevant ministries and other regulatory bodies

• For exploration, development & production of oil and gas reservoir

• To negotiate property sales and acquisitions

• To determine the market value

• To design facilities

• To obtain financing

• Evaluation of profit/interest

• Government regulations & taxation

• Planning & development of national energy policies

• Investment in oil/gas sector

• Reconcile dispute or arbitration involving reserves

2.4 Resources and Reserves

Resources, sometimes referred to as accumulations, are the total assumed quantities

of hydrocarbons found beneath the earth crust that could exist which may or may not

be produced in the future.

Reserves are estimated remaining quantities of oil and natural gas and related

substances anticipated to be recoverable from known accumulations, as of a given

date, based on the following:

• Analysis of drilling, geological, geophysical, and engineering data;

• The use of established technology;

• Specified economic conditions, which are generally accepted as being reasonable,

and shall be disclosed.

Hydrocarbon Resources

Resources are the total estimated quantities of hydrocarbons found beneath the earth

crust that could exist which may or may not be produced in the future. These are

commonly referred to as “Accumulations”. Resource is basically different from

reserve whose hydrocarbon deposit is known to exist with reasonable certainty

based on studies from geology and engineering. It encompasses all of the hydrocar￾bons that could exist, regardless of whether it is recoverable or known to exist.

Therefore, a resource can either be discovered or undiscovered (unknown and cannot

be estimated), economically recoverable or not economically recoverable. It includes

portions of hydrocarbons that are assumed to be present but are not measured

because they have not been explored or are located in inaccessible position.

The amount of naturally occurring accumulations of hydrocarbon estimated to be

originally in place is known as original resources. Hence, if the prospect has been

produced for a particular period of time, the original resources can also be defined on

a given date as the sum of the estimated quantities of hydrocarbon remaining in the

reservoir (naturally occurring accumulation) plus the quantities of the hydrocarbon

already produced plus quantities in the accumulations yet to be discovered if any.

Original resources can be classified as discovered or undiscovered and each of these

is further classified in the flow chart below (Fig. 2.2).

Contingent Resources

Contingent Resources are those potentially recoverable estimated quantities of

hydrocarbon from discovered accumulations on a given date, whose prospect or

project is not currently viable commercially or mature enough and are uneconomical

for development due to one or more uncertainties or contingencies. Some of these

contingencies may be that there is no current viable market(s) for the hydrocarbon, or

if commercial recovery of the hydrocarbon content is clinging on technology under

development, or evaluation of the accumulation is insufficient to clearly assess

commerciality.

Furthermore, the fact that contingent resource is not commercially viable does not

mean it cannot be seen as a reserve (that is, the movement from contingent resources

into reserves category) but if the key contingencies preventing commercial devel￾opment are adequately addressed or removed, then it can be called a hydrocarbon

reserve.

Classification of Contingent Resources

Development Not Viable

A discovered accumulation of hydrocarbons where viable processes of recovering

the hydrocarbon content have not yet been developed or a scenario where there are

no current plans to develop or to acquire additional data at the said time due to

limited production potential.

Development Unclarified or on Hold

A discovered accumulation of hydrocarbons of significant size where activities of

the project are not cleared or are on hold and/or where justification as a commercial

development may be subject to significant delay such as political, environmental,

technical or the dwindling market conditions.

Development Pending

This is an accumulation of discovered hydrocarbons where further data acquisitions

are required to confirm commerciality. In this case, the activities of the prospect are

presently happening or ongoing to provide an acceptable explanation of commercial

development in the anticipated or foreseeable future.

2.4.1.2 Prospective Resources

On the other hand, prospective resources which can be referred to as expected or

soon-to-be resources; are defined as the estimated volumes associated with

undiscovered accumulations or as estimated quantities of hydrocarbon as of a

given date to be potentially recoverable and are analyzed on the basis of indirect

evidence but have not yet been drilled. They are technically viable and economical to

produce but they present a higher risk than contingent resources since the risk of

discovery is also added.

Furthermore, we should note that while the engineers and geoscientists take into

consideration the possibility of hydrocarbons discovery and development when

determining the quantities of prospective resources, they also make some assump￾tions which include a range of uncertainty whether the hydrocarbons will be found.

The prospective resources are further classified as low, best and high estimate as

shown in Fig. 2.2.

Also, there can be a movement from prospective resources to contingent

resources, only if hydrocarbons are discovered and the accumulated discovery

must be further evaluated to determine an estimated quantity that would be recov￾erable under appropriate development projects.

Classification of Prospective Resources

According to the guidelines for the evaluation of petroleum reserves and resources by

Society of Petroleum Engineers (2001), prospective resources can be classified as:

Play

A project associated with a prospective trend of potential prospects, but requires more

data acquisition and/or evaluation to define specific leads or prospects. This is a

concept of exploration that includes a specific source rocks, reservoir rocks, migration

path and the type of trap to allow the discovery of recoverable quantity of hydrocarbon

(Norwegian Petroleum Directorate,1997).

Lead

A project associated with a potential accumulation that is currently poorly defined

and requires more data acquisition and/or evaluation to be classified as a prospect.

This implies that the data available is not enough to fully classify it as a prospect for

development.

Prospect

A project associated with a potential accumulation that is sufficiently well defined to

represent a viable drilling target. It implies a trap that has been identified and

adequately mapped but yet to be drilled. At this stage, there are some questions

asked to fully evaluate the play or prospect. These are:

• If we are certain of the hydrocarbon source, what then is the content (oil or/and

gas)?

• Can the content in the source rock migrate to the reservoir rock where it is

accumulated and how much of it?

• Does the reservoir have a storage capacity?

• What are the characteristics of the reservoir?

• Are there trapping mechanisms to help prevent the content of the reservoir from

further migration?

• If there is a trap, how efficient is it (seal or non-sealing)?

2.4.2 Hydrocarbon Reserves

Reserves are seen as the heart of the oil and gas business. These can be defined as the

estimated quantities of hydrocarbon such as crude oil, condensate, natural gas

(associated or non-associated gas) that are anticipated to be commercially recover￾able with the use of established technology on a known hydrocarbon accumulations

from a given date forward under existing economic conditions, established operating

conditions and current government regulations with a legal right to produce and a

production & transportation facilities to deliver the products to the market. Also, the

interpretations of reliable geologic, geophysics, drilling and engineering data avail￾able at the time of estimation are key factors that support the reserves definition.

Reserves estimates are generally revised as additional geologic or engineering data

becomes available or as economic conditions change.

In the previous statement, we established that contingent resources can be moved

to reserves. Therefore, based on development project(s), hydrocarbon reserves must

satisfy four criteria, and these are: discovered, recoverable, commercial, and

remaining quantity as at the date of evaluation (PRMS, 2017). Also, there must be

a reasonable expectation that all required internal and external approvals will be

forthcoming and evidence of company’s intention to proceed with the development

within a reasonable time frame; say 10 years to the international oil companies.

Generally, if they cannot develop it within this time frame, they might be mandated

by the regulatory body to farm-out to marginal field operators.

2.4.2.1 Hydrocarbon Reserves Classification

Classification by Development Operations

Oil and gas reserves can be classified to be on production, which implies that the

prospect is currently producing and the product delivered to the market for con￾sumption. It can be classified as being under development, which means that every

expedient approval has been obtained and the project development is in progress.

Furthermore, having satisfied all criteria for reserves, It can be classified has been

scheduled or outlined for development with substantial desire to develop but all

mandatory approvals have not be finalized or complete detailed development plan

have not been made.

Reserves are further classified according to the degree of certainty associated with

the estimation (Ross, 2001). These are: proved and unproved (probable and possible

reserves).

Classification by Degree of Uncertainty of Estimation

Proved Reserves

Proved reserves are those quantities of hydrocarbon reserves based on analysis of

geological and engineering data that can be estimated with a reasonably high degree

of certainty to be commercially recoverable from a given date forward from known

reservoirs and under current economic conditions, operating methods, and govern￾ment regulations. It is likely that the actual remaining quantities recovered will

exceed the estimated proved reserves. In general, reserves are considered proved if

the commercial producibility of the reservoir is supported by actual production or

formation tests. In its method of estimation, if probabilistic methods are used, there

should be at least a 90% probability that the quantities actually recovered will equal

or exceed the estimate and if deterministic methods are used, the term with reason￾able certainty is intended to express a high degree of confidence that the quantities

will be recovered.

Probable Reserves

Are those quantities of hydrocarbon based on geologic and/or engineering data

similar to that used in the estimation of proved reserves; but technical, contractual,

economic, or regulatory uncertainties deter such reserves from being classified as

proved. In this context, when probabilistic methods are used, there should be at least

a 50% probability that the quantities actually recovered will equal or exceed the sum

of estimated proved plus probable reserves.

Possible Reserves

Possible reserves are those additional reserves that are less certain to be recovered

than probable reserves. It is unlikely that the actual remaining quantities recovered

will exceed the sum of the estimated proved plus probable plus possible reserves.

They can also be defined as those unproved reserves which analysis of geological

and engineering data suggests that they are less likely to be recoverable than

probable reserves. In this context, when probabilistic methods are used, there should

be at least a 10% probability that the quantities actually recovered will equal or

exceed the sum of estimated proved plus probable plus possible reserves.

Introduction reservoir engineering 6 Productivity Index (PI or j) The productivity index

 The productivity index is calculated mathematically as

The productivity index is calculated mathematically as

Factors Affecting the Productivity Index

• Phase Behaviour of Fluids in the Reservoir

• Relative Permeability

• Oil Viscosity

• Oil Formation Volume Factor

• Skin

1.6.2 Phase Behaviour in Petroleum Reservoirs

As reservoir pressure drops below the bubble point, free gas begins to form and thus

the oil relative permeability (kro) is reduced. If a well is produced at a flow rate that

requires the wellbore flowing pressure (Pwf) to be less than the bubble point pressure

(Pb), the oil relative permeability and the productivity index (PI) will be decreased

around the wellbore.

1.6.3 Relative Permeability Behaviour

As free gas form in the pores of a reservoir rock, the ability of the liquid phase to

flow is decreased. Even though the gas saturation may not be great enough to allow

gas to flow, the space occupied by the gas reduces the effective flow area of the

liquid. Conversely, in gas reservoir, the relative permeability to gas will be decreased

if liquid saturation develops either as a result of retrograde condensation or water

formation in the pores.

1.6.4 Oil Viscosity Behaviour

The viscosity of oil saturated with gas at constant temperature will decrease as

pressure is decreased from an initial pressure to bubble point pressure (Pb). Below

Pb, the viscosity will increase as gas comes out of solution leaving the heavier

components of the hydrocarbon.

Oil Formation Volume Factor

As pressure is decreased in the reservoir, the hydrocarbon will expand and when the

bubble point pressure is reached for an oil reservoir, gas starts coming out of solution

which causes the oil to shrink thereby reducing the volume of the oil.

1.6.6 Skin

A well that is damaged results in low fluids flow potential. Thus, formation damage

is an impairment of reservoir permeability around the wellbore, leading to low or no

well production or injection. Or simply refers to the decrease in permeability that

occurs in the near wellbore region of a reservoir. Formation damage is often

quantified by “Skin” factor. Skin is strictly a measure of an excess pressure in the

producing formation as fluids flow into a well. Skin alters the flow of fluid; that is an

impairment to flow.

The excess pressure drop can occur from one or several of a wide variety of

causes such as drilling mud, cement, completion fluid filtrate invasion, solids

invasion, perforating damage, fines migration, formation compaction, swelling

clays, asphaltene/paraffin deposition, scale precipitation, emulsions, reservoir com￾paction, relative permeability effects, effects of stimulation treatments, etc.

Application of Dimensionless Parameters in Calculating

Flow Rate and Bottom Flowing Pressure

Now, let us write the pressure drop in dimensionless pressure

Shape Factors for Various Closed Single – Well Drainage Areas

Check for the flow regime at the given shape of the reservoir

Note, at any given time, the reservoir will behave like an infinite acting system,

that is, the reservoir is still undergoing transient flow condition if

tDA calculated ð Þ < tDA tabulated ð Þ

Thus, PD is calculated based on area as: